%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE021+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:12:52 AM UTC 2025
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE021+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.35 % Computer : n001.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Thu Jun 19 18:57:19 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(addition_type, type, (
% 0.21/0.44 addition: ( $i * $i ) > $i)).
% 0.21/0.44 tff(multiplication_type, type, (
% 0.21/0.44 multiplication: ( $i * $i ) > $i)).
% 0.21/0.44 tff(tptp_fun_X0_2_type, type, (
% 0.21/0.44 tptp_fun_X0_2: $i)).
% 0.21/0.44 tff(c_type, type, (
% 0.21/0.44 c: $i > $i)).
% 0.21/0.44 tff(tptp_fun_X1_0_type, type, (
% 0.21/0.44 tptp_fun_X1_0: $i > $i)).
% 0.21/0.44 tff(tptp_fun_X1_1_type, type, (
% 0.21/0.44 tptp_fun_X1_1: $i)).
% 0.21/0.44 tff(complement_type, type, (
% 0.21/0.44 complement: ( $i * $i ) > $o)).
% 0.21/0.44 tff(test_type, type, (
% 0.21/0.44 test: $i > $o)).
% 0.21/0.44 tff(one_type, type, (
% 0.21/0.44 one: $i)).
% 0.21/0.44 tff(zero_type, type, (
% 0.21/0.44 zero: $i)).
% 0.21/0.44 tff(1,plain,
% 0.21/0.44 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(4,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.44 tff(6,plain,(
% 0.21/0.44 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.44 inference(skolemize,[status(sab)],[5])).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 (addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 0.21/0.44 inference(symmetry,[status(thm)],[9])).
% 0.21/0.44 tff(11,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)).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (^[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)))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(13,plain,
% 0.21/0.44 (![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))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 (^[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)))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(15,plain,
% 0.21/0.44 (![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))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.44 tff(16,plain,
% 0.21/0.44 (![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))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[15, 13])).
% 0.21/0.44 tff(17,plain,
% 0.21/0.44 (^[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))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(18,plain,
% 0.21/0.44 (![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))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[17])).
% 0.21/0.44 tff(19,plain,
% 0.21/0.44 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(20,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_1')).
% 0.21/0.44 tff(21,plain,
% 0.21/0.44 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.44 tff(22,plain,(
% 0.21/0.44 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[21])).
% 0.21/0.44 tff(23,plain,
% 0.21/0.44 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.21/0.44 tff(24,plain,
% 0.21/0.44 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.21/0.44 tff(25,plain,
% 0.21/0.44 ((~![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: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(26,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[25, 24, 11])).
% 0.21/0.44 tff(27,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,[]))).
% 0.21/0.44 tff(28,plain,
% 0.21/0.44 (((~((~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))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(29,plain,
% 0.21/0.44 (test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.21/0.44 tff(30,assumption,(![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))), introduced(assumption)).
% 0.21/0.44 tff(31,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(34,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.44 tff(38,axiom,(![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_2')).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.21/0.44 tff(41,plain,(
% 0.21/0.44 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[40])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (((~![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)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 ((~(((~(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))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 ((((~(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)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 ((~(((~(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))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[46])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 ((~(((~(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))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[47, 45])).
% 0.21/0.44 tff(49,plain,
% 0.21/0.44 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(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)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[48])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(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)))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[49, 44])).
% 0.21/0.45 tff(51,plain,
% 0.21/0.45 ((~![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))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(52,plain,
% 0.21/0.45 ((~![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))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.45 tff(53,plain,
% 0.21/0.45 (~(((~(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)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[52, 43])).
% 0.21/0.45 tff(54,plain,
% 0.21/0.45 ((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))),
% 0.21/0.45 inference(commutativity,[status(thm)],[])).
% 0.21/0.45 tff(55,plain,
% 0.21/0.45 ((~![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)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(56,plain,
% 0.21/0.45 (~(((~(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))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[55, 43])).
% 0.21/0.45 tff(57,plain,
% 0.21/0.45 ((~![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))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(58,plain,
% 0.21/0.45 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[57, 24])).
% 0.21/0.45 tff(59,plain,
% 0.21/0.45 (((~((~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))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(60,plain,
% 0.21/0.45 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.21/0.45 tff(61,plain,
% 0.21/0.45 ((~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X1, X0), multiplication(c(X1), X0))))) <=> (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X1, X0), multiplication(c(X1), X0)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(62,plain,
% 0.21/0.45 ((~![X0: $i, X1: $i] : (test(X1) => (X0 = addition(multiplication(X1, X0), multiplication(c(X1), X0))))) <=> (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X1, X0), multiplication(c(X1), X0)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(63,axiom,(~![X0: $i, X1: $i] : (test(X1) => (X0 = addition(multiplication(X1, X0), multiplication(c(X1), X0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.21/0.45 tff(64,plain,
% 0.21/0.45 (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X1, X0), multiplication(c(X1), X0))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.45 tff(65,plain,
% 0.21/0.45 (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X1, X0), multiplication(c(X1), X0))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[64, 61])).
% 0.21/0.45 tff(66,plain,
% 0.21/0.45 (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X1, X0), multiplication(c(X1), X0))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.21/0.45 tff(67,plain,
% 0.21/0.45 (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X1, X0), multiplication(c(X1), X0))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[66, 61])).
% 0.21/0.45 tff(68,plain,(
% 0.21/0.45 ~((~test(X1!1)) | (X0!2 = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[67])).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 (test(X1!1)),
% 0.21/0.45 inference(or_elim,[status(thm)],[68])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[71, 60])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 ((((~(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))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 ((((~(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))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (~((~(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)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[74, 56])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 (((~(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)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 0.21/0.45 inference(symmetry,[status(thm)],[77])).
% 0.21/0.45 tff(79,plain,
% 0.21/0.45 ((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)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[78])).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 ((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))),
% 0.21/0.45 inference(transitivity,[status(thm)],[79, 54])).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 ((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)),
% 0.21/0.45 inference(symmetry,[status(thm)],[80])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 ((~![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))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[82, 7])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[83, 81])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 (((~(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)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[85, 75])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 (((~(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)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[87, 75])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 ((~((~(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))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(90,plain,
% 0.21/0.45 ((~((~(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))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[89, 88, 86])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 (~((~(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)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[90, 84])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 ((((~(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))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(93,plain,
% 0.21/0.45 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[92, 91, 53])).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 ((~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))) | (~complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[94, 93, 30])).
% 0.21/0.45 tff(96,plain,(~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 ((~(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)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(98,plain,
% 0.21/0.45 ((~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))) | test(tptp_fun_X1_0(X1!1))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.21/0.45 tff(99,plain,
% 0.21/0.45 (test(tptp_fun_X1_0(X1!1))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[98, 29])).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(101,plain,
% 0.21/0.45 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[100])).
% 0.21/0.45 tff(102,plain,
% 0.21/0.45 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(103,plain,
% 0.21/0.46 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(104,plain,
% 0.21/0.46 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[103])).
% 0.21/0.46 tff(105,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_3')).
% 0.21/0.46 tff(106,plain,
% 0.21/0.46 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.21/0.46 tff(107,plain,
% 0.21/0.46 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.21/0.46 tff(108,plain,(
% 0.21/0.46 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[107])).
% 0.21/0.46 tff(109,plain,
% 0.21/0.46 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.21/0.46 tff(110,plain,
% 0.21/0.46 (((~![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)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(111,plain,
% 0.21/0.46 ((~![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)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(112,plain,
% 0.21/0.46 ((~![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))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.46 tff(113,plain,
% 0.21/0.46 ((~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))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[112, 109])).
% 0.21/0.46 tff(114,plain,
% 0.21/0.46 ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[113, 99])).
% 0.21/0.46 tff(115,plain,
% 0.21/0.46 ((~((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))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(116,plain,
% 0.21/0.46 ((~((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)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[115, 72])).
% 0.21/0.46 tff(117,plain,
% 0.21/0.46 (c(tptp_fun_X1_0(X1!1)) = X1!1),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[116, 114])).
% 0.21/0.46 tff(118,plain,
% 0.21/0.46 (multiplication(c(tptp_fun_X1_0(X1!1)), X0!2) = multiplication(X1!1, X0!2)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.46 tff(119,plain,
% 0.21/0.46 (((~![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))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(120,plain,
% 0.21/0.46 ((~![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))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(121,plain,
% 0.21/0.46 ((~![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)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.46 tff(122,plain,
% 0.21/0.46 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[121, 109, 69])).
% 0.21/0.46 tff(123,plain,
% 0.21/0.46 ((~((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)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(124,plain,
% 0.21/0.46 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[123, 93, 122])).
% 0.21/0.46 tff(125,plain,
% 0.21/0.46 (tptp_fun_X1_0(X1!1) = c(X1!1)),
% 0.21/0.46 inference(symmetry,[status(thm)],[124])).
% 0.21/0.46 tff(126,plain,
% 0.21/0.46 (multiplication(tptp_fun_X1_0(X1!1), X0!2) = multiplication(c(X1!1), X0!2)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[125])).
% 0.21/0.46 tff(127,plain,
% 0.21/0.46 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[126, 118])).
% 0.21/0.46 tff(128,assumption,(multiplication(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), X0!2) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), X0!2))), introduced(assumption)).
% 0.21/0.46 tff(129,plain,
% 0.21/0.46 (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)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[125])).
% 0.21/0.46 tff(130,plain,
% 0.21/0.46 (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)))),
% 0.21/0.46 inference(symmetry,[status(thm)],[129])).
% 0.21/0.46 tff(131,plain,
% 0.21/0.46 (^[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))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(132,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[131])).
% 0.21/0.46 tff(133,plain,
% 0.21/0.46 (^[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)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(134,plain,
% 0.21/0.46 (![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)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[133])).
% 0.21/0.46 tff(135,plain,
% 0.21/0.46 (![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))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(136,plain,
% 0.21/0.46 (^[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)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(137,plain,
% 0.21/0.46 (![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))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[136])).
% 0.21/0.46 tff(138,axiom,(![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax','test_deMorgan2')).
% 0.21/0.46 tff(139,plain,
% 0.21/0.46 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.21/0.46 tff(140,plain,
% 0.21/0.46 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.21/0.46 tff(141,plain,(
% 0.21/0.46 ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[140])).
% 0.21/0.46 tff(142,plain,
% 0.21/0.46 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.21/0.46 tff(143,plain,
% 0.21/0.46 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[142, 132])).
% 0.21/0.46 tff(144,plain,
% 0.21/0.46 (((~![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)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(145,plain,
% 0.21/0.46 (((~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)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(146,plain,
% 0.21/0.46 (((~![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))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[145])).
% 0.21/0.46 tff(147,plain,
% 0.21/0.46 (((~![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)))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[146, 144])).
% 0.21/0.46 tff(148,plain,
% 0.21/0.46 ((~![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)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(149,plain,
% 0.21/0.46 ((~![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))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.21/0.46 tff(150,plain,
% 0.21/0.46 ((~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))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[149, 143, 69])).
% 0.21/0.46 tff(151,plain,
% 0.21/0.46 (c(multiplication(X1!1, tptp_fun_X1_0(X1!1))) = addition(c(X1!1), c(tptp_fun_X1_0(X1!1)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[150, 99])).
% 0.21/0.46 tff(152,plain,
% 0.21/0.46 (zero = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 0.21/0.46 inference(symmetry,[status(thm)],[86])).
% 0.21/0.46 tff(153,plain,
% 0.21/0.46 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 0.21/0.46 inference(transitivity,[status(thm)],[88, 152])).
% 0.21/0.46 tff(154,plain,
% 0.21/0.46 (c(multiplication(X1!1, tptp_fun_X1_0(X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[153])).
% 0.21/0.46 tff(155,plain,
% 0.21/0.46 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = c(multiplication(X1!1, tptp_fun_X1_0(X1!1)))),
% 0.21/0.46 inference(symmetry,[status(thm)],[154])).
% 0.21/0.46 tff(156,plain,
% 0.21/0.46 (((~![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))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(157,plain,
% 0.21/0.46 (((~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))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(158,plain,
% 0.21/0.46 (((~![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)))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[157])).
% 0.21/0.46 tff(159,plain,
% 0.21/0.46 (((~![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))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[158, 156])).
% 0.21/0.46 tff(160,plain,
% 0.21/0.46 ((~![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))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(161,plain,
% 0.21/0.46 ((~![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)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.46 tff(162,plain,
% 0.21/0.46 ((~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)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[161, 143, 69])).
% 0.21/0.46 tff(163,plain,
% 0.21/0.46 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[162, 99])).
% 0.21/0.46 tff(164,plain,
% 0.21/0.46 (addition(c(tptp_fun_X1_0(X1!1)), c(X1!1)) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 0.21/0.46 inference(symmetry,[status(thm)],[163])).
% 0.21/0.46 tff(165,plain,
% 0.21/0.46 (X1!1 = c(tptp_fun_X1_0(X1!1))),
% 0.21/0.46 inference(symmetry,[status(thm)],[117])).
% 0.21/0.46 tff(166,plain,
% 0.21/0.46 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[165, 125])).
% 0.21/0.47 tff(167,plain,
% 0.21/0.47 (one = addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[78, 166, 164, 155, 151, 130])).
% 0.21/0.47 tff(168,plain,
% 0.21/0.47 (multiplication(one, X0!2) = multiplication(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), X0!2)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[167])).
% 0.21/0.47 tff(169,plain,
% 0.21/0.47 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(170,plain,
% 0.21/0.47 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.21/0.47 inference(quant_intro,[status(thm)],[169])).
% 0.21/0.47 tff(171,plain,
% 0.21/0.47 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(172,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 0.21/0.47 tff(173,plain,
% 0.21/0.47 (![A: $i] : (multiplication(one, A) = A)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.21/0.47 tff(174,plain,(
% 0.21/0.47 ![A: $i] : (multiplication(one, A) = A)),
% 0.21/0.47 inference(skolemize,[status(sab)],[173])).
% 0.21/0.47 tff(175,plain,
% 0.21/0.47 (![A: $i] : (multiplication(one, A) = A)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.21/0.47 tff(176,plain,
% 0.21/0.47 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!2) = X0!2)),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(177,plain,
% 0.21/0.47 (multiplication(one, X0!2) = X0!2),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.21/0.47 tff(178,plain,
% 0.21/0.47 (X0!2 = multiplication(one, X0!2)),
% 0.21/0.47 inference(symmetry,[status(thm)],[177])).
% 0.21/0.47 tff(179,plain,
% 0.21/0.47 (X0!2 = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 0.21/0.47 inference(transitivity,[status(thm)],[178, 168, 128, 127, 10])).
% 0.21/0.47 tff(180,plain,
% 0.21/0.47 (~(X0!2 = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 0.21/0.47 inference(or_elim,[status(thm)],[68])).
% 0.21/0.47 tff(181,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.21/0.47 tff(182,plain,(~(multiplication(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), X0!2) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), X0!2)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(183,plain,
% 0.21/0.47 (^[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))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(184,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[183])).
% 0.21/0.47 tff(185,plain,
% 0.21/0.47 (![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)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(186,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','left_distributivity')).
% 0.21/0.47 tff(187,plain,
% 0.21/0.47 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.21/0.47 tff(188,plain,(
% 0.21/0.47 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[187])).
% 0.21/0.47 tff(189,plain,
% 0.21/0.47 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[188, 184])).
% 0.21/0.47 tff(190,plain,
% 0.21/0.47 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), X0!2) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), X0!2)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(191,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[190, 189, 182])).
% 0.21/0.47 % SZS output end Proof
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------