%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE009+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:12:50 AM UTC 2025
% Result : Theorem 9.26s 9.43s
% Output : Proof 9.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE009+2 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 18:49:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 9.26/9.43 % SZS status Theorem
% 9.26/9.43 % SZS output start Proof
% 9.26/9.43 tff(multiplication_type, type, (
% 9.26/9.43 multiplication: ( $i * $i ) > $i)).
% 9.26/9.43 tff(c_type, type, (
% 9.26/9.43 c: $i > $i)).
% 9.26/9.43 tff(tptp_fun_X1_1_type, type, (
% 9.26/9.43 tptp_fun_X1_1: $i)).
% 9.26/9.43 tff(tptp_fun_X0_2_type, type, (
% 9.26/9.43 tptp_fun_X0_2: $i)).
% 9.26/9.43 tff(tptp_fun_X1_0_type, type, (
% 9.26/9.43 tptp_fun_X1_0: $i > $i)).
% 9.26/9.43 tff(complement_type, type, (
% 9.26/9.43 complement: ( $i * $i ) > $o)).
% 9.26/9.43 tff(test_type, type, (
% 9.26/9.43 test: $i > $o)).
% 9.26/9.43 tff(one_type, type, (
% 9.26/9.43 one: $i)).
% 9.26/9.43 tff(addition_type, type, (
% 9.26/9.43 addition: ( $i * $i ) > $i)).
% 9.26/9.43 tff(zero_type, type, (
% 9.26/9.43 zero: $i)).
% 9.26/9.43 tff(1,assumption,((~((~test(tptp_fun_X1_0(X1!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))) | (~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))))), introduced(assumption)).
% 9.26/9.43 tff(2,plain,
% 9.26/9.43 (^[X0: $i] : refl((~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))))),
% 9.26/9.43 inference(bind,[status(th)],[])).
% 9.26/9.43 tff(3,plain,
% 9.26/9.43 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> ![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 9.26/9.43 inference(quant_intro,[status(thm)],[2])).
% 9.26/9.43 tff(4,plain,
% 9.26/9.43 (^[X0: $i] : rewrite((~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))))),
% 9.26/9.43 inference(bind,[status(th)],[])).
% 9.26/9.43 tff(5,plain,
% 9.26/9.43 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> ![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 9.26/9.43 inference(quant_intro,[status(thm)],[4])).
% 9.26/9.43 tff(6,plain,
% 9.26/9.43 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> ![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 9.26/9.43 inference(transitivity,[status(thm)],[5, 3])).
% 9.26/9.43 tff(7,plain,
% 9.26/9.43 (^[X0: $i] : trans(monotonicity(rewrite((test(X0) | ![X1: $i] : (~complement(X1, X0))) <=> (test(X0) | ![X1: $i] : (~complement(X1, X0)))), ((((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))) <=> (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))))), rewrite((((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))) <=> (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))), ((((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))) <=> (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))))),
% 9.26/9.43 inference(bind,[status(th)],[])).
% 9.26/9.43 tff(8,plain,
% 9.26/9.43 (![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))) <=> ![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 9.26/9.43 inference(quant_intro,[status(thm)],[7])).
% 9.26/9.43 tff(9,plain,
% 9.26/9.43 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 9.26/9.43 inference(rewrite,[status(thm)],[])).
% 9.26/9.43 tff(10,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_1')).
% 9.26/9.43 tff(11,plain,
% 9.26/9.43 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 9.26/9.43 inference(modus_ponens,[status(thm)],[10, 9])).
% 9.26/9.43 tff(12,plain,(
% 9.26/9.43 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 9.26/9.43 inference(skolemize,[status(sab)],[11])).
% 9.26/9.43 tff(13,plain,
% 9.26/9.43 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 9.26/9.43 inference(modus_ponens,[status(thm)],[12, 8])).
% 9.26/9.43 tff(14,plain,
% 9.26/9.43 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 9.26/9.43 inference(modus_ponens,[status(thm)],[13, 6])).
% 9.26/9.43 tff(15,plain,
% 9.26/9.43 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(tptp_fun_X1_0(X1!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))) | (~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))))))),
% 9.26/9.43 inference(quant_inst,[status(thm)],[])).
% 9.26/9.43 tff(16,plain,
% 9.26/9.43 ($false),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[15, 14, 1])).
% 9.26/9.43 tff(17,plain,(~((~((~test(tptp_fun_X1_0(X1!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))) | (~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))))), inference(lemma,lemma(discharge,[]))).
% 9.26/9.43 tff(18,plain,
% 9.26/9.43 (((~((~test(tptp_fun_X1_0(X1!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))) | (~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))))) | (test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))),
% 9.26/9.43 inference(tautology,[status(thm)],[])).
% 9.26/9.43 tff(19,plain,
% 9.26/9.43 (test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[18, 17])).
% 9.26/9.43 tff(20,assumption,(![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))), introduced(assumption)).
% 9.26/9.43 tff(21,plain,
% 9.26/9.43 (^[X0: $i, X1: $i] : refl((~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))))),
% 9.26/9.43 inference(bind,[status(th)],[])).
% 9.26/9.43 tff(22,plain,
% 9.26/9.43 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))) <=> ![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 9.26/9.43 inference(quant_intro,[status(thm)],[21])).
% 9.26/9.43 tff(23,plain,
% 9.26/9.43 (^[X0: $i, X1: $i] : trans(trans(monotonicity(rewrite(((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))), ((complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))))), rewrite((complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))), ((complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))))), rewrite((~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))), ((complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))))),
% 9.26/9.43 inference(bind,[status(th)],[])).
% 9.26/9.43 tff(24,plain,
% 9.26/9.43 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 9.26/9.43 inference(quant_intro,[status(thm)],[23])).
% 9.26/9.43 tff(25,plain,
% 9.26/9.43 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 9.26/9.43 inference(rewrite,[status(thm)],[])).
% 9.26/9.43 tff(26,plain,
% 9.26/9.43 (^[X0: $i, X1: $i] : rewrite((complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one))) <=> (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))))),
% 9.26/9.43 inference(bind,[status(th)],[])).
% 9.26/9.43 tff(27,plain,
% 9.26/9.43 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 9.26/9.43 inference(quant_intro,[status(thm)],[26])).
% 9.26/9.43 tff(28,axiom,(![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_2')).
% 9.26/9.43 tff(29,plain,
% 9.26/9.43 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 9.26/9.43 inference(modus_ponens,[status(thm)],[28, 27])).
% 9.26/9.43 tff(30,plain,
% 9.26/9.43 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 9.26/9.43 inference(modus_ponens,[status(thm)],[29, 25])).
% 9.26/9.43 tff(31,plain,(
% 9.26/9.43 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 9.26/9.43 inference(skolemize,[status(sab)],[30])).
% 9.26/9.43 tff(32,plain,
% 9.26/9.43 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 9.26/9.43 inference(modus_ponens,[status(thm)],[31, 24])).
% 9.26/9.43 tff(33,plain,
% 9.26/9.43 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 9.26/9.43 inference(modus_ponens,[status(thm)],[32, 22])).
% 9.26/9.43 tff(34,plain,
% 9.26/9.43 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.26/9.43 inference(rewrite,[status(thm)],[])).
% 9.26/9.43 tff(35,plain,
% 9.26/9.43 ((~(((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))) <=> (~(((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.26/9.43 inference(rewrite,[status(thm)],[])).
% 9.26/9.43 tff(36,plain,
% 9.26/9.43 ((((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))) <=> (((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.26/9.43 inference(rewrite,[status(thm)],[])).
% 9.26/9.43 tff(37,plain,
% 9.26/9.43 ((~(((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))) <=> (~(((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.26/9.43 inference(monotonicity,[status(thm)],[36])).
% 9.26/9.43 tff(38,plain,
% 9.26/9.43 ((~(((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))) <=> (~(((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.26/9.43 inference(transitivity,[status(thm)],[37, 35])).
% 9.26/9.43 tff(39,plain,
% 9.26/9.43 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.26/9.43 inference(monotonicity,[status(thm)],[38])).
% 9.26/9.43 tff(40,plain,
% 9.26/9.43 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.26/9.43 inference(transitivity,[status(thm)],[39, 34])).
% 9.26/9.43 tff(41,plain,
% 9.26/9.43 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.26/9.43 inference(quant_inst,[status(thm)],[])).
% 9.26/9.43 tff(42,plain,
% 9.26/9.43 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.26/9.43 inference(modus_ponens,[status(thm)],[41, 40])).
% 9.26/9.43 tff(43,plain,
% 9.26/9.43 (~(((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[42, 33])).
% 9.26/9.43 tff(44,plain,
% 9.26/9.43 ((addition(tptp_fun_X1_0(X1!1), X1!1) = addition(X1!1, tptp_fun_X1_0(X1!1))) <=> (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1))),
% 9.26/9.43 inference(commutativity,[status(thm)],[])).
% 9.26/9.43 tff(45,plain,
% 9.26/9.43 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), X1!1)))),
% 9.26/9.43 inference(quant_inst,[status(thm)],[])).
% 9.26/9.43 tff(46,plain,
% 9.26/9.43 (~(((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), X1!1))),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[45, 33])).
% 9.26/9.43 tff(47,plain,
% 9.26/9.43 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1))))))),
% 9.26/9.43 inference(quant_inst,[status(thm)],[])).
% 9.26/9.43 tff(48,plain,
% 9.26/9.43 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[47, 14])).
% 9.26/9.43 tff(49,plain,
% 9.26/9.43 (((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1))))) | ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))),
% 9.26/9.43 inference(tautology,[status(thm)],[])).
% 9.26/9.43 tff(50,plain,
% 9.26/9.43 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[49, 48])).
% 9.26/9.43 tff(51,plain,
% 9.26/9.43 ((~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))))))),
% 9.26/9.43 inference(rewrite,[status(thm)],[])).
% 9.26/9.43 tff(52,plain,
% 9.26/9.43 ((~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))))))),
% 9.26/9.43 inference(rewrite,[status(thm)],[])).
% 9.26/9.43 tff(53,axiom,(~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 9.26/9.43 tff(54,plain,
% 9.26/9.43 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 9.26/9.43 inference(modus_ponens,[status(thm)],[53, 52])).
% 9.26/9.43 tff(55,plain,
% 9.26/9.43 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 9.26/9.43 inference(modus_ponens,[status(thm)],[54, 51])).
% 9.26/9.43 tff(56,plain,
% 9.26/9.43 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 9.26/9.43 inference(modus_ponens,[status(thm)],[55, 51])).
% 9.26/9.43 tff(57,plain,
% 9.26/9.43 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 9.26/9.43 inference(modus_ponens,[status(thm)],[56, 51])).
% 9.26/9.43 tff(58,plain,(
% 9.26/9.43 ~((~(test(X1!1) & test(X0!2))) | (one = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 9.26/9.43 inference(skolemize,[status(sab)],[57])).
% 9.26/9.43 tff(59,plain,
% 9.26/9.43 (test(X1!1) & test(X0!2)),
% 9.26/9.43 inference(or_elim,[status(thm)],[58])).
% 9.26/9.43 tff(60,plain,
% 9.26/9.43 (test(X1!1)),
% 9.26/9.43 inference(and_elim,[status(thm)],[59])).
% 9.26/9.43 tff(61,plain,
% 9.26/9.43 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 9.26/9.43 inference(tautology,[status(thm)],[])).
% 9.26/9.43 tff(62,plain,
% 9.26/9.43 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[61, 60])).
% 9.26/9.43 tff(63,plain,
% 9.26/9.43 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[62, 50])).
% 9.26/9.43 tff(64,plain,
% 9.26/9.43 ((((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), X1!1)) | (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one)))) | (~complement(tptp_fun_X1_0(X1!1), X1!1))),
% 9.26/9.43 inference(tautology,[status(thm)],[])).
% 9.26/9.43 tff(65,plain,
% 9.26/9.43 ((((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), X1!1)) | (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))))),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[64, 63])).
% 9.26/9.43 tff(66,plain,
% 9.26/9.43 (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one)))),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[65, 46])).
% 9.26/9.43 tff(67,plain,
% 9.26/9.43 (((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))) | (addition(X1!1, tptp_fun_X1_0(X1!1)) = one)),
% 9.26/9.43 inference(tautology,[status(thm)],[])).
% 9.26/9.43 tff(68,plain,
% 9.26/9.43 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[67, 66])).
% 9.26/9.43 tff(69,plain,
% 9.26/9.43 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 9.26/9.43 inference(symmetry,[status(thm)],[68])).
% 9.26/9.43 tff(70,plain,
% 9.26/9.43 ((addition(tptp_fun_X1_0(X1!1), X1!1) = one) <=> (addition(tptp_fun_X1_0(X1!1), X1!1) = addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.26/9.43 inference(monotonicity,[status(thm)],[69])).
% 9.26/9.43 tff(71,plain,
% 9.26/9.43 ((addition(tptp_fun_X1_0(X1!1), X1!1) = one) <=> (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1))),
% 9.26/9.43 inference(transitivity,[status(thm)],[70, 44])).
% 9.26/9.43 tff(72,plain,
% 9.26/9.43 ((addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)) <=> (addition(tptp_fun_X1_0(X1!1), X1!1) = one)),
% 9.26/9.43 inference(symmetry,[status(thm)],[71])).
% 9.26/9.43 tff(73,plain,
% 9.26/9.43 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 9.26/9.43 inference(bind,[status(th)],[])).
% 9.26/9.43 tff(74,plain,
% 9.26/9.43 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 9.26/9.43 inference(quant_intro,[status(thm)],[73])).
% 9.26/9.43 tff(75,plain,
% 9.26/9.43 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 9.26/9.43 inference(rewrite,[status(thm)],[])).
% 9.26/9.43 tff(76,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 9.26/9.43 tff(77,plain,
% 9.26/9.43 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 9.26/9.43 inference(modus_ponens,[status(thm)],[76, 75])).
% 9.26/9.43 tff(78,plain,(
% 9.26/9.43 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 9.26/9.43 inference(skolemize,[status(sab)],[77])).
% 9.26/9.43 tff(79,plain,
% 9.26/9.43 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 9.26/9.43 inference(modus_ponens,[status(thm)],[78, 74])).
% 9.26/9.43 tff(80,plain,
% 9.26/9.43 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1))),
% 9.26/9.43 inference(quant_inst,[status(thm)],[])).
% 9.26/9.43 tff(81,plain,
% 9.26/9.43 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[80, 79])).
% 9.26/9.43 tff(82,plain,
% 9.26/9.43 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 9.26/9.43 inference(modus_ponens,[status(thm)],[81, 72])).
% 9.26/9.43 tff(83,plain,
% 9.26/9.43 (((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))) | (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)),
% 9.26/9.43 inference(tautology,[status(thm)],[])).
% 9.26/9.43 tff(84,plain,
% 9.26/9.43 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[83, 66])).
% 9.26/9.43 tff(85,plain,
% 9.26/9.43 (((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))) | (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)),
% 9.26/9.43 inference(tautology,[status(thm)],[])).
% 9.26/9.43 tff(86,plain,
% 9.26/9.43 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[85, 66])).
% 9.26/9.43 tff(87,plain,
% 9.26/9.43 ((~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))),
% 9.26/9.43 inference(tautology,[status(thm)],[])).
% 9.26/9.43 tff(88,plain,
% 9.26/9.43 ((~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[87, 86, 84])).
% 9.26/9.43 tff(89,plain,
% 9.26/9.43 (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[88, 82])).
% 9.26/9.43 tff(90,plain,
% 9.26/9.43 ((((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))) | ((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) | complement(X1!1, tptp_fun_X1_0(X1!1))),
% 9.26/9.43 inference(tautology,[status(thm)],[])).
% 9.26/9.43 tff(91,plain,
% 9.26/9.43 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[90, 89, 43])).
% 9.26/9.43 tff(92,plain,
% 9.26/9.43 ((~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))) | (~complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.26/9.43 inference(quant_inst,[status(thm)],[])).
% 9.26/9.43 tff(93,plain,
% 9.26/9.43 ($false),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[92, 91, 20])).
% 9.26/9.43 tff(94,plain,(~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))), inference(lemma,lemma(discharge,[]))).
% 9.26/9.43 tff(95,plain,
% 9.26/9.43 ((~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))) | test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))),
% 9.26/9.43 inference(tautology,[status(thm)],[])).
% 9.26/9.43 tff(96,plain,
% 9.26/9.43 ((~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))) | test(tptp_fun_X1_0(X1!1))),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[95, 94])).
% 9.26/9.43 tff(97,plain,
% 9.26/9.43 (test(tptp_fun_X1_0(X1!1))),
% 9.26/9.43 inference(unit_resolution,[status(thm)],[96, 19])).
% 9.26/9.43 tff(98,plain,
% 9.26/9.43 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 9.26/9.43 inference(bind,[status(th)],[])).
% 9.26/9.43 tff(99,plain,
% 9.26/9.43 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 9.26/9.44 inference(quant_intro,[status(thm)],[98])).
% 9.26/9.44 tff(100,plain,
% 9.26/9.44 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 9.26/9.44 inference(rewrite,[status(thm)],[])).
% 9.26/9.44 tff(101,plain,
% 9.26/9.44 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 9.26/9.44 inference(bind,[status(th)],[])).
% 9.26/9.44 tff(102,plain,
% 9.26/9.44 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 9.26/9.44 inference(quant_intro,[status(thm)],[101])).
% 9.26/9.44 tff(103,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_3')).
% 9.26/9.44 tff(104,plain,
% 9.26/9.44 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 9.26/9.44 inference(modus_ponens,[status(thm)],[103, 102])).
% 9.26/9.44 tff(105,plain,
% 9.26/9.44 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 9.26/9.44 inference(modus_ponens,[status(thm)],[104, 100])).
% 9.26/9.44 tff(106,plain,(
% 9.26/9.44 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 9.26/9.44 inference(skolemize,[status(sab)],[105])).
% 9.26/9.44 tff(107,plain,
% 9.26/9.44 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 9.26/9.44 inference(modus_ponens,[status(thm)],[106, 99])).
% 9.26/9.44 tff(108,plain,
% 9.26/9.44 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)))),
% 9.26/9.44 inference(rewrite,[status(thm)],[])).
% 9.26/9.44 tff(109,plain,
% 9.26/9.44 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)))),
% 9.26/9.44 inference(quant_inst,[status(thm)],[])).
% 9.26/9.44 tff(110,plain,
% 9.26/9.44 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1))),
% 9.26/9.44 inference(modus_ponens,[status(thm)],[109, 108])).
% 9.26/9.44 tff(111,plain,
% 9.26/9.44 ((~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1))),
% 9.26/9.44 inference(unit_resolution,[status(thm)],[110, 107])).
% 9.26/9.44 tff(112,plain,
% 9.26/9.44 ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)),
% 9.26/9.44 inference(unit_resolution,[status(thm)],[111, 97])).
% 9.26/9.44 tff(113,plain,
% 9.26/9.44 ((~((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1))) | (c(tptp_fun_X1_0(X1!1)) = X1!1) | (~complement(tptp_fun_X1_0(X1!1), X1!1))),
% 9.26/9.44 inference(tautology,[status(thm)],[])).
% 9.26/9.44 tff(114,plain,
% 9.26/9.44 ((~((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1))) | (c(tptp_fun_X1_0(X1!1)) = X1!1)),
% 9.26/9.44 inference(unit_resolution,[status(thm)],[113, 63])).
% 9.26/9.44 tff(115,plain,
% 9.26/9.44 (c(tptp_fun_X1_0(X1!1)) = X1!1),
% 9.26/9.44 inference(unit_resolution,[status(thm)],[114, 112])).
% 9.26/9.44 tff(116,plain,
% 9.26/9.44 (c(c(tptp_fun_X1_0(X1!1))) = c(X1!1)),
% 9.26/9.44 inference(monotonicity,[status(thm)],[115])).
% 9.26/9.44 tff(117,plain,
% 9.26/9.44 (c(X1!1) = c(c(tptp_fun_X1_0(X1!1)))),
% 9.26/9.44 inference(symmetry,[status(thm)],[116])).
% 9.26/9.44 tff(118,assumption,((~((~test(tptp_fun_X1_0(X0!2))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))) | (~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))))), introduced(assumption)).
% 9.26/9.44 tff(119,plain,
% 9.26/9.44 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(tptp_fun_X1_0(X0!2))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))) | (~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))))))),
% 9.26/9.44 inference(quant_inst,[status(thm)],[])).
% 9.26/9.44 tff(120,plain,
% 9.26/9.44 ($false),
% 9.26/9.44 inference(unit_resolution,[status(thm)],[119, 14, 118])).
% 9.26/9.44 tff(121,plain,(~((~((~test(tptp_fun_X1_0(X0!2))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))) | (~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2))))))), inference(lemma,lemma(discharge,[]))).
% 9.26/9.44 tff(122,plain,
% 9.26/9.44 (((~((~test(tptp_fun_X1_0(X0!2))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))) | (~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))))) | (test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2))))),
% 9.26/9.44 inference(tautology,[status(thm)],[])).
% 9.26/9.44 tff(123,plain,
% 9.26/9.44 (test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))),
% 9.26/9.44 inference(unit_resolution,[status(thm)],[122, 121])).
% 9.26/9.44 tff(124,assumption,(![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))), introduced(assumption)).
% 9.26/9.44 tff(125,plain,
% 9.26/9.44 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))))),
% 9.26/9.44 inference(rewrite,[status(thm)],[])).
% 9.26/9.44 tff(126,plain,
% 9.26/9.44 ((~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))) <=> (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 9.26/9.44 inference(rewrite,[status(thm)],[])).
% 9.26/9.44 tff(127,plain,
% 9.26/9.44 ((((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))) <=> (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 9.26/9.44 inference(rewrite,[status(thm)],[])).
% 9.26/9.44 tff(128,plain,
% 9.26/9.44 ((~(((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))) <=> (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 9.26/9.44 inference(monotonicity,[status(thm)],[127])).
% 9.26/9.44 tff(129,plain,
% 9.26/9.44 ((~(((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))) <=> (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 9.26/9.44 inference(transitivity,[status(thm)],[128, 126])).
% 9.26/9.44 tff(130,plain,
% 9.26/9.44 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))))),
% 9.29/9.44 inference(monotonicity,[status(thm)],[129])).
% 9.29/9.44 tff(131,plain,
% 9.29/9.44 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))))),
% 9.29/9.44 inference(transitivity,[status(thm)],[130, 125])).
% 9.29/9.44 tff(132,plain,
% 9.29/9.44 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 9.29/9.44 inference(quant_inst,[status(thm)],[])).
% 9.29/9.44 tff(133,plain,
% 9.29/9.44 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 9.29/9.44 inference(modus_ponens,[status(thm)],[132, 131])).
% 9.29/9.44 tff(134,plain,
% 9.29/9.44 (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[133, 33])).
% 9.29/9.44 tff(135,plain,
% 9.29/9.44 ((addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2))) <=> (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2))),
% 9.29/9.44 inference(commutativity,[status(thm)],[])).
% 9.29/9.44 tff(136,plain,
% 9.29/9.44 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) <=> complement(tptp_fun_X1_0(X0!2), X0!2)))),
% 9.29/9.44 inference(quant_inst,[status(thm)],[])).
% 9.29/9.44 tff(137,plain,
% 9.29/9.44 (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) <=> complement(tptp_fun_X1_0(X0!2), X0!2))),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[136, 33])).
% 9.29/9.44 tff(138,plain,
% 9.29/9.44 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2))))))),
% 9.29/9.44 inference(quant_inst,[status(thm)],[])).
% 9.29/9.44 tff(139,plain,
% 9.29/9.44 (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2)))))),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[138, 14])).
% 9.29/9.44 tff(140,plain,
% 9.29/9.44 (((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2))))) | ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))),
% 9.29/9.44 inference(tautology,[status(thm)],[])).
% 9.29/9.44 tff(141,plain,
% 9.29/9.44 ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[140, 139])).
% 9.29/9.44 tff(142,plain,
% 9.29/9.44 (test(X0!2)),
% 9.29/9.44 inference(and_elim,[status(thm)],[59])).
% 9.29/9.44 tff(143,plain,
% 9.29/9.44 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 9.29/9.44 inference(tautology,[status(thm)],[])).
% 9.29/9.44 tff(144,plain,
% 9.29/9.44 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[143, 142])).
% 9.29/9.44 tff(145,plain,
% 9.29/9.44 (complement(tptp_fun_X1_0(X0!2), X0!2)),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[144, 141])).
% 9.29/9.44 tff(146,plain,
% 9.29/9.44 ((((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) <=> complement(tptp_fun_X1_0(X0!2), X0!2)) | (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one)))) | (~complement(tptp_fun_X1_0(X0!2), X0!2))),
% 9.29/9.44 inference(tautology,[status(thm)],[])).
% 9.29/9.44 tff(147,plain,
% 9.29/9.44 ((((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) <=> complement(tptp_fun_X1_0(X0!2), X0!2)) | (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))))),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[146, 145])).
% 9.29/9.44 tff(148,plain,
% 9.29/9.44 (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one)))),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[147, 137])).
% 9.29/9.44 tff(149,plain,
% 9.29/9.44 (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) | (addition(X0!2, tptp_fun_X1_0(X0!2)) = one)),
% 9.29/9.44 inference(tautology,[status(thm)],[])).
% 9.29/9.44 tff(150,plain,
% 9.29/9.44 (addition(X0!2, tptp_fun_X1_0(X0!2)) = one),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[149, 148])).
% 9.29/9.44 tff(151,plain,
% 9.29/9.44 (one = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 9.29/9.44 inference(symmetry,[status(thm)],[150])).
% 9.29/9.44 tff(152,plain,
% 9.29/9.44 ((addition(tptp_fun_X1_0(X0!2), X0!2) = one) <=> (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2)))),
% 9.29/9.44 inference(monotonicity,[status(thm)],[151])).
% 9.29/9.44 tff(153,plain,
% 9.29/9.44 ((addition(tptp_fun_X1_0(X0!2), X0!2) = one) <=> (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2))),
% 9.29/9.44 inference(transitivity,[status(thm)],[152, 135])).
% 9.29/9.44 tff(154,plain,
% 9.29/9.44 ((addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)) <=> (addition(tptp_fun_X1_0(X0!2), X0!2) = one)),
% 9.29/9.44 inference(symmetry,[status(thm)],[153])).
% 9.29/9.44 tff(155,plain,
% 9.29/9.44 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2))),
% 9.29/9.44 inference(quant_inst,[status(thm)],[])).
% 9.29/9.44 tff(156,plain,
% 9.29/9.44 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[155, 79])).
% 9.29/9.44 tff(157,plain,
% 9.29/9.44 (addition(tptp_fun_X1_0(X0!2), X0!2) = one),
% 9.29/9.44 inference(modus_ponens,[status(thm)],[156, 154])).
% 9.29/9.44 tff(158,plain,
% 9.29/9.44 (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) | (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)),
% 9.29/9.44 inference(tautology,[status(thm)],[])).
% 9.29/9.44 tff(159,plain,
% 9.29/9.44 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[158, 148])).
% 9.29/9.44 tff(160,plain,
% 9.29/9.44 (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) | (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)),
% 9.29/9.44 inference(tautology,[status(thm)],[])).
% 9.29/9.44 tff(161,plain,
% 9.29/9.44 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[160, 148])).
% 9.29/9.44 tff(162,plain,
% 9.29/9.44 ((~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))),
% 9.29/9.44 inference(tautology,[status(thm)],[])).
% 9.29/9.44 tff(163,plain,
% 9.29/9.44 ((~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[162, 161, 159])).
% 9.29/9.44 tff(164,plain,
% 9.29/9.44 (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[163, 157])).
% 9.29/9.44 tff(165,plain,
% 9.29/9.44 ((((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))) | ((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) | complement(X0!2, tptp_fun_X1_0(X0!2))),
% 9.29/9.44 inference(tautology,[status(thm)],[])).
% 9.29/9.44 tff(166,plain,
% 9.29/9.44 (complement(X0!2, tptp_fun_X1_0(X0!2))),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[165, 164, 134])).
% 9.29/9.44 tff(167,plain,
% 9.29/9.44 ((~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))) | (~complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 9.29/9.44 inference(quant_inst,[status(thm)],[])).
% 9.29/9.44 tff(168,plain,
% 9.29/9.44 ($false),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[167, 166, 124])).
% 9.29/9.44 tff(169,plain,(~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))), inference(lemma,lemma(discharge,[]))).
% 9.29/9.44 tff(170,plain,
% 9.29/9.44 ((~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2))))) | test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))),
% 9.29/9.44 inference(tautology,[status(thm)],[])).
% 9.29/9.44 tff(171,plain,
% 9.29/9.44 ((~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2))))) | test(tptp_fun_X1_0(X0!2))),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[170, 169])).
% 9.29/9.44 tff(172,plain,
% 9.29/9.44 (test(tptp_fun_X1_0(X0!2))),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[171, 123])).
% 9.29/9.44 tff(173,plain,
% 9.29/9.44 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X0!2))) | ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X0!2))) | ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2)))),
% 9.29/9.44 inference(rewrite,[status(thm)],[])).
% 9.29/9.44 tff(174,plain,
% 9.29/9.44 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X0!2))) | ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2)))),
% 9.29/9.44 inference(quant_inst,[status(thm)],[])).
% 9.29/9.44 tff(175,plain,
% 9.29/9.44 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X0!2))) | ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2))),
% 9.29/9.44 inference(modus_ponens,[status(thm)],[174, 173])).
% 9.29/9.44 tff(176,plain,
% 9.29/9.44 ((~test(tptp_fun_X1_0(X0!2))) | ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2))),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[175, 107])).
% 9.29/9.44 tff(177,plain,
% 9.29/9.44 ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2)),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[176, 172])).
% 9.29/9.44 tff(178,plain,
% 9.29/9.44 ((~((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2))) | (c(tptp_fun_X1_0(X0!2)) = X0!2) | (~complement(tptp_fun_X1_0(X0!2), X0!2))),
% 9.29/9.44 inference(tautology,[status(thm)],[])).
% 9.29/9.44 tff(179,plain,
% 9.29/9.44 ((~((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2))) | (c(tptp_fun_X1_0(X0!2)) = X0!2)),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[178, 145])).
% 9.29/9.44 tff(180,plain,
% 9.29/9.44 (c(tptp_fun_X1_0(X0!2)) = X0!2),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[179, 177])).
% 9.29/9.44 tff(181,plain,
% 9.29/9.44 (c(c(tptp_fun_X1_0(X0!2))) = c(X0!2)),
% 9.29/9.44 inference(monotonicity,[status(thm)],[180])).
% 9.29/9.44 tff(182,plain,
% 9.29/9.44 (c(X0!2) = c(c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.44 inference(symmetry,[status(thm)],[181])).
% 9.29/9.44 tff(183,plain,
% 9.29/9.44 (multiplication(c(X0!2), c(X1!1)) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.44 inference(monotonicity,[status(thm)],[182, 117])).
% 9.29/9.44 tff(184,plain,
% 9.29/9.44 (multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1)))) = multiplication(c(X0!2), c(X1!1))),
% 9.29/9.44 inference(symmetry,[status(thm)],[183])).
% 9.29/9.44 tff(185,plain,
% 9.29/9.44 (test(c(tptp_fun_X1_0(X0!2))) <=> test(X0!2)),
% 9.29/9.44 inference(monotonicity,[status(thm)],[180])).
% 9.29/9.44 tff(186,plain,
% 9.29/9.44 (test(X0!2) <=> test(c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.44 inference(symmetry,[status(thm)],[185])).
% 9.29/9.44 tff(187,plain,
% 9.29/9.44 (test(c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.44 inference(modus_ponens,[status(thm)],[142, 186])).
% 9.29/9.44 tff(188,plain,
% 9.29/9.44 (test(c(tptp_fun_X1_0(X1!1))) <=> test(X1!1)),
% 9.29/9.44 inference(monotonicity,[status(thm)],[115])).
% 9.29/9.44 tff(189,plain,
% 9.29/9.44 (test(X1!1) <=> test(c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.44 inference(symmetry,[status(thm)],[188])).
% 9.29/9.44 tff(190,plain,
% 9.29/9.44 (test(c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.44 inference(modus_ponens,[status(thm)],[60, 189])).
% 9.29/9.44 tff(191,plain,
% 9.29/9.44 (^[X0: $i, X1: $i] : refl(((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))))),
% 9.29/9.44 inference(bind,[status(th)],[])).
% 9.29/9.44 tff(192,plain,
% 9.29/9.44 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 9.29/9.44 inference(quant_intro,[status(thm)],[191])).
% 9.29/9.44 tff(193,plain,
% 9.29/9.44 (^[X0: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((test(X0) & test(X1)) <=> (~((~test(X1)) | (~test(X0))))), ((~(test(X0) & test(X1))) <=> (~(~((~test(X1)) | (~test(X0))))))), rewrite((~(~((~test(X1)) | (~test(X0))))) <=> ((~test(X1)) | (~test(X0)))), ((~(test(X0) & test(X1))) <=> ((~test(X1)) | (~test(X0))))), (((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> (((~test(X1)) | (~test(X0))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))))), rewrite((((~test(X1)) | (~test(X0))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))), (((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))))),
% 9.29/9.44 inference(bind,[status(th)],[])).
% 9.29/9.44 tff(194,plain,
% 9.29/9.44 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 9.29/9.44 inference(quant_intro,[status(thm)],[193])).
% 9.29/9.44 tff(195,plain,
% 9.29/9.44 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 9.29/9.44 inference(rewrite,[status(thm)],[])).
% 9.29/9.44 tff(196,plain,
% 9.29/9.44 (^[X0: $i, X1: $i] : rewrite(((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))))),
% 9.29/9.44 inference(bind,[status(th)],[])).
% 9.29/9.44 tff(197,plain,
% 9.29/9.44 (![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 9.29/9.44 inference(quant_intro,[status(thm)],[196])).
% 9.29/9.44 tff(198,axiom,(![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+2.ax','test_deMorgan1')).
% 9.29/9.44 tff(199,plain,
% 9.29/9.44 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 9.29/9.44 inference(modus_ponens,[status(thm)],[198, 197])).
% 9.29/9.44 tff(200,plain,
% 9.29/9.44 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 9.29/9.44 inference(modus_ponens,[status(thm)],[199, 195])).
% 9.29/9.44 tff(201,plain,(
% 9.29/9.44 ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 9.29/9.44 inference(skolemize,[status(sab)],[200])).
% 9.29/9.44 tff(202,plain,
% 9.29/9.44 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 9.29/9.44 inference(modus_ponens,[status(thm)],[201, 194])).
% 9.29/9.44 tff(203,plain,
% 9.29/9.44 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 9.29/9.44 inference(modus_ponens,[status(thm)],[202, 192])).
% 9.29/9.44 tff(204,plain,
% 9.29/9.44 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1))))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.44 inference(rewrite,[status(thm)],[])).
% 9.29/9.44 tff(205,plain,
% 9.29/9.44 (((~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1))))) | (~test(c(tptp_fun_X1_0(X0!2))))) <=> ((~test(c(tptp_fun_X1_0(X1!1)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.44 inference(rewrite,[status(thm)],[])).
% 9.29/9.44 tff(206,plain,
% 9.29/9.44 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1))))) | (~test(c(tptp_fun_X1_0(X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1)))))))),
% 9.29/9.44 inference(monotonicity,[status(thm)],[205])).
% 9.29/9.44 tff(207,plain,
% 9.29/9.44 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1))))) | (~test(c(tptp_fun_X1_0(X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.44 inference(transitivity,[status(thm)],[206, 204])).
% 9.29/9.44 tff(208,plain,
% 9.29/9.44 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1))))) | (~test(c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.44 inference(quant_inst,[status(thm)],[])).
% 9.29/9.44 tff(209,plain,
% 9.29/9.44 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.44 inference(modus_ponens,[status(thm)],[208, 207])).
% 9.29/9.44 tff(210,plain,
% 9.29/9.44 ((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[209, 203, 190])).
% 9.29/9.44 tff(211,plain,
% 9.29/9.44 (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[210, 187])).
% 9.29/9.44 tff(212,plain,
% 9.29/9.44 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.29/9.44 inference(rewrite,[status(thm)],[])).
% 9.29/9.44 tff(213,plain,
% 9.29/9.44 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.29/9.44 inference(quant_inst,[status(thm)],[])).
% 9.29/9.44 tff(214,plain,
% 9.29/9.44 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.29/9.44 inference(modus_ponens,[status(thm)],[213, 212])).
% 9.29/9.44 tff(215,plain,
% 9.29/9.44 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[214, 107, 60])).
% 9.29/9.44 tff(216,plain,
% 9.29/9.44 ((~((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))) | (c(X1!1) = tptp_fun_X1_0(X1!1)) | (~complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.29/9.44 inference(tautology,[status(thm)],[])).
% 9.29/9.44 tff(217,plain,
% 9.29/9.44 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[216, 91, 215])).
% 9.29/9.44 tff(218,plain,
% 9.29/9.44 (c(c(X1!1)) = c(tptp_fun_X1_0(X1!1))),
% 9.29/9.44 inference(monotonicity,[status(thm)],[217])).
% 9.29/9.44 tff(219,plain,
% 9.29/9.44 (c(tptp_fun_X1_0(X1!1)) = c(c(X1!1))),
% 9.29/9.44 inference(symmetry,[status(thm)],[218])).
% 9.29/9.44 tff(220,plain,
% 9.29/9.44 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 9.29/9.44 inference(rewrite,[status(thm)],[])).
% 9.29/9.44 tff(221,plain,
% 9.29/9.44 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 9.29/9.44 inference(quant_inst,[status(thm)],[])).
% 9.29/9.44 tff(222,plain,
% 9.29/9.44 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 9.29/9.44 inference(modus_ponens,[status(thm)],[221, 220])).
% 9.29/9.44 tff(223,plain,
% 9.29/9.44 ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[222, 107, 142])).
% 9.29/9.44 tff(224,plain,
% 9.29/9.44 ((~((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))) | (c(X0!2) = tptp_fun_X1_0(X0!2)) | (~complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 9.29/9.44 inference(tautology,[status(thm)],[])).
% 9.29/9.44 tff(225,plain,
% 9.29/9.44 (c(X0!2) = tptp_fun_X1_0(X0!2)),
% 9.29/9.44 inference(unit_resolution,[status(thm)],[224, 166, 223])).
% 9.29/9.44 tff(226,plain,
% 9.29/9.44 (c(c(X0!2)) = c(tptp_fun_X1_0(X0!2))),
% 9.29/9.44 inference(monotonicity,[status(thm)],[225])).
% 9.29/9.44 tff(227,plain,
% 9.29/9.44 (c(tptp_fun_X1_0(X0!2)) = c(c(X0!2))),
% 9.29/9.44 inference(symmetry,[status(thm)],[226])).
% 9.29/9.45 tff(228,plain,
% 9.29/9.45 (addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))) = addition(c(c(X0!2)), c(c(X1!1)))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[227, 219])).
% 9.29/9.45 tff(229,plain,
% 9.29/9.45 (addition(c(c(X0!2)), c(c(X1!1))) = addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.45 inference(symmetry,[status(thm)],[228])).
% 9.29/9.45 tff(230,plain,
% 9.29/9.45 (X0!2 = c(tptp_fun_X1_0(X0!2))),
% 9.29/9.45 inference(symmetry,[status(thm)],[180])).
% 9.29/9.45 tff(231,plain,
% 9.29/9.45 (multiplication(X0!2, c(X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[230, 117])).
% 9.29/9.45 tff(232,plain,
% 9.29/9.45 (multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1)))) = multiplication(X0!2, c(X1!1))),
% 9.29/9.45 inference(symmetry,[status(thm)],[231])).
% 9.29/9.45 tff(233,plain,
% 9.29/9.45 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1))))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X0!2))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.45 inference(rewrite,[status(thm)],[])).
% 9.29/9.45 tff(234,plain,
% 9.29/9.45 (((~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1))))) | (~test(tptp_fun_X1_0(X0!2)))) <=> ((~test(tptp_fun_X1_0(X0!2))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.45 inference(rewrite,[status(thm)],[])).
% 9.29/9.45 tff(235,plain,
% 9.29/9.45 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1))))) | (~test(tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1)))))))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[234])).
% 9.29/9.45 tff(236,plain,
% 9.29/9.45 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1))))) | (~test(tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X0!2))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.45 inference(transitivity,[status(thm)],[235, 233])).
% 9.29/9.45 tff(237,plain,
% 9.29/9.45 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1))))) | (~test(tptp_fun_X1_0(X0!2))))),
% 9.29/9.45 inference(quant_inst,[status(thm)],[])).
% 9.29/9.45 tff(238,plain,
% 9.29/9.45 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X0!2))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.45 inference(modus_ponens,[status(thm)],[237, 236])).
% 9.29/9.45 tff(239,plain,
% 9.29/9.45 ((~test(tptp_fun_X1_0(X0!2))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.45 inference(unit_resolution,[status(thm)],[238, 203])).
% 9.29/9.45 tff(240,plain,
% 9.29/9.45 (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.45 inference(unit_resolution,[status(thm)],[239, 172, 190])).
% 9.29/9.45 tff(241,plain,
% 9.29/9.45 (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(X0!2, c(X1!1))),
% 9.29/9.45 inference(transitivity,[status(thm)],[240, 232])).
% 9.29/9.45 tff(242,plain,
% 9.29/9.45 (addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[241])).
% 9.29/9.45 tff(243,plain,
% 9.29/9.45 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.45 inference(symmetry,[status(thm)],[242])).
% 9.29/9.45 tff(244,plain,
% 9.29/9.45 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), tptp_fun_X1_0(X1!1))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[243])).
% 9.29/9.45 tff(245,plain,
% 9.29/9.45 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), tptp_fun_X1_0(X1!1)) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))),
% 9.29/9.45 inference(symmetry,[status(thm)],[244])).
% 9.29/9.45 tff(246,plain,
% 9.29/9.45 (^[A: $i, B: $i, C: $i] : refl((multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))))),
% 9.29/9.45 inference(bind,[status(th)],[])).
% 9.29/9.45 tff(247,plain,
% 9.29/9.45 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 9.29/9.45 inference(quant_intro,[status(thm)],[246])).
% 9.29/9.45 tff(248,plain,
% 9.29/9.45 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 9.29/9.45 inference(rewrite,[status(thm)],[])).
% 9.29/9.45 tff(249,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_distributivity')).
% 9.29/9.45 tff(250,plain,
% 9.29/9.45 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 9.29/9.45 inference(modus_ponens,[status(thm)],[249, 248])).
% 9.29/9.45 tff(251,plain,(
% 9.29/9.45 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 9.29/9.45 inference(skolemize,[status(sab)],[250])).
% 9.29/9.45 tff(252,plain,
% 9.29/9.45 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 9.29/9.45 inference(modus_ponens,[status(thm)],[251, 247])).
% 9.29/9.45 tff(253,plain,
% 9.29/9.45 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), tptp_fun_X1_0(X1!1)) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))))),
% 9.29/9.45 inference(quant_inst,[status(thm)],[])).
% 9.29/9.45 tff(254,plain,
% 9.29/9.45 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), tptp_fun_X1_0(X1!1)) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.45 inference(unit_resolution,[status(thm)],[253, 252])).
% 9.29/9.45 tff(255,plain,
% 9.29/9.45 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), tptp_fun_X1_0(X1!1))),
% 9.29/9.45 inference(symmetry,[status(thm)],[254])).
% 9.29/9.45 tff(256,plain,
% 9.29/9.45 (tptp_fun_X1_0(X1!1) = c(X1!1)),
% 9.29/9.45 inference(symmetry,[status(thm)],[217])).
% 9.29/9.45 tff(257,plain,
% 9.29/9.45 (tptp_fun_X1_0(X1!1) = c(c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.45 inference(transitivity,[status(thm)],[256, 117])).
% 9.29/9.45 tff(258,plain,
% 9.29/9.45 (multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[257])).
% 9.29/9.45 tff(259,plain,
% 9.29/9.45 (multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.45 inference(symmetry,[status(thm)],[258])).
% 9.29/9.45 tff(260,plain,
% 9.29/9.45 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X0!2))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.45 inference(rewrite,[status(thm)],[])).
% 9.29/9.45 tff(261,plain,
% 9.29/9.45 (((~test(tptp_fun_X1_0(X0!2))) | (c(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))) | (~test(c(tptp_fun_X1_0(X1!1))))) <=> ((~test(tptp_fun_X1_0(X0!2))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.45 inference(rewrite,[status(thm)],[])).
% 9.29/9.45 tff(262,plain,
% 9.29/9.45 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))) | (~test(c(tptp_fun_X1_0(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))))))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[261])).
% 9.29/9.45 tff(263,plain,
% 9.29/9.45 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))) | (~test(c(tptp_fun_X1_0(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X0!2))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.45 inference(transitivity,[status(thm)],[262, 260])).
% 9.29/9.45 tff(264,plain,
% 9.29/9.45 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))) | (~test(c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.45 inference(quant_inst,[status(thm)],[])).
% 9.29/9.45 tff(265,plain,
% 9.29/9.45 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X0!2))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.45 inference(modus_ponens,[status(thm)],[264, 263])).
% 9.29/9.45 tff(266,plain,
% 9.29/9.45 ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.45 inference(unit_resolution,[status(thm)],[265, 203, 190])).
% 9.29/9.45 tff(267,plain,
% 9.29/9.45 (c(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.45 inference(unit_resolution,[status(thm)],[266, 172])).
% 9.29/9.45 tff(268,plain,
% 9.29/9.45 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))) = addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 9.29/9.45 inference(quant_inst,[status(thm)],[])).
% 9.29/9.45 tff(269,plain,
% 9.29/9.45 (addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))) = addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.29/9.45 inference(unit_resolution,[status(thm)],[268, 79])).
% 9.29/9.45 tff(270,plain,
% 9.29/9.45 (addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.45 inference(symmetry,[status(thm)],[269])).
% 9.29/9.45 tff(271,plain,
% 9.29/9.45 (c(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[270])).
% 9.29/9.45 tff(272,plain,
% 9.29/9.45 (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = c(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 9.29/9.45 inference(symmetry,[status(thm)],[271])).
% 9.29/9.45 tff(273,plain,
% 9.29/9.45 (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.45 inference(transitivity,[status(thm)],[272, 267, 259])).
% 9.29/9.45 tff(274,plain,
% 9.29/9.45 (multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[273])).
% 9.29/9.45 tff(275,plain,
% 9.29/9.45 (multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))),
% 9.29/9.45 inference(symmetry,[status(thm)],[274])).
% 9.29/9.45 tff(276,plain,
% 9.29/9.45 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)))),
% 9.29/9.45 inference(bind,[status(th)],[])).
% 9.29/9.45 tff(277,plain,
% 9.29/9.45 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 9.29/9.45 inference(quant_intro,[status(thm)],[276])).
% 9.29/9.45 tff(278,plain,
% 9.29/9.45 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 9.29/9.45 inference(rewrite,[status(thm)],[])).
% 9.29/9.45 tff(279,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_associativity')).
% 9.29/9.45 tff(280,plain,
% 9.29/9.45 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 9.29/9.45 inference(modus_ponens,[status(thm)],[279, 278])).
% 9.29/9.45 tff(281,plain,(
% 9.29/9.45 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 9.29/9.45 inference(skolemize,[status(sab)],[280])).
% 9.29/9.45 tff(282,plain,
% 9.29/9.45 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 9.29/9.45 inference(modus_ponens,[status(thm)],[281, 277])).
% 9.29/9.45 tff(283,plain,
% 9.29/9.45 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.45 inference(quant_inst,[status(thm)],[])).
% 9.29/9.45 tff(284,plain,
% 9.29/9.45 (multiplication(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 9.29/9.45 inference(unit_resolution,[status(thm)],[283, 282])).
% 9.29/9.45 tff(285,plain,
% 9.29/9.45 (multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1)))) = c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.45 inference(symmetry,[status(thm)],[240])).
% 9.29/9.45 tff(286,plain,
% 9.29/9.45 (multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[257])).
% 9.29/9.45 tff(287,plain,
% 9.29/9.45 (multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.45 inference(transitivity,[status(thm)],[286, 285])).
% 9.29/9.45 tff(288,plain,
% 9.29/9.45 (multiplication(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X1!1), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[287])).
% 9.29/9.45 tff(289,plain,
% 9.29/9.45 (multiplication(tptp_fun_X1_0(X1!1), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.45 inference(symmetry,[status(thm)],[288])).
% 9.29/9.45 tff(290,plain,
% 9.29/9.45 (multiplication(tptp_fun_X1_0(X1!1), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[273])).
% 9.29/9.45 tff(291,plain,
% 9.29/9.45 (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(tptp_fun_X1_0(X1!1), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.45 inference(symmetry,[status(thm)],[290])).
% 9.29/9.45 tff(292,plain,
% 9.29/9.45 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.45 inference(quant_inst,[status(thm)],[])).
% 9.29/9.45 tff(293,plain,
% 9.29/9.45 (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.45 inference(unit_resolution,[status(thm)],[292, 282])).
% 9.29/9.45 tff(294,plain,
% 9.29/9.45 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.45 inference(symmetry,[status(thm)],[293])).
% 9.29/9.45 tff(295,plain,
% 9.29/9.45 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 9.29/9.45 inference(bind,[status(th)],[])).
% 9.29/9.45 tff(296,plain,
% 9.29/9.45 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 9.29/9.45 inference(quant_intro,[status(thm)],[295])).
% 9.29/9.45 tff(297,plain,
% 9.29/9.45 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 9.29/9.45 inference(rewrite,[status(thm)],[])).
% 9.29/9.45 tff(298,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 9.29/9.45 tff(299,plain,
% 9.29/9.45 (![A: $i] : (addition(A, A) = A)),
% 9.29/9.45 inference(modus_ponens,[status(thm)],[298, 297])).
% 9.29/9.45 tff(300,plain,(
% 9.29/9.45 ![A: $i] : (addition(A, A) = A)),
% 9.29/9.45 inference(skolemize,[status(sab)],[299])).
% 9.29/9.45 tff(301,plain,
% 9.29/9.45 (![A: $i] : (addition(A, A) = A)),
% 9.29/9.45 inference(modus_ponens,[status(thm)],[300, 296])).
% 9.29/9.45 tff(302,plain,
% 9.29/9.45 ((~![A: $i] : (addition(A, A) = A)) | (addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))) = c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.45 inference(quant_inst,[status(thm)],[])).
% 9.29/9.45 tff(303,plain,
% 9.29/9.45 (addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))) = c(tptp_fun_X1_0(X1!1))),
% 9.29/9.45 inference(unit_resolution,[status(thm)],[302, 301])).
% 9.29/9.45 tff(304,plain,
% 9.29/9.45 (addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))) = X1!1),
% 9.29/9.45 inference(transitivity,[status(thm)],[303, 115])).
% 9.29/9.45 tff(305,plain,
% 9.29/9.45 (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) = c(X1!1)),
% 9.29/9.45 inference(monotonicity,[status(thm)],[304])).
% 9.29/9.45 tff(306,plain,
% 9.29/9.45 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X1!1))))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.45 inference(rewrite,[status(thm)],[])).
% 9.29/9.45 tff(307,plain,
% 9.29/9.45 (((~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X1!1))))) | (~test(c(tptp_fun_X1_0(X1!1))))) <=> ((~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.45 inference(rewrite,[status(thm)],[])).
% 9.29/9.45 tff(308,plain,
% 9.29/9.45 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X1!1))))) | (~test(c(tptp_fun_X1_0(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X1!1)))))))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[307])).
% 9.29/9.45 tff(309,plain,
% 9.29/9.45 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X1!1))))) | (~test(c(tptp_fun_X1_0(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.45 inference(transitivity,[status(thm)],[308, 306])).
% 9.29/9.45 tff(310,plain,
% 9.29/9.45 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X1!1))))) | (~test(c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.45 inference(quant_inst,[status(thm)],[])).
% 9.29/9.45 tff(311,plain,
% 9.29/9.45 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.45 inference(modus_ponens,[status(thm)],[310, 309])).
% 9.29/9.45 tff(312,plain,
% 9.29/9.45 (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.45 inference(unit_resolution,[status(thm)],[311, 203, 190])).
% 9.29/9.45 tff(313,plain,
% 9.29/9.45 (multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X1!1)))) = c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.45 inference(symmetry,[status(thm)],[312])).
% 9.29/9.45 tff(314,plain,
% 9.29/9.45 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[257, 257])).
% 9.29/9.45 tff(315,plain,
% 9.29/9.45 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)) = c(c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.45 inference(transitivity,[status(thm)],[314, 313, 305, 117])).
% 9.29/9.45 tff(316,plain,
% 9.29/9.45 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[315])).
% 9.29/9.45 tff(317,plain,
% 9.29/9.45 (multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.45 inference(symmetry,[status(thm)],[316])).
% 9.29/9.45 tff(318,plain,
% 9.29/9.45 (multiplication(X0!2, c(X1!1)) = multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))),
% 9.29/9.45 inference(transitivity,[status(thm)],[231, 285, 272, 267, 317, 294, 291, 289, 284, 275])).
% 9.29/9.45 tff(319,plain,
% 9.29/9.45 ((~![A: $i] : (addition(A, A) = A)) | (addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.45 inference(quant_inst,[status(thm)],[])).
% 9.29/9.45 tff(320,plain,
% 9.29/9.45 (addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = c(tptp_fun_X1_0(X0!2))),
% 9.29/9.45 inference(unit_resolution,[status(thm)],[319, 301])).
% 9.29/9.45 tff(321,plain,
% 9.29/9.45 (addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = X0!2),
% 9.29/9.45 inference(transitivity,[status(thm)],[320, 180])).
% 9.29/9.45 tff(322,plain,
% 9.29/9.45 (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = c(X0!2)),
% 9.29/9.45 inference(monotonicity,[status(thm)],[321])).
% 9.29/9.45 tff(323,plain,
% 9.29/9.45 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X0!2))))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X0!2))))))),
% 9.29/9.45 inference(rewrite,[status(thm)],[])).
% 9.29/9.45 tff(324,plain,
% 9.29/9.45 (((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X0!2))))) | (~test(c(tptp_fun_X1_0(X0!2))))) <=> ((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X0!2))))))),
% 9.29/9.45 inference(rewrite,[status(thm)],[])).
% 9.29/9.45 tff(325,plain,
% 9.29/9.45 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X0!2))))) | (~test(c(tptp_fun_X1_0(X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X0!2)))))))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[324])).
% 9.29/9.45 tff(326,plain,
% 9.29/9.45 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X0!2))))) | (~test(c(tptp_fun_X1_0(X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X0!2))))))),
% 9.29/9.45 inference(transitivity,[status(thm)],[325, 323])).
% 9.29/9.45 tff(327,plain,
% 9.29/9.45 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X0!2))))) | (~test(c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.45 inference(quant_inst,[status(thm)],[])).
% 9.29/9.45 tff(328,plain,
% 9.29/9.45 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.45 inference(modus_ponens,[status(thm)],[327, 326])).
% 9.29/9.45 tff(329,plain,
% 9.29/9.45 (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.45 inference(unit_resolution,[status(thm)],[328, 203, 187])).
% 9.29/9.45 tff(330,plain,
% 9.29/9.45 (multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X0!2)))) = c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.45 inference(symmetry,[status(thm)],[329])).
% 9.29/9.45 tff(331,plain,
% 9.29/9.45 (tptp_fun_X1_0(X0!2) = c(X0!2)),
% 9.29/9.45 inference(symmetry,[status(thm)],[225])).
% 9.29/9.45 tff(332,plain,
% 9.29/9.45 (tptp_fun_X1_0(X0!2) = c(c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.45 inference(transitivity,[status(thm)],[331, 182])).
% 9.29/9.45 tff(333,plain,
% 9.29/9.45 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[332, 332])).
% 9.29/9.45 tff(334,plain,
% 9.29/9.45 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)) = c(X0!2)),
% 9.29/9.45 inference(transitivity,[status(thm)],[333, 330, 322])).
% 9.29/9.45 tff(335,plain,
% 9.29/9.45 (multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(c(X0!2), c(X1!1))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[334, 256])).
% 9.29/9.45 tff(336,plain,
% 9.29/9.45 (multiplication(c(X0!2), c(X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.45 inference(symmetry,[status(thm)],[335])).
% 9.29/9.45 tff(337,plain,
% 9.29/9.45 (multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[336])).
% 9.29/9.45 tff(338,plain,
% 9.29/9.45 (multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.45 inference(symmetry,[status(thm)],[337])).
% 9.29/9.45 tff(339,plain,
% 9.29/9.45 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))) = addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.45 inference(quant_inst,[status(thm)],[])).
% 9.29/9.45 tff(340,plain,
% 9.29/9.45 (addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))) = addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.45 inference(unit_resolution,[status(thm)],[339, 79])).
% 9.29/9.45 tff(341,plain,
% 9.29/9.45 (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[340])).
% 9.29/9.45 tff(342,plain,
% 9.29/9.45 (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.45 inference(symmetry,[status(thm)],[341])).
% 9.29/9.45 tff(343,plain,
% 9.29/9.45 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2))))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2))))))),
% 9.29/9.45 inference(rewrite,[status(thm)],[])).
% 9.29/9.45 tff(344,plain,
% 9.29/9.45 (((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2))))) | (~test(c(tptp_fun_X1_0(X1!1))))) <=> ((~test(c(tptp_fun_X1_0(X1!1)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2))))))),
% 9.29/9.45 inference(rewrite,[status(thm)],[])).
% 9.29/9.45 tff(345,plain,
% 9.29/9.45 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2))))) | (~test(c(tptp_fun_X1_0(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2)))))))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[344])).
% 9.29/9.45 tff(346,plain,
% 9.29/9.45 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2))))) | (~test(c(tptp_fun_X1_0(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2))))))),
% 9.29/9.45 inference(transitivity,[status(thm)],[345, 343])).
% 9.29/9.45 tff(347,plain,
% 9.29/9.45 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2))))) | (~test(c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.45 inference(quant_inst,[status(thm)],[])).
% 9.29/9.45 tff(348,plain,
% 9.29/9.45 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(tptp_fun_X1_0(X1!1)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.45 inference(modus_ponens,[status(thm)],[347, 346])).
% 9.29/9.45 tff(349,plain,
% 9.29/9.45 (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.45 inference(unit_resolution,[status(thm)],[348, 203, 190, 187])).
% 9.29/9.45 tff(350,plain,
% 9.29/9.45 (multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2)))) = c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.45 inference(symmetry,[status(thm)],[349])).
% 9.29/9.45 tff(351,plain,
% 9.29/9.45 (multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2)))) = multiplication(c(X1!1), c(X0!2))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[116, 181])).
% 9.29/9.45 tff(352,plain,
% 9.29/9.45 (multiplication(c(X1!1), c(X0!2)) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.45 inference(symmetry,[status(thm)],[351])).
% 9.29/9.45 tff(353,plain,
% 9.29/9.45 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(c(X1!1), c(X0!2))),
% 9.29/9.45 inference(monotonicity,[status(thm)],[256, 331])).
% 9.29/9.45 tff(354,plain,
% 9.29/9.45 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.45 inference(transitivity,[status(thm)],[353, 352, 350, 342, 211, 184, 336])).
% 9.29/9.45 tff(355,plain,
% 9.29/9.45 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[354])).
% 9.29/9.46 tff(356,plain,
% 9.29/9.46 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.46 inference(quant_inst,[status(thm)],[])).
% 9.29/9.46 tff(357,plain,
% 9.29/9.46 (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(unit_resolution,[status(thm)],[356, 282])).
% 9.29/9.46 tff(358,plain,
% 9.29/9.46 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)) = multiplication(c(X0!2), c(X1!1))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[331, 256])).
% 9.29/9.46 tff(359,plain,
% 9.29/9.46 (multiplication(c(X0!2), c(X1!1)) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(symmetry,[status(thm)],[358])).
% 9.29/9.46 tff(360,plain,
% 9.29/9.46 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 9.29/9.46 inference(bind,[status(th)],[])).
% 9.29/9.46 tff(361,plain,
% 9.29/9.46 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 9.29/9.46 inference(quant_intro,[status(thm)],[360])).
% 9.29/9.46 tff(362,plain,
% 9.29/9.46 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 9.29/9.46 inference(rewrite,[status(thm)],[])).
% 9.29/9.46 tff(363,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 9.29/9.46 tff(364,plain,
% 9.29/9.46 (![A: $i] : (addition(A, zero) = A)),
% 9.29/9.46 inference(modus_ponens,[status(thm)],[363, 362])).
% 9.29/9.46 tff(365,plain,(
% 9.29/9.46 ![A: $i] : (addition(A, zero) = A)),
% 9.29/9.46 inference(skolemize,[status(sab)],[364])).
% 9.29/9.46 tff(366,plain,
% 9.29/9.46 (![A: $i] : (addition(A, zero) = A)),
% 9.29/9.46 inference(modus_ponens,[status(thm)],[365, 361])).
% 9.29/9.46 tff(367,plain,
% 9.29/9.46 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), zero) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.46 inference(quant_inst,[status(thm)],[])).
% 9.29/9.46 tff(368,plain,
% 9.29/9.46 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), zero) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(unit_resolution,[status(thm)],[367, 366])).
% 9.29/9.46 tff(369,plain,
% 9.29/9.46 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 9.29/9.46 inference(bind,[status(th)],[])).
% 9.29/9.46 tff(370,plain,
% 9.29/9.46 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 9.29/9.46 inference(quant_intro,[status(thm)],[369])).
% 9.29/9.46 tff(371,plain,
% 9.29/9.46 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 9.29/9.46 inference(rewrite,[status(thm)],[])).
% 9.29/9.46 tff(372,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 9.29/9.46 tff(373,plain,
% 9.29/9.46 (![A: $i] : (multiplication(zero, A) = zero)),
% 9.29/9.46 inference(modus_ponens,[status(thm)],[372, 371])).
% 9.29/9.46 tff(374,plain,(
% 9.29/9.46 ![A: $i] : (multiplication(zero, A) = zero)),
% 9.29/9.46 inference(skolemize,[status(sab)],[373])).
% 9.29/9.46 tff(375,plain,
% 9.29/9.46 (![A: $i] : (multiplication(zero, A) = zero)),
% 9.29/9.46 inference(modus_ponens,[status(thm)],[374, 370])).
% 9.29/9.46 tff(376,plain,
% 9.29/9.46 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, tptp_fun_X1_0(X1!1)) = zero)),
% 9.29/9.46 inference(quant_inst,[status(thm)],[])).
% 9.29/9.46 tff(377,plain,
% 9.29/9.46 (multiplication(zero, tptp_fun_X1_0(X1!1)) = zero),
% 9.29/9.46 inference(unit_resolution,[status(thm)],[376, 375])).
% 9.29/9.46 tff(378,plain,
% 9.29/9.46 (X1!1 = c(tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(symmetry,[status(thm)],[115])).
% 9.29/9.46 tff(379,plain,
% 9.29/9.46 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[378, 256])).
% 9.29/9.46 tff(380,plain,
% 9.29/9.46 (multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1)) = multiplication(X1!1, tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(symmetry,[status(thm)],[379])).
% 9.29/9.46 tff(381,plain,
% 9.29/9.46 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1))))),
% 9.29/9.46 inference(rewrite,[status(thm)],[])).
% 9.29/9.46 tff(382,plain,
% 9.29/9.46 (((~test(X1!1)) | (c(addition(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1))) | (~test(tptp_fun_X1_0(X1!1)))) <=> ((~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1))))),
% 9.29/9.46 inference(rewrite,[status(thm)],[])).
% 9.29/9.46 tff(383,plain,
% 9.29/9.46 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(addition(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1))) | (~test(tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1)))))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[382])).
% 9.29/9.46 tff(384,plain,
% 9.29/9.46 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(addition(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1))) | (~test(tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1))))),
% 9.29/9.46 inference(transitivity,[status(thm)],[383, 381])).
% 9.29/9.46 tff(385,plain,
% 9.29/9.46 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(addition(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1))) | (~test(tptp_fun_X1_0(X1!1))))),
% 9.29/9.46 inference(quant_inst,[status(thm)],[])).
% 9.29/9.46 tff(386,plain,
% 9.29/9.46 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1)))),
% 9.29/9.46 inference(modus_ponens,[status(thm)],[385, 384])).
% 9.29/9.46 tff(387,plain,
% 9.29/9.46 ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1)))),
% 9.29/9.46 inference(unit_resolution,[status(thm)],[386, 203, 60])).
% 9.29/9.46 tff(388,plain,
% 9.29/9.46 (c(addition(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1))),
% 9.29/9.46 inference(unit_resolution,[status(thm)],[387, 97])).
% 9.29/9.46 tff(389,plain,
% 9.29/9.46 (addition(tptp_fun_X1_0(X1!1), X1!1) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(symmetry,[status(thm)],[81])).
% 9.29/9.46 tff(390,plain,
% 9.29/9.46 (c(addition(tptp_fun_X1_0(X1!1), X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[389])).
% 9.29/9.46 tff(391,plain,
% 9.29/9.46 (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = c(addition(tptp_fun_X1_0(X1!1), X1!1))),
% 9.29/9.46 inference(symmetry,[status(thm)],[390])).
% 9.29/9.46 tff(392,plain,
% 9.29/9.46 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(transitivity,[status(thm)],[150, 69])).
% 9.29/9.46 tff(393,plain,
% 9.29/9.46 (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[392])).
% 9.29/9.46 tff(394,plain,
% 9.29/9.46 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.46 inference(rewrite,[status(thm)],[])).
% 9.29/9.46 tff(395,plain,
% 9.29/9.46 (((~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))) | (~test(X0!2))) <=> ((~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.46 inference(rewrite,[status(thm)],[])).
% 9.29/9.46 tff(396,plain,
% 9.29/9.46 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))) | (~test(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2))))))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[395])).
% 9.29/9.46 tff(397,plain,
% 9.29/9.46 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))) | (~test(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.46 inference(transitivity,[status(thm)],[396, 394])).
% 9.29/9.46 tff(398,plain,
% 9.29/9.46 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))) | (~test(X0!2)))),
% 9.29/9.46 inference(quant_inst,[status(thm)],[])).
% 9.29/9.46 tff(399,plain,
% 9.29/9.46 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.46 inference(modus_ponens,[status(thm)],[398, 397])).
% 9.29/9.46 tff(400,plain,
% 9.29/9.46 ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.46 inference(unit_resolution,[status(thm)],[399, 203, 142])).
% 9.29/9.46 tff(401,plain,
% 9.29/9.46 (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.46 inference(unit_resolution,[status(thm)],[400, 172])).
% 9.29/9.46 tff(402,plain,
% 9.29/9.46 (multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2))) = c(addition(X0!2, tptp_fun_X1_0(X0!2)))),
% 9.29/9.46 inference(symmetry,[status(thm)],[401])).
% 9.29/9.46 tff(403,plain,
% 9.29/9.46 (multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[331])).
% 9.29/9.46 tff(404,plain,
% 9.29/9.46 (multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))) = zero),
% 9.29/9.46 inference(transitivity,[status(thm)],[403, 402, 393, 391, 388, 380, 86])).
% 9.29/9.46 tff(405,plain,
% 9.29/9.46 (multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = multiplication(zero, tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[404])).
% 9.29/9.46 tff(406,plain,
% 9.29/9.46 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.46 inference(quant_inst,[status(thm)],[])).
% 9.29/9.46 tff(407,plain,
% 9.29/9.46 (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(unit_resolution,[status(thm)],[406, 282])).
% 9.29/9.46 tff(408,plain,
% 9.29/9.46 (multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(symmetry,[status(thm)],[286])).
% 9.29/9.46 tff(409,plain,
% 9.29/9.46 (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(transitivity,[status(thm)],[240, 408])).
% 9.29/9.46 tff(410,plain,
% 9.29/9.46 (multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[409])).
% 9.29/9.46 tff(411,plain,
% 9.29/9.46 (multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = zero),
% 9.29/9.46 inference(transitivity,[status(thm)],[410, 407, 405, 377])).
% 9.29/9.46 tff(412,plain,
% 9.29/9.46 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.46 inference(quant_inst,[status(thm)],[])).
% 9.29/9.46 tff(413,plain,
% 9.29/9.46 (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(unit_resolution,[status(thm)],[412, 282])).
% 9.29/9.46 tff(414,plain,
% 9.29/9.46 (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[359])).
% 9.29/9.46 tff(415,plain,
% 9.29/9.46 (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(transitivity,[status(thm)],[414, 413])).
% 9.29/9.46 tff(416,plain,
% 9.29/9.46 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), zero)),
% 9.29/9.46 inference(monotonicity,[status(thm)],[415, 411])).
% 9.29/9.46 tff(417,plain,
% 9.29/9.46 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(transitivity,[status(thm)],[416, 368, 335, 359])).
% 9.29/9.46 tff(418,plain,
% 9.29/9.46 (multiplication(tptp_fun_X1_0(X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[417])).
% 9.29/9.46 tff(419,plain,
% 9.29/9.46 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), zero) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.46 inference(symmetry,[status(thm)],[416])).
% 9.29/9.46 tff(420,plain,
% 9.29/9.46 (multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), zero)),
% 9.29/9.46 inference(symmetry,[status(thm)],[368])).
% 9.29/9.46 tff(421,plain,
% 9.29/9.46 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.46 inference(transitivity,[status(thm)],[353, 352, 350, 342, 211, 184, 336, 420, 419])).
% 9.29/9.46 tff(422,plain,
% 9.29/9.46 (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[421])).
% 9.29/9.46 tff(423,plain,
% 9.29/9.46 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 9.29/9.46 inference(quant_inst,[status(thm)],[])).
% 9.29/9.46 tff(424,plain,
% 9.29/9.46 (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.29/9.46 inference(unit_resolution,[status(thm)],[423, 282])).
% 9.29/9.46 tff(425,plain,
% 9.29/9.46 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 9.29/9.46 inference(symmetry,[status(thm)],[424])).
% 9.29/9.46 tff(426,plain,
% 9.29/9.46 (multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X1!1)))) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(symmetry,[status(thm)],[314])).
% 9.29/9.46 tff(427,plain,
% 9.29/9.46 (c(X1!1) = c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.46 inference(symmetry,[status(thm)],[305])).
% 9.29/9.46 tff(428,plain,
% 9.29/9.46 (c(X1!1) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(transitivity,[status(thm)],[427, 312, 426])).
% 9.29/9.46 tff(429,plain,
% 9.29/9.46 (multiplication(c(X1!1), c(X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[428, 225])).
% 9.29/9.46 tff(430,plain,
% 9.29/9.46 (multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1)))) = c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.46 inference(symmetry,[status(thm)],[211])).
% 9.29/9.46 tff(431,plain,
% 9.29/9.46 (multiplication(c(X0!2), c(X1!1)) = multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(transitivity,[status(thm)],[183, 430, 341, 349, 351, 429, 425, 422, 418, 357, 355, 338])).
% 9.29/9.46 tff(432,plain,
% 9.29/9.46 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[431, 318])).
% 9.29/9.46 tff(433,plain,
% 9.29/9.46 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(transitivity,[status(thm)],[432, 255, 245])).
% 9.29/9.46 tff(434,plain,
% 9.29/9.46 (test(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) <=> test(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[433])).
% 9.29/9.46 tff(435,plain,
% 9.29/9.46 (test(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))) <=> test(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))))),
% 9.29/9.46 inference(symmetry,[status(thm)],[434])).
% 9.29/9.46 tff(436,plain,
% 9.29/9.46 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(transitivity,[status(thm)],[255, 245])).
% 9.29/9.46 tff(437,plain,
% 9.29/9.46 (test(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) <=> test(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[436])).
% 9.29/9.46 tff(438,plain,
% 9.29/9.46 (test(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) <=> test(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))))),
% 9.29/9.46 inference(transitivity,[status(thm)],[437, 435])).
% 9.29/9.46 tff(439,plain,
% 9.29/9.46 (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.46 inference(symmetry,[status(thm)],[414])).
% 9.29/9.46 tff(440,plain,
% 9.29/9.46 (multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 9.29/9.46 inference(symmetry,[status(thm)],[413])).
% 9.29/9.46 tff(441,plain,
% 9.29/9.46 (multiplication(c(X0!2), c(X1!1)) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.46 inference(transitivity,[status(thm)],[336, 440, 439])).
% 9.29/9.46 tff(442,plain,
% 9.29/9.46 (c(multiplication(c(X0!2), c(X1!1))) = c(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[441])).
% 9.29/9.46 tff(443,plain,
% 9.29/9.46 (c(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1)))) = c(multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.46 inference(symmetry,[status(thm)],[442])).
% 9.29/9.46 tff(444,plain,
% 9.29/9.46 (test(c(X1!1)) <=> test(tptp_fun_X1_0(X1!1))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[217])).
% 9.29/9.46 tff(445,plain,
% 9.29/9.46 (test(tptp_fun_X1_0(X1!1)) <=> test(c(X1!1))),
% 9.29/9.46 inference(symmetry,[status(thm)],[444])).
% 9.29/9.46 tff(446,plain,
% 9.29/9.46 (test(c(X1!1))),
% 9.29/9.46 inference(modus_ponens,[status(thm)],[97, 445])).
% 9.29/9.46 tff(447,plain,
% 9.29/9.46 (^[X0: $i, X1: $i] : refl(((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0))) <=> ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0))))),
% 9.29/9.46 inference(bind,[status(th)],[])).
% 9.29/9.46 tff(448,plain,
% 9.29/9.46 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 9.29/9.46 inference(quant_intro,[status(thm)],[447])).
% 9.29/9.46 tff(449,plain,
% 9.29/9.46 (^[X0: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((test(X0) & test(X1)) <=> (~((~test(X1)) | (~test(X0))))), ((~(test(X0) & test(X1))) <=> (~(~((~test(X1)) | (~test(X0))))))), rewrite((~(~((~test(X1)) | (~test(X0))))) <=> ((~test(X1)) | (~test(X0)))), ((~(test(X0) & test(X1))) <=> ((~test(X1)) | (~test(X0))))), (((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> (((~test(X1)) | (~test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))))), rewrite((((~test(X1)) | (~test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))), (((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))))),
% 9.29/9.46 inference(bind,[status(th)],[])).
% 9.29/9.46 tff(450,plain,
% 9.29/9.46 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 9.29/9.46 inference(quant_intro,[status(thm)],[449])).
% 9.29/9.46 tff(451,plain,
% 9.29/9.46 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 9.29/9.46 inference(rewrite,[status(thm)],[])).
% 9.29/9.46 tff(452,plain,
% 9.29/9.46 (^[X0: $i, X1: $i] : rewrite(((test(X0) & test(X1)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))))),
% 9.29/9.46 inference(bind,[status(th)],[])).
% 9.29/9.46 tff(453,plain,
% 9.29/9.46 (![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 9.29/9.46 inference(quant_intro,[status(thm)],[452])).
% 9.29/9.46 tff(454,axiom,(![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+2.ax','test_deMorgan2')).
% 9.29/9.46 tff(455,plain,
% 9.29/9.46 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 9.29/9.46 inference(modus_ponens,[status(thm)],[454, 453])).
% 9.29/9.46 tff(456,plain,
% 9.29/9.46 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 9.29/9.46 inference(modus_ponens,[status(thm)],[455, 451])).
% 9.29/9.46 tff(457,plain,(
% 9.29/9.46 ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 9.29/9.46 inference(skolemize,[status(sab)],[456])).
% 9.29/9.46 tff(458,plain,
% 9.29/9.46 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 9.29/9.46 inference(modus_ponens,[status(thm)],[457, 450])).
% 9.29/9.46 tff(459,plain,
% 9.29/9.46 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 9.29/9.46 inference(modus_ponens,[status(thm)],[458, 448])).
% 9.29/9.46 tff(460,plain,
% 9.29/9.46 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(c(X1!1))) | (c(multiplication(X0!2, c(X1!1))) = addition(c(X0!2), c(c(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(c(X1!1))) | (c(multiplication(X0!2, c(X1!1))) = addition(c(X0!2), c(c(X1!1)))))),
% 9.29/9.46 inference(rewrite,[status(thm)],[])).
% 9.29/9.46 tff(461,plain,
% 9.29/9.46 (((~test(c(X1!1))) | (c(multiplication(X0!2, c(X1!1))) = addition(c(X0!2), c(c(X1!1)))) | (~test(X0!2))) <=> ((~test(X0!2)) | (~test(c(X1!1))) | (c(multiplication(X0!2, c(X1!1))) = addition(c(X0!2), c(c(X1!1)))))),
% 9.29/9.46 inference(rewrite,[status(thm)],[])).
% 9.29/9.46 tff(462,plain,
% 9.29/9.46 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X1!1))) | (c(multiplication(X0!2, c(X1!1))) = addition(c(X0!2), c(c(X1!1)))) | (~test(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(c(X1!1))) | (c(multiplication(X0!2, c(X1!1))) = addition(c(X0!2), c(c(X1!1))))))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[461])).
% 9.29/9.46 tff(463,plain,
% 9.29/9.46 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X1!1))) | (c(multiplication(X0!2, c(X1!1))) = addition(c(X0!2), c(c(X1!1)))) | (~test(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(c(X1!1))) | (c(multiplication(X0!2, c(X1!1))) = addition(c(X0!2), c(c(X1!1)))))),
% 9.29/9.46 inference(transitivity,[status(thm)],[462, 460])).
% 9.29/9.46 tff(464,plain,
% 9.29/9.46 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X1!1))) | (c(multiplication(X0!2, c(X1!1))) = addition(c(X0!2), c(c(X1!1)))) | (~test(X0!2)))),
% 9.29/9.46 inference(quant_inst,[status(thm)],[])).
% 9.29/9.46 tff(465,plain,
% 9.29/9.46 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(c(X1!1))) | (c(multiplication(X0!2, c(X1!1))) = addition(c(X0!2), c(c(X1!1))))),
% 9.29/9.46 inference(modus_ponens,[status(thm)],[464, 463])).
% 9.29/9.46 tff(466,plain,
% 9.29/9.46 ((~test(c(X1!1))) | (c(multiplication(X0!2, c(X1!1))) = addition(c(X0!2), c(c(X1!1))))),
% 9.29/9.46 inference(unit_resolution,[status(thm)],[465, 459, 142])).
% 9.29/9.46 tff(467,plain,
% 9.29/9.46 (c(multiplication(X0!2, c(X1!1))) = addition(c(X0!2), c(c(X1!1)))),
% 9.29/9.46 inference(unit_resolution,[status(thm)],[466, 446])).
% 9.29/9.46 tff(468,plain,
% 9.29/9.46 (addition(c(X0!2), c(c(X1!1))) = c(multiplication(X0!2, c(X1!1)))),
% 9.29/9.46 inference(symmetry,[status(thm)],[467])).
% 9.29/9.46 tff(469,plain,
% 9.29/9.46 (multiplication(addition(c(X0!2), c(c(X1!1))), c(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))))) = multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1))))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[468, 443])).
% 9.29/9.46 tff(470,plain,
% 9.29/9.46 (multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1)))) = multiplication(addition(c(X0!2), c(c(X1!1))), c(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1)))))),
% 9.29/9.46 inference(symmetry,[status(thm)],[469])).
% 9.29/9.46 tff(471,plain,
% 9.29/9.46 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1))))),
% 9.29/9.46 inference(quant_inst,[status(thm)],[])).
% 9.29/9.46 tff(472,plain,
% 9.29/9.46 (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)))),
% 9.29/9.46 inference(unit_resolution,[status(thm)],[471, 79])).
% 9.29/9.46 tff(473,plain,
% 9.29/9.46 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.46 inference(symmetry,[status(thm)],[472])).
% 9.29/9.46 tff(474,plain,
% 9.29/9.46 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))) = addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 9.29/9.46 inference(quant_inst,[status(thm)],[])).
% 9.29/9.46 tff(475,plain,
% 9.29/9.46 (addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))) = addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))),
% 9.29/9.46 inference(unit_resolution,[status(thm)],[474, 79])).
% 9.29/9.46 tff(476,plain,
% 9.29/9.46 (addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1)))),
% 9.29/9.46 inference(symmetry,[status(thm)],[475])).
% 9.29/9.46 tff(477,plain,
% 9.29/9.46 (addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)) = addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[476])).
% 9.29/9.46 tff(478,plain,
% 9.29/9.46 (addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)) = addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))),
% 9.29/9.46 inference(symmetry,[status(thm)],[477])).
% 9.29/9.46 tff(479,plain,
% 9.29/9.46 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)))),
% 9.29/9.46 inference(monotonicity,[status(thm)],[478])).
% 9.29/9.46 tff(480,plain,
% 9.29/9.46 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)))),
% 9.29/9.47 inference(symmetry,[status(thm)],[479])).
% 9.29/9.47 tff(481,plain,
% 9.29/9.47 (^[C: $i, B: $i, A: $i] : refl((addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> (addition(A, addition(B, C)) = addition(addition(A, B), C)))),
% 9.29/9.47 inference(bind,[status(th)],[])).
% 9.29/9.47 tff(482,plain,
% 9.29/9.47 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 9.29/9.47 inference(quant_intro,[status(thm)],[481])).
% 9.29/9.47 tff(483,plain,
% 9.29/9.47 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 9.29/9.47 inference(rewrite,[status(thm)],[])).
% 9.29/9.47 tff(484,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_associativity')).
% 9.29/9.47 tff(485,plain,
% 9.29/9.47 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 9.29/9.47 inference(modus_ponens,[status(thm)],[484, 483])).
% 9.29/9.47 tff(486,plain,(
% 9.29/9.47 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 9.29/9.47 inference(skolemize,[status(sab)],[485])).
% 9.29/9.47 tff(487,plain,
% 9.29/9.47 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 9.29/9.47 inference(modus_ponens,[status(thm)],[486, 482])).
% 9.29/9.47 tff(488,plain,
% 9.29/9.47 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))), multiplication(c(X0!2), X1!1)))),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(489,plain,
% 9.29/9.47 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))), multiplication(c(X0!2), X1!1))),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[488, 487])).
% 9.29/9.47 tff(490,plain,
% 9.29/9.47 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)))),
% 9.29/9.47 inference(symmetry,[status(thm)],[489])).
% 9.29/9.47 tff(491,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1)) = c(addition(tptp_fun_X1_0(X1!1), X1!1))),
% 9.29/9.47 inference(symmetry,[status(thm)],[388])).
% 9.29/9.47 tff(492,plain,
% 9.29/9.47 (zero = multiplication(X1!1, tptp_fun_X1_0(X1!1))),
% 9.29/9.47 inference(symmetry,[status(thm)],[86])).
% 9.29/9.47 tff(493,plain,
% 9.29/9.47 (^[A: $i] : refl((multiplication(A, zero) = zero) <=> (multiplication(A, zero) = zero))),
% 9.29/9.47 inference(bind,[status(th)],[])).
% 9.29/9.47 tff(494,plain,
% 9.29/9.47 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 9.29/9.47 inference(quant_intro,[status(thm)],[493])).
% 9.29/9.47 tff(495,plain,
% 9.29/9.47 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 9.29/9.47 inference(rewrite,[status(thm)],[])).
% 9.29/9.47 tff(496,axiom,(![A: $i] : (multiplication(A, zero) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','right_annihilation')).
% 9.29/9.47 tff(497,plain,
% 9.29/9.47 (![A: $i] : (multiplication(A, zero) = zero)),
% 9.29/9.47 inference(modus_ponens,[status(thm)],[496, 495])).
% 9.29/9.47 tff(498,plain,(
% 9.29/9.47 ![A: $i] : (multiplication(A, zero) = zero)),
% 9.29/9.47 inference(skolemize,[status(sab)],[497])).
% 9.29/9.47 tff(499,plain,
% 9.29/9.47 (![A: $i] : (multiplication(A, zero) = zero)),
% 9.29/9.47 inference(modus_ponens,[status(thm)],[498, 494])).
% 9.29/9.47 tff(500,plain,
% 9.29/9.47 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(c(tptp_fun_X1_0(X1!1)), zero) = zero)),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(501,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), zero) = zero),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[500, 499])).
% 9.29/9.47 tff(502,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), zero)),
% 9.29/9.47 inference(monotonicity,[status(thm)],[404])).
% 9.29/9.47 tff(503,plain,
% 9.29/9.47 (multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.47 inference(symmetry,[status(thm)],[403])).
% 9.29/9.47 tff(504,plain,
% 9.29/9.47 (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = c(addition(X0!2, tptp_fun_X1_0(X0!2)))),
% 9.29/9.47 inference(symmetry,[status(thm)],[393])).
% 9.29/9.47 tff(505,plain,
% 9.29/9.47 ((~![A: $i] : (addition(A, A) = A)) | (addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(506,plain,
% 9.29/9.47 (addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[505, 301])).
% 9.29/9.47 tff(507,plain,
% 9.29/9.47 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, c(tptp_fun_X1_0(X0!2))) = zero)),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(508,plain,
% 9.29/9.47 (multiplication(zero, c(tptp_fun_X1_0(X0!2))) = zero),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[507, 375])).
% 9.29/9.47 tff(509,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[256])).
% 9.29/9.47 tff(510,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = zero),
% 9.29/9.47 inference(transitivity,[status(thm)],[509, 380, 86])).
% 9.29/9.47 tff(511,plain,
% 9.29/9.47 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(zero, c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[510])).
% 9.29/9.47 tff(512,plain,
% 9.29/9.47 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(513,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[512, 282])).
% 9.29/9.47 tff(514,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[273])).
% 9.29/9.47 tff(515,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.29/9.47 inference(transitivity,[status(thm)],[514, 513, 511, 508, 492, 379, 491, 390])).
% 9.29/9.47 tff(516,plain,
% 9.29/9.47 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(tptp_fun_X1_0(X0!2), zero) = zero)),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(517,plain,
% 9.29/9.47 (multiplication(tptp_fun_X1_0(X0!2), zero) = zero),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[516, 499])).
% 9.29/9.47 tff(518,plain,
% 9.29/9.47 (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), zero)),
% 9.29/9.47 inference(monotonicity,[status(thm)],[510])).
% 9.29/9.47 tff(519,plain,
% 9.29/9.47 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(520,plain,
% 9.29/9.47 (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1))),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[519, 282])).
% 9.29/9.47 tff(521,plain,
% 9.29/9.47 (multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.47 inference(symmetry,[status(thm)],[520])).
% 9.29/9.47 tff(522,plain,
% 9.29/9.47 (multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), X1!1)),
% 9.29/9.47 inference(monotonicity,[status(thm)],[331, 115])).
% 9.29/9.47 tff(523,plain,
% 9.29/9.47 (multiplication(c(X0!2), X1!1) = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.47 inference(symmetry,[status(thm)],[522])).
% 9.29/9.47 tff(524,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[523])).
% 9.29/9.47 tff(525,plain,
% 9.29/9.47 (multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), X1!1)),
% 9.29/9.47 inference(monotonicity,[status(thm)],[181, 115])).
% 9.29/9.47 tff(526,plain,
% 9.29/9.47 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X1!1))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.47 inference(rewrite,[status(thm)],[])).
% 9.29/9.47 tff(527,plain,
% 9.29/9.47 (((~test(tptp_fun_X1_0(X1!1))) | (c(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1)))) | (~test(c(tptp_fun_X1_0(X0!2))))) <=> ((~test(tptp_fun_X1_0(X1!1))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.47 inference(rewrite,[status(thm)],[])).
% 9.29/9.47 tff(528,plain,
% 9.29/9.47 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1)))) | (~test(c(tptp_fun_X1_0(X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[527])).
% 9.29/9.47 tff(529,plain,
% 9.29/9.47 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1)))) | (~test(c(tptp_fun_X1_0(X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X1!1))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.47 inference(transitivity,[status(thm)],[528, 526])).
% 9.29/9.47 tff(530,plain,
% 9.29/9.47 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1)))) | (~test(c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(531,plain,
% 9.29/9.47 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X1!1))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.47 inference(modus_ponens,[status(thm)],[530, 529])).
% 9.29/9.47 tff(532,plain,
% 9.29/9.47 ((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[531, 203, 97])).
% 9.29/9.47 tff(533,plain,
% 9.29/9.47 (c(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[532, 187])).
% 9.29/9.47 tff(534,plain,
% 9.29/9.47 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(535,plain,
% 9.29/9.47 (addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[534, 79])).
% 9.29/9.47 tff(536,plain,
% 9.29/9.47 (addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))) = addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.47 inference(symmetry,[status(thm)],[535])).
% 9.29/9.47 tff(537,plain,
% 9.29/9.47 (c(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = c(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[536])).
% 9.29/9.47 tff(538,plain,
% 9.29/9.47 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2))))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X1!1))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2))))))),
% 9.29/9.47 inference(rewrite,[status(thm)],[])).
% 9.29/9.47 tff(539,plain,
% 9.29/9.47 (((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2))))) | (~test(tptp_fun_X1_0(X1!1)))) <=> ((~test(tptp_fun_X1_0(X1!1))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2))))))),
% 9.29/9.47 inference(rewrite,[status(thm)],[])).
% 9.29/9.47 tff(540,plain,
% 9.29/9.47 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2))))) | (~test(tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2)))))))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[539])).
% 9.29/9.47 tff(541,plain,
% 9.29/9.47 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2))))) | (~test(tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X1!1))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2))))))),
% 9.29/9.47 inference(transitivity,[status(thm)],[540, 538])).
% 9.29/9.47 tff(542,plain,
% 9.29/9.47 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2))))) | (~test(tptp_fun_X1_0(X1!1))))),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(543,plain,
% 9.29/9.47 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X1!1))) | (~test(c(tptp_fun_X1_0(X0!2)))) | (c(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.47 inference(modus_ponens,[status(thm)],[542, 541])).
% 9.29/9.47 tff(544,plain,
% 9.29/9.47 (c(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[543, 203, 97, 187])).
% 9.29/9.47 tff(545,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2)))) = c(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.47 inference(symmetry,[status(thm)],[544])).
% 9.29/9.47 tff(546,plain,
% 9.29/9.47 (multiplication(X1!1, c(X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[378, 182])).
% 9.29/9.47 tff(547,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(X1!1, c(X0!2))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[115, 331])).
% 9.29/9.47 tff(548,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(c(X0!2), X1!1)),
% 9.29/9.47 inference(transitivity,[status(thm)],[547, 546, 545, 537, 533, 525])).
% 9.29/9.47 tff(549,plain,
% 9.29/9.47 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[548])).
% 9.29/9.47 tff(550,plain,
% 9.29/9.47 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(551,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[550, 282])).
% 9.29/9.47 tff(552,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[359])).
% 9.29/9.47 tff(553,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.29/9.47 inference(transitivity,[status(thm)],[552, 551, 549, 524, 521, 518, 517, 492, 379, 491, 390])).
% 9.29/9.47 tff(554,plain,
% 9.29/9.47 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(c(tptp_fun_X1_0(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[553, 515])).
% 9.29/9.47 tff(555,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.47 inference(symmetry,[status(thm)],[514])).
% 9.29/9.47 tff(556,plain,
% 9.29/9.47 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.47 inference(symmetry,[status(thm)],[513])).
% 9.29/9.47 tff(557,plain,
% 9.29/9.47 (multiplication(zero, c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.47 inference(symmetry,[status(thm)],[511])).
% 9.29/9.47 tff(558,plain,
% 9.29/9.47 (zero = multiplication(zero, c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.47 inference(symmetry,[status(thm)],[508])).
% 9.29/9.47 tff(559,plain,
% 9.29/9.47 (multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1)))) = multiplication(c(X0!2), c(X1!1))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[181, 116])).
% 9.29/9.47 tff(560,plain,
% 9.29/9.47 (addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.47 inference(symmetry,[status(thm)],[340])).
% 9.29/9.47 tff(561,plain,
% 9.29/9.47 (c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[560])).
% 9.29/9.47 tff(562,plain,
% 9.29/9.47 (multiplication(c(X1!1), c(X0!2)) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[117, 182])).
% 9.29/9.47 tff(563,plain,
% 9.29/9.47 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(c(X0!2), c(X1!1))),
% 9.29/9.47 inference(transitivity,[status(thm)],[353, 562, 350, 561, 211, 559])).
% 9.29/9.47 tff(564,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[563])).
% 9.29/9.47 tff(565,plain,
% 9.29/9.47 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(566,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[565, 282])).
% 9.29/9.47 tff(567,plain,
% 9.29/9.47 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 9.29/9.47 inference(symmetry,[status(thm)],[566])).
% 9.29/9.47 tff(568,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), c(X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.47 inference(symmetry,[status(thm)],[509])).
% 9.29/9.47 tff(569,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.47 inference(transitivity,[status(thm)],[524, 521, 518, 517, 492, 379, 568])).
% 9.29/9.47 tff(570,plain,
% 9.29/9.47 (multiplication(multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[569])).
% 9.29/9.47 tff(571,plain,
% 9.29/9.47 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(multiplication(c(X0!2), X1!1), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(572,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[571, 282])).
% 9.29/9.47 tff(573,plain,
% 9.29/9.47 (multiplication(c(X1!1), c(X0!2)) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))),
% 9.29/9.47 inference(symmetry,[status(thm)],[353])).
% 9.29/9.47 tff(574,plain,
% 9.29/9.47 (multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2)))) = multiplication(c(X1!1), c(X0!2))),
% 9.29/9.47 inference(symmetry,[status(thm)],[562])).
% 9.29/9.47 tff(575,plain,
% 9.29/9.47 (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = c(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.47 inference(symmetry,[status(thm)],[561])).
% 9.29/9.47 tff(576,plain,
% 9.29/9.47 (multiplication(c(X0!2), c(X1!1)) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.47 inference(symmetry,[status(thm)],[559])).
% 9.29/9.47 tff(577,plain,
% 9.29/9.47 (multiplication(c(X0!2), c(X1!1)) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))),
% 9.29/9.47 inference(transitivity,[status(thm)],[576, 430, 575, 349, 574, 573])).
% 9.29/9.47 tff(578,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = multiplication(multiplication(c(X0!2), X1!1), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[577])).
% 9.29/9.47 tff(579,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.47 inference(transitivity,[status(thm)],[578, 572, 570, 567, 564, 552, 551, 549, 524, 521, 518, 517, 558, 557, 556, 555])).
% 9.29/9.47 tff(580,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.47 inference(symmetry,[status(thm)],[552])).
% 9.29/9.47 tff(581,plain,
% 9.29/9.47 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 9.29/9.47 inference(symmetry,[status(thm)],[551])).
% 9.29/9.47 tff(582,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.47 inference(symmetry,[status(thm)],[549])).
% 9.29/9.47 tff(583,plain,
% 9.29/9.47 (multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1))),
% 9.29/9.47 inference(symmetry,[status(thm)],[524])).
% 9.29/9.47 tff(584,plain,
% 9.29/9.47 (multiplication(tptp_fun_X1_0(X0!2), zero) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.47 inference(symmetry,[status(thm)],[518])).
% 9.29/9.47 tff(585,plain,
% 9.29/9.47 (zero = multiplication(tptp_fun_X1_0(X0!2), zero)),
% 9.29/9.47 inference(symmetry,[status(thm)],[517])).
% 9.29/9.47 tff(586,plain,
% 9.29/9.47 (multiplication(multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[569])).
% 9.29/9.47 tff(587,plain,
% 9.29/9.47 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(multiplication(c(X0!2), X1!1), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(588,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[587, 282])).
% 9.29/9.47 tff(589,plain,
% 9.29/9.47 (multiplication(X0!2, c(X1!1)) = multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.47 inference(transitivity,[status(thm)],[231, 285, 272, 267, 259])).
% 9.29/9.47 tff(590,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), multiplication(X0!2, c(X1!1))) = multiplication(multiplication(c(X0!2), X1!1), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[589])).
% 9.29/9.47 tff(591,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(multiplication(c(X0!2), X1!1), multiplication(X0!2, c(X1!1)))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[241])).
% 9.29/9.47 tff(592,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.47 inference(transitivity,[status(thm)],[591, 590, 588, 586, 511, 508, 585, 584, 520, 583, 582, 581, 580])).
% 9.29/9.47 tff(593,plain,
% 9.29/9.47 (addition(multiplication(multiplication(c(X0!2), X1!1), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), multiplication(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(c(tptp_fun_X1_0(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[592, 579])).
% 9.29/9.47 tff(594,plain,
% 9.29/9.47 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))))),
% 9.29/9.47 inference(bind,[status(th)],[])).
% 9.29/9.47 tff(595,plain,
% 9.29/9.47 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 9.29/9.47 inference(quant_intro,[status(thm)],[594])).
% 9.29/9.47 tff(596,plain,
% 9.29/9.47 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 9.29/9.47 inference(rewrite,[status(thm)],[])).
% 9.29/9.47 tff(597,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','right_distributivity')).
% 9.29/9.47 tff(598,plain,
% 9.29/9.47 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 9.29/9.47 inference(modus_ponens,[status(thm)],[597, 596])).
% 9.29/9.47 tff(599,plain,(
% 9.29/9.47 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 9.29/9.47 inference(skolemize,[status(sab)],[598])).
% 9.29/9.47 tff(600,plain,
% 9.29/9.47 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 9.29/9.47 inference(modus_ponens,[status(thm)],[599, 595])).
% 9.29/9.47 tff(601,plain,
% 9.29/9.47 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(multiplication(c(X0!2), X1!1), addition(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(multiplication(c(X0!2), X1!1), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), multiplication(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(602,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), addition(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(multiplication(c(X0!2), X1!1), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), multiplication(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[601, 600])).
% 9.29/9.47 tff(603,plain,
% 9.29/9.47 (addition(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[241])).
% 9.29/9.47 tff(604,plain,
% 9.29/9.47 (addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.47 inference(symmetry,[status(thm)],[603])).
% 9.29/9.47 tff(605,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(multiplication(c(X0!2), X1!1), addition(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), multiplication(c(X0!2), c(X1!1))))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[604])).
% 9.29/9.47 tff(606,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = zero),
% 9.29/9.47 inference(transitivity,[status(thm)],[605, 602, 593, 554, 506, 391, 388, 380, 86])).
% 9.29/9.47 tff(607,assumption,(~(multiplication(multiplication(c(X0!2), X1!1), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = zero)), introduced(assumption)).
% 9.29/9.47 tff(608,plain,
% 9.29/9.47 ($false),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[607, 606])).
% 9.29/9.47 tff(609,plain,(multiplication(multiplication(c(X0!2), X1!1), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = zero), inference(lemma,lemma(discharge,[]))).
% 9.29/9.47 tff(610,plain,
% 9.29/9.47 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))))),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(611,plain,
% 9.29/9.47 (addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[610, 79])).
% 9.29/9.47 tff(612,plain,
% 9.29/9.47 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.47 inference(symmetry,[status(thm)],[611])).
% 9.29/9.47 tff(613,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = multiplication(multiplication(c(X0!2), X1!1), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[612])).
% 9.29/9.47 tff(614,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.47 inference(transitivity,[status(thm)],[613, 609, 492, 379, 491, 390, 504, 401, 503])).
% 9.29/9.47 tff(615,plain,
% 9.29/9.47 (multiplication(multiplication(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[614])).
% 9.29/9.47 tff(616,plain,
% 9.29/9.47 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(multiplication(c(X0!2), X1!1), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.47 inference(quant_inst,[status(thm)],[])).
% 9.29/9.47 tff(617,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1))),
% 9.29/9.47 inference(unit_resolution,[status(thm)],[616, 282])).
% 9.29/9.47 tff(618,plain,
% 9.29/9.47 (multiplication(multiplication(c(X0!2), X1!1), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.47 inference(transitivity,[status(thm)],[617, 615, 405, 377, 492, 379, 491, 390, 504, 401, 503])).
% 9.29/9.47 tff(619,plain,
% 9.29/9.47 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(multiplication(c(X0!2), X1!1), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.47 inference(monotonicity,[status(thm)],[618])).
% 9.29/9.47 tff(620,plain,
% 9.29/9.47 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(multiplication(c(X0!2), X1!1), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))))),
% 9.29/9.48 inference(quant_inst,[status(thm)],[])).
% 9.29/9.48 tff(621,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(multiplication(c(X0!2), X1!1), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.48 inference(unit_resolution,[status(thm)],[620, 282])).
% 9.29/9.48 tff(622,plain,
% 9.29/9.48 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(multiplication(c(X0!2), X1!1), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))))),
% 9.29/9.48 inference(symmetry,[status(thm)],[621])).
% 9.29/9.48 tff(623,plain,
% 9.29/9.48 (c(X1!1) = c(c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[378])).
% 9.29/9.48 tff(624,plain,
% 9.29/9.48 (multiplication(X0!2, c(X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[230, 623])).
% 9.29/9.48 tff(625,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1)))) = multiplication(X0!2, c(X1!1))),
% 9.29/9.48 inference(symmetry,[status(thm)],[624])).
% 9.29/9.48 tff(626,plain,
% 9.29/9.48 (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(X0!2, c(X1!1))),
% 9.29/9.48 inference(transitivity,[status(thm)],[240, 625])).
% 9.29/9.48 tff(627,plain,
% 9.29/9.48 (addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[626])).
% 9.29/9.48 tff(628,plain,
% 9.29/9.48 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.48 inference(symmetry,[status(thm)],[627])).
% 9.29/9.48 tff(629,plain,
% 9.29/9.48 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), tptp_fun_X1_0(X1!1))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[628])).
% 9.29/9.48 tff(630,plain,
% 9.29/9.48 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), tptp_fun_X1_0(X1!1)) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))),
% 9.29/9.48 inference(symmetry,[status(thm)],[629])).
% 9.29/9.48 tff(631,plain,
% 9.29/9.48 (multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = c(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(symmetry,[status(thm)],[267])).
% 9.29/9.48 tff(632,plain,
% 9.29/9.48 (tptp_fun_X1_0(X1!1) = c(c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.48 inference(transitivity,[status(thm)],[256, 623])).
% 9.29/9.48 tff(633,plain,
% 9.29/9.48 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[632, 632])).
% 9.29/9.48 tff(634,plain,
% 9.29/9.48 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)) = c(c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.48 inference(transitivity,[status(thm)],[633, 313, 305, 623])).
% 9.29/9.48 tff(635,plain,
% 9.29/9.48 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[634])).
% 9.29/9.48 tff(636,plain,
% 9.29/9.48 (multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[632])).
% 9.29/9.48 tff(637,plain,
% 9.29/9.48 (multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(symmetry,[status(thm)],[636])).
% 9.29/9.48 tff(638,plain,
% 9.29/9.48 (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(transitivity,[status(thm)],[272, 267, 637])).
% 9.29/9.48 tff(639,plain,
% 9.29/9.48 (multiplication(tptp_fun_X1_0(X1!1), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[638])).
% 9.29/9.48 tff(640,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[632])).
% 9.29/9.48 tff(641,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.48 inference(transitivity,[status(thm)],[640, 285])).
% 9.29/9.48 tff(642,plain,
% 9.29/9.48 (multiplication(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X1!1), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[641])).
% 9.29/9.48 tff(643,plain,
% 9.29/9.48 (multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = multiplication(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.48 inference(symmetry,[status(thm)],[284])).
% 9.29/9.48 tff(644,plain,
% 9.29/9.48 (multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[638])).
% 9.29/9.48 tff(645,plain,
% 9.29/9.48 (multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)) = multiplication(X0!2, c(X1!1))),
% 9.29/9.48 inference(transitivity,[status(thm)],[644, 643, 642, 639, 293, 635, 631, 271, 240, 625])).
% 9.29/9.48 tff(646,plain,
% 9.29/9.48 (multiplication(c(X0!2), c(X1!1)) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[182, 623])).
% 9.29/9.48 tff(647,plain,
% 9.29/9.48 (multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1)))) = multiplication(c(X0!2), c(X1!1))),
% 9.29/9.48 inference(symmetry,[status(thm)],[646])).
% 9.29/9.48 tff(648,plain,
% 9.29/9.48 (c(c(tptp_fun_X1_0(X1!1))) = c(X1!1)),
% 9.29/9.48 inference(symmetry,[status(thm)],[623])).
% 9.29/9.48 tff(649,plain,
% 9.29/9.48 (multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2)))) = multiplication(c(X1!1), c(X0!2))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[648, 181])).
% 9.29/9.48 tff(650,plain,
% 9.29/9.48 (multiplication(c(X1!1), c(X0!2)) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.48 inference(symmetry,[status(thm)],[649])).
% 9.29/9.48 tff(651,plain,
% 9.29/9.48 (multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X1!1)))) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))),
% 9.29/9.48 inference(symmetry,[status(thm)],[633])).
% 9.29/9.48 tff(652,plain,
% 9.29/9.48 (c(X1!1) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))),
% 9.29/9.48 inference(transitivity,[status(thm)],[427, 312, 651])).
% 9.29/9.48 tff(653,plain,
% 9.29/9.48 (multiplication(c(X1!1), c(X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[652, 225])).
% 9.29/9.48 tff(654,plain,
% 9.29/9.48 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(c(X1!1), c(X0!2))),
% 9.29/9.48 inference(symmetry,[status(thm)],[653])).
% 9.29/9.48 tff(655,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.48 inference(symmetry,[status(thm)],[640])).
% 9.29/9.48 tff(656,plain,
% 9.29/9.48 (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.48 inference(transitivity,[status(thm)],[240, 655])).
% 9.29/9.48 tff(657,plain,
% 9.29/9.48 (multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[656])).
% 9.29/9.48 tff(658,plain,
% 9.29/9.48 (multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = zero),
% 9.29/9.48 inference(transitivity,[status(thm)],[657, 407, 405, 377])).
% 9.29/9.48 tff(659,plain,
% 9.29/9.48 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), zero)),
% 9.29/9.48 inference(monotonicity,[status(thm)],[415, 658])).
% 9.29/9.48 tff(660,plain,
% 9.29/9.48 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), zero) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.48 inference(symmetry,[status(thm)],[659])).
% 9.29/9.48 tff(661,plain,
% 9.29/9.48 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.48 inference(transitivity,[status(thm)],[353, 650, 350, 342, 211, 647, 336, 420, 660])).
% 9.29/9.48 tff(662,plain,
% 9.29/9.48 (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[661])).
% 9.29/9.48 tff(663,plain,
% 9.29/9.48 (multiplication(tptp_fun_X1_0(X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(symmetry,[status(thm)],[662])).
% 9.29/9.48 tff(664,plain,
% 9.29/9.48 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 9.29/9.48 inference(transitivity,[status(thm)],[659, 368, 335, 359])).
% 9.29/9.48 tff(665,plain,
% 9.29/9.48 (multiplication(tptp_fun_X1_0(X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[664])).
% 9.29/9.48 tff(666,plain,
% 9.29/9.48 (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))))),
% 9.29/9.48 inference(symmetry,[status(thm)],[665])).
% 9.29/9.48 tff(667,plain,
% 9.29/9.48 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 9.29/9.48 inference(symmetry,[status(thm)],[357])).
% 9.29/9.48 tff(668,plain,
% 9.29/9.48 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.48 inference(transitivity,[status(thm)],[353, 650, 350, 342, 211, 647, 336])).
% 9.29/9.48 tff(669,plain,
% 9.29/9.48 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[668])).
% 9.29/9.48 tff(670,plain,
% 9.29/9.48 (multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.48 inference(symmetry,[status(thm)],[669])).
% 9.29/9.48 tff(671,plain,
% 9.29/9.48 (multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)) = multiplication(c(X0!2), c(X1!1))),
% 9.29/9.48 inference(transitivity,[status(thm)],[337, 670, 667, 666, 663, 424, 654, 650, 350, 342, 211, 647])).
% 9.29/9.48 tff(672,plain,
% 9.29/9.48 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[671, 645])).
% 9.29/9.48 tff(673,plain,
% 9.29/9.48 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.48 inference(symmetry,[status(thm)],[672])).
% 9.29/9.48 tff(674,assumption,(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one), introduced(assumption)).
% 9.29/9.48 tff(675,plain,
% 9.29/9.48 (one = addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))),
% 9.29/9.48 inference(symmetry,[status(thm)],[674])).
% 9.29/9.48 tff(676,plain,
% 9.29/9.48 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[378, 256])).
% 9.29/9.48 tff(677,plain,
% 9.29/9.48 (addition(c(tptp_fun_X1_0(X1!1)), c(X1!1)) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 9.29/9.48 inference(symmetry,[status(thm)],[676])).
% 9.29/9.48 tff(678,plain,
% 9.29/9.48 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1))))),
% 9.29/9.48 inference(rewrite,[status(thm)],[])).
% 9.29/9.48 tff(679,plain,
% 9.29/9.48 (((~test(X1!1)) | (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1))) | (~test(tptp_fun_X1_0(X1!1)))) <=> ((~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1))))),
% 9.29/9.48 inference(rewrite,[status(thm)],[])).
% 9.29/9.48 tff(680,plain,
% 9.29/9.48 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1))) | (~test(tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1)))))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[679])).
% 9.29/9.48 tff(681,plain,
% 9.29/9.48 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1))) | (~test(tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1))))),
% 9.29/9.48 inference(transitivity,[status(thm)],[680, 678])).
% 9.29/9.48 tff(682,plain,
% 9.29/9.48 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1))) | (~test(tptp_fun_X1_0(X1!1))))),
% 9.29/9.48 inference(quant_inst,[status(thm)],[])).
% 9.29/9.48 tff(683,plain,
% 9.29/9.48 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1)))),
% 9.29/9.48 inference(modus_ponens,[status(thm)],[682, 681])).
% 9.29/9.48 tff(684,plain,
% 9.29/9.48 ((~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1)))),
% 9.29/9.48 inference(unit_resolution,[status(thm)],[683, 459, 60])).
% 9.29/9.48 tff(685,plain,
% 9.29/9.48 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1))),
% 9.29/9.48 inference(unit_resolution,[status(thm)],[684, 97])).
% 9.29/9.48 tff(686,plain,
% 9.29/9.48 (zero = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 9.29/9.48 inference(symmetry,[status(thm)],[84])).
% 9.29/9.48 tff(687,plain,
% 9.29/9.48 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 9.29/9.48 inference(transitivity,[status(thm)],[161, 686])).
% 9.29/9.48 tff(688,plain,
% 9.29/9.48 (c(multiplication(X0!2, tptp_fun_X1_0(X0!2))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[687])).
% 9.29/9.48 tff(689,plain,
% 9.29/9.48 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(X0!2, tptp_fun_X1_0(X0!2))) = addition(c(X0!2), c(tptp_fun_X1_0(X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(X0!2, tptp_fun_X1_0(X0!2))) = addition(c(X0!2), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.48 inference(rewrite,[status(thm)],[])).
% 9.29/9.48 tff(690,plain,
% 9.29/9.48 (((~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(X0!2, tptp_fun_X1_0(X0!2))) = addition(c(X0!2), c(tptp_fun_X1_0(X0!2)))) | (~test(X0!2))) <=> ((~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(X0!2, tptp_fun_X1_0(X0!2))) = addition(c(X0!2), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.48 inference(rewrite,[status(thm)],[])).
% 9.29/9.48 tff(691,plain,
% 9.29/9.48 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(X0!2, tptp_fun_X1_0(X0!2))) = addition(c(X0!2), c(tptp_fun_X1_0(X0!2)))) | (~test(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(X0!2, tptp_fun_X1_0(X0!2))) = addition(c(X0!2), c(tptp_fun_X1_0(X0!2))))))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[690])).
% 9.29/9.48 tff(692,plain,
% 9.29/9.48 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(X0!2, tptp_fun_X1_0(X0!2))) = addition(c(X0!2), c(tptp_fun_X1_0(X0!2)))) | (~test(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(X0!2, tptp_fun_X1_0(X0!2))) = addition(c(X0!2), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.48 inference(transitivity,[status(thm)],[691, 689])).
% 9.29/9.48 tff(693,plain,
% 9.29/9.48 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(X0!2, tptp_fun_X1_0(X0!2))) = addition(c(X0!2), c(tptp_fun_X1_0(X0!2)))) | (~test(X0!2)))),
% 9.29/9.48 inference(quant_inst,[status(thm)],[])).
% 9.29/9.48 tff(694,plain,
% 9.29/9.48 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(X0!2, tptp_fun_X1_0(X0!2))) = addition(c(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.48 inference(modus_ponens,[status(thm)],[693, 692])).
% 9.29/9.48 tff(695,plain,
% 9.29/9.48 ((~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(X0!2, tptp_fun_X1_0(X0!2))) = addition(c(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.48 inference(unit_resolution,[status(thm)],[694, 459, 142])).
% 9.29/9.48 tff(696,plain,
% 9.29/9.48 (c(multiplication(X0!2, tptp_fun_X1_0(X0!2))) = addition(c(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(unit_resolution,[status(thm)],[695, 172])).
% 9.29/9.48 tff(697,plain,
% 9.29/9.48 (addition(c(X0!2), c(tptp_fun_X1_0(X0!2))) = c(multiplication(X0!2, tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(symmetry,[status(thm)],[696])).
% 9.29/9.48 tff(698,plain,
% 9.29/9.48 (addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))) = addition(c(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[331])).
% 9.29/9.48 tff(699,plain,
% 9.29/9.48 (addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))),
% 9.29/9.48 inference(transitivity,[status(thm)],[698, 697, 688, 685, 677, 68, 675, 673, 255, 630])).
% 9.29/9.48 tff(700,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[523])).
% 9.29/9.48 tff(701,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), X1!1))),
% 9.29/9.48 inference(symmetry,[status(thm)],[700])).
% 9.29/9.48 tff(702,plain,
% 9.29/9.48 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.48 inference(quant_inst,[status(thm)],[])).
% 9.29/9.48 tff(703,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.48 inference(unit_resolution,[status(thm)],[702, 282])).
% 9.29/9.48 tff(704,plain,
% 9.29/9.48 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.48 inference(symmetry,[status(thm)],[703])).
% 9.29/9.48 tff(705,plain,
% 9.29/9.48 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), X1!1))),
% 9.29/9.48 inference(transitivity,[status(thm)],[704, 701])).
% 9.29/9.48 tff(706,plain,
% 9.29/9.48 (multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[705, 699])).
% 9.29/9.48 tff(707,plain,
% 9.29/9.48 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)), multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.48 inference(quant_inst,[status(thm)],[])).
% 9.29/9.48 tff(708,plain,
% 9.29/9.48 (multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)), multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.48 inference(unit_resolution,[status(thm)],[707, 600])).
% 9.29/9.48 tff(709,plain,
% 9.29/9.48 (addition(multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)), multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.48 inference(symmetry,[status(thm)],[708])).
% 9.29/9.48 tff(710,plain,
% 9.29/9.48 (multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[705])).
% 9.29/9.48 tff(711,plain,
% 9.29/9.48 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(symmetry,[status(thm)],[710])).
% 9.29/9.48 tff(712,plain,
% 9.29/9.48 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(multiplication(c(X0!2), X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.48 inference(quant_inst,[status(thm)],[])).
% 9.29/9.48 tff(713,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(multiplication(c(X0!2), X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(unit_resolution,[status(thm)],[712, 282])).
% 9.29/9.48 tff(714,plain,
% 9.29/9.48 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.48 inference(quant_inst,[status(thm)],[])).
% 9.29/9.48 tff(715,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(unit_resolution,[status(thm)],[714, 282])).
% 9.29/9.48 tff(716,plain,
% 9.29/9.48 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.48 inference(symmetry,[status(thm)],[715])).
% 9.29/9.48 tff(717,plain,
% 9.29/9.48 (multiplication(X1!1, c(X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.29/9.48 inference(symmetry,[status(thm)],[547])).
% 9.29/9.48 tff(718,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2)))) = multiplication(X1!1, c(X0!2))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[115, 181])).
% 9.29/9.48 tff(719,plain,
% 9.29/9.48 (c(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = c(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[535])).
% 9.29/9.48 tff(720,plain,
% 9.29/9.48 (multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1))) = c(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.48 inference(symmetry,[status(thm)],[533])).
% 9.29/9.48 tff(721,plain,
% 9.29/9.48 (multiplication(c(X0!2), X1!1) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[182, 378])).
% 9.29/9.48 tff(722,plain,
% 9.29/9.48 (multiplication(c(X0!2), X1!1) = multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.29/9.48 inference(transitivity,[status(thm)],[721, 720, 719, 544, 718, 717])).
% 9.29/9.48 tff(723,plain,
% 9.29/9.48 (multiplication(multiplication(c(X0!2), X1!1), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[722])).
% 9.29/9.48 tff(724,plain,
% 9.29/9.48 (multiplication(multiplication(c(X0!2), X1!1), c(tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(transitivity,[status(thm)],[723, 716, 502, 501, 492, 379, 491, 390, 504, 401, 503])).
% 9.29/9.48 tff(725,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(multiplication(c(X0!2), X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[724])).
% 9.29/9.48 tff(726,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(multiplication(c(X0!2), X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.48 inference(symmetry,[status(thm)],[725])).
% 9.29/9.48 tff(727,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X1!1)), zero) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.48 inference(symmetry,[status(thm)],[502])).
% 9.29/9.48 tff(728,plain,
% 9.29/9.48 (zero = multiplication(c(tptp_fun_X1_0(X1!1)), zero)),
% 9.29/9.48 inference(symmetry,[status(thm)],[501])).
% 9.29/9.48 tff(729,plain,
% 9.29/9.48 (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(transitivity,[status(thm)],[391, 388, 380, 86, 728, 727, 726, 713, 711])).
% 9.29/9.48 tff(730,plain,
% 9.29/9.48 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(quant_inst,[status(thm)],[])).
% 9.29/9.48 tff(731,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2))),
% 9.29/9.48 inference(unit_resolution,[status(thm)],[730, 282])).
% 9.29/9.48 tff(732,plain,
% 9.29/9.48 (multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), X1!1)),
% 9.29/9.48 inference(symmetry,[status(thm)],[721])).
% 9.29/9.48 tff(733,plain,
% 9.29/9.48 (c(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = c(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.48 inference(symmetry,[status(thm)],[719])).
% 9.29/9.48 tff(734,plain,
% 9.29/9.48 (multiplication(X1!1, c(X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.48 inference(symmetry,[status(thm)],[718])).
% 9.29/9.48 tff(735,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(c(X0!2), X1!1)),
% 9.29/9.48 inference(transitivity,[status(thm)],[547, 734, 545, 733, 533, 732])).
% 9.29/9.48 tff(736,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), X1!1))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[735])).
% 9.29/9.48 tff(737,plain,
% 9.29/9.48 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(symmetry,[status(thm)],[736])).
% 9.29/9.48 tff(738,plain,
% 9.29/9.48 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2))),
% 9.29/9.48 inference(transitivity,[status(thm)],[704, 701, 737, 731])).
% 9.29/9.48 tff(739,plain,
% 9.29/9.48 (multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[738])).
% 9.29/9.48 tff(740,plain,
% 9.29/9.48 (multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2))),
% 9.29/9.48 inference(symmetry,[status(thm)],[739])).
% 9.29/9.48 tff(741,plain,
% 9.29/9.48 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(quant_inst,[status(thm)],[])).
% 9.29/9.48 tff(742,plain,
% 9.29/9.48 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 9.29/9.48 inference(unit_resolution,[status(thm)],[741, 282])).
% 9.29/9.48 tff(743,plain,
% 9.29/9.48 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)) = tptp_fun_X1_0(X0!2)),
% 9.29/9.48 inference(transitivity,[status(thm)],[333, 330, 322, 225])).
% 9.29/9.48 tff(744,plain,
% 9.29/9.48 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[743])).
% 9.29/9.48 tff(745,plain,
% 9.29/9.48 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)))),
% 9.29/9.48 inference(symmetry,[status(thm)],[744])).
% 9.29/9.48 tff(746,plain,
% 9.29/9.48 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))) = multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2))),
% 9.29/9.48 inference(transitivity,[status(thm)],[704, 701, 737, 731, 745, 742, 740])).
% 9.29/9.48 tff(747,plain,
% 9.29/9.48 (addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)), multiplication(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[746, 729])).
% 9.29/9.48 tff(748,plain,
% 9.29/9.48 (zero = c(addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.29/9.48 inference(transitivity,[status(thm)],[492, 379, 491, 390])).
% 9.29/9.48 tff(749,plain,
% 9.29/9.48 (addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), zero) = addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.29/9.48 inference(monotonicity,[status(thm)],[748])).
% 9.29/9.48 tff(750,plain,
% 9.29/9.48 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), zero) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.48 inference(quant_inst,[status(thm)],[])).
% 9.29/9.48 tff(751,plain,
% 9.29/9.48 (addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), zero) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.48 inference(unit_resolution,[status(thm)],[750, 366])).
% 9.29/9.48 tff(752,plain,
% 9.29/9.48 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))) = addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), zero)),
% 9.29/9.49 inference(symmetry,[status(thm)],[751])).
% 9.29/9.49 tff(753,plain,
% 9.29/9.49 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 9.29/9.49 inference(symmetry,[status(thm)],[731])).
% 9.29/9.49 tff(754,plain,
% 9.29/9.49 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.49 inference(rewrite,[status(thm)],[])).
% 9.29/9.49 tff(755,plain,
% 9.29/9.49 (((~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) | (~test(tptp_fun_X1_0(X1!1)))) <=> ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.49 inference(rewrite,[status(thm)],[])).
% 9.29/9.49 tff(756,plain,
% 9.29/9.49 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) | (~test(tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[755])).
% 9.29/9.49 tff(757,plain,
% 9.29/9.49 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) | (~test(tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.49 inference(transitivity,[status(thm)],[756, 754])).
% 9.29/9.49 tff(758,plain,
% 9.29/9.49 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) | (~test(tptp_fun_X1_0(X1!1))))),
% 9.29/9.49 inference(quant_inst,[status(thm)],[])).
% 9.29/9.49 tff(759,plain,
% 9.29/9.49 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.49 inference(modus_ponens,[status(thm)],[758, 757])).
% 9.29/9.49 tff(760,plain,
% 9.29/9.49 (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(unit_resolution,[status(thm)],[759, 203, 97])).
% 9.29/9.49 tff(761,plain,
% 9.29/9.49 ((~![A: $i] : (addition(A, A) = A)) | (addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)) = tptp_fun_X1_0(X1!1))),
% 9.29/9.49 inference(quant_inst,[status(thm)],[])).
% 9.29/9.49 tff(762,plain,
% 9.29/9.49 (addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)) = tptp_fun_X1_0(X1!1)),
% 9.29/9.49 inference(unit_resolution,[status(thm)],[761, 301])).
% 9.29/9.49 tff(763,plain,
% 9.29/9.49 (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = c(tptp_fun_X1_0(X1!1))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[762])).
% 9.29/9.49 tff(764,plain,
% 9.29/9.49 (c(tptp_fun_X1_0(X1!1)) = c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(symmetry,[status(thm)],[763])).
% 9.29/9.49 tff(765,plain,
% 9.29/9.49 (X1!1 = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(transitivity,[status(thm)],[378, 764, 760])).
% 9.29/9.49 tff(766,plain,
% 9.29/9.49 (multiplication(X1!1, c(X0!2)) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[765, 225])).
% 9.29/9.49 tff(767,plain,
% 9.29/9.49 (multiplication(c(X0!2), X1!1) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(transitivity,[status(thm)],[721, 720, 719, 544, 718, 766, 753, 736, 700, 703, 752, 749, 747, 709, 706, 622, 619, 502, 501, 492, 379, 491, 390])).
% 9.29/9.49 tff(768,plain,
% 9.29/9.49 (addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[335])).
% 9.29/9.49 tff(769,plain,
% 9.29/9.49 (addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(symmetry,[status(thm)],[768])).
% 9.29/9.49 tff(770,plain,
% 9.29/9.49 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))) = addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 9.29/9.49 inference(quant_inst,[status(thm)],[])).
% 9.29/9.49 tff(771,plain,
% 9.29/9.49 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))) = addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.49 inference(unit_resolution,[status(thm)],[770, 79])).
% 9.29/9.49 tff(772,plain,
% 9.29/9.49 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))) = addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(transitivity,[status(thm)],[771, 769])).
% 9.29/9.49 tff(773,plain,
% 9.29/9.49 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))), multiplication(c(X0!2), X1!1)) = addition(addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[772, 767])).
% 9.29/9.49 tff(774,plain,
% 9.29/9.49 (addition(addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))), multiplication(c(X0!2), X1!1))),
% 9.29/9.49 inference(symmetry,[status(thm)],[773])).
% 9.29/9.49 tff(775,plain,
% 9.29/9.49 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.29/9.49 inference(quant_inst,[status(thm)],[])).
% 9.29/9.49 tff(776,plain,
% 9.29/9.49 (addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.29/9.49 inference(unit_resolution,[status(thm)],[775, 487])).
% 9.29/9.49 tff(777,plain,
% 9.29/9.49 (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.49 inference(symmetry,[status(thm)],[657])).
% 9.29/9.49 tff(778,plain,
% 9.29/9.49 (multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(symmetry,[status(thm)],[407])).
% 9.29/9.49 tff(779,plain,
% 9.29/9.49 (multiplication(zero, tptp_fun_X1_0(X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 9.29/9.49 inference(symmetry,[status(thm)],[405])).
% 9.29/9.49 tff(780,plain,
% 9.29/9.49 (zero = multiplication(zero, tptp_fun_X1_0(X1!1))),
% 9.29/9.49 inference(symmetry,[status(thm)],[377])).
% 9.29/9.49 tff(781,plain,
% 9.29/9.49 (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.49 inference(transitivity,[status(thm)],[391, 388, 380, 86, 780, 779, 778, 777])).
% 9.29/9.49 tff(782,plain,
% 9.29/9.49 (multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.49 inference(transitivity,[status(thm)],[440, 439])).
% 9.29/9.49 tff(783,plain,
% 9.29/9.49 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[782, 781])).
% 9.29/9.49 tff(784,plain,
% 9.29/9.49 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = multiplication(c(X0!2), c(X1!1))),
% 9.29/9.49 inference(transitivity,[status(thm)],[783, 659, 368, 335])).
% 9.29/9.49 tff(785,plain,
% 9.29/9.49 (addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[784])).
% 9.29/9.49 tff(786,plain,
% 9.29/9.49 (addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.29/9.49 inference(symmetry,[status(thm)],[785])).
% 9.29/9.49 tff(787,plain,
% 9.29/9.49 (addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))) = addition(c(X1!1), c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[256])).
% 9.29/9.49 tff(788,plain,
% 9.29/9.49 (addition(c(X1!1), c(tptp_fun_X1_0(X1!1))) = addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(symmetry,[status(thm)],[787])).
% 9.29/9.49 tff(789,plain,
% 9.29/9.49 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(X1!1, tptp_fun_X1_0(X1!1))) = addition(c(X1!1), c(tptp_fun_X1_0(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(X1!1, tptp_fun_X1_0(X1!1))) = addition(c(X1!1), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.49 inference(rewrite,[status(thm)],[])).
% 9.29/9.49 tff(790,plain,
% 9.29/9.49 (((~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(X1!1, tptp_fun_X1_0(X1!1))) = addition(c(X1!1), c(tptp_fun_X1_0(X1!1)))) | (~test(X1!1))) <=> ((~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(X1!1, tptp_fun_X1_0(X1!1))) = addition(c(X1!1), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.49 inference(rewrite,[status(thm)],[])).
% 9.29/9.49 tff(791,plain,
% 9.29/9.49 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(X1!1, tptp_fun_X1_0(X1!1))) = addition(c(X1!1), c(tptp_fun_X1_0(X1!1)))) | (~test(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(X1!1, tptp_fun_X1_0(X1!1))) = addition(c(X1!1), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[790])).
% 9.29/9.49 tff(792,plain,
% 9.29/9.49 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(X1!1, tptp_fun_X1_0(X1!1))) = addition(c(X1!1), c(tptp_fun_X1_0(X1!1)))) | (~test(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(X1!1, tptp_fun_X1_0(X1!1))) = addition(c(X1!1), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.49 inference(transitivity,[status(thm)],[791, 789])).
% 9.29/9.49 tff(793,plain,
% 9.29/9.49 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(X1!1, tptp_fun_X1_0(X1!1))) = addition(c(X1!1), c(tptp_fun_X1_0(X1!1)))) | (~test(X1!1)))),
% 9.29/9.49 inference(quant_inst,[status(thm)],[])).
% 9.29/9.49 tff(794,plain,
% 9.29/9.49 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(X1!1, tptp_fun_X1_0(X1!1))) = addition(c(X1!1), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.49 inference(modus_ponens,[status(thm)],[793, 792])).
% 9.29/9.49 tff(795,plain,
% 9.29/9.49 ((~test(tptp_fun_X1_0(X1!1))) | (c(multiplication(X1!1, tptp_fun_X1_0(X1!1))) = addition(c(X1!1), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.49 inference(unit_resolution,[status(thm)],[794, 459, 60])).
% 9.29/9.49 tff(796,plain,
% 9.29/9.49 (c(multiplication(X1!1, tptp_fun_X1_0(X1!1))) = addition(c(X1!1), c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(unit_resolution,[status(thm)],[795, 97])).
% 9.29/9.49 tff(797,plain,
% 9.29/9.49 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 9.29/9.49 inference(transitivity,[status(thm)],[86, 686])).
% 9.29/9.49 tff(798,plain,
% 9.29/9.49 (c(multiplication(X1!1, tptp_fun_X1_0(X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[797])).
% 9.29/9.49 tff(799,plain,
% 9.29/9.49 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = c(multiplication(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(symmetry,[status(thm)],[798])).
% 9.29/9.49 tff(800,plain,
% 9.29/9.49 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(transitivity,[status(thm)],[799, 796, 788])).
% 9.29/9.49 tff(801,plain,
% 9.29/9.49 (multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[800])).
% 9.29/9.49 tff(802,plain,
% 9.29/9.49 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 9.29/9.49 inference(symmetry,[status(thm)],[801])).
% 9.29/9.49 tff(803,plain,
% 9.29/9.49 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.49 inference(quant_inst,[status(thm)],[])).
% 9.29/9.49 tff(804,plain,
% 9.29/9.49 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.49 inference(unit_resolution,[status(thm)],[803, 600])).
% 9.29/9.49 tff(805,plain,
% 9.29/9.49 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.49 inference(symmetry,[status(thm)],[804])).
% 9.29/9.49 tff(806,plain,
% 9.29/9.49 (X1!1 = c(c(X1!1))),
% 9.29/9.49 inference(transitivity,[status(thm)],[378, 219])).
% 9.29/9.49 tff(807,plain,
% 9.29/9.49 (X0!2 = c(c(X0!2))),
% 9.29/9.49 inference(transitivity,[status(thm)],[230, 227])).
% 9.29/9.49 tff(808,plain,
% 9.29/9.49 (multiplication(X0!2, X1!1) = multiplication(c(c(X0!2)), c(c(X1!1)))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[807, 806])).
% 9.29/9.49 tff(809,plain,
% 9.29/9.49 (multiplication(c(c(X0!2)), c(c(X1!1))) = multiplication(X0!2, X1!1)),
% 9.29/9.49 inference(symmetry,[status(thm)],[808])).
% 9.29/9.49 tff(810,plain,
% 9.29/9.49 (multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))) = multiplication(c(c(X0!2)), c(c(X1!1)))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[227, 219])).
% 9.29/9.49 tff(811,plain,
% 9.29/9.49 (multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))) = multiplication(X0!2, X1!1)),
% 9.29/9.49 inference(transitivity,[status(thm)],[810, 809])).
% 9.29/9.49 tff(812,plain,
% 9.29/9.49 (multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(X0!2, c(X1!1))),
% 9.29/9.49 inference(transitivity,[status(thm)],[640, 625])).
% 9.29/9.49 tff(813,plain,
% 9.29/9.49 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[812, 811])).
% 9.29/9.49 tff(814,plain,
% 9.29/9.49 (addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.49 inference(symmetry,[status(thm)],[813])).
% 9.29/9.49 tff(815,plain,
% 9.29/9.49 (addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 9.29/9.49 inference(transitivity,[status(thm)],[814, 805, 802])).
% 9.29/9.49 tff(816,plain,
% 9.29/9.49 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))),
% 9.29/9.49 inference(transitivity,[status(thm)],[685, 677, 68, 675, 673, 255, 630])).
% 9.29/9.49 tff(817,plain,
% 9.29/9.49 (multiplication(tptp_fun_X1_0(X0!2), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[816])).
% 9.29/9.49 tff(818,plain,
% 9.29/9.49 (multiplication(tptp_fun_X1_0(X0!2), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 9.29/9.49 inference(symmetry,[status(thm)],[817])).
% 9.29/9.49 tff(819,plain,
% 9.29/9.49 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X0!2), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(quant_inst,[status(thm)],[])).
% 9.29/9.49 tff(820,plain,
% 9.29/9.49 (multiplication(tptp_fun_X1_0(X0!2), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1))),
% 9.29/9.49 inference(unit_resolution,[status(thm)],[819, 282])).
% 9.29/9.49 tff(821,plain,
% 9.29/9.49 (multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)) = multiplication(tptp_fun_X1_0(X0!2), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(symmetry,[status(thm)],[820])).
% 9.29/9.49 tff(822,plain,
% 9.29/9.49 (multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[628])).
% 9.29/9.49 tff(823,plain,
% 9.29/9.49 (multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))))),
% 9.29/9.49 inference(symmetry,[status(thm)],[822])).
% 9.29/9.49 tff(824,plain,
% 9.29/9.49 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))))),
% 9.29/9.49 inference(quant_inst,[status(thm)],[])).
% 9.29/9.49 tff(825,plain,
% 9.29/9.49 (multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.49 inference(unit_resolution,[status(thm)],[824, 600])).
% 9.29/9.49 tff(826,plain,
% 9.29/9.49 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.49 inference(symmetry,[status(thm)],[825])).
% 9.29/9.49 tff(827,plain,
% 9.29/9.49 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))))),
% 9.29/9.49 inference(transitivity,[status(thm)],[826, 823])).
% 9.29/9.49 tff(828,plain,
% 9.29/9.49 (multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[827])).
% 9.29/9.49 tff(829,plain,
% 9.29/9.49 (multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.49 inference(transitivity,[status(thm)],[420, 660])).
% 9.29/9.49 tff(830,plain,
% 9.29/9.49 (multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))), tptp_fun_X1_0(X1!1))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[829])).
% 9.29/9.49 tff(831,plain,
% 9.29/9.49 (multiplication(c(X0!2), c(X1!1)) = multiplication(tptp_fun_X1_0(X0!2), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 9.29/9.49 inference(transitivity,[status(thm)],[646, 430, 341, 349, 649, 653, 425, 662, 665, 357, 669, 830, 828, 821, 818])).
% 9.29/9.49 tff(832,plain,
% 9.29/9.49 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[831, 815])).
% 9.29/9.49 tff(833,plain,
% 9.29/9.49 (addition(multiplication(tptp_fun_X1_0(X0!2), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 9.29/9.49 inference(symmetry,[status(thm)],[832])).
% 9.29/9.49 tff(834,plain,
% 9.29/9.49 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))))),
% 9.29/9.49 inference(quant_inst,[status(thm)],[])).
% 9.29/9.49 tff(835,plain,
% 9.29/9.49 (multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))),
% 9.29/9.49 inference(unit_resolution,[status(thm)],[834, 252])).
% 9.29/9.49 tff(836,plain,
% 9.29/9.49 (multiplication(c(tptp_fun_X1_0(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[638])).
% 9.29/9.49 tff(837,plain,
% 9.29/9.49 (multiplication(c(tptp_fun_X1_0(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 9.29/9.49 inference(transitivity,[status(thm)],[836, 513, 511, 508, 686])).
% 9.29/9.49 tff(838,plain,
% 9.29/9.49 (c(multiplication(c(tptp_fun_X1_0(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[837])).
% 9.29/9.49 tff(839,plain,
% 9.29/9.49 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = c(multiplication(c(tptp_fun_X1_0(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.49 inference(symmetry,[status(thm)],[838])).
% 9.29/9.49 tff(840,plain,
% 9.29/9.49 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[735])).
% 9.29/9.49 tff(841,plain,
% 9.29/9.49 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))) = multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1))),
% 9.29/9.49 inference(transitivity,[status(thm)],[552, 551, 840])).
% 9.29/9.49 tff(842,plain,
% 9.29/9.49 (c(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))) = c(multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[841])).
% 9.29/9.49 tff(843,plain,
% 9.29/9.49 (c(multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1))) = c(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 9.29/9.49 inference(symmetry,[status(thm)],[842])).
% 9.29/9.49 tff(844,plain,
% 9.29/9.49 (multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1)) = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 9.29/9.49 inference(transitivity,[status(thm)],[524, 521, 518, 517, 686])).
% 9.29/9.49 tff(845,plain,
% 9.29/9.49 (c(multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[844])).
% 9.29/9.49 tff(846,plain,
% 9.29/9.49 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = c(multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1)))),
% 9.29/9.49 inference(symmetry,[status(thm)],[845])).
% 9.29/9.49 tff(847,plain,
% 9.29/9.49 (addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))) = c(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 9.29/9.49 inference(transitivity,[status(thm)],[698, 697, 688, 846, 843])).
% 9.29/9.49 tff(848,plain,
% 9.29/9.49 (multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = multiplication(c(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))), c(multiplication(c(tptp_fun_X1_0(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[847, 839])).
% 9.29/9.49 tff(849,plain,
% 9.29/9.49 (multiplication(c(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))), c(multiplication(c(tptp_fun_X1_0(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))) = multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 9.29/9.49 inference(symmetry,[status(thm)],[848])).
% 9.29/9.49 tff(850,plain,
% 9.29/9.49 (addition(c(X0!2), c(tptp_fun_X1_0(X0!2))) = addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.49 inference(symmetry,[status(thm)],[698])).
% 9.29/9.49 tff(851,plain,
% 9.29/9.49 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = c(multiplication(X0!2, tptp_fun_X1_0(X0!2)))),
% 9.29/9.49 inference(symmetry,[status(thm)],[688])).
% 9.29/9.49 tff(852,plain,
% 9.29/9.49 (c(multiplication(c(tptp_fun_X1_0(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.49 inference(transitivity,[status(thm)],[838, 851, 696, 850])).
% 9.29/9.49 tff(853,plain,
% 9.29/9.49 (c(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 9.29/9.49 inference(transitivity,[status(thm)],[842, 845])).
% 9.29/9.49 tff(854,plain,
% 9.29/9.49 (multiplication(c(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))), c(multiplication(c(tptp_fun_X1_0(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))) = multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.49 inference(monotonicity,[status(thm)],[853, 852])).
% 9.29/9.49 tff(855,plain,
% 9.29/9.49 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))), c(multiplication(c(tptp_fun_X1_0(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))))),
% 9.29/9.49 inference(symmetry,[status(thm)],[854])).
% 9.29/9.49 tff(856,plain,
% 9.29/9.49 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.49 inference(quant_inst,[status(thm)],[])).
% 9.29/9.49 tff(857,plain,
% 9.29/9.49 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.49 inference(unit_resolution,[status(thm)],[856, 600])).
% 9.29/9.49 tff(858,plain,
% 9.29/9.49 (addition(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.49 inference(symmetry,[status(thm)],[857])).
% 9.29/9.49 tff(859,plain,
% 9.29/9.49 (c(c(tptp_fun_X1_0(X1!1))) = tptp_fun_X1_0(X1!1)),
% 9.29/9.49 inference(transitivity,[status(thm)],[648, 217])).
% 9.29/9.49 tff(860,plain,
% 9.29/9.49 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.50 inference(rewrite,[status(thm)],[])).
% 9.29/9.50 tff(861,plain,
% 9.29/9.50 (((~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) | (~test(tptp_fun_X1_0(X0!2)))) <=> ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.50 inference(rewrite,[status(thm)],[])).
% 9.29/9.50 tff(862,plain,
% 9.29/9.50 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) | (~test(tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))))))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[861])).
% 9.29/9.50 tff(863,plain,
% 9.29/9.50 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) | (~test(tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.50 inference(transitivity,[status(thm)],[862, 860])).
% 9.29/9.50 tff(864,plain,
% 9.29/9.50 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) | (~test(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(865,plain,
% 9.29/9.50 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(modus_ponens,[status(thm)],[864, 863])).
% 9.29/9.50 tff(866,plain,
% 9.29/9.50 (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[865, 203, 172])).
% 9.29/9.50 tff(867,plain,
% 9.29/9.50 ((~![A: $i] : (addition(A, A) = A)) | (addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)) = tptp_fun_X1_0(X0!2))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(868,plain,
% 9.29/9.50 (addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)) = tptp_fun_X1_0(X0!2)),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[867, 301])).
% 9.29/9.50 tff(869,plain,
% 9.29/9.50 (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = c(tptp_fun_X1_0(X0!2))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[868])).
% 9.29/9.50 tff(870,plain,
% 9.29/9.50 (c(tptp_fun_X1_0(X0!2)) = c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(symmetry,[status(thm)],[869])).
% 9.29/9.50 tff(871,plain,
% 9.29/9.50 (c(tptp_fun_X1_0(X0!2)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(transitivity,[status(thm)],[870, 866])).
% 9.29/9.50 tff(872,plain,
% 9.29/9.50 (multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1)))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[871, 859])).
% 9.29/9.50 tff(873,plain,
% 9.29/9.50 (multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.50 inference(symmetry,[status(thm)],[872])).
% 9.29/9.50 tff(874,plain,
% 9.29/9.50 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(875,plain,
% 9.29/9.50 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[874, 282])).
% 9.29/9.50 tff(876,plain,
% 9.29/9.50 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[641])).
% 9.29/9.50 tff(877,plain,
% 9.29/9.50 (multiplication(c(tptp_fun_X1_0(X0!2)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.50 inference(symmetry,[status(thm)],[876])).
% 9.29/9.50 tff(878,plain,
% 9.29/9.50 (multiplication(c(tptp_fun_X1_0(X0!2)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[638])).
% 9.29/9.50 tff(879,plain,
% 9.29/9.50 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.50 inference(symmetry,[status(thm)],[878])).
% 9.29/9.50 tff(880,plain,
% 9.29/9.50 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(881,plain,
% 9.29/9.50 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[880, 282])).
% 9.29/9.50 tff(882,plain,
% 9.29/9.50 (multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(symmetry,[status(thm)],[881])).
% 9.29/9.50 tff(883,plain,
% 9.29/9.50 (multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[641])).
% 9.29/9.50 tff(884,plain,
% 9.29/9.50 (multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(symmetry,[status(thm)],[883])).
% 9.29/9.50 tff(885,plain,
% 9.29/9.50 (multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))) = c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.50 inference(transitivity,[status(thm)],[884, 882, 879, 877, 875, 873, 285])).
% 9.29/9.50 tff(886,plain,
% 9.29/9.50 (multiplication(multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[885])).
% 9.29/9.50 tff(887,plain,
% 9.29/9.50 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))), zero) = multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(888,plain,
% 9.29/9.50 (addition(multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))), zero) = multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[887, 366])).
% 9.29/9.50 tff(889,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))) = c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.50 inference(transitivity,[status(thm)],[636, 631, 271])).
% 9.29/9.50 tff(890,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[889])).
% 9.29/9.50 tff(891,plain,
% 9.29/9.50 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(892,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[891, 282])).
% 9.29/9.50 tff(893,plain,
% 9.29/9.50 (multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(symmetry,[status(thm)],[892])).
% 9.29/9.50 tff(894,plain,
% 9.29/9.50 (multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[359])).
% 9.29/9.50 tff(895,plain,
% 9.29/9.50 (multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))) = zero),
% 9.29/9.50 inference(transitivity,[status(thm)],[894, 893, 890, 657, 407, 405, 377])).
% 9.29/9.50 tff(896,plain,
% 9.29/9.50 (addition(multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))), zero)),
% 9.29/9.50 inference(monotonicity,[status(thm)],[895])).
% 9.29/9.50 tff(897,plain,
% 9.29/9.50 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), multiplication(c(X0!2), c(X1!1))), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(898,plain,
% 9.29/9.50 (multiplication(addition(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), multiplication(c(X0!2), c(X1!1))), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[897, 252])).
% 9.29/9.50 tff(899,plain,
% 9.29/9.50 (addition(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[626])).
% 9.29/9.50 tff(900,plain,
% 9.29/9.50 (addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.50 inference(symmetry,[status(thm)],[899])).
% 9.29/9.50 tff(901,plain,
% 9.29/9.50 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = addition(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.50 inference(transitivity,[status(thm)],[612, 900])).
% 9.29/9.50 tff(902,plain,
% 9.29/9.50 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(addition(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), multiplication(c(X0!2), c(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[901])).
% 9.29/9.50 tff(903,plain,
% 9.29/9.50 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(transitivity,[status(thm)],[902, 898, 896, 888])).
% 9.29/9.50 tff(904,plain,
% 9.29/9.50 (multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[903])).
% 9.29/9.50 tff(905,plain,
% 9.29/9.50 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(906,plain,
% 9.29/9.50 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[905, 282])).
% 9.29/9.50 tff(907,plain,
% 9.29/9.50 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[656])).
% 9.29/9.50 tff(908,plain,
% 9.29/9.50 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[889])).
% 9.29/9.50 tff(909,plain,
% 9.29/9.50 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(910,plain,
% 9.29/9.50 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[909, 282])).
% 9.29/9.50 tff(911,plain,
% 9.29/9.50 (multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(symmetry,[status(thm)],[910])).
% 9.29/9.50 tff(912,plain,
% 9.29/9.50 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[816])).
% 9.29/9.50 tff(913,plain,
% 9.29/9.50 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(X0!2, c(X1!1))),
% 9.29/9.50 inference(transitivity,[status(thm)],[912, 911, 908, 907, 906, 904, 886, 644, 643, 642, 639, 293, 635, 631, 271, 240, 625])).
% 9.29/9.50 tff(914,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 9.29/9.50 inference(transitivity,[status(thm)],[353, 650, 350, 342, 211, 647, 359])).
% 9.29/9.50 tff(915,plain,
% 9.29/9.50 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[914])).
% 9.29/9.50 tff(916,plain,
% 9.29/9.50 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(917,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[916, 282])).
% 9.29/9.50 tff(918,plain,
% 9.29/9.50 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 9.29/9.50 inference(symmetry,[status(thm)],[156])).
% 9.29/9.50 tff(919,plain,
% 9.29/9.50 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 9.29/9.50 inference(transitivity,[status(thm)],[918, 150, 69])).
% 9.29/9.50 tff(920,plain,
% 9.29/9.50 (c(addition(tptp_fun_X1_0(X0!2), X0!2)) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[919])).
% 9.29/9.50 tff(921,plain,
% 9.29/9.50 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X0!2))))),
% 9.29/9.50 inference(rewrite,[status(thm)],[])).
% 9.29/9.50 tff(922,plain,
% 9.29/9.50 (((~test(X0!2)) | (c(addition(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X0!2))) | (~test(tptp_fun_X1_0(X0!2)))) <=> ((~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X0!2))))),
% 9.29/9.50 inference(rewrite,[status(thm)],[])).
% 9.29/9.50 tff(923,plain,
% 9.29/9.50 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(addition(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X0!2))) | (~test(tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X0!2)))))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[922])).
% 9.29/9.50 tff(924,plain,
% 9.29/9.50 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(addition(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X0!2))) | (~test(tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X0!2))))),
% 9.29/9.50 inference(transitivity,[status(thm)],[923, 921])).
% 9.29/9.50 tff(925,plain,
% 9.29/9.50 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(addition(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X0!2))) | (~test(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(926,plain,
% 9.29/9.50 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X0!2)))),
% 9.29/9.50 inference(modus_ponens,[status(thm)],[925, 924])).
% 9.29/9.50 tff(927,plain,
% 9.29/9.50 ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X0!2)))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[926, 203, 142])).
% 9.29/9.50 tff(928,plain,
% 9.29/9.50 (c(addition(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X0!2))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[927, 172])).
% 9.29/9.50 tff(929,plain,
% 9.29/9.50 (multiplication(c(tptp_fun_X1_0(X0!2)), c(X0!2)) = c(addition(tptp_fun_X1_0(X0!2), X0!2))),
% 9.29/9.50 inference(symmetry,[status(thm)],[928])).
% 9.29/9.50 tff(930,plain,
% 9.29/9.50 (multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X0!2))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[331])).
% 9.29/9.50 tff(931,plain,
% 9.29/9.50 (multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(transitivity,[status(thm)],[930, 929, 920, 504, 401, 503])).
% 9.29/9.50 tff(932,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[931])).
% 9.29/9.50 tff(933,plain,
% 9.29/9.50 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(934,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[933, 282])).
% 9.29/9.50 tff(935,plain,
% 9.29/9.50 (multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(symmetry,[status(thm)],[934])).
% 9.29/9.50 tff(936,plain,
% 9.29/9.50 (multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[638])).
% 9.29/9.50 tff(937,plain,
% 9.29/9.50 (multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.50 inference(transitivity,[status(thm)],[936, 935, 932, 917, 915, 893, 890])).
% 9.29/9.50 tff(938,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(c(X0!2), c(X1!1))),
% 9.29/9.50 inference(transitivity,[status(thm)],[353, 650, 350, 342, 211, 647])).
% 9.29/9.50 tff(939,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[938])).
% 9.29/9.50 tff(940,plain,
% 9.29/9.50 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(941,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[940, 282])).
% 9.29/9.50 tff(942,plain,
% 9.29/9.50 (multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(symmetry,[status(thm)],[941])).
% 9.29/9.50 tff(943,plain,
% 9.29/9.50 (multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[359])).
% 9.29/9.50 tff(944,plain,
% 9.29/9.50 (multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.50 inference(transitivity,[status(thm)],[943, 942, 939])).
% 9.29/9.50 tff(945,plain,
% 9.29/9.50 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[944, 937])).
% 9.29/9.50 tff(946,plain,
% 9.29/9.50 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), tptp_fun_X1_0(X0!2)) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(947,plain,
% 9.29/9.50 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), tptp_fun_X1_0(X0!2)) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[946, 252])).
% 9.29/9.50 tff(948,plain,
% 9.29/9.50 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X0!2)) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), tptp_fun_X1_0(X0!2))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[628])).
% 9.29/9.50 tff(949,plain,
% 9.29/9.50 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.50 inference(transitivity,[status(thm)],[948, 947, 945, 659, 368])).
% 9.29/9.50 tff(950,plain,
% 9.29/9.50 (multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[949])).
% 9.29/9.50 tff(951,plain,
% 9.29/9.50 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(952,plain,
% 9.29/9.50 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[951, 282])).
% 9.29/9.50 tff(953,plain,
% 9.29/9.50 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[914])).
% 9.29/9.50 tff(954,plain,
% 9.29/9.50 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(955,plain,
% 9.29/9.50 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[954, 282])).
% 9.29/9.50 tff(956,plain,
% 9.29/9.50 (multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(symmetry,[status(thm)],[955])).
% 9.29/9.50 tff(957,plain,
% 9.29/9.50 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[816])).
% 9.29/9.50 tff(958,plain,
% 9.29/9.50 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(c(X0!2), c(X1!1))),
% 9.29/9.50 inference(transitivity,[status(thm)],[957, 956, 953, 952, 950, 670, 667, 666, 663, 424, 654, 650, 350, 342, 211, 647])).
% 9.29/9.50 tff(959,plain,
% 9.29/9.50 (addition(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[958, 913])).
% 9.29/9.50 tff(960,plain,
% 9.29/9.50 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = addition(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(symmetry,[status(thm)],[959])).
% 9.29/9.50 tff(961,plain,
% 9.29/9.50 (one = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.50 inference(transitivity,[status(thm)],[675, 960, 858, 855, 849, 835, 833, 771, 786, 776, 774, 490, 480, 473])).
% 9.29/9.50 tff(962,plain,
% 9.29/9.50 (~(one = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 9.29/9.50 inference(or_elim,[status(thm)],[58])).
% 9.29/9.50 tff(963,plain,
% 9.29/9.50 ($false),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[962, 961])).
% 9.29/9.50 tff(964,plain,(~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one)), inference(lemma,lemma(discharge,[]))).
% 9.29/9.50 tff(965,plain,
% 9.29/9.50 (c(X0!2) = c(c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[230])).
% 9.29/9.50 tff(966,plain,
% 9.29/9.50 (c(c(tptp_fun_X1_0(X0!2))) = c(X0!2)),
% 9.29/9.50 inference(symmetry,[status(thm)],[965])).
% 9.29/9.50 tff(967,plain,
% 9.29/9.50 (multiplication(c(X0!2), c(X1!1)) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[965, 623])).
% 9.29/9.50 tff(968,plain,
% 9.29/9.50 (multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X1!1)))) = multiplication(c(X0!2), c(X1!1))),
% 9.29/9.50 inference(symmetry,[status(thm)],[967])).
% 9.29/9.50 tff(969,plain,
% 9.29/9.50 (multiplication(c(X1!1), c(X0!2)) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[623, 965])).
% 9.29/9.50 tff(970,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 9.29/9.50 inference(transitivity,[status(thm)],[353, 969, 350, 561, 211, 968, 359])).
% 9.29/9.50 tff(971,plain,
% 9.29/9.50 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[970])).
% 9.29/9.50 tff(972,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(transitivity,[status(thm)],[657, 407, 405, 377, 492, 379, 491, 390, 504, 401, 503])).
% 9.29/9.50 tff(973,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[972])).
% 9.29/9.50 tff(974,plain,
% 9.29/9.50 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.50 inference(quant_inst,[status(thm)],[])).
% 9.29/9.50 tff(975,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.50 inference(unit_resolution,[status(thm)],[974, 282])).
% 9.29/9.50 tff(976,plain,
% 9.29/9.50 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.50 inference(symmetry,[status(thm)],[975])).
% 9.29/9.50 tff(977,plain,
% 9.29/9.50 (multiplication(X0!2, c(X1!1)) = c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.50 inference(transitivity,[status(thm)],[624, 285])).
% 9.29/9.50 tff(978,plain,
% 9.29/9.50 (multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2)))) = multiplication(c(X1!1), c(X0!2))),
% 9.29/9.50 inference(symmetry,[status(thm)],[969])).
% 9.29/9.50 tff(979,plain,
% 9.29/9.50 (multiplication(c(X0!2), c(X1!1)) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))),
% 9.29/9.50 inference(transitivity,[status(thm)],[967, 430, 575, 349, 978, 573])).
% 9.29/9.50 tff(980,plain,
% 9.29/9.50 (multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[979, 977])).
% 9.29/9.50 tff(981,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))) = multiplication(X0!2, c(X1!1))),
% 9.29/9.50 inference(transitivity,[status(thm)],[636, 631, 271, 240, 625])).
% 9.29/9.50 tff(982,plain,
% 9.29/9.50 (tptp_fun_X1_0(X0!2) = c(c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.50 inference(transitivity,[status(thm)],[331, 965])).
% 9.29/9.50 tff(983,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.50 inference(monotonicity,[status(thm)],[982, 982])).
% 9.29/9.50 tff(984,plain,
% 9.29/9.50 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)) = c(X0!2)),
% 9.29/9.50 inference(transitivity,[status(thm)],[983, 330, 322])).
% 9.29/9.50 tff(985,plain,
% 9.29/9.50 (multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(c(X0!2), c(X1!1))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[984, 256])).
% 9.29/9.51 tff(986,plain,
% 9.29/9.51 (multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[985, 981])).
% 9.29/9.51 tff(987,plain,
% 9.29/9.51 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.51 inference(quant_inst,[status(thm)],[])).
% 9.29/9.51 tff(988,plain,
% 9.29/9.51 (multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.51 inference(unit_resolution,[status(thm)],[987, 282])).
% 9.29/9.51 tff(989,plain,
% 9.29/9.51 (multiplication(multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.51 inference(symmetry,[status(thm)],[988])).
% 9.29/9.51 tff(990,plain,
% 9.29/9.51 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(transitivity,[status(thm)],[659, 368])).
% 9.29/9.51 tff(991,plain,
% 9.29/9.51 (multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[990])).
% 9.29/9.51 tff(992,plain,
% 9.29/9.51 (multiplication(multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[991])).
% 9.29/9.51 tff(993,plain,
% 9.29/9.51 (multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(symmetry,[status(thm)],[991])).
% 9.29/9.51 tff(994,plain,
% 9.29/9.51 (multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))),
% 9.29/9.51 inference(transitivity,[status(thm)],[985, 967, 430, 575, 349, 978, 573])).
% 9.29/9.51 tff(995,plain,
% 9.29/9.51 (multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[994])).
% 9.29/9.51 tff(996,plain,
% 9.29/9.51 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(symmetry,[status(thm)],[995])).
% 9.29/9.51 tff(997,plain,
% 9.29/9.51 (multiplication(c(X0!2), c(X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(symmetry,[status(thm)],[985])).
% 9.29/9.51 tff(998,plain,
% 9.29/9.51 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.51 inference(transitivity,[status(thm)],[358, 997, 420, 660])).
% 9.29/9.51 tff(999,plain,
% 9.29/9.51 (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[998])).
% 9.29/9.51 tff(1000,plain,
% 9.29/9.51 (multiplication(tptp_fun_X1_0(X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 9.29/9.51 inference(symmetry,[status(thm)],[999])).
% 9.29/9.51 tff(1001,plain,
% 9.29/9.51 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))),
% 9.29/9.51 inference(transitivity,[status(thm)],[659, 368, 985, 967, 430, 575, 349, 978, 573])).
% 9.29/9.51 tff(1002,plain,
% 9.29/9.51 (multiplication(tptp_fun_X1_0(X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1001])).
% 9.29/9.51 tff(1003,plain,
% 9.29/9.51 (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1002])).
% 9.29/9.51 tff(1004,plain,
% 9.29/9.51 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)) = c(X1!1)),
% 9.29/9.51 inference(transitivity,[status(thm)],[633, 313, 305])).
% 9.29/9.51 tff(1005,plain,
% 9.29/9.51 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(c(X1!1), c(X0!2))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1004, 331])).
% 9.29/9.51 tff(1006,plain,
% 9.29/9.51 (multiplication(c(X1!1), c(X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1005])).
% 9.29/9.51 tff(1007,assumption,(~(c(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1)))))), introduced(assumption)).
% 9.29/9.51 tff(1008,plain,
% 9.29/9.51 (multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(symmetry,[status(thm)],[644])).
% 9.29/9.51 tff(1009,plain,
% 9.29/9.51 (multiplication(tptp_fun_X1_0(X1!1), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.51 inference(symmetry,[status(thm)],[642])).
% 9.29/9.51 tff(1010,plain,
% 9.29/9.51 (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(tptp_fun_X1_0(X1!1), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.51 inference(symmetry,[status(thm)],[639])).
% 9.29/9.51 tff(1011,plain,
% 9.29/9.51 (multiplication(c(c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.51 inference(symmetry,[status(thm)],[635])).
% 9.29/9.51 tff(1012,plain,
% 9.29/9.51 (multiplication(X0!2, c(X1!1)) = multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(transitivity,[status(thm)],[624, 285, 272, 267, 1011, 294, 1010, 1009, 284, 1008])).
% 9.29/9.51 tff(1013,plain,
% 9.29/9.51 (multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[997])).
% 9.29/9.51 tff(1014,plain,
% 9.29/9.51 (multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1013])).
% 9.29/9.51 tff(1015,plain,
% 9.29/9.51 (multiplication(c(X0!2), c(X1!1)) = multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(transitivity,[status(thm)],[967, 430, 575, 349, 978, 1006, 425, 1003, 1000, 357, 996, 1014])).
% 9.29/9.51 tff(1016,plain,
% 9.29/9.51 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1015, 1012])).
% 9.29/9.51 tff(1017,plain,
% 9.29/9.51 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1016])).
% 9.29/9.51 tff(1018,plain,
% 9.29/9.51 (multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.51 inference(transitivity,[status(thm)],[822, 825])).
% 9.29/9.51 tff(1019,plain,
% 9.29/9.51 (multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)) = multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1018])).
% 9.29/9.51 tff(1020,plain,
% 9.29/9.51 (multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(transitivity,[status(thm)],[1019, 991, 1014])).
% 9.29/9.51 tff(1021,plain,
% 9.29/9.51 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1020])).
% 9.29/9.51 tff(1022,plain,
% 9.29/9.51 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))),
% 9.29/9.51 inference(transitivity,[status(thm)],[1021, 1017])).
% 9.29/9.51 tff(1023,plain,
% 9.29/9.51 ((addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = one) <=> (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one)),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1022])).
% 9.29/9.51 tff(1024,plain,
% 9.29/9.51 ((addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one) <=> (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = one)),
% 9.29/9.51 inference(symmetry,[status(thm)],[1023])).
% 9.29/9.51 tff(1025,plain,
% 9.29/9.51 ((~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one)) <=> (~(addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = one))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1024])).
% 9.29/9.51 tff(1026,assumption,(~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one)), introduced(assumption)).
% 9.29/9.51 tff(1027,plain,
% 9.29/9.51 (~(addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = one)),
% 9.29/9.51 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 9.29/9.51 tff(1028,assumption,(c(multiplication(X0!2, c(X1!1))) = zero), introduced(assumption)).
% 9.29/9.51 tff(1029,plain,
% 9.29/9.51 (addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))) = addition(c(X0!2), c(c(X1!1)))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[331, 219])).
% 9.29/9.51 tff(1030,plain,
% 9.29/9.51 (addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 9.29/9.51 inference(transitivity,[status(thm)],[1029, 468, 1028, 686])).
% 9.29/9.51 tff(1031,plain,
% 9.29/9.51 (c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1030])).
% 9.29/9.51 tff(1032,plain,
% 9.29/9.51 (multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)))),
% 9.29/9.51 inference(symmetry,[status(thm)],[866])).
% 9.29/9.51 tff(1033,plain,
% 9.29/9.51 (multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = c(tptp_fun_X1_0(X0!2))),
% 9.29/9.51 inference(transitivity,[status(thm)],[1032, 869])).
% 9.29/9.51 tff(1034,plain,
% 9.29/9.51 (multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1033, 632])).
% 9.29/9.51 tff(1035,plain,
% 9.29/9.51 (multiplication(c(tptp_fun_X1_0(X0!2)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[656])).
% 9.29/9.51 tff(1036,plain,
% 9.29/9.51 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[889])).
% 9.29/9.51 tff(1037,plain,
% 9.29/9.51 (multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[656])).
% 9.29/9.51 tff(1038,plain,
% 9.29/9.51 (multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))) = c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.51 inference(transitivity,[status(thm)],[1037, 882, 1036, 1035, 875, 1034, 285])).
% 9.29/9.51 tff(1039,plain,
% 9.29/9.51 (multiplication(multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1038])).
% 9.29/9.51 tff(1040,plain,
% 9.29/9.51 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), c(tptp_fun_X1_0(X0!2))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[627])).
% 9.29/9.51 tff(1041,plain,
% 9.29/9.51 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.51 inference(quant_inst,[status(thm)],[])).
% 9.29/9.51 tff(1042,plain,
% 9.29/9.51 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.51 inference(unit_resolution,[status(thm)],[1041, 252])).
% 9.29/9.51 tff(1043,plain,
% 9.29/9.51 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2)))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1042])).
% 9.29/9.51 tff(1044,plain,
% 9.29/9.51 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2)))) = c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.51 inference(transitivity,[status(thm)],[1043, 1040, 902, 898, 896, 888, 1037, 882, 1036, 1035, 875, 1034, 285])).
% 9.29/9.51 tff(1045,plain,
% 9.29/9.51 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1044])).
% 9.29/9.51 tff(1046,plain,
% 9.29/9.51 (multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2)))) = multiplication(c(X1!1), c(X0!2))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[648, 966])).
% 9.29/9.51 tff(1047,plain,
% 9.29/9.51 (multiplication(c(X1!1), c(X0!2)) = multiplication(c(c(tptp_fun_X1_0(X1!1))), c(c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1046])).
% 9.29/9.51 tff(1048,plain,
% 9.29/9.51 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.51 inference(transitivity,[status(thm)],[353, 1047, 350, 342, 211, 968, 997, 420, 660])).
% 9.29/9.51 tff(1049,plain,
% 9.29/9.51 (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1048])).
% 9.29/9.51 tff(1050,plain,
% 9.29/9.51 (multiplication(tptp_fun_X1_0(X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1049])).
% 9.29/9.51 tff(1051,plain,
% 9.29/9.51 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(transitivity,[status(thm)],[659, 368, 985, 359])).
% 9.29/9.51 tff(1052,plain,
% 9.29/9.51 (multiplication(tptp_fun_X1_0(X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1051])).
% 9.29/9.51 tff(1053,plain,
% 9.29/9.51 (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X1!1), addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1052])).
% 9.29/9.51 tff(1054,plain,
% 9.29/9.51 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(transitivity,[status(thm)],[353, 1047, 350, 342, 211, 968, 997])).
% 9.29/9.51 tff(1055,plain,
% 9.29/9.51 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1054])).
% 9.29/9.51 tff(1056,plain,
% 9.29/9.51 (multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1055])).
% 9.29/9.51 tff(1057,plain,
% 9.29/9.51 (multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)) = multiplication(c(X0!2), c(X1!1))),
% 9.29/9.51 inference(transitivity,[status(thm)],[1013, 1056, 667, 1053, 1050, 424, 654, 1047, 350, 342, 211, 968])).
% 9.29/9.51 tff(1058,plain,
% 9.29/9.51 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1057, 645])).
% 9.29/9.51 tff(1059,plain,
% 9.29/9.51 (multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1058])).
% 9.29/9.51 tff(1060,plain,
% 9.29/9.51 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1040])).
% 9.29/9.51 tff(1061,plain,
% 9.29/9.51 (multiplication(addition(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), multiplication(c(X0!2), c(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.51 inference(symmetry,[status(thm)],[902])).
% 9.29/9.51 tff(1062,plain,
% 9.29/9.51 (addition(multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(addition(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), multiplication(c(X0!2), c(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.51 inference(symmetry,[status(thm)],[898])).
% 9.29/9.51 tff(1063,plain,
% 9.29/9.51 (addition(multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))), zero) = addition(multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.51 inference(symmetry,[status(thm)],[896])).
% 9.29/9.51 tff(1064,plain,
% 9.29/9.51 (multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))), zero)),
% 9.29/9.51 inference(symmetry,[status(thm)],[888])).
% 9.29/9.51 tff(1065,plain,
% 9.29/9.51 (multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1037])).
% 9.29/9.51 tff(1066,plain,
% 9.29/9.51 (multiplication(c(tptp_fun_X1_0(X0!2)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1036])).
% 9.29/9.51 tff(1067,plain,
% 9.29/9.51 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1035])).
% 9.29/9.51 tff(1068,plain,
% 9.29/9.51 (multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.51 inference(symmetry,[status(thm)],[875])).
% 9.29/9.51 tff(1069,plain,
% 9.29/9.51 (multiplication(c(tptp_fun_X1_0(X0!2)), c(c(tptp_fun_X1_0(X1!1)))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1034])).
% 9.29/9.51 tff(1070,plain,
% 9.29/9.51 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1031])).
% 9.29/9.51 tff(1071,plain,
% 9.29/9.51 (addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.51 inference(transitivity,[status(thm)],[698, 697, 688, 1070, 240, 1069, 1068, 1067, 1066, 881, 1065, 1064, 1063, 1062, 1061, 1060, 1042])).
% 9.29/9.51 tff(1072,plain,
% 9.29/9.51 (multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1071])).
% 9.29/9.51 tff(1073,plain,
% 9.29/9.51 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)), multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))))),
% 9.29/9.51 inference(quant_inst,[status(thm)],[])).
% 9.29/9.51 tff(1074,plain,
% 9.29/9.51 (multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)), multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.51 inference(unit_resolution,[status(thm)],[1073, 600])).
% 9.29/9.51 tff(1075,plain,
% 9.29/9.51 (addition(multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)), multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))) = multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1074])).
% 9.29/9.51 tff(1076,plain,
% 9.29/9.51 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))),
% 9.29/9.51 inference(transitivity,[status(thm)],[255, 630])).
% 9.29/9.51 tff(1077,plain,
% 9.29/9.51 (multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.51 inference(monotonicity,[status(thm)],[1076])).
% 9.29/9.51 tff(1078,plain,
% 9.29/9.51 (multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.51 inference(symmetry,[status(thm)],[1077])).
% 9.29/9.51 tff(1079,plain,
% 9.29/9.51 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.51 inference(symmetry,[status(thm)],[908])).
% 9.29/9.51 tff(1080,plain,
% 9.29/9.51 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.51 inference(symmetry,[status(thm)],[907])).
% 9.29/9.51 tff(1081,plain,
% 9.29/9.51 (multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.52 inference(symmetry,[status(thm)],[906])).
% 9.29/9.52 tff(1082,plain,
% 9.29/9.52 (multiplication(multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 9.29/9.52 inference(symmetry,[status(thm)],[904])).
% 9.29/9.52 tff(1083,plain,
% 9.29/9.52 (multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 9.29/9.52 inference(symmetry,[status(thm)],[1039])).
% 9.29/9.52 tff(1084,plain,
% 9.29/9.52 (multiplication(X0!2, c(X1!1)) = multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.52 inference(transitivity,[status(thm)],[624, 285, 272, 267, 1011, 294, 1010, 1009, 284, 1008, 1083, 1082, 1081, 1080, 1079, 910, 1078])).
% 9.29/9.52 tff(1085,plain,
% 9.29/9.52 (multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1076])).
% 9.29/9.52 tff(1086,plain,
% 9.29/9.52 (multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2))),
% 9.29/9.52 inference(symmetry,[status(thm)],[1085])).
% 9.29/9.52 tff(1087,plain,
% 9.29/9.52 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 9.29/9.52 inference(transitivity,[status(thm)],[353, 1047, 350, 342, 211, 968, 359])).
% 9.29/9.52 tff(1088,plain,
% 9.29/9.52 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1087])).
% 9.29/9.52 tff(1089,plain,
% 9.29/9.52 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 9.29/9.52 inference(symmetry,[status(thm)],[1088])).
% 9.29/9.52 tff(1090,plain,
% 9.29/9.52 (multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 9.29/9.52 inference(symmetry,[status(thm)],[952])).
% 9.29/9.52 tff(1091,plain,
% 9.29/9.52 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1087])).
% 9.29/9.52 tff(1092,plain,
% 9.29/9.52 (multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.29/9.52 inference(transitivity,[status(thm)],[936, 935, 932, 917, 1091, 893, 890])).
% 9.29/9.52 tff(1093,plain,
% 9.29/9.52 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(c(X0!2), c(X1!1))),
% 9.29/9.52 inference(transitivity,[status(thm)],[353, 1047, 350, 342, 211, 968])).
% 9.29/9.52 tff(1094,plain,
% 9.29/9.52 (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1093])).
% 9.29/9.52 tff(1095,plain,
% 9.29/9.52 (multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.52 inference(transitivity,[status(thm)],[943, 942, 1094])).
% 9.29/9.52 tff(1096,plain,
% 9.29/9.52 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1095, 1092])).
% 9.29/9.52 tff(1097,plain,
% 9.29/9.52 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.52 inference(transitivity,[status(thm)],[948, 947, 1096, 659, 368])).
% 9.29/9.52 tff(1098,plain,
% 9.29/9.52 (multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1097])).
% 9.29/9.52 tff(1099,plain,
% 9.29/9.52 (multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.52 inference(symmetry,[status(thm)],[1098])).
% 9.29/9.52 tff(1100,plain,
% 9.29/9.52 (multiplication(c(X0!2), c(X1!1)) = multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2))),
% 9.29/9.52 inference(transitivity,[status(thm)],[967, 430, 341, 349, 1046, 653, 425, 1049, 1052, 357, 1055, 1099, 1090, 1089, 955, 1086])).
% 9.29/9.52 tff(1101,plain,
% 9.29/9.52 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = addition(multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)), multiplication(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1100, 1084])).
% 9.29/9.52 tff(1102,plain,
% 9.29/9.52 (multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.52 inference(symmetry,[status(thm)],[830])).
% 9.29/9.52 tff(1103,plain,
% 9.29/9.52 (multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.52 inference(transitivity,[status(thm)],[1019, 1102, 1014])).
% 9.29/9.52 tff(1104,plain,
% 9.29/9.52 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1103])).
% 9.29/9.52 tff(1105,plain,
% 9.29/9.52 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = one),
% 9.29/9.52 inference(transitivity,[status(thm)],[1104, 1058, 1101, 1075, 1072, 1059, 1045, 907, 906, 904, 1039, 644, 643, 642, 639, 293, 635, 631, 271, 1031, 685, 677, 68])).
% 9.29/9.52 tff(1106,assumption,(~(addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = one)), introduced(assumption)).
% 9.29/9.52 tff(1107,plain,
% 9.29/9.52 ($false),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1106, 1105])).
% 9.29/9.52 tff(1108,plain,((~(c(multiplication(X0!2, c(X1!1))) = zero)) | (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = one)), inference(lemma,lemma(discharge,[]))).
% 9.29/9.52 tff(1109,plain,
% 9.29/9.52 (~(c(multiplication(X0!2, c(X1!1))) = zero)),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1108, 1027])).
% 9.29/9.52 tff(1110,plain,
% 9.29/9.52 (^[X0: $i] : refl((test(X0) | (c(X0) = zero)) <=> (test(X0) | (c(X0) = zero)))),
% 9.29/9.52 inference(bind,[status(th)],[])).
% 9.29/9.52 tff(1111,plain,
% 9.29/9.52 (![X0: $i] : (test(X0) | (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 9.29/9.52 inference(quant_intro,[status(thm)],[1110])).
% 9.29/9.52 tff(1112,plain,
% 9.29/9.52 (![X0: $i] : (test(X0) | (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 9.29/9.52 inference(rewrite,[status(thm)],[])).
% 9.29/9.52 tff(1113,plain,
% 9.29/9.52 (^[X0: $i] : rewrite(((~test(X0)) => (c(X0) = zero)) <=> (test(X0) | (c(X0) = zero)))),
% 9.29/9.52 inference(bind,[status(th)],[])).
% 9.29/9.52 tff(1114,plain,
% 9.29/9.52 (![X0: $i] : ((~test(X0)) => (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 9.29/9.52 inference(quant_intro,[status(thm)],[1113])).
% 9.29/9.52 tff(1115,axiom,(![X0: $i] : ((~test(X0)) => (c(X0) = zero))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_4')).
% 9.29/9.52 tff(1116,plain,
% 9.29/9.52 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 9.29/9.52 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 9.29/9.52 tff(1117,plain,
% 9.29/9.52 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 9.29/9.52 inference(modus_ponens,[status(thm)],[1116, 1112])).
% 9.29/9.52 tff(1118,plain,(
% 9.29/9.52 ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 9.29/9.52 inference(skolemize,[status(sab)],[1117])).
% 9.29/9.52 tff(1119,plain,
% 9.29/9.52 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 9.29/9.52 inference(modus_ponens,[status(thm)],[1118, 1111])).
% 9.29/9.52 tff(1120,plain,
% 9.29/9.52 (((~![X0: $i] : (test(X0) | (c(X0) = zero))) | (test(multiplication(X0!2, c(X1!1))) | (c(multiplication(X0!2, c(X1!1))) = zero))) <=> ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | test(multiplication(X0!2, c(X1!1))) | (c(multiplication(X0!2, c(X1!1))) = zero))),
% 9.29/9.52 inference(rewrite,[status(thm)],[])).
% 9.29/9.52 tff(1121,plain,
% 9.29/9.52 ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | (test(multiplication(X0!2, c(X1!1))) | (c(multiplication(X0!2, c(X1!1))) = zero))),
% 9.29/9.52 inference(quant_inst,[status(thm)],[])).
% 9.29/9.52 tff(1122,plain,
% 9.29/9.52 ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | test(multiplication(X0!2, c(X1!1))) | (c(multiplication(X0!2, c(X1!1))) = zero)),
% 9.29/9.52 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 9.29/9.52 tff(1123,plain,
% 9.29/9.52 (test(multiplication(X0!2, c(X1!1))) | (c(multiplication(X0!2, c(X1!1))) = zero)),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1122, 1119])).
% 9.29/9.52 tff(1124,plain,
% 9.29/9.52 (test(multiplication(X0!2, c(X1!1)))),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1123, 1109])).
% 9.29/9.52 tff(1125,plain,
% 9.29/9.52 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(multiplication(X0!2, c(X1!1)))) | (~test(multiplication(c(X0!2), c(X1!1)))) | (c(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1))))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(multiplication(X0!2, c(X1!1)))) | (~test(multiplication(c(X0!2), c(X1!1)))) | (c(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1))))))),
% 9.29/9.52 inference(rewrite,[status(thm)],[])).
% 9.29/9.52 tff(1126,plain,
% 9.29/9.52 (((~test(multiplication(c(X0!2), c(X1!1)))) | (c(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1))))) | (~test(multiplication(X0!2, c(X1!1))))) <=> ((~test(multiplication(X0!2, c(X1!1)))) | (~test(multiplication(c(X0!2), c(X1!1)))) | (c(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1))))))),
% 9.29/9.52 inference(rewrite,[status(thm)],[])).
% 9.29/9.52 tff(1127,plain,
% 9.29/9.52 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(multiplication(c(X0!2), c(X1!1)))) | (c(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1))))) | (~test(multiplication(X0!2, c(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(multiplication(X0!2, c(X1!1)))) | (~test(multiplication(c(X0!2), c(X1!1)))) | (c(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1)))))))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1126])).
% 9.29/9.52 tff(1128,plain,
% 9.29/9.52 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(multiplication(c(X0!2), c(X1!1)))) | (c(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1))))) | (~test(multiplication(X0!2, c(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(multiplication(X0!2, c(X1!1)))) | (~test(multiplication(c(X0!2), c(X1!1)))) | (c(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1))))))),
% 9.29/9.52 inference(transitivity,[status(thm)],[1127, 1125])).
% 9.29/9.52 tff(1129,plain,
% 9.29/9.52 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(multiplication(c(X0!2), c(X1!1)))) | (c(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1))))) | (~test(multiplication(X0!2, c(X1!1)))))),
% 9.29/9.52 inference(quant_inst,[status(thm)],[])).
% 9.29/9.52 tff(1130,plain,
% 9.29/9.52 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(multiplication(X0!2, c(X1!1)))) | (~test(multiplication(c(X0!2), c(X1!1)))) | (c(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1)))))),
% 9.29/9.52 inference(modus_ponens,[status(thm)],[1129, 1128])).
% 9.29/9.52 tff(1131,plain,
% 9.29/9.52 ((~test(multiplication(X0!2, c(X1!1)))) | (~test(multiplication(c(X0!2), c(X1!1)))) | (c(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1)))))),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1130, 203])).
% 9.29/9.52 tff(1132,plain,
% 9.29/9.52 (~test(multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1131, 1124, 1007])).
% 9.29/9.52 tff(1133,plain,
% 9.29/9.52 (((~![X0: $i] : (test(X0) | (c(X0) = zero))) | (test(multiplication(c(X0!2), c(X1!1))) | (c(multiplication(c(X0!2), c(X1!1))) = zero))) <=> ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | test(multiplication(c(X0!2), c(X1!1))) | (c(multiplication(c(X0!2), c(X1!1))) = zero))),
% 9.29/9.52 inference(rewrite,[status(thm)],[])).
% 9.29/9.52 tff(1134,plain,
% 9.29/9.52 ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | (test(multiplication(c(X0!2), c(X1!1))) | (c(multiplication(c(X0!2), c(X1!1))) = zero))),
% 9.29/9.52 inference(quant_inst,[status(thm)],[])).
% 9.29/9.52 tff(1135,plain,
% 9.29/9.52 ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | test(multiplication(c(X0!2), c(X1!1))) | (c(multiplication(c(X0!2), c(X1!1))) = zero)),
% 9.29/9.52 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 9.29/9.52 tff(1136,plain,
% 9.29/9.52 (test(multiplication(c(X0!2), c(X1!1))) | (c(multiplication(c(X0!2), c(X1!1))) = zero)),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1135, 1119])).
% 9.29/9.52 tff(1137,plain,
% 9.29/9.52 (c(multiplication(c(X0!2), c(X1!1))) = zero),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1136, 1132])).
% 9.29/9.52 tff(1138,plain,
% 9.29/9.52 (test(c(X0!2)) <=> test(tptp_fun_X1_0(X0!2))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[225])).
% 9.29/9.52 tff(1139,plain,
% 9.29/9.52 (test(tptp_fun_X1_0(X0!2)) <=> test(c(X0!2))),
% 9.29/9.52 inference(symmetry,[status(thm)],[1138])).
% 9.29/9.52 tff(1140,plain,
% 9.29/9.52 (test(c(X0!2))),
% 9.29/9.52 inference(modus_ponens,[status(thm)],[172, 1139])).
% 9.29/9.52 tff(1141,plain,
% 9.29/9.52 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X1!1))) | (~test(c(X0!2))) | (c(multiplication(c(X0!2), c(X1!1))) = addition(c(c(X0!2)), c(c(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(c(X1!1))) | (~test(c(X0!2))) | (c(multiplication(c(X0!2), c(X1!1))) = addition(c(c(X0!2)), c(c(X1!1)))))),
% 9.29/9.52 inference(rewrite,[status(thm)],[])).
% 9.29/9.52 tff(1142,plain,
% 9.29/9.52 (((~test(c(X1!1))) | (c(multiplication(c(X0!2), c(X1!1))) = addition(c(c(X0!2)), c(c(X1!1)))) | (~test(c(X0!2)))) <=> ((~test(c(X1!1))) | (~test(c(X0!2))) | (c(multiplication(c(X0!2), c(X1!1))) = addition(c(c(X0!2)), c(c(X1!1)))))),
% 9.29/9.52 inference(rewrite,[status(thm)],[])).
% 9.29/9.52 tff(1143,plain,
% 9.29/9.52 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X1!1))) | (c(multiplication(c(X0!2), c(X1!1))) = addition(c(c(X0!2)), c(c(X1!1)))) | (~test(c(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X1!1))) | (~test(c(X0!2))) | (c(multiplication(c(X0!2), c(X1!1))) = addition(c(c(X0!2)), c(c(X1!1))))))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1142])).
% 9.29/9.52 tff(1144,plain,
% 9.29/9.52 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X1!1))) | (c(multiplication(c(X0!2), c(X1!1))) = addition(c(c(X0!2)), c(c(X1!1)))) | (~test(c(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(c(X1!1))) | (~test(c(X0!2))) | (c(multiplication(c(X0!2), c(X1!1))) = addition(c(c(X0!2)), c(c(X1!1)))))),
% 9.29/9.52 inference(transitivity,[status(thm)],[1143, 1141])).
% 9.29/9.52 tff(1145,plain,
% 9.29/9.52 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X1!1))) | (c(multiplication(c(X0!2), c(X1!1))) = addition(c(c(X0!2)), c(c(X1!1)))) | (~test(c(X0!2))))),
% 9.29/9.52 inference(quant_inst,[status(thm)],[])).
% 9.29/9.52 tff(1146,plain,
% 9.29/9.52 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(c(X1!1))) | (~test(c(X0!2))) | (c(multiplication(c(X0!2), c(X1!1))) = addition(c(c(X0!2)), c(c(X1!1))))),
% 9.29/9.52 inference(modus_ponens,[status(thm)],[1145, 1144])).
% 9.29/9.52 tff(1147,plain,
% 9.29/9.52 ((~test(c(X1!1))) | (~test(c(X0!2))) | (c(multiplication(c(X0!2), c(X1!1))) = addition(c(c(X0!2)), c(c(X1!1))))),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1146, 459])).
% 9.29/9.52 tff(1148,plain,
% 9.29/9.52 (c(multiplication(c(X0!2), c(X1!1))) = addition(c(c(X0!2)), c(c(X1!1)))),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1147, 1140, 446])).
% 9.29/9.52 tff(1149,plain,
% 9.29/9.52 (addition(c(c(X0!2)), c(c(X1!1))) = c(multiplication(c(X0!2), c(X1!1)))),
% 9.29/9.52 inference(symmetry,[status(thm)],[1148])).
% 9.29/9.52 tff(1150,plain,
% 9.29/9.52 (addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 9.29/9.52 inference(transitivity,[status(thm)],[228, 1149, 1137, 686])).
% 9.29/9.52 tff(1151,plain,
% 9.29/9.52 (c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1150])).
% 9.29/9.52 tff(1152,plain,
% 9.29/9.52 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))),
% 9.29/9.52 inference(symmetry,[status(thm)],[1151])).
% 9.29/9.52 tff(1153,plain,
% 9.29/9.52 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))), tptp_fun_X1_0(X1!1))),
% 9.29/9.52 inference(transitivity,[status(thm)],[1152, 575, 349, 978, 1006, 425, 1003, 1000, 357, 996, 993])).
% 9.29/9.52 tff(1154,plain,
% 9.29/9.52 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1153])).
% 9.29/9.52 tff(1155,plain,
% 9.29/9.52 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = zero),
% 9.29/9.52 inference(transitivity,[status(thm)],[1154, 992, 989, 986, 980, 976, 973, 917, 971, 893, 890, 657, 407, 405, 377])).
% 9.29/9.52 tff(1156,plain,
% 9.29/9.52 (multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[931])).
% 9.29/9.52 tff(1157,plain,
% 9.29/9.52 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.52 inference(quant_inst,[status(thm)],[])).
% 9.29/9.52 tff(1158,plain,
% 9.29/9.52 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1157, 282])).
% 9.29/9.52 tff(1159,plain,
% 9.29/9.52 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[359])).
% 9.29/9.52 tff(1160,plain,
% 9.29/9.52 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.52 inference(transitivity,[status(thm)],[1159, 1158, 1156, 405, 377, 492, 379, 491, 390, 504, 401, 503])).
% 9.29/9.52 tff(1161,plain,
% 9.29/9.52 (multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1160])).
% 9.29/9.52 tff(1162,plain,
% 9.29/9.52 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))), tptp_fun_X1_0(X1!1)))),
% 9.29/9.52 inference(quant_inst,[status(thm)],[])).
% 9.29/9.52 tff(1163,plain,
% 9.29/9.52 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))), tptp_fun_X1_0(X1!1))),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1162, 282])).
% 9.29/9.52 tff(1164,plain,
% 9.29/9.52 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.29/9.52 inference(transitivity,[status(thm)],[1152, 575, 349, 978, 1006, 425, 1003, 1000, 357, 996, 1014])).
% 9.29/9.52 tff(1165,plain,
% 9.29/9.52 (multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1164])).
% 9.29/9.52 tff(1166,plain,
% 9.29/9.52 (multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero),
% 9.29/9.52 inference(transitivity,[status(thm)],[1165, 1163, 1161, 405, 377])).
% 9.29/9.52 tff(1167,plain,
% 9.29/9.52 (addition(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = addition(c(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[331, 320])).
% 9.29/9.52 tff(1168,plain,
% 9.29/9.52 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = addition(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.52 inference(quant_inst,[status(thm)],[])).
% 9.29/9.52 tff(1169,plain,
% 9.29/9.52 (addition(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = addition(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1168, 487])).
% 9.29/9.52 tff(1170,plain,
% 9.29/9.52 (addition(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X0!2))) = addition(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))))),
% 9.29/9.52 inference(symmetry,[status(thm)],[1169])).
% 9.29/9.52 tff(1171,plain,
% 9.29/9.52 (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 9.29/9.52 inference(transitivity,[status(thm)],[391, 388, 380, 86, 686])).
% 9.29/9.52 tff(1172,plain,
% 9.29/9.52 (c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1171])).
% 9.29/9.52 tff(1173,plain,
% 9.29/9.52 (c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.52 inference(transitivity,[status(thm)],[1172, 851, 696, 850])).
% 9.29/9.52 tff(1174,plain,
% 9.29/9.52 (addition(c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))) = addition(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1173])).
% 9.29/9.52 tff(1175,plain,
% 9.29/9.52 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = c(c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.29/9.52 inference(symmetry,[status(thm)],[1172])).
% 9.29/9.52 tff(1176,plain,
% 9.29/9.52 (addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = addition(c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2)))),
% 9.29/9.52 inference(monotonicity,[status(thm)],[1175])).
% 9.29/9.52 tff(1177,plain,
% 9.29/9.52 (addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = one),
% 9.29/9.52 inference(transitivity,[status(thm)],[1176, 1174, 1170, 1167, 697, 688, 685, 677, 68])).
% 9.29/9.52 tff(1178,plain,
% 9.29/9.52 ((~((~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = zero)) | (~(multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = one)))) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = zero)) | (~(multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = one))),
% 9.29/9.52 inference(tautology,[status(thm)],[])).
% 9.29/9.52 tff(1179,plain,
% 9.29/9.52 ((~((~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = zero)) | (~(multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = one)))) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = zero)) | (~(multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero))),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1178, 1177])).
% 9.29/9.52 tff(1180,plain,
% 9.29/9.52 (~((~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = zero)) | (~(multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = one)))),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1179, 1166, 1155])).
% 9.29/9.52 tff(1181,plain,
% 9.29/9.52 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = zero)) | (~(multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = one))) <=> complement(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))))),
% 9.29/9.52 inference(quant_inst,[status(thm)],[])).
% 9.29/9.52 tff(1182,plain,
% 9.29/9.52 (~(((~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = zero)) | (~(multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = one))) <=> complement(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1181, 33])).
% 9.29/9.52 tff(1183,plain,
% 9.29/9.52 ((((~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = zero)) | (~(multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = one))) <=> complement(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))) | ((~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = zero)) | (~(multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = one))) | complement(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 9.29/9.52 inference(tautology,[status(thm)],[])).
% 9.29/9.52 tff(1184,plain,
% 9.29/9.52 (((~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = zero)) | (~(multiplication(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X0!2))) = one))) | complement(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1183, 1182])).
% 9.29/9.52 tff(1185,plain,
% 9.29/9.52 (complement(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 9.29/9.52 inference(unit_resolution,[status(thm)],[1184, 1180])).
% 9.29/9.52 tff(1186,plain,
% 9.29/9.52 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(c(tptp_fun_X1_0(X0!2)))) | ((c(c(tptp_fun_X1_0(X0!2))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> complement(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | ((c(c(tptp_fun_X1_0(X0!2))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> complement(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))))),
% 9.29/9.52 inference(rewrite,[status(thm)],[])).
% 9.29/9.52 tff(1187,plain,
% 9.29/9.52 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(c(tptp_fun_X1_0(X0!2)))) | ((c(c(tptp_fun_X1_0(X0!2))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> complement(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))))),
% 9.29/9.52 inference(quant_inst,[status(thm)],[])).
% 9.37/9.52 tff(1188,plain,
% 9.37/9.52 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(c(tptp_fun_X1_0(X0!2)))) | ((c(c(tptp_fun_X1_0(X0!2))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> complement(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))),
% 9.37/9.52 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 9.37/9.52 tff(1189,plain,
% 9.37/9.52 ((c(c(tptp_fun_X1_0(X0!2))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> complement(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 9.37/9.52 inference(unit_resolution,[status(thm)],[1188, 107, 187])).
% 9.37/9.52 tff(1190,plain,
% 9.37/9.52 ((~((c(c(tptp_fun_X1_0(X0!2))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> complement(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))) | (c(c(tptp_fun_X1_0(X0!2))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) | (~complement(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))),
% 9.37/9.52 inference(tautology,[status(thm)],[])).
% 9.37/9.52 tff(1191,plain,
% 9.37/9.52 ((c(c(tptp_fun_X1_0(X0!2))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) | (~complement(c(tptp_fun_X1_0(X0!2)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))),
% 9.37/9.52 inference(unit_resolution,[status(thm)],[1190, 1189])).
% 9.37/9.52 tff(1192,plain,
% 9.37/9.52 (c(c(tptp_fun_X1_0(X0!2))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 9.37/9.52 inference(unit_resolution,[status(thm)],[1191, 1185])).
% 9.37/9.52 tff(1193,plain,
% 9.37/9.52 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = c(c(tptp_fun_X1_0(X0!2)))),
% 9.37/9.52 inference(symmetry,[status(thm)],[1192])).
% 9.37/9.52 tff(1194,plain,
% 9.37/9.52 (multiplication(c(X0!2), X1!1) = multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.52 inference(monotonicity,[status(thm)],[965, 378])).
% 9.37/9.52 tff(1195,plain,
% 9.37/9.52 (multiplication(c(c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), X1!1)),
% 9.37/9.52 inference(symmetry,[status(thm)],[1194])).
% 9.37/9.52 tff(1196,plain,
% 9.37/9.52 (multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2)))) = multiplication(X1!1, c(X0!2))),
% 9.37/9.52 inference(monotonicity,[status(thm)],[115, 966])).
% 9.37/9.53 tff(1197,plain,
% 9.37/9.53 (multiplication(X1!1, c(X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(c(tptp_fun_X1_0(X0!2))))),
% 9.37/9.53 inference(symmetry,[status(thm)],[1196])).
% 9.37/9.53 tff(1198,plain,
% 9.37/9.53 (multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(c(X0!2), X1!1)),
% 9.37/9.53 inference(transitivity,[status(thm)],[547, 1197, 545, 733, 533, 1195])).
% 9.37/9.53 tff(1199,plain,
% 9.37/9.53 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(c(X0!2), X1!1), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1198])).
% 9.37/9.53 tff(1200,plain,
% 9.37/9.53 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))))),
% 9.37/9.53 inference(quant_inst,[status(thm)],[])).
% 9.37/9.53 tff(1201,plain,
% 9.37/9.53 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(unit_resolution,[status(thm)],[1200, 282])).
% 9.37/9.53 tff(1202,plain,
% 9.37/9.53 (multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1))),
% 9.37/9.53 inference(symmetry,[status(thm)],[1019])).
% 9.37/9.53 tff(1203,plain,
% 9.37/9.53 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(tptp_fun_X1_0(X0!2), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(transitivity,[status(thm)],[1152, 575, 349, 978, 1006, 425, 1003, 1000, 357, 996, 993, 1202, 821])).
% 9.37/9.53 tff(1204,plain,
% 9.37/9.53 (multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1203])).
% 9.37/9.53 tff(1205,plain,
% 9.37/9.53 (multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero),
% 9.37/9.53 inference(transitivity,[status(thm)],[1204, 1201, 1199, 617, 615, 405, 377])).
% 9.37/9.53 tff(1206,plain,
% 9.37/9.53 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1198])).
% 9.37/9.53 tff(1207,plain,
% 9.37/9.53 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(c(X0!2), c(X1!1))),
% 9.37/9.53 inference(transitivity,[status(thm)],[353, 969, 350, 561, 211, 968])).
% 9.37/9.53 tff(1208,plain,
% 9.37/9.53 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1207])).
% 9.37/9.53 tff(1209,plain,
% 9.37/9.53 (multiplication(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = multiplication(multiplication(c(X0!2), X1!1), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[979])).
% 9.37/9.53 tff(1210,plain,
% 9.37/9.53 (multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1))) = multiplication(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[522])).
% 9.37/9.53 tff(1211,plain,
% 9.37/9.53 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1))))),
% 9.37/9.53 inference(quant_inst,[status(thm)],[])).
% 9.37/9.53 tff(1212,plain,
% 9.37/9.53 (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1)))),
% 9.37/9.53 inference(unit_resolution,[status(thm)],[1211, 282])).
% 9.37/9.53 tff(1213,plain,
% 9.37/9.53 (multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 9.37/9.53 inference(symmetry,[status(thm)],[1206])).
% 9.37/9.53 tff(1214,plain,
% 9.37/9.53 (multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.37/9.53 inference(transitivity,[status(thm)],[1213, 581, 580])).
% 9.37/9.53 tff(1215,plain,
% 9.37/9.53 (multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1214])).
% 9.37/9.53 tff(1216,plain,
% 9.37/9.53 (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.37/9.53 inference(transitivity,[status(thm)],[391, 388, 568])).
% 9.37/9.53 tff(1217,plain,
% 9.37/9.53 (multiplication(tptp_fun_X1_0(X0!2), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1216])).
% 9.37/9.53 tff(1218,plain,
% 9.37/9.53 (multiplication(tptp_fun_X1_0(X0!2), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1))),
% 9.37/9.53 inference(transitivity,[status(thm)],[1217, 520, 583])).
% 9.37/9.53 tff(1219,plain,
% 9.37/9.53 (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X0!2), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(c(X0!2), X1!1), tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1218])).
% 9.37/9.53 tff(1220,plain,
% 9.37/9.53 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X0!2), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.53 inference(quant_inst,[status(thm)],[])).
% 9.37/9.53 tff(1221,plain,
% 9.37/9.53 (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X0!2), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.53 inference(unit_resolution,[status(thm)],[1220, 282])).
% 9.37/9.53 tff(1222,plain,
% 9.37/9.53 (multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X0!2), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.53 inference(symmetry,[status(thm)],[1221])).
% 9.37/9.53 tff(1223,plain,
% 9.37/9.53 (multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.37/9.53 inference(transitivity,[status(thm)],[1222, 1219, 1215, 1212, 1210, 1209, 572, 570, 567, 1208, 552, 551, 1206, 524, 521, 518, 517, 492, 379, 491, 390, 504, 401, 503])).
% 9.37/9.53 tff(1224,plain,
% 9.37/9.53 (multiplication(tptp_fun_X1_0(X1!1), multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1223])).
% 9.37/9.53 tff(1225,plain,
% 9.37/9.53 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X1!1), multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.53 inference(quant_inst,[status(thm)],[])).
% 9.37/9.53 tff(1226,plain,
% 9.37/9.53 (multiplication(tptp_fun_X1_0(X1!1), multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.53 inference(unit_resolution,[status(thm)],[1225, 282])).
% 9.37/9.53 tff(1227,plain,
% 9.37/9.53 (multiplication(multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.53 inference(symmetry,[status(thm)],[1226])).
% 9.37/9.53 tff(1228,plain,
% 9.37/9.53 (multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(transitivity,[status(thm)],[657, 407, 405, 377, 492, 379, 491, 390])).
% 9.37/9.53 tff(1229,plain,
% 9.37/9.53 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))),
% 9.37/9.53 inference(quant_inst,[status(thm)],[])).
% 9.37/9.53 tff(1230,plain,
% 9.37/9.53 (multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 9.37/9.53 inference(unit_resolution,[status(thm)],[1229, 282])).
% 9.37/9.53 tff(1231,plain,
% 9.37/9.53 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)))),
% 9.37/9.53 inference(symmetry,[status(thm)],[1230])).
% 9.37/9.53 tff(1232,plain,
% 9.37/9.53 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1207])).
% 9.37/9.53 tff(1233,plain,
% 9.37/9.53 (multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 9.37/9.53 inference(symmetry,[status(thm)],[1232])).
% 9.37/9.53 tff(1234,plain,
% 9.37/9.53 (multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.37/9.53 inference(symmetry,[status(thm)],[943])).
% 9.37/9.53 tff(1235,plain,
% 9.37/9.53 (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1)))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1207])).
% 9.37/9.53 tff(1236,plain,
% 9.37/9.53 (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 9.37/9.53 inference(symmetry,[status(thm)],[1235])).
% 9.37/9.53 tff(1237,plain,
% 9.37/9.53 (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)))),
% 9.37/9.53 inference(transitivity,[status(thm)],[1236, 941, 1234, 1233, 1231])).
% 9.37/9.53 tff(1238,plain,
% 9.37/9.53 (multiplication(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1237, 1228])).
% 9.37/9.53 tff(1239,plain,
% 9.37/9.53 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X1!1)))))),
% 9.37/9.53 inference(rewrite,[status(thm)],[])).
% 9.37/9.53 tff(1240,plain,
% 9.37/9.53 (((~test(tptp_fun_X1_0(X1!1))) | (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X1!1)))) | (~test(X1!1))) <=> ((~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X1!1)))))),
% 9.37/9.53 inference(rewrite,[status(thm)],[])).
% 9.37/9.53 tff(1241,plain,
% 9.37/9.53 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X1!1)))) | (~test(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X1!1))))))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1240])).
% 9.37/9.53 tff(1242,plain,
% 9.37/9.53 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X1!1)))) | (~test(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X1!1)))))),
% 9.37/9.53 inference(transitivity,[status(thm)],[1241, 1239])).
% 9.37/9.53 tff(1243,plain,
% 9.37/9.53 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X1!1)))) | (~test(X1!1)))),
% 9.37/9.53 inference(quant_inst,[status(thm)],[])).
% 9.37/9.53 tff(1244,plain,
% 9.37/9.53 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X1!1))))),
% 9.37/9.53 inference(modus_ponens,[status(thm)],[1243, 1242])).
% 9.37/9.53 tff(1245,plain,
% 9.37/9.53 ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X1!1))))),
% 9.37/9.53 inference(unit_resolution,[status(thm)],[1244, 203, 60])).
% 9.37/9.53 tff(1246,plain,
% 9.37/9.53 (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(unit_resolution,[status(thm)],[1245, 97])).
% 9.37/9.53 tff(1247,plain,
% 9.37/9.53 (multiplication(c(X1!1), c(tptp_fun_X1_0(X1!1))) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(symmetry,[status(thm)],[1246])).
% 9.37/9.53 tff(1248,plain,
% 9.37/9.53 (multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[256])).
% 9.37/9.53 tff(1249,plain,
% 9.37/9.53 (multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.37/9.53 inference(transitivity,[status(thm)],[1248, 1247, 391, 388, 380, 86, 780, 779, 778, 777])).
% 9.37/9.53 tff(1250,plain,
% 9.37/9.53 (multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[782, 1249])).
% 9.37/9.53 tff(1251,plain,
% 9.37/9.53 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))) = multiplication(multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))))),
% 9.37/9.53 inference(quant_inst,[status(thm)],[])).
% 9.37/9.53 tff(1252,plain,
% 9.37/9.53 (multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))) = multiplication(multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(unit_resolution,[status(thm)],[1251, 282])).
% 9.37/9.53 tff(1253,plain,
% 9.37/9.53 (multiplication(multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))) = multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))))),
% 9.37/9.53 inference(symmetry,[status(thm)],[1252])).
% 9.37/9.53 tff(1254,plain,
% 9.37/9.53 (multiplication(multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))) = multiplication(multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[991])).
% 9.37/9.53 tff(1255,plain,
% 9.37/9.53 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = multiplication(multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1153])).
% 9.37/9.53 tff(1256,plain,
% 9.37/9.53 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero),
% 9.37/9.53 inference(transitivity,[status(thm)],[1255, 1254, 1253, 1250, 1238, 1227, 1224, 917, 971, 893, 890, 657, 407, 405, 377])).
% 9.37/9.53 tff(1257,plain,
% 9.37/9.53 (addition(c(X1!1), c(tptp_fun_X1_0(X1!1))) = c(multiplication(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(symmetry,[status(thm)],[796])).
% 9.37/9.53 tff(1258,plain,
% 9.37/9.53 (addition(tptp_fun_X1_0(X1!1), addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) = addition(c(X1!1), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[256, 303])).
% 9.37/9.53 tff(1259,plain,
% 9.37/9.53 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X1!1), addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) = addition(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X1!1))))),
% 9.37/9.53 inference(quant_inst,[status(thm)],[])).
% 9.37/9.53 tff(1260,plain,
% 9.37/9.53 (addition(tptp_fun_X1_0(X1!1), addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))) = addition(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(unit_resolution,[status(thm)],[1259, 487])).
% 9.37/9.53 tff(1261,plain,
% 9.37/9.53 (addition(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X1!1))) = addition(tptp_fun_X1_0(X1!1), addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))))),
% 9.37/9.53 inference(symmetry,[status(thm)],[1260])).
% 9.37/9.53 tff(1262,plain,
% 9.37/9.53 (c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(transitivity,[status(thm)],[1172, 799, 796, 788])).
% 9.37/9.53 tff(1263,plain,
% 9.37/9.53 (addition(c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X1!1))) = addition(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1262])).
% 9.37/9.53 tff(1264,plain,
% 9.37/9.53 (addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = addition(c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1175])).
% 9.37/9.53 tff(1265,plain,
% 9.37/9.53 (addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one),
% 9.37/9.53 inference(transitivity,[status(thm)],[1264, 1263, 1261, 1258, 1257, 798, 685, 677, 68])).
% 9.37/9.53 tff(1266,plain,
% 9.37/9.53 ((~((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one)))) | (~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))),
% 9.37/9.53 inference(tautology,[status(thm)],[])).
% 9.37/9.53 tff(1267,plain,
% 9.37/9.53 ((~((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one)))) | (~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero))),
% 9.37/9.53 inference(unit_resolution,[status(thm)],[1266, 1265])).
% 9.37/9.53 tff(1268,plain,
% 9.37/9.53 (~((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one)))),
% 9.37/9.53 inference(unit_resolution,[status(thm)],[1267, 1256, 1205])).
% 9.37/9.53 tff(1269,plain,
% 9.37/9.53 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))))),
% 9.37/9.53 inference(rewrite,[status(thm)],[])).
% 9.37/9.53 tff(1270,plain,
% 9.37/9.53 ((~(((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))) <=> (~(((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))))),
% 9.37/9.53 inference(rewrite,[status(thm)],[])).
% 9.37/9.53 tff(1271,plain,
% 9.37/9.53 ((((~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))) <=> (((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))),
% 9.37/9.53 inference(rewrite,[status(thm)],[])).
% 9.37/9.53 tff(1272,plain,
% 9.37/9.53 ((~(((~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))) <=> (~(((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1271])).
% 9.37/9.53 tff(1273,plain,
% 9.37/9.53 ((~(((~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))) <=> (~(((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))))),
% 9.37/9.53 inference(transitivity,[status(thm)],[1272, 1270])).
% 9.37/9.53 tff(1274,plain,
% 9.37/9.53 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))))),
% 9.37/9.53 inference(monotonicity,[status(thm)],[1273])).
% 9.37/9.53 tff(1275,plain,
% 9.37/9.53 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))))),
% 9.37/9.53 inference(transitivity,[status(thm)],[1274, 1269])).
% 9.37/9.53 tff(1276,plain,
% 9.37/9.53 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))))),
% 9.37/9.53 inference(quant_inst,[status(thm)],[])).
% 9.37/9.53 tff(1277,plain,
% 9.37/9.53 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))))),
% 9.37/9.53 inference(modus_ponens,[status(thm)],[1276, 1275])).
% 9.37/9.53 tff(1278,plain,
% 9.37/9.53 (~(((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))),
% 9.37/9.53 inference(unit_resolution,[status(thm)],[1277, 33])).
% 9.37/9.53 tff(1279,plain,
% 9.37/9.53 ((((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))) | ((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) | complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 9.37/9.53 inference(tautology,[status(thm)],[])).
% 9.37/9.53 tff(1280,plain,
% 9.37/9.53 (((~(multiplication(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = zero)) | (~(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = zero)) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = one))) | complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 9.37/9.53 inference(unit_resolution,[status(thm)],[1279, 1278])).
% 9.37/9.53 tff(1281,plain,
% 9.37/9.53 (complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 9.37/9.53 inference(unit_resolution,[status(thm)],[1280, 1268])).
% 9.37/9.53 tff(1282,plain,
% 9.37/9.53 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | ((c(c(tptp_fun_X1_0(X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(c(tptp_fun_X1_0(X1!1)))) | ((c(c(tptp_fun_X1_0(X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))))),
% 9.37/9.53 inference(rewrite,[status(thm)],[])).
% 9.37/9.53 tff(1283,plain,
% 9.37/9.53 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(c(tptp_fun_X1_0(X1!1)))) | ((c(c(tptp_fun_X1_0(X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))))),
% 9.37/9.53 inference(quant_inst,[status(thm)],[])).
% 9.37/9.53 tff(1284,plain,
% 9.37/9.53 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(c(tptp_fun_X1_0(X1!1)))) | ((c(c(tptp_fun_X1_0(X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))),
% 9.37/9.53 inference(modus_ponens,[status(thm)],[1283, 1282])).
% 9.37/9.53 tff(1285,plain,
% 9.37/9.53 ((c(c(tptp_fun_X1_0(X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 9.37/9.53 inference(unit_resolution,[status(thm)],[1284, 107, 190])).
% 9.37/9.53 tff(1286,plain,
% 9.37/9.53 ((~((c(c(tptp_fun_X1_0(X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))) | (c(c(tptp_fun_X1_0(X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) | (~complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))),
% 9.37/9.54 inference(tautology,[status(thm)],[])).
% 9.37/9.54 tff(1287,plain,
% 9.37/9.54 ((c(c(tptp_fun_X1_0(X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) | (~complement(c(tptp_fun_X1_0(X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1286, 1285])).
% 9.37/9.54 tff(1288,plain,
% 9.37/9.54 (c(c(tptp_fun_X1_0(X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1287, 1281])).
% 9.37/9.54 tff(1289,plain,
% 9.37/9.54 (c(X1!1) = c(X0!2)),
% 9.37/9.54 inference(transitivity,[status(thm)],[623, 1288, 1193, 966])).
% 9.37/9.54 tff(1290,plain,
% 9.37/9.54 (multiplication(c(X0!2), c(X1!1)) = one),
% 9.37/9.54 inference(transitivity,[status(thm)],[967, 430, 1151, 685, 677, 68])).
% 9.37/9.54 tff(1291,plain,
% 9.37/9.54 (addition(c(X0!2), X1!1) = addition(c(X0!2), c(c(X1!1)))),
% 9.37/9.54 inference(monotonicity,[status(thm)],[806])).
% 9.37/9.54 tff(1292,plain,
% 9.37/9.54 (addition(c(X0!2), c(c(X1!1))) = addition(c(X0!2), X1!1)),
% 9.37/9.54 inference(symmetry,[status(thm)],[1291])).
% 9.37/9.54 tff(1293,plain,
% 9.37/9.54 (c(multiplication(X0!2, c(X1!1))) = addition(c(X0!2), X1!1)),
% 9.37/9.54 inference(transitivity,[status(thm)],[467, 1292])).
% 9.37/9.54 tff(1294,plain,
% 9.37/9.54 ((c(multiplication(X0!2, c(X1!1))) = multiplication(c(X0!2), c(X1!1))) <=> (addition(c(X0!2), X1!1) = one)),
% 9.37/9.54 inference(monotonicity,[status(thm)],[1293, 1290])).
% 9.37/9.54 tff(1295,plain,
% 9.37/9.54 ((~(c(multiplication(X0!2, c(X1!1))) = multiplication(c(X0!2), c(X1!1)))) <=> (~(addition(c(X0!2), X1!1) = one))),
% 9.37/9.54 inference(monotonicity,[status(thm)],[1294])).
% 9.37/9.54 tff(1296,plain,
% 9.37/9.54 (((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) | (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one)),
% 9.37/9.54 inference(tautology,[status(thm)],[])).
% 9.37/9.54 tff(1297,plain,
% 9.37/9.54 ((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1296, 1026])).
% 9.37/9.54 tff(1298,plain,
% 9.37/9.54 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))))))),
% 9.37/9.54 inference(rewrite,[status(thm)],[])).
% 9.37/9.54 tff(1299,plain,
% 9.37/9.54 ((~(((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))))) <=> (~(((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 9.37/9.54 inference(rewrite,[status(thm)],[])).
% 9.37/9.54 tff(1300,plain,
% 9.37/9.54 ((((~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 9.37/9.54 inference(rewrite,[status(thm)],[])).
% 9.37/9.54 tff(1301,plain,
% 9.37/9.54 ((~(((~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))))) <=> (~(((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 9.37/9.54 inference(monotonicity,[status(thm)],[1300])).
% 9.37/9.54 tff(1302,plain,
% 9.37/9.54 ((~(((~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))))) <=> (~(((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 9.37/9.54 inference(transitivity,[status(thm)],[1301, 1299])).
% 9.37/9.54 tff(1303,plain,
% 9.37/9.54 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))))))),
% 9.37/9.54 inference(monotonicity,[status(thm)],[1302])).
% 9.37/9.54 tff(1304,plain,
% 9.37/9.54 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))))))),
% 9.37/9.54 inference(transitivity,[status(thm)],[1303, 1298])).
% 9.37/9.54 tff(1305,plain,
% 9.37/9.54 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 9.37/9.54 inference(quant_inst,[status(thm)],[])).
% 9.37/9.54 tff(1306,plain,
% 9.37/9.54 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 9.37/9.54 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 9.37/9.54 tff(1307,plain,
% 9.37/9.54 (~(((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1306, 33])).
% 9.37/9.54 tff(1308,plain,
% 9.37/9.54 ((((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) | (~((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one)))) | (~complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 9.37/9.54 inference(tautology,[status(thm)],[])).
% 9.37/9.54 tff(1309,plain,
% 9.37/9.54 ((~((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one)))) | (~complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1308, 1307])).
% 9.37/9.54 tff(1310,plain,
% 9.37/9.54 (~complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1309, 1297])).
% 9.37/9.54 tff(1311,plain,
% 9.37/9.54 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(multiplication(X0!2, c(X1!1)))) | ((c(multiplication(X0!2, c(X1!1))) = multiplication(c(X0!2), c(X1!1))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(multiplication(X0!2, c(X1!1)))) | ((c(multiplication(X0!2, c(X1!1))) = multiplication(c(X0!2), c(X1!1))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 9.37/9.54 inference(rewrite,[status(thm)],[])).
% 9.37/9.54 tff(1312,plain,
% 9.37/9.54 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(multiplication(X0!2, c(X1!1)))) | ((c(multiplication(X0!2, c(X1!1))) = multiplication(c(X0!2), c(X1!1))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 9.37/9.54 inference(quant_inst,[status(thm)],[])).
% 9.37/9.54 tff(1313,plain,
% 9.37/9.54 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(multiplication(X0!2, c(X1!1)))) | ((c(multiplication(X0!2, c(X1!1))) = multiplication(c(X0!2), c(X1!1))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 9.37/9.54 inference(modus_ponens,[status(thm)],[1312, 1311])).
% 9.37/9.54 tff(1314,plain,
% 9.37/9.54 ((~test(multiplication(X0!2, c(X1!1)))) | ((c(multiplication(X0!2, c(X1!1))) = multiplication(c(X0!2), c(X1!1))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1313, 107])).
% 9.37/9.54 tff(1315,plain,
% 9.37/9.54 ((c(multiplication(X0!2, c(X1!1))) = multiplication(c(X0!2), c(X1!1))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1314, 1124])).
% 9.37/9.54 tff(1316,plain,
% 9.37/9.54 ((~((c(multiplication(X0!2, c(X1!1))) = multiplication(c(X0!2), c(X1!1))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~(c(multiplication(X0!2, c(X1!1))) = multiplication(c(X0!2), c(X1!1)))) | complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.37/9.54 inference(tautology,[status(thm)],[])).
% 9.37/9.54 tff(1317,plain,
% 9.37/9.54 (~(c(multiplication(X0!2, c(X1!1))) = multiplication(c(X0!2), c(X1!1)))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1316, 1315, 1310])).
% 9.37/9.54 tff(1318,plain,
% 9.37/9.54 (~(addition(c(X0!2), X1!1) = one)),
% 9.37/9.54 inference(modus_ponens,[status(thm)],[1317, 1295])).
% 9.37/9.54 tff(1319,plain,
% 9.37/9.54 (((~(multiplication(X1!1, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X1!1) = zero)) | (~(addition(c(X0!2), X1!1) = one))) | (addition(c(X0!2), X1!1) = one)),
% 9.37/9.54 inference(tautology,[status(thm)],[])).
% 9.37/9.54 tff(1320,plain,
% 9.37/9.54 ((~(multiplication(X1!1, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X1!1) = zero)) | (~(addition(c(X0!2), X1!1) = one))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1319, 1318])).
% 9.37/9.54 tff(1321,plain,
% 9.37/9.54 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!1, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X1!1) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!1, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X1!1) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2)))))),
% 9.37/9.54 inference(rewrite,[status(thm)],[])).
% 9.37/9.54 tff(1322,plain,
% 9.37/9.54 ((~(((~(multiplication(X1!1, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X1!1) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2)))) <=> (~(((~(multiplication(X1!1, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X1!1) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2))))),
% 9.37/9.54 inference(rewrite,[status(thm)],[])).
% 9.37/9.54 tff(1323,plain,
% 9.37/9.54 ((((~(multiplication(c(X0!2), X1!1) = zero)) | (~(multiplication(X1!1, c(X0!2)) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2))) <=> (((~(multiplication(X1!1, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X1!1) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2)))),
% 9.37/9.54 inference(rewrite,[status(thm)],[])).
% 9.37/9.54 tff(1324,plain,
% 9.37/9.54 ((~(((~(multiplication(c(X0!2), X1!1) = zero)) | (~(multiplication(X1!1, c(X0!2)) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2)))) <=> (~(((~(multiplication(X1!1, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X1!1) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2))))),
% 9.37/9.54 inference(monotonicity,[status(thm)],[1323])).
% 9.37/9.54 tff(1325,plain,
% 9.37/9.54 ((~(((~(multiplication(c(X0!2), X1!1) = zero)) | (~(multiplication(X1!1, c(X0!2)) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2)))) <=> (~(((~(multiplication(X1!1, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X1!1) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2))))),
% 9.37/9.54 inference(transitivity,[status(thm)],[1324, 1322])).
% 9.37/9.54 tff(1326,plain,
% 9.37/9.54 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(X0!2), X1!1) = zero)) | (~(multiplication(X1!1, c(X0!2)) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!1, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X1!1) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2)))))),
% 9.37/9.54 inference(monotonicity,[status(thm)],[1325])).
% 9.37/9.54 tff(1327,plain,
% 9.37/9.54 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(X0!2), X1!1) = zero)) | (~(multiplication(X1!1, c(X0!2)) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!1, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X1!1) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2)))))),
% 9.37/9.54 inference(transitivity,[status(thm)],[1326, 1321])).
% 9.37/9.54 tff(1328,plain,
% 9.37/9.54 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(X0!2), X1!1) = zero)) | (~(multiplication(X1!1, c(X0!2)) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2))))),
% 9.37/9.54 inference(quant_inst,[status(thm)],[])).
% 9.37/9.54 tff(1329,plain,
% 9.37/9.54 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!1, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X1!1) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2))))),
% 9.37/9.54 inference(modus_ponens,[status(thm)],[1328, 1327])).
% 9.37/9.54 tff(1330,plain,
% 9.37/9.54 (~(((~(multiplication(X1!1, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X1!1) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2)))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1329, 33])).
% 9.37/9.54 tff(1331,plain,
% 9.37/9.54 ((((~(multiplication(X1!1, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X1!1) = zero)) | (~(addition(c(X0!2), X1!1) = one))) <=> complement(X1!1, c(X0!2))) | (~((~(multiplication(X1!1, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X1!1) = zero)) | (~(addition(c(X0!2), X1!1) = one)))) | (~complement(X1!1, c(X0!2)))),
% 9.37/9.54 inference(tautology,[status(thm)],[])).
% 9.37/9.54 tff(1332,plain,
% 9.37/9.54 ((~((~(multiplication(X1!1, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X1!1) = zero)) | (~(addition(c(X0!2), X1!1) = one)))) | (~complement(X1!1, c(X0!2)))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1331, 1330])).
% 9.37/9.54 tff(1333,plain,
% 9.37/9.54 (~complement(X1!1, c(X0!2))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1332, 1320])).
% 9.37/9.54 tff(1334,plain,
% 9.37/9.54 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = c(X0!2)) <=> complement(X1!1, c(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | ((c(X1!1) = c(X0!2)) <=> complement(X1!1, c(X0!2))))),
% 9.37/9.54 inference(rewrite,[status(thm)],[])).
% 9.37/9.54 tff(1335,plain,
% 9.37/9.54 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = c(X0!2)) <=> complement(X1!1, c(X0!2))))),
% 9.37/9.54 inference(quant_inst,[status(thm)],[])).
% 9.37/9.54 tff(1336,plain,
% 9.37/9.54 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | ((c(X1!1) = c(X0!2)) <=> complement(X1!1, c(X0!2)))),
% 9.37/9.54 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 9.37/9.54 tff(1337,plain,
% 9.37/9.54 ((c(X1!1) = c(X0!2)) <=> complement(X1!1, c(X0!2))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1336, 107, 60])).
% 9.37/9.54 tff(1338,plain,
% 9.37/9.54 ((~((c(X1!1) = c(X0!2)) <=> complement(X1!1, c(X0!2)))) | (~(c(X1!1) = c(X0!2))) | complement(X1!1, c(X0!2))),
% 9.37/9.54 inference(tautology,[status(thm)],[])).
% 9.37/9.54 tff(1339,plain,
% 9.37/9.54 ((~(c(X1!1) = c(X0!2))) | complement(X1!1, c(X0!2))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1338, 1337])).
% 9.37/9.54 tff(1340,plain,
% 9.37/9.54 (~(c(X1!1) = c(X0!2))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1339, 1333])).
% 9.37/9.54 tff(1341,plain,
% 9.37/9.54 ($false),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1340, 1289])).
% 9.37/9.54 tff(1342,plain,((addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one) | (c(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1)))))), inference(lemma,lemma(discharge,[]))).
% 9.37/9.54 tff(1343,plain,
% 9.37/9.54 (c(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1))))),
% 9.37/9.54 inference(unit_resolution,[status(thm)],[1342, 964])).
% 9.37/9.54 tff(1344,plain,
% 9.37/9.54 (c(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = c(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))))),
% 9.37/9.54 inference(monotonicity,[status(thm)],[611])).
% 9.37/9.54 tff(1345,plain,
% 9.37/9.54 (c(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = c(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 9.37/9.54 inference(symmetry,[status(thm)],[1344])).
% 9.37/9.54 tff(1346,plain,
% 9.37/9.54 (c(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = c(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)))),
% 9.37/9.54 inference(monotonicity,[status(thm)],[433])).
% 9.37/9.54 tff(1347,plain,
% 9.37/9.54 (c(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1))) = c(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))))),
% 9.37/9.54 inference(symmetry,[status(thm)],[1346])).
% 9.37/9.54 tff(1348,plain,
% 9.37/9.54 (c(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) = c(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), tptp_fun_X1_0(X1!1)))),
% 9.37/9.54 inference(monotonicity,[status(thm)],[436])).
% 9.37/9.54 tff(1349,plain,
% 9.37/9.54 (c(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) = multiplication(addition(c(X0!2), c(c(X1!1))), c(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1)))))),
% 9.37/9.54 inference(transitivity,[status(thm)],[1348, 1347, 1345, 1343, 470])).
% 9.37/9.54 tff(1350,plain,
% 9.37/9.54 ((c(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) = zero) <=> (multiplication(addition(c(X0!2), c(c(X1!1))), c(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))))) = zero)),
% 9.37/9.54 inference(monotonicity,[status(thm)],[1349])).
% 9.37/9.54 tff(1351,plain,
% 9.37/9.54 ((multiplication(addition(c(X0!2), c(c(X1!1))), c(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))))) = zero) <=> (c(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) = zero)),
% 9.37/9.55 inference(symmetry,[status(thm)],[1350])).
% 9.37/9.55 tff(1352,plain,
% 9.37/9.55 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 9.37/9.55 inference(bind,[status(th)],[])).
% 9.37/9.55 tff(1353,plain,
% 9.37/9.55 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 9.37/9.55 inference(quant_intro,[status(thm)],[1352])).
% 9.37/9.55 tff(1354,plain,
% 9.37/9.55 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 9.37/9.55 inference(rewrite,[status(thm)],[])).
% 9.37/9.55 tff(1355,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 9.37/9.55 tff(1356,plain,
% 9.37/9.55 (![A: $i] : (multiplication(one, A) = A)),
% 9.37/9.55 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 9.37/9.55 tff(1357,plain,(
% 9.37/9.55 ![A: $i] : (multiplication(one, A) = A)),
% 9.37/9.55 inference(skolemize,[status(sab)],[1356])).
% 9.37/9.55 tff(1358,plain,
% 9.37/9.55 (![A: $i] : (multiplication(one, A) = A)),
% 9.37/9.55 inference(modus_ponens,[status(thm)],[1357, 1353])).
% 9.37/9.55 tff(1359,plain,
% 9.37/9.55 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.55 inference(quant_inst,[status(thm)],[])).
% 9.37/9.55 tff(1360,plain,
% 9.37/9.55 (multiplication(one, addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.55 inference(unit_resolution,[status(thm)],[1359, 1358])).
% 9.37/9.55 tff(1361,plain,
% 9.37/9.55 ((~![A: $i] : (addition(A, zero) = A)) | (addition(c(tptp_fun_X1_0(X1!1)), zero) = c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.55 inference(quant_inst,[status(thm)],[])).
% 9.37/9.55 tff(1362,plain,
% 9.37/9.55 (addition(c(tptp_fun_X1_0(X1!1)), zero) = c(tptp_fun_X1_0(X1!1))),
% 9.37/9.55 inference(unit_resolution,[status(thm)],[1361, 366])).
% 9.37/9.55 tff(1363,plain,
% 9.37/9.55 (addition(c(tptp_fun_X1_0(X1!1)), zero) = addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[748])).
% 9.37/9.55 tff(1364,plain,
% 9.37/9.55 (addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(c(tptp_fun_X1_0(X1!1)), zero)),
% 9.37/9.55 inference(symmetry,[status(thm)],[1363])).
% 9.37/9.55 tff(1365,plain,
% 9.37/9.55 (addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(tptp_fun_X1_0(X1!1))),
% 9.37/9.55 inference(transitivity,[status(thm)],[1364, 1362])).
% 9.37/9.55 tff(1366,plain,
% 9.37/9.55 (addition(c(tptp_fun_X1_0(X1!1)), c(X1!1)) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 9.37/9.55 inference(symmetry,[status(thm)],[685])).
% 9.37/9.55 tff(1367,plain,
% 9.37/9.55 (one = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 9.37/9.55 inference(transitivity,[status(thm)],[69, 676, 1366])).
% 9.37/9.55 tff(1368,plain,
% 9.37/9.55 (multiplication(one, addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1367, 1365])).
% 9.37/9.55 tff(1369,plain,
% 9.37/9.55 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = multiplication(one, addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1368])).
% 9.37/9.55 tff(1370,plain,
% 9.37/9.55 (c(tptp_fun_X1_0(X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), zero)),
% 9.37/9.55 inference(symmetry,[status(thm)],[1362])).
% 9.37/9.55 tff(1371,plain,
% 9.37/9.55 (c(tptp_fun_X1_0(X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.55 inference(transitivity,[status(thm)],[1370, 1363])).
% 9.37/9.55 tff(1372,plain,
% 9.37/9.55 (c(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = c(multiplication(X0!2, c(X1!1)))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[241])).
% 9.37/9.55 tff(1373,plain,
% 9.37/9.55 (c(multiplication(X0!2, c(X1!1))) = c(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1372])).
% 9.37/9.55 tff(1374,plain,
% 9.37/9.55 (addition(c(X0!2), c(c(X1!1))) = c(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.37/9.55 inference(transitivity,[status(thm)],[468, 1373])).
% 9.37/9.55 tff(1375,plain,
% 9.37/9.55 (addition(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X0!2))) = addition(c(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), c(tptp_fun_X1_0(X0!2)))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1374])).
% 9.37/9.55 tff(1376,plain,
% 9.37/9.55 (addition(c(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), c(tptp_fun_X1_0(X0!2))) = addition(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1375])).
% 9.37/9.55 tff(1377,plain,
% 9.37/9.55 (addition(c(X0!2), c(c(X1!1))) = addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1029])).
% 9.37/9.55 tff(1378,plain,
% 9.37/9.55 (c(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 9.37/9.55 inference(transitivity,[status(thm)],[1372, 467, 1377, 269])).
% 9.37/9.55 tff(1379,plain,
% 9.37/9.55 (addition(c(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), c(tptp_fun_X1_0(X0!2))) = addition(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1378])).
% 9.37/9.55 tff(1380,plain,
% 9.37/9.55 (addition(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = addition(c(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))), c(tptp_fun_X1_0(X0!2)))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1379])).
% 9.37/9.55 tff(1381,plain,
% 9.37/9.55 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = addition(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))))),
% 9.37/9.55 inference(quant_inst,[status(thm)],[])).
% 9.37/9.55 tff(1382,plain,
% 9.37/9.55 (addition(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = addition(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))),
% 9.37/9.55 inference(unit_resolution,[status(thm)],[1381, 487])).
% 9.37/9.55 tff(1383,plain,
% 9.37/9.55 (addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))) = c(c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.55 inference(transitivity,[status(thm)],[698, 697, 688, 1175])).
% 9.37/9.55 tff(1384,plain,
% 9.37/9.55 (addition(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = addition(c(tptp_fun_X1_0(X1!1)), c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1383])).
% 9.37/9.55 tff(1385,plain,
% 9.37/9.55 (addition(c(tptp_fun_X1_0(X1!1)), c(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1384])).
% 9.37/9.55 tff(1386,plain,
% 9.37/9.55 (addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[256])).
% 9.37/9.55 tff(1387,plain,
% 9.37/9.55 (addition(c(tptp_fun_X1_0(X1!1)), c(X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1386])).
% 9.37/9.55 tff(1388,plain,
% 9.37/9.55 (c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.37/9.55 inference(transitivity,[status(thm)],[1172, 685, 1387])).
% 9.37/9.55 tff(1389,plain,
% 9.37/9.55 (addition(c(tptp_fun_X1_0(X1!1)), c(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(c(tptp_fun_X1_0(X1!1)), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1388])).
% 9.37/9.55 tff(1390,plain,
% 9.37/9.55 (addition(c(tptp_fun_X1_0(X1!1)), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = addition(c(tptp_fun_X1_0(X1!1)), c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1389])).
% 9.37/9.55 tff(1391,plain,
% 9.37/9.55 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(c(tptp_fun_X1_0(X1!1)), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = addition(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)))),
% 9.37/9.55 inference(quant_inst,[status(thm)],[])).
% 9.37/9.55 tff(1392,plain,
% 9.37/9.55 (addition(c(tptp_fun_X1_0(X1!1)), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = addition(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1))),
% 9.37/9.55 inference(unit_resolution,[status(thm)],[1391, 487])).
% 9.37/9.55 tff(1393,plain,
% 9.37/9.55 (addition(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1392])).
% 9.37/9.55 tff(1394,plain,
% 9.37/9.55 (addition(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[303, 256])).
% 9.37/9.55 tff(1395,plain,
% 9.37/9.55 (addition(c(tptp_fun_X1_0(X1!1)), c(X1!1)) = addition(addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1394])).
% 9.37/9.55 tff(1396,plain,
% 9.37/9.55 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = addition(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.37/9.55 inference(transitivity,[status(thm)],[685, 1395, 1393, 1390, 1385, 1382, 1380, 1376])).
% 9.37/9.55 tff(1397,plain,
% 9.37/9.55 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = multiplication(addition(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X0!2))), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1396, 1371])).
% 9.37/9.55 tff(1398,plain,
% 9.37/9.55 (multiplication(addition(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X0!2))), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1397])).
% 9.37/9.55 tff(1399,plain,
% 9.37/9.55 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X0!2))), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(multiplication(addition(c(X0!2), c(c(X1!1))), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))))),
% 9.37/9.55 inference(quant_inst,[status(thm)],[])).
% 9.37/9.55 tff(1400,plain,
% 9.37/9.55 (multiplication(addition(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X0!2))), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(multiplication(addition(c(X0!2), c(c(X1!1))), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 9.37/9.55 inference(unit_resolution,[status(thm)],[1399, 252])).
% 9.37/9.55 tff(1401,plain,
% 9.37/9.55 (addition(multiplication(addition(c(X0!2), c(c(X1!1))), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) = multiplication(addition(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X0!2))), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1400])).
% 9.37/9.55 tff(1402,plain,
% 9.37/9.55 (multiplication(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1377])).
% 9.37/9.55 tff(1403,plain,
% 9.37/9.55 (multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1402])).
% 9.37/9.55 tff(1404,plain,
% 9.37/9.55 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))))),
% 9.37/9.55 inference(quant_inst,[status(thm)],[])).
% 9.37/9.55 tff(1405,plain,
% 9.37/9.55 (multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.37/9.55 inference(unit_resolution,[status(thm)],[1404, 252])).
% 9.37/9.55 tff(1406,plain,
% 9.37/9.55 (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1405])).
% 9.37/9.55 tff(1407,plain,
% 9.37/9.55 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X1!1))) | (~test(c(X0!2))) | (c(addition(c(X0!2), c(X1!1))) = multiplication(c(c(X0!2)), c(c(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(X1!1))) | (~test(c(X0!2))) | (c(addition(c(X0!2), c(X1!1))) = multiplication(c(c(X0!2)), c(c(X1!1)))))),
% 9.37/9.55 inference(rewrite,[status(thm)],[])).
% 9.37/9.55 tff(1408,plain,
% 9.37/9.55 (((~test(c(X1!1))) | (c(addition(c(X0!2), c(X1!1))) = multiplication(c(c(X0!2)), c(c(X1!1)))) | (~test(c(X0!2)))) <=> ((~test(c(X1!1))) | (~test(c(X0!2))) | (c(addition(c(X0!2), c(X1!1))) = multiplication(c(c(X0!2)), c(c(X1!1)))))),
% 9.37/9.55 inference(rewrite,[status(thm)],[])).
% 9.37/9.55 tff(1409,plain,
% 9.37/9.55 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X1!1))) | (c(addition(c(X0!2), c(X1!1))) = multiplication(c(c(X0!2)), c(c(X1!1)))) | (~test(c(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X1!1))) | (~test(c(X0!2))) | (c(addition(c(X0!2), c(X1!1))) = multiplication(c(c(X0!2)), c(c(X1!1))))))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1408])).
% 9.37/9.55 tff(1410,plain,
% 9.37/9.55 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X1!1))) | (c(addition(c(X0!2), c(X1!1))) = multiplication(c(c(X0!2)), c(c(X1!1)))) | (~test(c(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(X1!1))) | (~test(c(X0!2))) | (c(addition(c(X0!2), c(X1!1))) = multiplication(c(c(X0!2)), c(c(X1!1)))))),
% 9.37/9.55 inference(transitivity,[status(thm)],[1409, 1407])).
% 9.37/9.55 tff(1411,plain,
% 9.37/9.55 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X1!1))) | (c(addition(c(X0!2), c(X1!1))) = multiplication(c(c(X0!2)), c(c(X1!1)))) | (~test(c(X0!2))))),
% 9.37/9.55 inference(quant_inst,[status(thm)],[])).
% 9.37/9.55 tff(1412,plain,
% 9.37/9.55 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(X1!1))) | (~test(c(X0!2))) | (c(addition(c(X0!2), c(X1!1))) = multiplication(c(c(X0!2)), c(c(X1!1))))),
% 9.37/9.55 inference(modus_ponens,[status(thm)],[1411, 1410])).
% 9.37/9.55 tff(1413,plain,
% 9.37/9.55 ((~test(c(X1!1))) | (~test(c(X0!2))) | (c(addition(c(X0!2), c(X1!1))) = multiplication(c(c(X0!2)), c(c(X1!1))))),
% 9.37/9.55 inference(unit_resolution,[status(thm)],[1412, 203])).
% 9.37/9.55 tff(1414,plain,
% 9.37/9.55 (c(addition(c(X0!2), c(X1!1))) = multiplication(c(c(X0!2)), c(c(X1!1)))),
% 9.37/9.55 inference(unit_resolution,[status(thm)],[1413, 1140, 446])).
% 9.37/9.55 tff(1415,plain,
% 9.37/9.55 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(c(X0!2), c(X1!1)) = addition(c(X1!1), c(X0!2)))),
% 9.37/9.55 inference(quant_inst,[status(thm)],[])).
% 9.37/9.55 tff(1416,plain,
% 9.37/9.55 (addition(c(X0!2), c(X1!1)) = addition(c(X1!1), c(X0!2))),
% 9.37/9.55 inference(unit_resolution,[status(thm)],[1415, 79])).
% 9.37/9.55 tff(1417,plain,
% 9.37/9.55 (addition(c(X1!1), c(X0!2)) = addition(c(X0!2), c(X1!1))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1416])).
% 9.37/9.55 tff(1418,plain,
% 9.37/9.55 (c(addition(c(X1!1), c(X0!2))) = c(addition(c(X0!2), c(X1!1)))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1417])).
% 9.37/9.55 tff(1419,plain,
% 9.37/9.55 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X1!1))) | (~test(c(X0!2))) | (c(addition(c(X1!1), c(X0!2))) = multiplication(c(c(X1!1)), c(c(X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(X1!1))) | (~test(c(X0!2))) | (c(addition(c(X1!1), c(X0!2))) = multiplication(c(c(X1!1)), c(c(X0!2)))))),
% 9.37/9.55 inference(rewrite,[status(thm)],[])).
% 9.37/9.55 tff(1420,plain,
% 9.37/9.55 (((~test(c(X0!2))) | (c(addition(c(X1!1), c(X0!2))) = multiplication(c(c(X1!1)), c(c(X0!2)))) | (~test(c(X1!1)))) <=> ((~test(c(X1!1))) | (~test(c(X0!2))) | (c(addition(c(X1!1), c(X0!2))) = multiplication(c(c(X1!1)), c(c(X0!2)))))),
% 9.37/9.55 inference(rewrite,[status(thm)],[])).
% 9.37/9.55 tff(1421,plain,
% 9.37/9.55 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X0!2))) | (c(addition(c(X1!1), c(X0!2))) = multiplication(c(c(X1!1)), c(c(X0!2)))) | (~test(c(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X1!1))) | (~test(c(X0!2))) | (c(addition(c(X1!1), c(X0!2))) = multiplication(c(c(X1!1)), c(c(X0!2))))))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1420])).
% 9.37/9.55 tff(1422,plain,
% 9.37/9.55 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X0!2))) | (c(addition(c(X1!1), c(X0!2))) = multiplication(c(c(X1!1)), c(c(X0!2)))) | (~test(c(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(X1!1))) | (~test(c(X0!2))) | (c(addition(c(X1!1), c(X0!2))) = multiplication(c(c(X1!1)), c(c(X0!2)))))),
% 9.37/9.55 inference(transitivity,[status(thm)],[1421, 1419])).
% 9.37/9.55 tff(1423,plain,
% 9.37/9.55 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(c(X0!2))) | (c(addition(c(X1!1), c(X0!2))) = multiplication(c(c(X1!1)), c(c(X0!2)))) | (~test(c(X1!1))))),
% 9.37/9.55 inference(quant_inst,[status(thm)],[])).
% 9.37/9.55 tff(1424,plain,
% 9.37/9.55 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(c(X1!1))) | (~test(c(X0!2))) | (c(addition(c(X1!1), c(X0!2))) = multiplication(c(c(X1!1)), c(c(X0!2))))),
% 9.37/9.55 inference(modus_ponens,[status(thm)],[1423, 1422])).
% 9.37/9.55 tff(1425,plain,
% 9.37/9.55 ((~test(c(X1!1))) | (~test(c(X0!2))) | (c(addition(c(X1!1), c(X0!2))) = multiplication(c(c(X1!1)), c(c(X0!2))))),
% 9.37/9.55 inference(unit_resolution,[status(thm)],[1424, 203])).
% 9.37/9.55 tff(1426,plain,
% 9.37/9.55 (c(addition(c(X1!1), c(X0!2))) = multiplication(c(c(X1!1)), c(c(X0!2)))),
% 9.37/9.55 inference(unit_resolution,[status(thm)],[1425, 1140, 446])).
% 9.37/9.55 tff(1427,plain,
% 9.37/9.55 (multiplication(c(c(X1!1)), c(c(X0!2))) = c(addition(c(X1!1), c(X0!2)))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1426])).
% 9.37/9.55 tff(1428,plain,
% 9.37/9.55 (multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(c(c(X1!1)), c(c(X0!2)))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[219, 227])).
% 9.37/9.55 tff(1429,plain,
% 9.37/9.55 (multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(c(c(X0!2)), c(c(X1!1)))),
% 9.37/9.55 inference(transitivity,[status(thm)],[1428, 1427, 1418, 1414])).
% 9.37/9.55 tff(1430,plain,
% 9.37/9.55 (multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.37/9.55 inference(transitivity,[status(thm)],[403, 402, 393])).
% 9.37/9.55 tff(1431,plain,
% 9.37/9.55 (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), multiplication(c(c(X0!2)), c(c(X1!1))))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1430, 1429])).
% 9.37/9.55 tff(1432,plain,
% 9.37/9.55 (addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), multiplication(c(c(X0!2)), c(c(X1!1)))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1431])).
% 9.37/9.55 tff(1433,plain,
% 9.37/9.55 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), multiplication(c(c(X0!2)), c(c(X1!1)))) = addition(multiplication(c(c(X0!2)), c(c(X1!1))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.55 inference(quant_inst,[status(thm)],[])).
% 9.37/9.55 tff(1434,plain,
% 9.37/9.55 (addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), multiplication(c(c(X0!2)), c(c(X1!1)))) = addition(multiplication(c(c(X0!2)), c(c(X1!1))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.55 inference(unit_resolution,[status(thm)],[1433, 79])).
% 9.37/9.55 tff(1435,plain,
% 9.37/9.55 (addition(multiplication(c(c(X0!2)), c(c(X1!1))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), multiplication(c(c(X0!2)), c(c(X1!1))))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1434])).
% 9.37/9.55 tff(1436,plain,
% 9.37/9.55 (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = zero),
% 9.37/9.55 inference(transitivity,[status(thm)],[391, 388, 380, 86])).
% 9.37/9.55 tff(1437,plain,
% 9.37/9.55 (addition(multiplication(c(c(X0!2)), c(c(X1!1))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(multiplication(c(c(X0!2)), c(c(X1!1))), zero)),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1436])).
% 9.37/9.55 tff(1438,plain,
% 9.37/9.55 (addition(multiplication(c(c(X0!2)), c(c(X1!1))), zero) = addition(multiplication(c(c(X0!2)), c(c(X1!1))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1437])).
% 9.37/9.55 tff(1439,plain,
% 9.37/9.55 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(c(c(X0!2)), c(c(X1!1))), zero) = multiplication(c(c(X0!2)), c(c(X1!1))))),
% 9.37/9.55 inference(quant_inst,[status(thm)],[])).
% 9.37/9.55 tff(1440,plain,
% 9.37/9.55 (addition(multiplication(c(c(X0!2)), c(c(X1!1))), zero) = multiplication(c(c(X0!2)), c(c(X1!1)))),
% 9.37/9.55 inference(unit_resolution,[status(thm)],[1439, 366])).
% 9.37/9.55 tff(1441,plain,
% 9.37/9.55 (multiplication(c(c(X0!2)), c(c(X1!1))) = addition(multiplication(c(c(X0!2)), c(c(X1!1))), zero)),
% 9.37/9.55 inference(symmetry,[status(thm)],[1440])).
% 9.37/9.55 tff(1442,plain,
% 9.37/9.55 (addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(c(X1!1))),
% 9.37/9.55 inference(transitivity,[status(thm)],[1364, 1362, 219])).
% 9.37/9.55 tff(1443,plain,
% 9.37/9.55 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(c(c(X0!2)), c(c(X1!1)))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[227, 1442])).
% 9.37/9.55 tff(1444,plain,
% 9.37/9.55 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 9.37/9.55 inference(transitivity,[status(thm)],[1443, 1441, 1438, 1435, 1432, 1406, 1403])).
% 9.37/9.55 tff(1445,plain,
% 9.37/9.55 (multiplication(addition(c(X0!2), c(c(X1!1))), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1365])).
% 9.37/9.55 tff(1446,plain,
% 9.37/9.55 (addition(multiplication(addition(c(X0!2), c(c(X1!1))), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) = addition(multiplication(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X1!1))), multiplication(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X0!2))))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1445, 1444])).
% 9.37/9.55 tff(1447,plain,
% 9.37/9.55 (addition(multiplication(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X1!1))), multiplication(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(addition(c(X0!2), c(c(X1!1))), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1446])).
% 9.37/9.55 tff(1448,plain,
% 9.37/9.55 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(addition(c(X0!2), c(c(X1!1))), addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X1!1))), multiplication(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X0!2)))))),
% 9.37/9.55 inference(quant_inst,[status(thm)],[])).
% 9.37/9.55 tff(1449,plain,
% 9.37/9.55 (multiplication(addition(c(X0!2), c(c(X1!1))), addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X1!1))), multiplication(addition(c(X0!2), c(c(X1!1))), c(tptp_fun_X1_0(X0!2))))),
% 9.37/9.55 inference(unit_resolution,[status(thm)],[1448, 600])).
% 9.37/9.55 tff(1450,plain,
% 9.37/9.55 (addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = c(multiplication(c(X0!2), c(X1!1)))),
% 9.37/9.55 inference(transitivity,[status(thm)],[560, 228, 1149])).
% 9.37/9.55 tff(1451,plain,
% 9.37/9.55 (multiplication(addition(c(X0!2), c(c(X1!1))), addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1))))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[468, 1450])).
% 9.37/9.55 tff(1452,plain,
% 9.37/9.55 (multiplication(c(multiplication(X0!2, c(X1!1))), c(multiplication(c(X0!2), c(X1!1)))) = multiplication(addition(c(X0!2), c(c(X1!1))), addition(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1451])).
% 9.37/9.55 tff(1453,plain,
% 9.37/9.55 (multiplication(addition(c(X0!2), c(c(X1!1))), c(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))))) = addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.55 inference(transitivity,[status(thm)],[469, 1452, 1449, 1447, 1401, 1398, 1369, 1360])).
% 9.37/9.55 tff(1454,plain,
% 9.37/9.55 ((multiplication(addition(c(X0!2), c(c(X1!1))), c(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))))) = zero) <=> (addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1453, 748])).
% 9.37/9.55 tff(1455,plain,
% 9.37/9.55 ((addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))) <=> (multiplication(addition(c(X0!2), c(c(X1!1))), c(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))))) = zero)),
% 9.37/9.55 inference(symmetry,[status(thm)],[1454])).
% 9.37/9.55 tff(1456,plain,
% 9.37/9.55 ((addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))) <=> (c(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) = zero)),
% 9.37/9.55 inference(transitivity,[status(thm)],[1455, 1351])).
% 9.37/9.55 tff(1457,plain,
% 9.37/9.55 ((~(addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(addition(X1!1, tptp_fun_X1_0(X1!1))))) <=> (~(c(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) = zero))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1456])).
% 9.37/9.55 tff(1458,plain,
% 9.37/9.55 ((addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))) <=> (c(tptp_fun_X1_0(X1!1)) = zero)),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1365, 1436])).
% 9.37/9.55 tff(1459,plain,
% 9.37/9.55 ((c(tptp_fun_X1_0(X1!1)) = zero) <=> (addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.55 inference(symmetry,[status(thm)],[1458])).
% 9.37/9.55 tff(1460,plain,
% 9.37/9.55 ((c(tptp_fun_X1_0(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))) <=> (c(tptp_fun_X1_0(X1!1)) = zero)),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1436])).
% 9.37/9.55 tff(1461,plain,
% 9.37/9.55 ((c(tptp_fun_X1_0(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))) <=> (addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.55 inference(transitivity,[status(thm)],[1460, 1459])).
% 9.37/9.55 tff(1462,plain,
% 9.37/9.55 ((~(c(tptp_fun_X1_0(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1))))) <=> (~(addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.55 inference(monotonicity,[status(thm)],[1461])).
% 9.37/9.55 tff(1463,assumption,(~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one)), introduced(assumption)).
% 9.37/9.55 tff(1464,plain,
% 9.37/9.55 (((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) | (addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one)),
% 9.37/9.55 inference(tautology,[status(thm)],[])).
% 9.37/9.55 tff(1465,plain,
% 9.37/9.55 ((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))),
% 9.37/9.55 inference(unit_resolution,[status(thm)],[1464, 1463])).
% 9.37/9.55 tff(1466,plain,
% 9.37/9.55 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))))),
% 9.37/9.55 inference(rewrite,[status(thm)],[])).
% 9.37/9.55 tff(1467,plain,
% 9.37/9.55 ((~(((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) <=> (~(((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 9.37/9.55 inference(rewrite,[status(thm)],[])).
% 9.37/9.55 tff(1468,plain,
% 9.37/9.55 ((((~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) <=> (((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.55 inference(rewrite,[status(thm)],[])).
% 9.37/9.55 tff(1469,plain,
% 9.37/9.55 ((~(((~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) <=> (~(((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 9.37/9.56 inference(monotonicity,[status(thm)],[1468])).
% 9.37/9.56 tff(1470,plain,
% 9.37/9.56 ((~(((~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) <=> (~(((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 9.37/9.56 inference(transitivity,[status(thm)],[1469, 1467])).
% 9.37/9.56 tff(1471,plain,
% 9.37/9.56 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))))),
% 9.37/9.56 inference(monotonicity,[status(thm)],[1470])).
% 9.37/9.56 tff(1472,plain,
% 9.37/9.56 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))))),
% 9.37/9.56 inference(transitivity,[status(thm)],[1471, 1466])).
% 9.37/9.56 tff(1473,plain,
% 9.37/9.56 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 9.37/9.56 inference(quant_inst,[status(thm)],[])).
% 9.37/9.56 tff(1474,plain,
% 9.37/9.56 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 9.37/9.56 inference(modus_ponens,[status(thm)],[1473, 1472])).
% 9.37/9.56 tff(1475,plain,
% 9.37/9.56 (~(((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.56 inference(unit_resolution,[status(thm)],[1474, 33])).
% 9.37/9.56 tff(1476,plain,
% 9.37/9.56 ((((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | (~((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one)))) | (~complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.56 inference(tautology,[status(thm)],[])).
% 9.37/9.56 tff(1477,plain,
% 9.37/9.56 ((~((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one)))) | (~complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.56 inference(unit_resolution,[status(thm)],[1476, 1475])).
% 9.37/9.56 tff(1478,plain,
% 9.37/9.56 (~complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.56 inference(unit_resolution,[status(thm)],[1477, 1465])).
% 9.37/9.56 tff(1479,plain,
% 9.37/9.56 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 9.37/9.56 inference(rewrite,[status(thm)],[])).
% 9.37/9.56 tff(1480,plain,
% 9.37/9.56 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 9.37/9.56 inference(quant_inst,[status(thm)],[])).
% 9.37/9.56 tff(1481,plain,
% 9.37/9.56 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.56 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 9.37/9.56 tff(1482,plain,
% 9.37/9.56 ((c(tptp_fun_X1_0(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.56 inference(unit_resolution,[status(thm)],[1481, 107, 97])).
% 9.37/9.56 tff(1483,plain,
% 9.37/9.56 ((~((c(tptp_fun_X1_0(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) | (~(c(tptp_fun_X1_0(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.56 inference(tautology,[status(thm)],[])).
% 9.37/9.56 tff(1484,plain,
% 9.37/9.56 ((~(c(tptp_fun_X1_0(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.56 inference(unit_resolution,[status(thm)],[1483, 1482])).
% 9.37/9.56 tff(1485,plain,
% 9.37/9.56 (~(c(tptp_fun_X1_0(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.56 inference(unit_resolution,[status(thm)],[1484, 1478])).
% 9.37/9.56 tff(1486,plain,
% 9.37/9.56 (~(addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.56 inference(modus_ponens,[status(thm)],[1485, 1462])).
% 9.37/9.56 tff(1487,plain,
% 9.37/9.56 (~(c(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) = zero)),
% 9.37/9.56 inference(modus_ponens,[status(thm)],[1486, 1457])).
% 9.37/9.56 tff(1488,plain,
% 9.37/9.56 (((~![X0: $i] : (test(X0) | (c(X0) = zero))) | (test(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) | (c(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) = zero))) <=> ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | test(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) | (c(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) = zero))),
% 9.37/9.56 inference(rewrite,[status(thm)],[])).
% 9.37/9.56 tff(1489,plain,
% 9.37/9.56 ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | (test(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) | (c(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) = zero))),
% 9.37/9.56 inference(quant_inst,[status(thm)],[])).
% 9.37/9.56 tff(1490,plain,
% 9.37/9.56 ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | test(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) | (c(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) = zero)),
% 9.37/9.56 inference(modus_ponens,[status(thm)],[1489, 1488])).
% 9.37/9.56 tff(1491,plain,
% 9.37/9.56 (test(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) | (c(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))) = zero)),
% 9.37/9.56 inference(unit_resolution,[status(thm)],[1490, 1119])).
% 9.37/9.56 tff(1492,plain,
% 9.37/9.56 (test(addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))))),
% 9.37/9.56 inference(unit_resolution,[status(thm)],[1491, 1487])).
% 9.37/9.56 tff(1493,plain,
% 9.37/9.56 (test(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))))),
% 9.37/9.56 inference(modus_ponens,[status(thm)],[1492, 438])).
% 9.37/9.56 tff(1494,plain,
% 9.37/9.56 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 9.37/9.56 inference(quant_inst,[status(thm)],[])).
% 9.37/9.56 tff(1495,plain,
% 9.37/9.56 (addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))),
% 9.37/9.56 inference(unit_resolution,[status(thm)],[1494, 79])).
% 9.37/9.56 tff(1496,plain,
% 9.37/9.56 (multiplication(c(c(X0!2)), c(c(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.56 inference(symmetry,[status(thm)],[1443])).
% 9.37/9.56 tff(1497,plain,
% 9.37/9.56 (multiplication(X0!2, X1!1) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.56 inference(transitivity,[status(thm)],[808, 1496])).
% 9.37/9.56 tff(1498,plain,
% 9.37/9.56 (addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = X1!1),
% 9.37/9.56 inference(transitivity,[status(thm)],[1364, 1362, 115])).
% 9.37/9.56 tff(1499,plain,
% 9.37/9.56 (multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(c(X0!2), X1!1)),
% 9.37/9.56 inference(monotonicity,[status(thm)],[331, 1498])).
% 9.37/9.56 tff(1500,plain,
% 9.37/9.56 (multiplication(c(X0!2), X1!1) = multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.56 inference(symmetry,[status(thm)],[1499])).
% 9.37/9.56 tff(1501,plain,
% 9.37/9.56 (addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 9.37/9.56 inference(monotonicity,[status(thm)],[1500, 1497])).
% 9.37/9.56 tff(1502,plain,
% 9.37/9.56 (addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) = addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))),
% 9.37/9.56 inference(symmetry,[status(thm)],[1501])).
% 9.37/9.56 tff(1503,plain,
% 9.37/9.56 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))))),
% 9.37/9.56 inference(quant_inst,[status(thm)],[])).
% 9.37/9.56 tff(1504,plain,
% 9.37/9.56 (multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 9.37/9.56 inference(unit_resolution,[status(thm)],[1503, 252])).
% 9.37/9.56 tff(1505,plain,
% 9.37/9.56 (addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 9.37/9.56 inference(transitivity,[status(thm)],[698, 697, 688])).
% 9.37/9.56 tff(1506,plain,
% 9.37/9.56 (multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.56 inference(monotonicity,[status(thm)],[1505, 1365])).
% 9.37/9.56 tff(1507,plain,
% 9.37/9.56 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(tptp_fun_X1_0(X1!1))) = multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), addition(c(tptp_fun_X1_0(X1!1)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.56 inference(symmetry,[status(thm)],[1506])).
% 9.37/9.56 tff(1508,plain,
% 9.37/9.56 (c(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))),
% 9.37/9.56 inference(transitivity,[status(thm)],[1345, 1343, 1452, 1449, 1447, 1401, 1398, 1507, 1504, 1502, 1495])).
% 9.37/9.56 tff(1509,plain,
% 9.37/9.56 (complement(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) <=> complement(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 9.37/9.56 inference(monotonicity,[status(thm)],[612])).
% 9.37/9.56 tff(1510,plain,
% 9.37/9.56 (complement(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) <=> complement(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 9.37/9.56 inference(symmetry,[status(thm)],[1509])).
% 9.37/9.56 tff(1511,plain,
% 9.37/9.56 ((~complement(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) <=> (~complement(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 9.37/9.56 inference(monotonicity,[status(thm)],[1510])).
% 9.37/9.56 tff(1512,plain,
% 9.37/9.56 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = zero)) | (~(multiplication(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = zero)) | (~(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = one))) <=> complement(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))))),
% 9.37/9.56 inference(quant_inst,[status(thm)],[])).
% 9.37/9.56 tff(1513,plain,
% 9.37/9.56 (~(((~(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = zero)) | (~(multiplication(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = zero)) | (~(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = one))) <=> complement(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 9.37/9.56 inference(unit_resolution,[status(thm)],[1512, 33])).
% 9.37/9.56 tff(1514,plain,
% 9.37/9.56 ((addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = one) <=> (one = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 9.37/9.56 inference(commutativity,[status(thm)],[])).
% 9.37/9.56 tff(1515,plain,
% 9.37/9.56 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1)))))),
% 9.37/9.56 inference(quant_inst,[status(thm)],[])).
% 9.37/9.56 tff(1516,plain,
% 9.37/9.56 (addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))))),
% 9.37/9.56 inference(unit_resolution,[status(thm)],[1515, 79])).
% 9.37/9.56 tff(1517,plain,
% 9.37/9.56 (addition(multiplication(c(X0!2), X1!1), addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1)))) = addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1))),
% 9.37/9.56 inference(symmetry,[status(thm)],[1516])).
% 9.37/9.56 tff(1518,plain,
% 9.37/9.56 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X0!2), X1!1), addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), multiplication(X0!2, c(X1!1))))),
% 9.37/9.56 inference(quant_inst,[status(thm)],[])).
% 9.37/9.56 tff(1519,plain,
% 9.37/9.56 (addition(multiplication(c(X0!2), X1!1), addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), multiplication(X0!2, c(X1!1)))),
% 9.37/9.56 inference(unit_resolution,[status(thm)],[1518, 487])).
% 9.37/9.56 tff(1520,plain,
% 9.37/9.56 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), multiplication(X0!2, c(X1!1))) = addition(multiplication(c(X0!2), X1!1), addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))))),
% 9.37/9.56 inference(symmetry,[status(thm)],[1519])).
% 9.37/9.56 tff(1521,plain,
% 9.37/9.56 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), multiplication(X0!2, c(X1!1))) = addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1))),
% 9.37/9.56 inference(transitivity,[status(thm)],[1520, 1517])).
% 9.37/9.56 tff(1522,plain,
% 9.37/9.56 (addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), c(X1!1))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.37/9.56 inference(monotonicity,[status(thm)],[1521])).
% 9.37/9.56 tff(1523,plain,
% 9.37/9.56 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), c(X1!1))))),
% 9.37/9.56 inference(quant_inst,[status(thm)],[])).
% 9.37/9.56 tff(1524,plain,
% 9.37/9.56 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), c(X1!1)))),
% 9.37/9.56 inference(unit_resolution,[status(thm)],[1523, 487])).
% 9.37/9.56 tff(1525,plain,
% 9.37/9.56 (addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))),
% 9.37/9.56 inference(symmetry,[status(thm)],[1495])).
% 9.37/9.56 tff(1526,plain,
% 9.37/9.56 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 9.37/9.56 inference(monotonicity,[status(thm)],[1525])).
% 9.37/9.56 tff(1527,plain,
% 9.37/9.56 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.37/9.56 inference(transitivity,[status(thm)],[1526, 1524, 1522])).
% 9.37/9.56 tff(1528,plain,
% 9.37/9.56 ((addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = one) <=> (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = one)),
% 9.37/9.56 inference(monotonicity,[status(thm)],[1527])).
% 9.37/9.56 tff(1529,plain,
% 9.37/9.56 ((addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = one) <=> (one = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 9.37/9.56 inference(transitivity,[status(thm)],[1528, 1514])).
% 9.37/9.56 tff(1530,plain,
% 9.37/9.56 ((one = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = one)),
% 9.37/9.56 inference(symmetry,[status(thm)],[1529])).
% 9.37/9.56 tff(1531,plain,
% 9.37/9.56 ((~(one = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) <=> (~(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = one))),
% 9.37/9.56 inference(monotonicity,[status(thm)],[1530])).
% 9.37/9.56 tff(1532,plain,
% 9.37/9.56 (~(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = one)),
% 9.37/9.56 inference(modus_ponens,[status(thm)],[962, 1531])).
% 9.37/9.56 tff(1533,plain,
% 9.37/9.56 (((~(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = zero)) | (~(multiplication(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = zero)) | (~(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = one))) | (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = one)),
% 9.37/9.56 inference(tautology,[status(thm)],[])).
% 9.37/9.56 tff(1534,plain,
% 9.37/9.56 ((~(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = zero)) | (~(multiplication(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = zero)) | (~(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = one))),
% 9.37/9.56 inference(unit_resolution,[status(thm)],[1533, 1532])).
% 9.37/9.56 tff(1535,plain,
% 9.37/9.56 ((((~(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = zero)) | (~(multiplication(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = zero)) | (~(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = one))) <=> complement(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (~((~(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = zero)) | (~(multiplication(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = zero)) | (~(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = one)))) | (~complement(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 9.37/9.56 inference(tautology,[status(thm)],[])).
% 9.37/9.56 tff(1536,plain,
% 9.37/9.56 (~complement(addition(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 9.37/9.56 inference(unit_resolution,[status(thm)],[1535, 1534, 1513])).
% 9.37/9.56 tff(1537,plain,
% 9.37/9.56 (~complement(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 9.37/9.56 inference(modus_ponens,[status(thm)],[1536, 1511])).
% 9.37/9.56 tff(1538,plain,
% 9.37/9.56 ((~((c(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) <=> complement(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))) | (~(c(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | complement(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 9.37/9.57 inference(tautology,[status(thm)],[])).
% 9.37/9.57 tff(1539,plain,
% 9.37/9.57 ((~((c(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) <=> complement(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))) | (~(c(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 9.37/9.57 inference(unit_resolution,[status(thm)],[1538, 1537])).
% 9.37/9.57 tff(1540,plain,
% 9.37/9.57 (~((c(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) <=> complement(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 9.37/9.57 inference(unit_resolution,[status(thm)],[1539, 1508])).
% 9.37/9.57 tff(1541,plain,
% 9.37/9.57 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))))) | ((c(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) <=> complement(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))))) | ((c(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) <=> complement(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))))),
% 9.37/9.57 inference(rewrite,[status(thm)],[])).
% 9.37/9.57 tff(1542,plain,
% 9.37/9.57 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))))) | ((c(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) <=> complement(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))))),
% 9.37/9.57 inference(quant_inst,[status(thm)],[])).
% 9.37/9.57 tff(1543,plain,
% 9.37/9.57 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))))) | ((c(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) <=> complement(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 9.37/9.57 inference(modus_ponens,[status(thm)],[1542, 1541])).
% 9.37/9.57 tff(1544,plain,
% 9.37/9.57 ((~test(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))))) | ((c(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) <=> complement(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 9.37/9.57 inference(unit_resolution,[status(thm)],[1543, 107])).
% 9.37/9.57 tff(1545,plain,
% 9.37/9.57 (~test(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))))),
% 9.37/9.57 inference(unit_resolution,[status(thm)],[1544, 1540])).
% 9.37/9.57 tff(1546,plain,
% 9.37/9.57 ($false),
% 9.37/9.57 inference(unit_resolution,[status(thm)],[1545, 1493])).
% 9.37/9.57 tff(1547,plain,(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one), inference(lemma,lemma(discharge,[]))).
% 9.37/9.57 tff(1548,plain,
% 9.37/9.57 (multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))) = c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 9.37/9.57 inference(transitivity,[status(thm)],[258, 631, 271])).
% 9.37/9.57 tff(1549,plain,
% 9.37/9.57 (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))) = multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.37/9.57 inference(monotonicity,[status(thm)],[1548])).
% 9.37/9.57 tff(1550,plain,
% 9.37/9.57 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 9.37/9.57 inference(transitivity,[status(thm)],[353, 352, 350, 342, 211, 184, 359])).
% 9.37/9.57 tff(1551,plain,
% 9.37/9.57 (multiplication(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 9.37/9.57 inference(monotonicity,[status(thm)],[1550])).
% 9.37/9.57 tff(1552,plain,
% 9.37/9.57 (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 9.37/9.57 inference(transitivity,[status(thm)],[504, 401, 503])).
% 9.37/9.57 tff(1553,plain,
% 9.37/9.57 (multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = multiplication(tptp_fun_X1_0(X1!1), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 9.37/9.57 inference(monotonicity,[status(thm)],[1552])).
% 9.37/9.57 tff(1554,plain,
% 9.37/9.57 (multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.37/9.57 inference(transitivity,[status(thm)],[1553, 917, 1551, 893, 1549])).
% 9.37/9.57 tff(1555,plain,
% 9.37/9.57 ((multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero) <=> (multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = zero)),
% 9.37/9.57 inference(monotonicity,[status(thm)],[1554])).
% 9.37/9.57 tff(1556,plain,
% 9.37/9.57 ((multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = zero) <=> (multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)),
% 9.37/9.57 inference(symmetry,[status(thm)],[1555])).
% 9.37/9.57 tff(1557,plain,
% 9.37/9.57 (multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero),
% 9.37/9.57 inference(modus_ponens,[status(thm)],[411, 1556])).
% 9.37/9.57 tff(1558,plain,
% 9.37/9.57 (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.37/9.57 inference(symmetry,[status(thm)],[410])).
% 9.37/9.57 tff(1559,plain,
% 9.37/9.57 (multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 9.37/9.57 inference(monotonicity,[status(thm)],[1552])).
% 9.37/9.57 tff(1560,plain,
% 9.37/9.57 (multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 9.37/9.57 inference(transitivity,[status(thm)],[1559, 778, 1558])).
% 9.37/9.57 tff(1561,plain,
% 9.37/9.57 ((multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero) <=> (multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = zero)),
% 9.37/9.57 inference(monotonicity,[status(thm)],[1560])).
% 9.37/9.57 tff(1562,plain,
% 9.37/9.57 ((multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = zero) <=> (multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)),
% 9.37/9.57 inference(symmetry,[status(thm)],[1561])).
% 9.37/9.57 tff(1563,plain,
% 9.37/9.57 (multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero),
% 9.37/9.57 inference(modus_ponens,[status(thm)],[411, 1562])).
% 9.37/9.57 tff(1564,plain,
% 9.37/9.57 ((~((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one)))) | (~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))),
% 9.37/9.57 inference(tautology,[status(thm)],[])).
% 9.37/9.57 tff(1565,plain,
% 9.37/9.57 ((~((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one)))) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))),
% 9.37/9.57 inference(unit_resolution,[status(thm)],[1564, 1563, 1557])).
% 9.37/9.57 tff(1566,plain,
% 9.37/9.57 (~((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one)))),
% 9.37/9.57 inference(unit_resolution,[status(thm)],[1565, 1547])).
% 9.37/9.57 tff(1567,plain,
% 9.37/9.57 ((((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | ((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) | complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.57 inference(tautology,[status(thm)],[])).
% 9.37/9.57 tff(1568,plain,
% 9.37/9.57 (((~(multiplication(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = one))) | complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.57 inference(unit_resolution,[status(thm)],[1567, 1475])).
% 9.37/9.57 tff(1569,plain,
% 9.37/9.57 (complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.57 inference(unit_resolution,[status(thm)],[1568, 1566])).
% 9.37/9.57 tff(1570,plain,
% 9.37/9.57 ((~((c(tptp_fun_X1_0(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))) <=> complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) | (c(tptp_fun_X1_0(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))) | (~complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.57 inference(tautology,[status(thm)],[])).
% 9.37/9.57 tff(1571,plain,
% 9.37/9.57 ((c(tptp_fun_X1_0(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))) | (~complement(tptp_fun_X1_0(X1!1), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 9.37/9.57 inference(unit_resolution,[status(thm)],[1570, 1482])).
% 9.37/9.57 tff(1572,plain,
% 9.37/9.57 (c(tptp_fun_X1_0(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.37/9.57 inference(unit_resolution,[status(thm)],[1571, 1569])).
% 9.37/9.57 tff(1573,plain,
% 9.37/9.57 (c(c(X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 9.37/9.57 inference(transitivity,[status(thm)],[218, 1572])).
% 9.37/9.57 tff(1574,plain,
% 9.37/9.57 (addition(c(c(X0!2)), c(c(X1!1))) = addition(c(tptp_fun_X1_0(X0!2)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.57 inference(monotonicity,[status(thm)],[226, 1573])).
% 9.37/9.57 tff(1575,plain,
% 9.37/9.57 (addition(c(tptp_fun_X1_0(X0!2)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(c(c(X0!2)), c(c(X1!1)))),
% 9.37/9.57 inference(symmetry,[status(thm)],[1574])).
% 9.37/9.57 tff(1576,plain,
% 9.37/9.57 (addition(c(tptp_fun_X1_0(X0!2)), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(c(tptp_fun_X1_0(X0!2)), zero)),
% 9.37/9.57 inference(monotonicity,[status(thm)],[1436])).
% 9.37/9.57 tff(1577,plain,
% 9.37/9.57 (addition(c(tptp_fun_X1_0(X0!2)), zero) = addition(c(tptp_fun_X1_0(X0!2)), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.57 inference(symmetry,[status(thm)],[1576])).
% 9.37/9.57 tff(1578,plain,
% 9.37/9.57 ((~![A: $i] : (addition(A, zero) = A)) | (addition(c(tptp_fun_X1_0(X0!2)), zero) = c(tptp_fun_X1_0(X0!2)))),
% 9.37/9.57 inference(quant_inst,[status(thm)],[])).
% 9.37/9.57 tff(1579,plain,
% 9.37/9.57 (addition(c(tptp_fun_X1_0(X0!2)), zero) = c(tptp_fun_X1_0(X0!2))),
% 9.37/9.57 inference(unit_resolution,[status(thm)],[1578, 366])).
% 9.37/9.57 tff(1580,plain,
% 9.37/9.57 (c(tptp_fun_X1_0(X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), zero)),
% 9.37/9.57 inference(symmetry,[status(thm)],[1579])).
% 9.37/9.57 tff(1581,plain,
% 9.37/9.57 (X0!2 = addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))),
% 9.37/9.57 inference(transitivity,[status(thm)],[230, 1580, 1577, 1575, 229])).
% 9.37/9.57 tff(1582,plain,
% 9.37/9.57 (c(X0!2) = c(addition(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))),
% 9.37/9.57 inference(monotonicity,[status(thm)],[1581])).
% 9.37/9.57 tff(1583,plain,
% 9.37/9.57 ((~![A: $i] : (addition(A, zero) = A)) | (addition(tptp_fun_X1_0(X0!2), zero) = tptp_fun_X1_0(X0!2))),
% 9.37/9.57 inference(quant_inst,[status(thm)],[])).
% 9.37/9.57 tff(1584,plain,
% 9.37/9.57 (addition(tptp_fun_X1_0(X0!2), zero) = tptp_fun_X1_0(X0!2)),
% 9.37/9.57 inference(unit_resolution,[status(thm)],[1583, 366])).
% 9.37/9.57 tff(1585,plain,
% 9.37/9.57 (addition(tptp_fun_X1_0(X0!2), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(tptp_fun_X1_0(X0!2), zero)),
% 9.37/9.57 inference(monotonicity,[status(thm)],[1436])).
% 9.37/9.57 tff(1586,plain,
% 9.37/9.57 (addition(c(X0!2), c(c(X1!1))) = addition(tptp_fun_X1_0(X0!2), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 9.37/9.57 inference(monotonicity,[status(thm)],[225, 1573])).
% 9.37/9.57 tff(1587,plain,
% 9.37/9.57 (c(multiplication(X0!2, c(X1!1))) = multiplication(c(X0!2), c(X1!1))),
% 9.37/9.57 inference(transitivity,[status(thm)],[467, 1586, 1585, 1584, 331, 1582, 211, 184])).
% 9.37/9.57 tff(1588,plain,
% 9.37/9.57 ((~(multiplication(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(multiplication(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one))),
% 9.37/9.57 inference(unit_resolution,[status(thm)],[1296, 964])).
% 9.37/9.57 tff(1589,plain,
% 9.37/9.57 (~complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.37/9.57 inference(unit_resolution,[status(thm)],[1309, 1588])).
% 9.37/9.57 tff(1590,plain,
% 9.37/9.57 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))),
% 9.37/9.57 inference(symmetry,[status(thm)],[432])).
% 9.37/9.57 tff(1591,plain,
% 9.37/9.57 (multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.37/9.57 inference(transitivity,[status(thm)],[420, 419])).
% 9.37/9.57 tff(1592,plain,
% 9.37/9.57 (multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))), tptp_fun_X1_0(X1!1))),
% 9.37/9.57 inference(monotonicity,[status(thm)],[1591])).
% 9.37/9.57 tff(1593,plain,
% 9.37/9.57 (multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.37/9.57 inference(symmetry,[status(thm)],[1592])).
% 9.37/9.57 tff(1594,plain,
% 9.37/9.57 (multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))) = multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 9.37/9.57 inference(monotonicity,[status(thm)],[243])).
% 9.37/9.57 tff(1595,plain,
% 9.37/9.57 (multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))))),
% 9.37/9.57 inference(symmetry,[status(thm)],[1594])).
% 9.37/9.57 tff(1596,plain,
% 9.37/9.57 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))))),
% 9.37/9.57 inference(transitivity,[status(thm)],[826, 1595])).
% 9.37/9.57 tff(1597,plain,
% 9.37/9.57 (multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1))),
% 9.37/9.57 inference(monotonicity,[status(thm)],[1596])).
% 9.37/9.57 tff(1598,plain,
% 9.37/9.57 (multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)) = multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(tptp_fun_X1_0(X0!2), c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))), tptp_fun_X1_0(X1!1))),
% 9.37/9.57 inference(symmetry,[status(thm)],[1597])).
% 9.37/9.57 tff(1599,plain,
% 9.37/9.57 (multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))),
% 9.37/9.57 inference(transitivity,[status(thm)],[1598, 1593, 338])).
% 9.37/9.57 tff(1600,plain,
% 9.37/9.57 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1)))),
% 9.37/9.57 inference(monotonicity,[status(thm)],[1599])).
% 9.37/9.57 tff(1601,plain,
% 9.37/9.57 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))),
% 9.37/9.57 inference(transitivity,[status(thm)],[1600, 1590])).
% 9.37/9.57 tff(1602,plain,
% 9.37/9.57 ((addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = one) <=> (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one)),
% 9.37/9.57 inference(monotonicity,[status(thm)],[1601])).
% 9.37/9.57 tff(1603,plain,
% 9.37/9.57 ((addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one) <=> (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = one)),
% 9.37/9.57 inference(symmetry,[status(thm)],[1602])).
% 9.37/9.57 tff(1604,plain,
% 9.37/9.57 ((~(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1))) = one)) <=> (~(addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = one))),
% 9.37/9.58 inference(monotonicity,[status(thm)],[1603])).
% 9.37/9.58 tff(1605,plain,
% 9.37/9.58 (~(addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, c(X1!1)))), tptp_fun_X1_0(X1!1)), multiplication(c(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X1!1))) = one)),
% 9.37/9.58 inference(modus_ponens,[status(thm)],[964, 1604])).
% 9.37/9.58 tff(1606,plain,
% 9.37/9.58 (~(c(multiplication(X0!2, c(X1!1))) = zero)),
% 9.37/9.58 inference(unit_resolution,[status(thm)],[1108, 1605])).
% 9.37/9.58 tff(1607,plain,
% 9.37/9.58 (test(multiplication(X0!2, c(X1!1)))),
% 9.37/9.58 inference(unit_resolution,[status(thm)],[1123, 1606])).
% 9.37/9.58 tff(1608,plain,
% 9.37/9.58 ((c(multiplication(X0!2, c(X1!1))) = multiplication(c(X0!2), c(X1!1))) <=> complement(multiplication(X0!2, c(X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 9.37/9.58 inference(unit_resolution,[status(thm)],[1314, 1607])).
% 9.37/9.58 tff(1609,plain,
% 9.37/9.58 (~(c(multiplication(X0!2, c(X1!1))) = multiplication(c(X0!2), c(X1!1)))),
% 9.37/9.58 inference(unit_resolution,[status(thm)],[1316, 1608, 1589])).
% 9.37/9.58 tff(1610,plain,
% 9.37/9.58 ($false),
% 9.37/9.58 inference(unit_resolution,[status(thm)],[1609, 1587])).
% 9.37/9.58 % SZS output end Proof
% 9.43/9.58 % E exiting
%------------------------------------------------------------------------------