%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE007+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:12:50 AM UTC 2025
% Result : Theorem 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE007+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 18:50:42 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.38 % SZS status Theorem
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 tff(complement_type, type, (
% 0.18/0.38 complement: ( $i * $i ) > $o)).
% 0.18/0.38 tff(tptp_fun_X1_1_type, type, (
% 0.18/0.38 tptp_fun_X1_1: $i)).
% 0.18/0.38 tff(tptp_fun_X1_0_type, type, (
% 0.18/0.38 tptp_fun_X1_0: $i > $i)).
% 0.18/0.38 tff(multiplication_type, type, (
% 0.18/0.38 multiplication: ( $i * $i ) > $i)).
% 0.18/0.38 tff(addition_type, type, (
% 0.18/0.38 addition: ( $i * $i ) > $i)).
% 0.18/0.38 tff(c_type, type, (
% 0.18/0.38 c: $i > $i)).
% 0.18/0.38 tff(tptp_fun_X0_2_type, type, (
% 0.18/0.38 tptp_fun_X0_2: $i)).
% 0.18/0.38 tff(one_type, type, (
% 0.18/0.38 one: $i)).
% 0.18/0.38 tff(zero_type, type, (
% 0.18/0.38 zero: $i)).
% 0.18/0.38 tff(test_type, type, (
% 0.18/0.38 test: $i > $o)).
% 0.18/0.38 tff(1,plain,
% 0.18/0.38 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(2,plain,
% 0.18/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.38 tff(3,plain,
% 0.18/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(4,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 0.18/0.38 tff(5,plain,
% 0.18/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.38 tff(6,plain,(
% 0.18/0.38 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.18/0.38 inference(skolemize,[status(sab)],[5])).
% 0.18/0.38 tff(7,plain,
% 0.18/0.38 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.38 tff(8,plain,
% 0.18/0.38 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, c(X0!2)) = addition(c(X0!2), X0!2))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(9,plain,
% 0.18/0.38 (addition(X0!2, c(X0!2)) = addition(c(X0!2), X0!2)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.38 tff(10,plain,
% 0.18/0.38 (addition(c(X0!2), X0!2) = addition(X0!2, c(X0!2))),
% 0.18/0.38 inference(symmetry,[status(thm)],[9])).
% 0.18/0.38 tff(11,plain,
% 0.18/0.38 (^[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))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(12,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.18/0.38 tff(13,plain,
% 0.18/0.38 (^[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)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(14,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.38 tff(15,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(16,plain,
% 0.18/0.38 (^[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))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(17,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.38 tff(18,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')).
% 0.18/0.38 tff(19,plain,
% 0.18/0.38 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.38 tff(20,plain,
% 0.18/0.38 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.18/0.38 tff(21,plain,(
% 0.18/0.38 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[20])).
% 0.18/0.38 tff(22,plain,
% 0.18/0.38 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.18/0.38 tff(23,plain,
% 0.18/0.38 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2)))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 ((~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2)))) <=> (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 ((((~(multiplication(c(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, c(X0!2)) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))) <=> (((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(27,plain,
% 0.18/0.39 ((~(((~(multiplication(c(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, c(X0!2)) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2)))) <=> (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[26])).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 ((~(((~(multiplication(c(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, c(X0!2)) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2)))) <=> (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[27, 25])).
% 0.18/0.39 tff(29,plain,
% 0.18/0.39 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, c(X0!2)) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2)))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[28])).
% 0.18/0.39 tff(30,plain,
% 0.18/0.39 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, c(X0!2)) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2)))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[29, 24])).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, c(X0!2)) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(32,plain,
% 0.18/0.39 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.18/0.39 tff(33,plain,
% 0.18/0.39 (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[32, 23])).
% 0.18/0.39 tff(34,plain,
% 0.18/0.39 ((~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(35,plain,
% 0.18/0.39 ((~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (one = addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(36,axiom,(~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (one = addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.18/0.39 tff(37,plain,
% 0.18/0.39 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.18/0.39 tff(38,plain,
% 0.18/0.39 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.18/0.39 tff(40,plain,
% 0.18/0.39 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[39, 34])).
% 0.18/0.39 tff(41,plain,(
% 0.18/0.39 ~((~(test(X1!1) & test(X0!2))) | (one = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1)))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[40])).
% 0.18/0.39 tff(42,plain,
% 0.18/0.39 (test(X1!1) & test(X0!2)),
% 0.18/0.39 inference(or_elim,[status(thm)],[41])).
% 0.18/0.39 tff(43,plain,
% 0.18/0.39 (test(X0!2)),
% 0.18/0.39 inference(and_elim,[status(thm)],[42])).
% 0.18/0.39 tff(44,plain,
% 0.18/0.39 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(45,plain,
% 0.18/0.39 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[44])).
% 0.18/0.39 tff(46,plain,
% 0.18/0.39 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(47,plain,
% 0.18/0.39 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(48,plain,
% 0.18/0.39 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[47])).
% 0.18/0.39 tff(49,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_3')).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.18/0.39 tff(52,plain,(
% 0.18/0.39 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[51])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | complement(X0!2, c(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | complement(X0!2, c(X0!2)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 (((~test(X0!2)) | ((c(X0!2) = c(X0!2)) <=> complement(X0!2, c(X0!2)))) <=> ((~test(X0!2)) | complement(X0!2, c(X0!2)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = c(X0!2)) <=> complement(X0!2, c(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | complement(X0!2, c(X0!2))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[55])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = c(X0!2)) <=> complement(X0!2, c(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | complement(X0!2, c(X0!2)))),
% 0.18/0.39 inference(transitivity,[status(thm)],[56, 54])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = c(X0!2)) <=> complement(X0!2, c(X0!2))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | complement(X0!2, c(X0!2))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 (complement(X0!2, c(X0!2))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[59, 53, 43])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 ((((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))) | (~((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one)))) | (~complement(X0!2, c(X0!2)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (~((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[61, 60, 33])).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 (((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) | (addition(c(X0!2), X0!2) = one)),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 (addition(c(X0!2), X0!2) = one),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 (one = addition(c(X0!2), X0!2)),
% 0.18/0.39 inference(symmetry,[status(thm)],[64])).
% 0.18/0.39 tff(66,plain,
% 0.18/0.39 (one = addition(X0!2, c(X0!2))),
% 0.18/0.39 inference(transitivity,[status(thm)],[65, 10])).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 (multiplication(one, X1!1) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 0.18/0.39 inference(monotonicity,[status(thm)],[66])).
% 0.18/0.39 tff(68,plain,
% 0.18/0.39 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.18/0.39 inference(quant_intro,[status(thm)],[68])).
% 0.18/0.39 tff(70,plain,
% 0.18/0.39 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(71,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 0.18/0.39 tff(72,plain,
% 0.18/0.39 (![A: $i] : (multiplication(one, A) = A)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.18/0.39 tff(73,plain,(
% 0.18/0.39 ![A: $i] : (multiplication(one, A) = A)),
% 0.18/0.39 inference(skolemize,[status(sab)],[72])).
% 0.18/0.39 tff(74,plain,
% 0.18/0.39 (![A: $i] : (multiplication(one, A) = A)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.18/0.39 tff(75,plain,
% 0.18/0.39 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X1!1) = X1!1)),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(76,plain,
% 0.18/0.39 (multiplication(one, X1!1) = X1!1),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.18/0.39 tff(77,plain,
% 0.18/0.39 (X1!1 = multiplication(one, X1!1)),
% 0.18/0.39 inference(symmetry,[status(thm)],[76])).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 (X1!1 = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 0.18/0.39 inference(transitivity,[status(thm)],[77, 67])).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 (multiplication(one, c(X1!1)) = multiplication(addition(X0!2, c(X0!2)), c(X1!1))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[66])).
% 0.18/0.39 tff(80,plain,
% 0.18/0.39 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, c(X1!1)) = c(X1!1))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(81,plain,
% 0.18/0.39 (multiplication(one, c(X1!1)) = c(X1!1)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[80, 74])).
% 0.18/0.39 tff(82,plain,
% 0.18/0.39 (c(X1!1) = multiplication(one, c(X1!1))),
% 0.18/0.39 inference(symmetry,[status(thm)],[81])).
% 0.18/0.39 tff(83,plain,
% 0.18/0.39 (test(X1!1)),
% 0.18/0.39 inference(and_elim,[status(thm)],[42])).
% 0.18/0.39 tff(84,plain,
% 0.18/0.39 (((~![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))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(85,plain,
% 0.18/0.39 ((~![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))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(86,plain,
% 0.18/0.39 ((~![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)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.18/0.39 tff(87,plain,
% 0.18/0.39 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[86, 53, 83])).
% 0.18/0.39 tff(88,plain,
% 0.18/0.39 (((~![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)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(89,plain,
% 0.18/0.39 ((~(((~(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))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(90,plain,
% 0.18/0.39 ((((~(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)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(91,plain,
% 0.18/0.39 ((~(((~(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))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[90])).
% 0.18/0.39 tff(92,plain,
% 0.18/0.39 ((~(((~(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))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[91, 89])).
% 0.18/0.40 tff(93,plain,
% 0.18/0.40 (((~![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)))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[92])).
% 0.18/0.40 tff(94,plain,
% 0.18/0.40 (((~![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)))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[93, 88])).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 ((~![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))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(96,plain,
% 0.18/0.40 ((~![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))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.18/0.40 tff(97,plain,
% 0.18/0.40 (~(((~(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)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[96, 23])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 ((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))),
% 0.18/0.40 inference(commutativity,[status(thm)],[])).
% 0.18/0.40 tff(99,plain,
% 0.18/0.40 ((~![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)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(100,plain,
% 0.18/0.40 (~(((~(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))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[99, 23])).
% 0.18/0.40 tff(101,plain,
% 0.18/0.40 (^[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)))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 (![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))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[101])).
% 0.18/0.40 tff(103,plain,
% 0.18/0.40 (^[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)))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(104,plain,
% 0.18/0.40 (![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))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[103])).
% 0.18/0.40 tff(105,plain,
% 0.18/0.40 (![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))))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[104, 102])).
% 0.18/0.40 tff(106,plain,
% 0.18/0.40 (^[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))))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(107,plain,
% 0.18/0.40 (![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))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[106])).
% 0.18/0.40 tff(108,plain,
% 0.18/0.40 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(109,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_1')).
% 0.18/0.40 tff(110,plain,
% 0.18/0.40 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.18/0.40 tff(111,plain,(
% 0.18/0.40 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[110])).
% 0.18/0.40 tff(112,plain,
% 0.18/0.40 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.18/0.40 tff(113,plain,
% 0.18/0.40 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.18/0.40 tff(114,plain,
% 0.18/0.40 ((~![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))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(115,plain,
% 0.18/0.40 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.18/0.40 tff(116,plain,
% 0.18/0.40 (((~((~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))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(117,plain,
% 0.18/0.40 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.18/0.40 tff(118,plain,
% 0.18/0.40 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(119,plain,
% 0.18/0.40 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[118, 83])).
% 0.18/0.40 tff(120,plain,
% 0.18/0.40 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[119, 117])).
% 0.18/0.40 tff(121,plain,
% 0.18/0.40 ((((~(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))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(122,plain,
% 0.18/0.40 ((((~(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))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.18/0.40 tff(123,plain,
% 0.18/0.40 (~((~(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)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[122, 100])).
% 0.18/0.40 tff(124,plain,
% 0.18/0.40 (((~(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)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(125,plain,
% 0.18/0.40 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.18/0.40 tff(126,plain,
% 0.18/0.40 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 0.18/0.40 inference(symmetry,[status(thm)],[125])).
% 0.18/0.40 tff(127,plain,
% 0.18/0.40 ((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)))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[126])).
% 0.18/0.40 tff(128,plain,
% 0.18/0.40 ((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))),
% 0.18/0.40 inference(transitivity,[status(thm)],[127, 98])).
% 0.18/0.40 tff(129,plain,
% 0.18/0.40 ((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)),
% 0.18/0.40 inference(symmetry,[status(thm)],[128])).
% 0.18/0.40 tff(130,plain,
% 0.18/0.40 ((~![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))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(131,plain,
% 0.18/0.40 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[130, 7])).
% 0.18/0.40 tff(132,plain,
% 0.18/0.40 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[131, 129])).
% 0.18/0.40 tff(133,plain,
% 0.18/0.40 (((~(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)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(134,plain,
% 0.18/0.40 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[133, 123])).
% 0.18/0.40 tff(135,plain,
% 0.18/0.40 (((~(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)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(136,plain,
% 0.18/0.41 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[135, 123])).
% 0.18/0.41 tff(137,plain,
% 0.18/0.41 ((~((~(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))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(138,plain,
% 0.18/0.41 ((~((~(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))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[137, 136, 134])).
% 0.18/0.41 tff(139,plain,
% 0.18/0.41 (~((~(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)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[138, 132])).
% 0.18/0.41 tff(140,plain,
% 0.18/0.41 ((((~(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))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(141,plain,
% 0.18/0.41 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[140, 139, 97])).
% 0.18/0.41 tff(142,plain,
% 0.18/0.41 ((~((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)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(143,plain,
% 0.18/0.41 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[142, 141, 87])).
% 0.18/0.41 tff(144,plain,
% 0.18/0.41 (tptp_fun_X1_0(X1!1) = c(X1!1)),
% 0.18/0.41 inference(symmetry,[status(thm)],[143])).
% 0.18/0.41 tff(145,plain,
% 0.18/0.41 (tptp_fun_X1_0(X1!1) = multiplication(addition(X0!2, c(X0!2)), c(X1!1))),
% 0.18/0.41 inference(transitivity,[status(thm)],[144, 82, 79])).
% 0.18/0.41 tff(146,plain,
% 0.18/0.41 (complement(tptp_fun_X1_0(X1!1), X1!1) <=> complement(multiplication(addition(X0!2, c(X0!2)), c(X1!1)), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[145, 78])).
% 0.18/0.41 tff(147,plain,
% 0.18/0.41 (complement(multiplication(addition(X0!2, c(X0!2)), c(X1!1)), multiplication(addition(X0!2, c(X0!2)), X1!1)) <=> complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.18/0.41 inference(symmetry,[status(thm)],[146])).
% 0.18/0.41 tff(148,plain,
% 0.18/0.41 ((~complement(multiplication(addition(X0!2, c(X0!2)), c(X1!1)), multiplication(addition(X0!2, c(X0!2)), X1!1))) <=> (~complement(tptp_fun_X1_0(X1!1), X1!1))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[147])).
% 0.18/0.41 tff(149,plain,
% 0.18/0.41 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = zero)) | (~(multiplication(multiplication(addition(X0!2, c(X0!2)), c(X1!1)), multiplication(addition(X0!2, c(X0!2)), X1!1)) = zero)) | (~(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = one))) <=> complement(multiplication(addition(X0!2, c(X0!2)), c(X1!1)), multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(150,plain,
% 0.18/0.41 (~(((~(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = zero)) | (~(multiplication(multiplication(addition(X0!2, c(X0!2)), c(X1!1)), multiplication(addition(X0!2, c(X0!2)), X1!1)) = zero)) | (~(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = one))) <=> complement(multiplication(addition(X0!2, c(X0!2)), c(X1!1)), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[149, 23])).
% 0.18/0.41 tff(151,plain,
% 0.18/0.41 ((addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = one) <=> (one = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))))),
% 0.18/0.41 inference(commutativity,[status(thm)],[])).
% 0.18/0.41 tff(152,plain,
% 0.18/0.41 ((one = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1)))) <=> (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = one)),
% 0.18/0.41 inference(symmetry,[status(thm)],[151])).
% 0.18/0.41 tff(153,plain,
% 0.18/0.41 ((~(one = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))))) <=> (~(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = one))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[152])).
% 0.18/0.41 tff(154,plain,
% 0.18/0.41 (~(one = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))))),
% 0.18/0.41 inference(or_elim,[status(thm)],[41])).
% 0.18/0.41 tff(155,plain,
% 0.18/0.41 (~(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = one)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.18/0.41 tff(156,plain,
% 0.18/0.41 (((~(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = zero)) | (~(multiplication(multiplication(addition(X0!2, c(X0!2)), c(X1!1)), multiplication(addition(X0!2, c(X0!2)), X1!1)) = zero)) | (~(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = one))) | (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = one)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(157,plain,
% 0.18/0.41 ((~(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = zero)) | (~(multiplication(multiplication(addition(X0!2, c(X0!2)), c(X1!1)), multiplication(addition(X0!2, c(X0!2)), X1!1)) = zero)) | (~(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = one))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.18/0.41 tff(158,plain,
% 0.18/0.41 ((((~(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = zero)) | (~(multiplication(multiplication(addition(X0!2, c(X0!2)), c(X1!1)), multiplication(addition(X0!2, c(X0!2)), X1!1)) = zero)) | (~(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = one))) <=> complement(multiplication(addition(X0!2, c(X0!2)), c(X1!1)), multiplication(addition(X0!2, c(X0!2)), X1!1))) | (~((~(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = zero)) | (~(multiplication(multiplication(addition(X0!2, c(X0!2)), c(X1!1)), multiplication(addition(X0!2, c(X0!2)), X1!1)) = zero)) | (~(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = one)))) | (~complement(multiplication(addition(X0!2, c(X0!2)), c(X1!1)), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(159,plain,
% 0.18/0.41 (~complement(multiplication(addition(X0!2, c(X0!2)), c(X1!1)), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[158, 157, 150])).
% 0.18/0.41 tff(160,plain,
% 0.18/0.41 (~complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[159, 148])).
% 0.18/0.41 tff(161,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[120, 160])).
% 0.18/0.41 % SZS output end Proof
% 0.18/0.41 % E exiting
%------------------------------------------------------------------------------