%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE021+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 05:12:52 AM UTC 2025
% Result : Theorem 1.37s 1.58s
% Output : Proof 1.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE021+2 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 18:51:56 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.37/1.58 % SZS status Theorem
% 1.37/1.58 % SZS output start Proof
% 1.37/1.58 tff(tptp_fun_X0_2_type, type, (
% 1.37/1.58 tptp_fun_X0_2: $i)).
% 1.37/1.58 tff(multiplication_type, type, (
% 1.37/1.58 multiplication: ( $i * $i ) > $i)).
% 1.37/1.58 tff(one_type, type, (
% 1.37/1.58 one: $i)).
% 1.37/1.58 tff(leq_type, type, (
% 1.37/1.58 leq: ( $i * $i ) > $o)).
% 1.37/1.58 tff(addition_type, type, (
% 1.37/1.58 addition: ( $i * $i ) > $i)).
% 1.37/1.58 tff(c_type, type, (
% 1.37/1.58 c: $i > $i)).
% 1.37/1.58 tff(tptp_fun_X1_1_type, type, (
% 1.37/1.58 tptp_fun_X1_1: $i)).
% 1.37/1.58 tff(tptp_fun_X1_0_type, type, (
% 1.37/1.58 tptp_fun_X1_0: $i > $i)).
% 1.37/1.58 tff(zero_type, type, (
% 1.37/1.58 zero: $i)).
% 1.37/1.58 tff(complement_type, type, (
% 1.37/1.58 complement: ( $i * $i ) > $o)).
% 1.37/1.58 tff(test_type, type, (
% 1.37/1.58 test: $i > $o)).
% 1.37/1.58 tff(1,assumption,(multiplication(one, X0!2) = X0!2), introduced(assumption)).
% 1.37/1.58 tff(2,plain,
% 1.37/1.58 (^[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))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(3,plain,
% 1.37/1.58 (![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)))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[2])).
% 1.37/1.58 tff(4,plain,
% 1.37/1.58 (^[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)))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(5,plain,
% 1.37/1.58 (![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)))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[4])).
% 1.37/1.58 tff(6,plain,
% 1.37/1.58 (![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)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(7,plain,
% 1.37/1.58 (^[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))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(8,plain,
% 1.37/1.58 (![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)))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[7])).
% 1.37/1.58 tff(9,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')).
% 1.37/1.58 tff(10,plain,
% 1.37/1.58 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[9, 8])).
% 1.37/1.58 tff(11,plain,
% 1.37/1.58 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[10, 6])).
% 1.37/1.58 tff(12,plain,(
% 1.37/1.58 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 1.37/1.58 inference(skolemize,[status(sab)],[11])).
% 1.37/1.58 tff(13,plain,
% 1.37/1.58 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[12, 5])).
% 1.37/1.58 tff(14,plain,
% 1.37/1.58 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[13, 3])).
% 1.37/1.58 tff(15,plain,
% 1.37/1.58 ((~![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)))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(16,plain,
% 1.37/1.58 (~(((~(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))),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[15, 14])).
% 1.37/1.58 tff(17,plain,
% 1.37/1.58 (^[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)))))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(18,plain,
% 1.37/1.58 (![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))))))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[17])).
% 1.37/1.58 tff(19,plain,
% 1.37/1.58 (^[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)))))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(20,plain,
% 1.37/1.58 (![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))))))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[19])).
% 1.37/1.58 tff(21,plain,
% 1.37/1.58 (![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))))))),
% 1.37/1.58 inference(transitivity,[status(thm)],[20, 18])).
% 1.37/1.58 tff(22,plain,
% 1.37/1.58 (^[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))))))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(23,plain,
% 1.37/1.58 (![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))))))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[22])).
% 1.37/1.58 tff(24,plain,
% 1.37/1.58 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(25,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_1')).
% 1.37/1.58 tff(26,plain,
% 1.37/1.58 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[25, 24])).
% 1.37/1.58 tff(27,plain,(
% 1.37/1.58 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 1.37/1.58 inference(skolemize,[status(sab)],[26])).
% 1.37/1.58 tff(28,plain,
% 1.37/1.58 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[27, 23])).
% 1.37/1.58 tff(29,plain,
% 1.37/1.58 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[28, 21])).
% 1.37/1.58 tff(30,plain,
% 1.37/1.58 ((~![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))))))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(31,plain,
% 1.37/1.58 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[30, 29])).
% 1.37/1.58 tff(32,plain,
% 1.37/1.58 (((~((~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))),
% 1.37/1.58 inference(tautology,[status(thm)],[])).
% 1.37/1.58 tff(33,plain,
% 1.37/1.58 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[32, 31])).
% 1.37/1.58 tff(34,plain,
% 1.37/1.58 ((~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))) <=> (~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0))))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(35,plain,
% 1.37/1.58 ((~![X0: $i, X1: $i] : (test(X1) => (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))) <=> (~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0))))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(36,axiom,(~![X0: $i, X1: $i] : (test(X1) => (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 1.37/1.58 tff(37,plain,
% 1.37/1.58 (~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.37/1.58 tff(38,plain,
% 1.37/1.58 (~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[37, 34])).
% 1.37/1.58 tff(39,plain,
% 1.37/1.58 (~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[38, 34])).
% 1.37/1.58 tff(40,plain,
% 1.37/1.58 (~![X0: $i, X1: $i] : ((~test(X1)) | (leq(X0, addition(multiplication(X1, X0), multiplication(c(X1), X0))) & leq(addition(multiplication(X1, X0), multiplication(c(X1), X0)), X0)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[39, 34])).
% 1.37/1.58 tff(41,plain,(
% 1.37/1.58 ~((~test(X1!1)) | (leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) & leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2)))),
% 1.37/1.58 inference(skolemize,[status(sab)],[40])).
% 1.37/1.58 tff(42,plain,
% 1.37/1.58 (test(X1!1)),
% 1.37/1.58 inference(or_elim,[status(thm)],[41])).
% 1.37/1.58 tff(43,plain,
% 1.37/1.58 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 1.37/1.58 inference(tautology,[status(thm)],[])).
% 1.37/1.58 tff(44,plain,
% 1.37/1.58 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[43, 42])).
% 1.37/1.58 tff(45,plain,
% 1.37/1.58 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[44, 33])).
% 1.37/1.58 tff(46,plain,
% 1.37/1.58 ((((~(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))),
% 1.37/1.58 inference(tautology,[status(thm)],[])).
% 1.37/1.58 tff(47,plain,
% 1.37/1.58 ((((~(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))))),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[46, 45])).
% 1.37/1.58 tff(48,plain,
% 1.37/1.58 (~((~(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)))),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[47, 16])).
% 1.37/1.58 tff(49,plain,
% 1.37/1.58 (((~(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)),
% 1.37/1.58 inference(tautology,[status(thm)],[])).
% 1.37/1.58 tff(50,plain,
% 1.37/1.58 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[49, 48])).
% 1.37/1.58 tff(51,plain,
% 1.37/1.58 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = multiplication(one, X0!2)),
% 1.37/1.58 inference(monotonicity,[status(thm)],[50])).
% 1.37/1.58 tff(52,plain,
% 1.37/1.58 (^[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))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(53,plain,
% 1.37/1.58 (![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)))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[52])).
% 1.37/1.58 tff(54,plain,
% 1.37/1.58 (![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)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(55,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')).
% 1.37/1.58 tff(56,plain,
% 1.37/1.58 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.37/1.58 tff(57,plain,(
% 1.37/1.58 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 1.37/1.58 inference(skolemize,[status(sab)],[56])).
% 1.37/1.58 tff(58,plain,
% 1.37/1.58 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[57, 53])).
% 1.37/1.58 tff(59,plain,
% 1.37/1.58 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)))),
% 1.37/1.58 inference(quant_inst,[status(thm)],[])).
% 1.37/1.58 tff(60,plain,
% 1.37/1.58 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 1.37/1.58 inference(unit_resolution,[status(thm)],[59, 58])).
% 1.37/1.58 tff(61,plain,
% 1.37/1.58 (addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2)),
% 1.37/1.58 inference(symmetry,[status(thm)],[60])).
% 1.37/1.58 tff(62,plain,
% 1.37/1.58 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(63,plain,
% 1.37/1.58 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[62])).
% 1.37/1.58 tff(64,plain,
% 1.37/1.58 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(65,plain,
% 1.37/1.58 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 1.37/1.58 inference(bind,[status(th)],[])).
% 1.37/1.58 tff(66,plain,
% 1.37/1.58 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 1.37/1.58 inference(quant_intro,[status(thm)],[65])).
% 1.37/1.58 tff(67,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_3')).
% 1.37/1.58 tff(68,plain,
% 1.37/1.58 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.37/1.58 tff(69,plain,
% 1.37/1.58 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[68, 64])).
% 1.37/1.58 tff(70,plain,(
% 1.37/1.58 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 1.37/1.58 inference(skolemize,[status(sab)],[69])).
% 1.37/1.58 tff(71,plain,
% 1.37/1.58 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 1.37/1.58 inference(modus_ponens,[status(thm)],[70, 63])).
% 1.37/1.58 tff(72,plain,
% 1.37/1.58 (((~![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))))),
% 1.37/1.58 inference(rewrite,[status(thm)],[])).
% 1.37/1.58 tff(73,plain,
% 1.37/1.58 ((~![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))))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(74,plain,
% 1.37/1.59 ((~![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)))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.37/1.59 tff(75,plain,
% 1.37/1.59 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[74, 71, 42])).
% 1.37/1.59 tff(76,plain,
% 1.37/1.59 (((~![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)))))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(77,plain,
% 1.37/1.59 ((~(((~(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))))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(78,plain,
% 1.37/1.59 ((((~(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)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(79,plain,
% 1.37/1.59 ((~(((~(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))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[78])).
% 1.37/1.59 tff(80,plain,
% 1.37/1.59 ((~(((~(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))))),
% 1.37/1.59 inference(transitivity,[status(thm)],[79, 77])).
% 1.37/1.59 tff(81,plain,
% 1.37/1.59 (((~![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)))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[80])).
% 1.37/1.59 tff(82,plain,
% 1.37/1.59 (((~![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)))))),
% 1.37/1.59 inference(transitivity,[status(thm)],[81, 76])).
% 1.37/1.59 tff(83,plain,
% 1.37/1.59 ((~![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))))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(84,plain,
% 1.37/1.59 ((~![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))))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.37/1.59 tff(85,plain,
% 1.37/1.59 (~(((~(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)))),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[84, 14])).
% 1.37/1.59 tff(86,plain,
% 1.37/1.59 ((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))),
% 1.37/1.59 inference(commutativity,[status(thm)],[])).
% 1.37/1.59 tff(87,plain,
% 1.37/1.59 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 1.37/1.59 inference(symmetry,[status(thm)],[50])).
% 1.37/1.59 tff(88,plain,
% 1.37/1.59 ((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)))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[87])).
% 1.37/1.59 tff(89,plain,
% 1.37/1.59 ((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))),
% 1.37/1.59 inference(transitivity,[status(thm)],[88, 86])).
% 1.37/1.59 tff(90,plain,
% 1.37/1.59 ((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)),
% 1.37/1.59 inference(symmetry,[status(thm)],[89])).
% 1.37/1.59 tff(91,plain,
% 1.37/1.59 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 1.37/1.59 inference(bind,[status(th)],[])).
% 1.37/1.59 tff(92,plain,
% 1.37/1.59 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.37/1.59 inference(quant_intro,[status(thm)],[91])).
% 1.37/1.59 tff(93,plain,
% 1.37/1.59 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(94,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 1.37/1.59 tff(95,plain,
% 1.37/1.59 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[94, 93])).
% 1.37/1.59 tff(96,plain,(
% 1.37/1.59 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.37/1.59 inference(skolemize,[status(sab)],[95])).
% 1.37/1.59 tff(97,plain,
% 1.37/1.59 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[96, 92])).
% 1.37/1.59 tff(98,plain,
% 1.37/1.59 ((~![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))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(99,plain,
% 1.37/1.59 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[98, 97])).
% 1.37/1.59 tff(100,plain,
% 1.37/1.59 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[99, 90])).
% 1.37/1.59 tff(101,plain,
% 1.37/1.59 (((~(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)),
% 1.37/1.59 inference(tautology,[status(thm)],[])).
% 1.37/1.59 tff(102,plain,
% 1.37/1.59 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[101, 48])).
% 1.37/1.59 tff(103,plain,
% 1.37/1.59 (((~(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)),
% 1.37/1.59 inference(tautology,[status(thm)],[])).
% 1.37/1.59 tff(104,plain,
% 1.37/1.59 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[103, 48])).
% 1.37/1.59 tff(105,plain,
% 1.37/1.59 ((~((~(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))),
% 1.37/1.59 inference(tautology,[status(thm)],[])).
% 1.37/1.59 tff(106,plain,
% 1.37/1.59 ((~((~(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))),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[105, 104, 102])).
% 1.37/1.59 tff(107,plain,
% 1.37/1.59 (~((~(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)))),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[106, 100])).
% 1.37/1.59 tff(108,plain,
% 1.37/1.59 ((((~(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))),
% 1.37/1.59 inference(tautology,[status(thm)],[])).
% 1.37/1.59 tff(109,plain,
% 1.37/1.59 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[108, 107, 85])).
% 1.37/1.59 tff(110,plain,
% 1.37/1.59 ((~((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)))),
% 1.37/1.59 inference(tautology,[status(thm)],[])).
% 1.37/1.59 tff(111,plain,
% 1.37/1.59 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[110, 109, 75])).
% 1.37/1.59 tff(112,plain,
% 1.37/1.59 (tptp_fun_X1_0(X1!1) = c(X1!1)),
% 1.37/1.59 inference(symmetry,[status(thm)],[111])).
% 1.37/1.59 tff(113,plain,
% 1.37/1.59 (multiplication(tptp_fun_X1_0(X1!1), X0!2) = multiplication(c(X1!1), X0!2)),
% 1.37/1.59 inference(monotonicity,[status(thm)],[112])).
% 1.37/1.59 tff(114,plain,
% 1.37/1.59 (multiplication(c(X1!1), X0!2) = multiplication(tptp_fun_X1_0(X1!1), X0!2)),
% 1.37/1.59 inference(symmetry,[status(thm)],[113])).
% 1.37/1.59 tff(115,plain,
% 1.37/1.59 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[114])).
% 1.37/1.59 tff(116,plain,
% 1.37/1.59 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = X0!2),
% 1.37/1.59 inference(transitivity,[status(thm)],[115, 61, 51, 1])).
% 1.37/1.59 tff(117,plain,
% 1.37/1.59 (leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) <=> leq(X0!2, X0!2)),
% 1.37/1.59 inference(monotonicity,[status(thm)],[116])).
% 1.37/1.59 tff(118,plain,
% 1.37/1.59 (leq(X0!2, X0!2) <=> leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.37/1.59 inference(symmetry,[status(thm)],[117])).
% 1.37/1.59 tff(119,plain,
% 1.37/1.59 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 1.37/1.59 inference(bind,[status(th)],[])).
% 1.37/1.59 tff(120,plain,
% 1.37/1.59 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 1.37/1.59 inference(quant_intro,[status(thm)],[119])).
% 1.37/1.59 tff(121,plain,
% 1.37/1.59 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(122,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','order')).
% 1.37/1.59 tff(123,plain,
% 1.37/1.59 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[122, 121])).
% 1.37/1.59 tff(124,plain,(
% 1.37/1.59 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 1.37/1.59 inference(skolemize,[status(sab)],[123])).
% 1.37/1.59 tff(125,plain,
% 1.37/1.59 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[124, 120])).
% 1.37/1.59 tff(126,plain,
% 1.37/1.59 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!2, X0!2) <=> (addition(X0!2, X0!2) = X0!2))),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(127,plain,
% 1.37/1.59 (leq(X0!2, X0!2) <=> (addition(X0!2, X0!2) = X0!2)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[126, 125])).
% 1.37/1.59 tff(128,plain,
% 1.37/1.59 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 1.37/1.59 inference(bind,[status(th)],[])).
% 1.37/1.59 tff(129,plain,
% 1.37/1.59 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 1.37/1.59 inference(quant_intro,[status(thm)],[128])).
% 1.37/1.59 tff(130,plain,
% 1.37/1.59 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(131,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 1.37/1.59 tff(132,plain,
% 1.37/1.59 (![A: $i] : (addition(A, A) = A)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[131, 130])).
% 1.37/1.59 tff(133,plain,(
% 1.37/1.59 ![A: $i] : (addition(A, A) = A)),
% 1.37/1.59 inference(skolemize,[status(sab)],[132])).
% 1.37/1.59 tff(134,plain,
% 1.37/1.59 (![A: $i] : (addition(A, A) = A)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[133, 129])).
% 1.37/1.59 tff(135,plain,
% 1.37/1.59 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!2, X0!2) = X0!2)),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(136,plain,
% 1.37/1.59 (addition(X0!2, X0!2) = X0!2),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[135, 134])).
% 1.37/1.59 tff(137,plain,
% 1.37/1.59 ((~(leq(X0!2, X0!2) <=> (addition(X0!2, X0!2) = X0!2))) | leq(X0!2, X0!2) | (~(addition(X0!2, X0!2) = X0!2))),
% 1.37/1.59 inference(tautology,[status(thm)],[])).
% 1.37/1.59 tff(138,plain,
% 1.37/1.59 (leq(X0!2, X0!2)),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[137, 136, 127])).
% 1.37/1.59 tff(139,plain,
% 1.37/1.59 (leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[138, 118])).
% 1.37/1.59 tff(140,plain,
% 1.37/1.59 (leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2) <=> leq(X0!2, X0!2)),
% 1.37/1.59 inference(monotonicity,[status(thm)],[116])).
% 1.37/1.59 tff(141,plain,
% 1.37/1.59 (leq(X0!2, X0!2) <=> leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2)),
% 1.37/1.59 inference(symmetry,[status(thm)],[140])).
% 1.37/1.59 tff(142,plain,
% 1.37/1.59 (leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[138, 141])).
% 1.37/1.59 tff(143,plain,
% 1.37/1.59 ((~(~((~leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (~leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2))))) <=> ((~leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (~leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2)))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(144,plain,
% 1.37/1.59 ((leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) & leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2)) <=> (~((~leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (~leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2))))),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(145,plain,
% 1.37/1.59 ((~(leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) & leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2))) <=> (~(~((~leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (~leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2)))))),
% 1.37/1.59 inference(monotonicity,[status(thm)],[144])).
% 1.37/1.59 tff(146,plain,
% 1.37/1.59 ((~(leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) & leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2))) <=> ((~leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (~leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2)))),
% 1.37/1.59 inference(transitivity,[status(thm)],[145, 143])).
% 1.37/1.59 tff(147,plain,
% 1.37/1.59 (~(leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) & leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2))),
% 1.37/1.59 inference(or_elim,[status(thm)],[41])).
% 1.37/1.59 tff(148,plain,
% 1.37/1.59 ((~leq(X0!2, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (~leq(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), X0!2))),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[147, 146])).
% 1.37/1.59 tff(149,plain,
% 1.37/1.59 ($false),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[148, 142, 139])).
% 1.37/1.59 tff(150,plain,(~(multiplication(one, X0!2) = X0!2)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.59 tff(151,plain,
% 1.37/1.59 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 1.37/1.59 inference(bind,[status(th)],[])).
% 1.37/1.59 tff(152,plain,
% 1.37/1.59 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 1.37/1.59 inference(quant_intro,[status(thm)],[151])).
% 1.37/1.59 tff(153,plain,
% 1.37/1.59 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 1.37/1.59 inference(rewrite,[status(thm)],[])).
% 1.37/1.59 tff(154,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 1.37/1.59 tff(155,plain,
% 1.37/1.59 (![A: $i] : (multiplication(one, A) = A)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[154, 153])).
% 1.37/1.59 tff(156,plain,(
% 1.37/1.59 ![A: $i] : (multiplication(one, A) = A)),
% 1.37/1.59 inference(skolemize,[status(sab)],[155])).
% 1.37/1.59 tff(157,plain,
% 1.37/1.59 (![A: $i] : (multiplication(one, A) = A)),
% 1.37/1.59 inference(modus_ponens,[status(thm)],[156, 152])).
% 1.37/1.59 tff(158,plain,
% 1.37/1.59 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!2) = X0!2)),
% 1.37/1.59 inference(quant_inst,[status(thm)],[])).
% 1.37/1.59 tff(159,plain,
% 1.37/1.59 ($false),
% 1.37/1.59 inference(unit_resolution,[status(thm)],[158, 157, 150])).
% 1.37/1.59 % SZS output end Proof
% 1.37/1.59 % E exiting
%------------------------------------------------------------------------------