%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE024+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:12:53 AM UTC 2025
% Result : Theorem 4.12s 4.34s
% Output : Proof 4.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE024+2 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 18:54:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.12/4.34 % SZS status Theorem
% 4.12/4.34 % SZS output start Proof
% 4.12/4.34 tff(zero_type, type, (
% 4.12/4.34 zero: $i)).
% 4.12/4.34 tff(multiplication_type, type, (
% 4.12/4.34 multiplication: ( $i * $i ) > $i)).
% 4.12/4.34 tff(c_type, type, (
% 4.12/4.34 c: $i > $i)).
% 4.12/4.34 tff(tptp_fun_X2_1_type, type, (
% 4.12/4.34 tptp_fun_X2_1: $i)).
% 4.12/4.34 tff(tptp_fun_X0_3_type, type, (
% 4.12/4.34 tptp_fun_X0_3: $i)).
% 4.12/4.34 tff(tptp_fun_X1_2_type, type, (
% 4.12/4.34 tptp_fun_X1_2: $i)).
% 4.12/4.34 tff(tptp_fun_X1_0_type, type, (
% 4.12/4.34 tptp_fun_X1_0: $i > $i)).
% 4.12/4.34 tff(addition_type, type, (
% 4.12/4.34 addition: ( $i * $i ) > $i)).
% 4.12/4.34 tff(complement_type, type, (
% 4.12/4.34 complement: ( $i * $i ) > $o)).
% 4.12/4.34 tff(test_type, type, (
% 4.12/4.34 test: $i > $o)).
% 4.12/4.34 tff(one_type, type, (
% 4.12/4.34 one: $i)).
% 4.12/4.34 tff(1,assumption,(~(multiplication(zero, multiplication(c(X1!2), X0!3)) = zero)), introduced(assumption)).
% 4.12/4.34 tff(2,plain,
% 4.12/4.34 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 4.12/4.34 inference(bind,[status(th)],[])).
% 4.12/4.34 tff(3,plain,
% 4.12/4.34 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 4.12/4.34 inference(quant_intro,[status(thm)],[2])).
% 4.12/4.35 tff(4,plain,
% 4.12/4.35 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 4.12/4.35 inference(rewrite,[status(thm)],[])).
% 4.12/4.35 tff(5,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 4.12/4.35 tff(6,plain,
% 4.12/4.35 (![A: $i] : (multiplication(zero, A) = zero)),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[5, 4])).
% 4.12/4.35 tff(7,plain,(
% 4.12/4.35 ![A: $i] : (multiplication(zero, A) = zero)),
% 4.12/4.35 inference(skolemize,[status(sab)],[6])).
% 4.12/4.35 tff(8,plain,
% 4.12/4.35 (![A: $i] : (multiplication(zero, A) = zero)),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[7, 3])).
% 4.12/4.35 tff(9,plain,
% 4.12/4.35 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, multiplication(c(X1!2), X0!3)) = zero)),
% 4.12/4.35 inference(quant_inst,[status(thm)],[])).
% 4.12/4.35 tff(10,plain,
% 4.12/4.35 ($false),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 4.12/4.35 tff(11,plain,(multiplication(zero, multiplication(c(X1!2), X0!3)) = zero), inference(lemma,lemma(discharge,[]))).
% 4.12/4.35 tff(12,plain,
% 4.12/4.35 ((~((multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero) | (~(test(X1!2) & test(X2!1))) | (~(addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3)) = multiplication(c(X1!2), X0!3))))) <=> (~((multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero) | (~(test(X1!2) & test(X2!1))) | (~(addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3)) = multiplication(c(X1!2), X0!3)))))),
% 4.12/4.35 inference(rewrite,[status(thm)],[])).
% 4.12/4.35 tff(13,plain,
% 4.12/4.35 ((~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0))))) <=> (~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0)))))),
% 4.12/4.35 inference(rewrite,[status(thm)],[])).
% 4.12/4.35 tff(14,plain,
% 4.12/4.35 ((~![X0: $i, X1: $i, X2: $i] : ((test(X1) & test(X2)) => ((addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0)) => (multiplication(multiplication(X1, X0), c(X2)) = zero)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0)))))),
% 4.12/4.35 inference(rewrite,[status(thm)],[])).
% 4.12/4.35 tff(15,axiom,(~![X0: $i, X1: $i, X2: $i] : ((test(X1) & test(X2)) => ((addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0)) => (multiplication(multiplication(X1, X0), c(X2)) = zero)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 4.12/4.35 tff(16,plain,
% 4.12/4.35 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0))))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[15, 14])).
% 4.12/4.35 tff(17,plain,
% 4.12/4.35 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0))))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[16, 13])).
% 4.12/4.35 tff(18,plain,
% 4.12/4.35 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0))))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[17, 13])).
% 4.12/4.35 tff(19,plain,
% 4.12/4.35 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0))))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[18, 13])).
% 4.12/4.35 tff(20,plain,(
% 4.12/4.35 ~((multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero) | (~(test(X1!2) & test(X2!1))) | (~(addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3)) = multiplication(c(X1!2), X0!3))))),
% 4.12/4.35 inference(skolemize,[status(sab)],[19])).
% 4.12/4.35 tff(21,plain,
% 4.12/4.35 (~((multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero) | (~(test(X1!2) & test(X2!1))) | (~(addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3)) = multiplication(c(X1!2), X0!3))))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[20, 12])).
% 4.12/4.35 tff(22,plain,
% 4.12/4.35 (test(X1!2) & test(X2!1)),
% 4.12/4.35 inference(or_elim,[status(thm)],[21])).
% 4.12/4.35 tff(23,plain,
% 4.12/4.35 (test(X1!2)),
% 4.12/4.35 inference(and_elim,[status(thm)],[22])).
% 4.12/4.35 tff(24,plain,
% 4.12/4.35 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 4.12/4.35 inference(bind,[status(th)],[])).
% 4.12/4.35 tff(25,plain,
% 4.12/4.35 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.12/4.35 inference(quant_intro,[status(thm)],[24])).
% 4.12/4.35 tff(26,plain,
% 4.12/4.35 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.12/4.35 inference(rewrite,[status(thm)],[])).
% 4.12/4.35 tff(27,plain,
% 4.12/4.35 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 4.12/4.35 inference(bind,[status(th)],[])).
% 4.12/4.35 tff(28,plain,
% 4.12/4.35 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.12/4.35 inference(quant_intro,[status(thm)],[27])).
% 4.12/4.35 tff(29,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_3')).
% 4.12/4.35 tff(30,plain,
% 4.12/4.35 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[29, 28])).
% 4.12/4.35 tff(31,plain,
% 4.12/4.35 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[30, 26])).
% 4.12/4.35 tff(32,plain,(
% 4.12/4.35 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.12/4.35 inference(skolemize,[status(sab)],[31])).
% 4.12/4.35 tff(33,plain,
% 4.12/4.35 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[32, 25])).
% 4.12/4.35 tff(34,plain,
% 4.12/4.35 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!2)) | ((c(X1!2) = tptp_fun_X1_0(X1!2)) <=> complement(X1!2, tptp_fun_X1_0(X1!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!2)) | ((c(X1!2) = tptp_fun_X1_0(X1!2)) <=> complement(X1!2, tptp_fun_X1_0(X1!2))))),
% 4.12/4.35 inference(rewrite,[status(thm)],[])).
% 4.12/4.35 tff(35,plain,
% 4.12/4.35 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!2)) | ((c(X1!2) = tptp_fun_X1_0(X1!2)) <=> complement(X1!2, tptp_fun_X1_0(X1!2))))),
% 4.12/4.35 inference(quant_inst,[status(thm)],[])).
% 4.12/4.35 tff(36,plain,
% 4.12/4.35 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!2)) | ((c(X1!2) = tptp_fun_X1_0(X1!2)) <=> complement(X1!2, tptp_fun_X1_0(X1!2)))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[35, 34])).
% 4.12/4.35 tff(37,plain,
% 4.12/4.35 ((c(X1!2) = tptp_fun_X1_0(X1!2)) <=> complement(X1!2, tptp_fun_X1_0(X1!2))),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[36, 33, 23])).
% 4.12/4.35 tff(38,plain,
% 4.12/4.35 (^[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))))),
% 4.12/4.35 inference(bind,[status(th)],[])).
% 4.12/4.35 tff(39,plain,
% 4.12/4.35 (![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)))),
% 4.12/4.35 inference(quant_intro,[status(thm)],[38])).
% 4.12/4.35 tff(40,plain,
% 4.12/4.35 (^[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)))))),
% 4.12/4.35 inference(bind,[status(th)],[])).
% 4.12/4.35 tff(41,plain,
% 4.12/4.35 (![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)))),
% 4.12/4.35 inference(quant_intro,[status(thm)],[40])).
% 4.12/4.35 tff(42,plain,
% 4.12/4.35 (![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)))),
% 4.12/4.35 inference(rewrite,[status(thm)],[])).
% 4.12/4.35 tff(43,plain,
% 4.12/4.35 (^[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))))),
% 4.12/4.35 inference(bind,[status(th)],[])).
% 4.12/4.35 tff(44,plain,
% 4.12/4.35 (![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)))),
% 4.12/4.35 inference(quant_intro,[status(thm)],[43])).
% 4.12/4.35 tff(45,axiom,(![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_2')).
% 4.12/4.35 tff(46,plain,
% 4.12/4.35 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[45, 44])).
% 4.12/4.35 tff(47,plain,
% 4.12/4.35 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[46, 42])).
% 4.12/4.35 tff(48,plain,(
% 4.12/4.35 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 4.12/4.35 inference(skolemize,[status(sab)],[47])).
% 4.12/4.35 tff(49,plain,
% 4.12/4.35 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[48, 41])).
% 4.12/4.35 tff(50,plain,
% 4.12/4.35 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[49, 39])).
% 4.12/4.35 tff(51,plain,
% 4.12/4.35 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2)))))),
% 4.12/4.35 inference(rewrite,[status(thm)],[])).
% 4.12/4.35 tff(52,plain,
% 4.12/4.35 ((~(((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2)))) <=> (~(((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2))))),
% 4.12/4.35 inference(rewrite,[status(thm)],[])).
% 4.12/4.35 tff(53,plain,
% 4.12/4.35 ((((~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2))) <=> (((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2)))),
% 4.12/4.35 inference(rewrite,[status(thm)],[])).
% 4.12/4.35 tff(54,plain,
% 4.12/4.35 ((~(((~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2)))) <=> (~(((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2))))),
% 4.12/4.35 inference(monotonicity,[status(thm)],[53])).
% 4.12/4.35 tff(55,plain,
% 4.12/4.35 ((~(((~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2)))) <=> (~(((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2))))),
% 4.12/4.35 inference(transitivity,[status(thm)],[54, 52])).
% 4.12/4.35 tff(56,plain,
% 4.12/4.35 (((~![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!2), X1!2) = zero)) | (~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2)))))),
% 4.12/4.35 inference(monotonicity,[status(thm)],[55])).
% 4.12/4.35 tff(57,plain,
% 4.12/4.35 (((~![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!2), X1!2) = zero)) | (~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2)))))),
% 4.12/4.35 inference(transitivity,[status(thm)],[56, 51])).
% 4.12/4.35 tff(58,plain,
% 4.12/4.35 ((~![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!2), X1!2) = zero)) | (~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2))))),
% 4.12/4.35 inference(quant_inst,[status(thm)],[])).
% 4.12/4.35 tff(59,plain,
% 4.12/4.35 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2))))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[58, 57])).
% 4.12/4.35 tff(60,plain,
% 4.12/4.35 (~(((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2)))),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[59, 50])).
% 4.12/4.35 tff(61,plain,
% 4.12/4.35 ((addition(tptp_fun_X1_0(X1!2), X1!2) = addition(X1!2, tptp_fun_X1_0(X1!2))) <=> (addition(X1!2, tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), X1!2))),
% 4.12/4.35 inference(commutativity,[status(thm)],[])).
% 4.12/4.35 tff(62,plain,
% 4.12/4.35 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))) <=> complement(tptp_fun_X1_0(X1!2), X1!2)))),
% 4.12/4.35 inference(quant_inst,[status(thm)],[])).
% 4.12/4.35 tff(63,plain,
% 4.12/4.35 (~(((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))) <=> complement(tptp_fun_X1_0(X1!2), X1!2))),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[62, 50])).
% 4.12/4.35 tff(64,plain,
% 4.12/4.35 (^[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)))))))),
% 4.12/4.35 inference(bind,[status(th)],[])).
% 4.12/4.35 tff(65,plain,
% 4.12/4.35 (![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))))))),
% 4.12/4.35 inference(quant_intro,[status(thm)],[64])).
% 4.12/4.35 tff(66,plain,
% 4.12/4.35 (^[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)))))))),
% 4.12/4.35 inference(bind,[status(th)],[])).
% 4.12/4.35 tff(67,plain,
% 4.12/4.35 (![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))))))),
% 4.12/4.35 inference(quant_intro,[status(thm)],[66])).
% 4.12/4.35 tff(68,plain,
% 4.12/4.35 (![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))))))),
% 4.12/4.35 inference(transitivity,[status(thm)],[67, 65])).
% 4.12/4.35 tff(69,plain,
% 4.12/4.35 (^[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))))))))),
% 4.12/4.35 inference(bind,[status(th)],[])).
% 4.12/4.35 tff(70,plain,
% 4.12/4.35 (![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))))))),
% 4.12/4.35 inference(quant_intro,[status(thm)],[69])).
% 4.12/4.35 tff(71,plain,
% 4.12/4.35 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 4.12/4.35 inference(rewrite,[status(thm)],[])).
% 4.12/4.35 tff(72,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_1')).
% 4.12/4.35 tff(73,plain,
% 4.12/4.35 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[72, 71])).
% 4.12/4.35 tff(74,plain,(
% 4.12/4.35 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 4.12/4.35 inference(skolemize,[status(sab)],[73])).
% 4.12/4.35 tff(75,plain,
% 4.12/4.35 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[74, 70])).
% 4.12/4.35 tff(76,plain,
% 4.12/4.35 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[75, 68])).
% 4.12/4.35 tff(77,plain,
% 4.12/4.35 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | (~(test(X1!2) | ![X1: $i] : (~complement(X1, X1!2))))))),
% 4.12/4.35 inference(quant_inst,[status(thm)],[])).
% 4.12/4.35 tff(78,plain,
% 4.12/4.35 (~((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | (~(test(X1!2) | ![X1: $i] : (~complement(X1, X1!2)))))),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[77, 76])).
% 4.12/4.35 tff(79,plain,
% 4.12/4.35 (((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | (~(test(X1!2) | ![X1: $i] : (~complement(X1, X1!2))))) | ((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))),
% 4.12/4.35 inference(tautology,[status(thm)],[])).
% 4.12/4.35 tff(80,plain,
% 4.12/4.35 ((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2)),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[79, 78])).
% 4.12/4.35 tff(81,plain,
% 4.12/4.35 ((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | (~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2)),
% 4.12/4.35 inference(tautology,[status(thm)],[])).
% 4.12/4.35 tff(82,plain,
% 4.12/4.35 ((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | complement(tptp_fun_X1_0(X1!2), X1!2)),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[81, 23])).
% 4.12/4.35 tff(83,plain,
% 4.12/4.35 (complement(tptp_fun_X1_0(X1!2), X1!2)),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[82, 80])).
% 4.12/4.35 tff(84,plain,
% 4.12/4.35 ((((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))) <=> complement(tptp_fun_X1_0(X1!2), X1!2)) | (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one)))) | (~complement(tptp_fun_X1_0(X1!2), X1!2))),
% 4.12/4.35 inference(tautology,[status(thm)],[])).
% 4.12/4.35 tff(85,plain,
% 4.12/4.35 ((((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))) <=> complement(tptp_fun_X1_0(X1!2), X1!2)) | (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))))),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[84, 83])).
% 4.12/4.35 tff(86,plain,
% 4.12/4.35 (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one)))),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[85, 63])).
% 4.12/4.35 tff(87,plain,
% 4.12/4.35 (((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))) | (addition(X1!2, tptp_fun_X1_0(X1!2)) = one)),
% 4.12/4.35 inference(tautology,[status(thm)],[])).
% 4.12/4.35 tff(88,plain,
% 4.12/4.35 (addition(X1!2, tptp_fun_X1_0(X1!2)) = one),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[87, 86])).
% 4.12/4.35 tff(89,plain,
% 4.12/4.35 (one = addition(X1!2, tptp_fun_X1_0(X1!2))),
% 4.12/4.35 inference(symmetry,[status(thm)],[88])).
% 4.12/4.35 tff(90,plain,
% 4.12/4.35 ((addition(tptp_fun_X1_0(X1!2), X1!2) = one) <=> (addition(tptp_fun_X1_0(X1!2), X1!2) = addition(X1!2, tptp_fun_X1_0(X1!2)))),
% 4.12/4.35 inference(monotonicity,[status(thm)],[89])).
% 4.12/4.35 tff(91,plain,
% 4.12/4.35 ((addition(tptp_fun_X1_0(X1!2), X1!2) = one) <=> (addition(X1!2, tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), X1!2))),
% 4.12/4.35 inference(transitivity,[status(thm)],[90, 61])).
% 4.12/4.35 tff(92,plain,
% 4.12/4.35 ((addition(X1!2, tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), X1!2)) <=> (addition(tptp_fun_X1_0(X1!2), X1!2) = one)),
% 4.12/4.35 inference(symmetry,[status(thm)],[91])).
% 4.12/4.35 tff(93,plain,
% 4.12/4.35 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 4.12/4.35 inference(bind,[status(th)],[])).
% 4.12/4.35 tff(94,plain,
% 4.12/4.35 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 4.12/4.35 inference(quant_intro,[status(thm)],[93])).
% 4.12/4.35 tff(95,plain,
% 4.12/4.35 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 4.12/4.35 inference(rewrite,[status(thm)],[])).
% 4.12/4.35 tff(96,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 4.12/4.35 tff(97,plain,
% 4.12/4.35 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[96, 95])).
% 4.12/4.35 tff(98,plain,(
% 4.12/4.35 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 4.12/4.35 inference(skolemize,[status(sab)],[97])).
% 4.12/4.35 tff(99,plain,
% 4.12/4.35 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[98, 94])).
% 4.12/4.35 tff(100,plain,
% 4.12/4.35 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!2, tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), X1!2))),
% 4.12/4.35 inference(quant_inst,[status(thm)],[])).
% 4.12/4.35 tff(101,plain,
% 4.12/4.35 (addition(X1!2, tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), X1!2)),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[100, 99])).
% 4.12/4.35 tff(102,plain,
% 4.12/4.35 (addition(tptp_fun_X1_0(X1!2), X1!2) = one),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[101, 92])).
% 4.12/4.35 tff(103,plain,
% 4.12/4.35 (((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))) | (multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)),
% 4.12/4.35 inference(tautology,[status(thm)],[])).
% 4.12/4.35 tff(104,plain,
% 4.12/4.35 (multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[103, 86])).
% 4.12/4.35 tff(105,plain,
% 4.12/4.35 (((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))) | (multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)),
% 4.12/4.35 inference(tautology,[status(thm)],[])).
% 4.12/4.35 tff(106,plain,
% 4.12/4.35 (multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[105, 86])).
% 4.12/4.35 tff(107,plain,
% 4.12/4.35 ((~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one)))) | (~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))),
% 4.12/4.35 inference(tautology,[status(thm)],[])).
% 4.12/4.35 tff(108,plain,
% 4.12/4.35 ((~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one)))) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[107, 106, 104])).
% 4.12/4.35 tff(109,plain,
% 4.12/4.35 (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one)))),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[108, 102])).
% 4.12/4.35 tff(110,plain,
% 4.12/4.35 ((((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) <=> complement(X1!2, tptp_fun_X1_0(X1!2))) | ((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))) | complement(X1!2, tptp_fun_X1_0(X1!2))),
% 4.12/4.35 inference(tautology,[status(thm)],[])).
% 4.12/4.35 tff(111,plain,
% 4.12/4.35 (complement(X1!2, tptp_fun_X1_0(X1!2))),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[110, 109, 60])).
% 4.12/4.35 tff(112,plain,
% 4.12/4.35 ((~((c(X1!2) = tptp_fun_X1_0(X1!2)) <=> complement(X1!2, tptp_fun_X1_0(X1!2)))) | (c(X1!2) = tptp_fun_X1_0(X1!2)) | (~complement(X1!2, tptp_fun_X1_0(X1!2)))),
% 4.12/4.35 inference(tautology,[status(thm)],[])).
% 4.12/4.35 tff(113,plain,
% 4.12/4.35 (c(X1!2) = tptp_fun_X1_0(X1!2)),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[112, 111, 37])).
% 4.12/4.35 tff(114,plain,
% 4.12/4.35 (tptp_fun_X1_0(X1!2) = c(X1!2)),
% 4.12/4.35 inference(symmetry,[status(thm)],[113])).
% 4.12/4.35 tff(115,plain,
% 4.12/4.35 (multiplication(tptp_fun_X1_0(X1!2), X0!3) = multiplication(c(X1!2), X0!3)),
% 4.12/4.35 inference(monotonicity,[status(thm)],[114])).
% 4.12/4.35 tff(116,plain,
% 4.12/4.35 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))) <=> complement(tptp_fun_X1_0(X2!1), X2!1)))),
% 4.12/4.35 inference(quant_inst,[status(thm)],[])).
% 4.12/4.35 tff(117,plain,
% 4.12/4.35 (~(((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))) <=> complement(tptp_fun_X1_0(X2!1), X2!1))),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[116, 50])).
% 4.12/4.35 tff(118,plain,
% 4.12/4.35 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | (~(test(X2!1) | ![X1: $i] : (~complement(X1, X2!1))))))),
% 4.12/4.35 inference(quant_inst,[status(thm)],[])).
% 4.12/4.35 tff(119,plain,
% 4.12/4.35 (~((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | (~(test(X2!1) | ![X1: $i] : (~complement(X1, X2!1)))))),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[118, 76])).
% 4.12/4.35 tff(120,plain,
% 4.12/4.35 (((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | (~(test(X2!1) | ![X1: $i] : (~complement(X1, X2!1))))) | ((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))),
% 4.12/4.35 inference(tautology,[status(thm)],[])).
% 4.12/4.35 tff(121,plain,
% 4.12/4.35 ((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1)),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[120, 119])).
% 4.12/4.35 tff(122,plain,
% 4.12/4.35 (test(X2!1)),
% 4.12/4.35 inference(and_elim,[status(thm)],[22])).
% 4.12/4.35 tff(123,plain,
% 4.12/4.35 ((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | (~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1)),
% 4.12/4.35 inference(tautology,[status(thm)],[])).
% 4.12/4.35 tff(124,plain,
% 4.12/4.35 ((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | complement(tptp_fun_X1_0(X2!1), X2!1)),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[123, 122])).
% 4.12/4.35 tff(125,plain,
% 4.12/4.35 (complement(tptp_fun_X1_0(X2!1), X2!1)),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[124, 121])).
% 4.12/4.35 tff(126,plain,
% 4.12/4.35 ((((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))) <=> complement(tptp_fun_X1_0(X2!1), X2!1)) | (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one)))) | (~complement(tptp_fun_X1_0(X2!1), X2!1))),
% 4.12/4.35 inference(tautology,[status(thm)],[])).
% 4.12/4.35 tff(127,plain,
% 4.12/4.35 ((((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))) <=> complement(tptp_fun_X1_0(X2!1), X2!1)) | (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))))),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[126, 125])).
% 4.12/4.35 tff(128,plain,
% 4.12/4.35 (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one)))),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[127, 117])).
% 4.12/4.35 tff(129,plain,
% 4.12/4.35 (((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))) | (multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)),
% 4.12/4.35 inference(tautology,[status(thm)],[])).
% 4.12/4.35 tff(130,plain,
% 4.12/4.35 (multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[129, 128])).
% 4.12/4.35 tff(131,plain,
% 4.12/4.35 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X2!1)) | ((c(X2!1) = tptp_fun_X1_0(X2!1)) <=> complement(X2!1, tptp_fun_X1_0(X2!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X2!1)) | ((c(X2!1) = tptp_fun_X1_0(X2!1)) <=> complement(X2!1, tptp_fun_X1_0(X2!1))))),
% 4.12/4.35 inference(rewrite,[status(thm)],[])).
% 4.12/4.35 tff(132,plain,
% 4.12/4.35 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X2!1)) | ((c(X2!1) = tptp_fun_X1_0(X2!1)) <=> complement(X2!1, tptp_fun_X1_0(X2!1))))),
% 4.12/4.35 inference(quant_inst,[status(thm)],[])).
% 4.12/4.35 tff(133,plain,
% 4.12/4.35 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X2!1)) | ((c(X2!1) = tptp_fun_X1_0(X2!1)) <=> complement(X2!1, tptp_fun_X1_0(X2!1)))),
% 4.12/4.35 inference(modus_ponens,[status(thm)],[132, 131])).
% 4.12/4.35 tff(134,plain,
% 4.12/4.35 ((c(X2!1) = tptp_fun_X1_0(X2!1)) <=> complement(X2!1, tptp_fun_X1_0(X2!1))),
% 4.12/4.35 inference(unit_resolution,[status(thm)],[133, 33, 122])).
% 4.12/4.35 tff(135,plain,
% 4.12/4.35 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1)))))),
% 4.12/4.36 inference(rewrite,[status(thm)],[])).
% 4.12/4.36 tff(136,plain,
% 4.12/4.36 ((~(((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1)))) <=> (~(((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1))))),
% 4.12/4.36 inference(rewrite,[status(thm)],[])).
% 4.12/4.36 tff(137,plain,
% 4.12/4.36 ((((~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1))) <=> (((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1)))),
% 4.12/4.36 inference(rewrite,[status(thm)],[])).
% 4.12/4.36 tff(138,plain,
% 4.12/4.36 ((~(((~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1)))) <=> (~(((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1))))),
% 4.12/4.36 inference(monotonicity,[status(thm)],[137])).
% 4.12/4.36 tff(139,plain,
% 4.12/4.36 ((~(((~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1)))) <=> (~(((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1))))),
% 4.12/4.36 inference(transitivity,[status(thm)],[138, 136])).
% 4.12/4.36 tff(140,plain,
% 4.12/4.36 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1)))))),
% 4.12/4.36 inference(monotonicity,[status(thm)],[139])).
% 4.12/4.36 tff(141,plain,
% 4.12/4.36 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1)))))),
% 4.12/4.36 inference(transitivity,[status(thm)],[140, 135])).
% 4.12/4.36 tff(142,plain,
% 4.12/4.36 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1))))),
% 4.12/4.36 inference(quant_inst,[status(thm)],[])).
% 4.12/4.36 tff(143,plain,
% 4.12/4.36 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1))))),
% 4.12/4.36 inference(modus_ponens,[status(thm)],[142, 141])).
% 4.12/4.36 tff(144,plain,
% 4.12/4.36 (~(((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1)))),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[143, 50])).
% 4.12/4.36 tff(145,plain,
% 4.12/4.36 ((addition(tptp_fun_X1_0(X2!1), X2!1) = addition(X2!1, tptp_fun_X1_0(X2!1))) <=> (addition(X2!1, tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), X2!1))),
% 4.12/4.36 inference(commutativity,[status(thm)],[])).
% 4.12/4.36 tff(146,plain,
% 4.12/4.36 (((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))) | (addition(X2!1, tptp_fun_X1_0(X2!1)) = one)),
% 4.12/4.36 inference(tautology,[status(thm)],[])).
% 4.12/4.36 tff(147,plain,
% 4.12/4.36 (addition(X2!1, tptp_fun_X1_0(X2!1)) = one),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[146, 128])).
% 4.12/4.36 tff(148,plain,
% 4.12/4.36 (one = addition(X2!1, tptp_fun_X1_0(X2!1))),
% 4.12/4.36 inference(symmetry,[status(thm)],[147])).
% 4.12/4.36 tff(149,plain,
% 4.12/4.36 ((addition(tptp_fun_X1_0(X2!1), X2!1) = one) <=> (addition(tptp_fun_X1_0(X2!1), X2!1) = addition(X2!1, tptp_fun_X1_0(X2!1)))),
% 4.12/4.36 inference(monotonicity,[status(thm)],[148])).
% 4.12/4.36 tff(150,plain,
% 4.12/4.36 ((addition(tptp_fun_X1_0(X2!1), X2!1) = one) <=> (addition(X2!1, tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), X2!1))),
% 4.12/4.36 inference(transitivity,[status(thm)],[149, 145])).
% 4.12/4.36 tff(151,plain,
% 4.12/4.36 ((addition(X2!1, tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), X2!1)) <=> (addition(tptp_fun_X1_0(X2!1), X2!1) = one)),
% 4.12/4.36 inference(symmetry,[status(thm)],[150])).
% 4.12/4.36 tff(152,plain,
% 4.12/4.36 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X2!1, tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), X2!1))),
% 4.12/4.36 inference(quant_inst,[status(thm)],[])).
% 4.12/4.36 tff(153,plain,
% 4.12/4.36 (addition(X2!1, tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), X2!1)),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[152, 99])).
% 4.12/4.36 tff(154,plain,
% 4.12/4.36 (addition(tptp_fun_X1_0(X2!1), X2!1) = one),
% 4.12/4.36 inference(modus_ponens,[status(thm)],[153, 151])).
% 4.12/4.36 tff(155,plain,
% 4.12/4.36 (((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))) | (multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)),
% 4.12/4.36 inference(tautology,[status(thm)],[])).
% 4.12/4.36 tff(156,plain,
% 4.12/4.36 (multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[155, 128])).
% 4.12/4.36 tff(157,plain,
% 4.12/4.36 ((~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one)))) | (~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))),
% 4.12/4.36 inference(tautology,[status(thm)],[])).
% 4.12/4.36 tff(158,plain,
% 4.12/4.36 ((~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one)))) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[157, 130, 156])).
% 4.12/4.36 tff(159,plain,
% 4.12/4.36 (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one)))),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[158, 154])).
% 4.12/4.36 tff(160,plain,
% 4.12/4.36 ((((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) <=> complement(X2!1, tptp_fun_X1_0(X2!1))) | ((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))) | complement(X2!1, tptp_fun_X1_0(X2!1))),
% 4.12/4.36 inference(tautology,[status(thm)],[])).
% 4.12/4.36 tff(161,plain,
% 4.12/4.36 (complement(X2!1, tptp_fun_X1_0(X2!1))),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[160, 159, 144])).
% 4.12/4.36 tff(162,plain,
% 4.12/4.36 ((~((c(X2!1) = tptp_fun_X1_0(X2!1)) <=> complement(X2!1, tptp_fun_X1_0(X2!1)))) | (c(X2!1) = tptp_fun_X1_0(X2!1)) | (~complement(X2!1, tptp_fun_X1_0(X2!1)))),
% 4.12/4.36 inference(tautology,[status(thm)],[])).
% 4.12/4.36 tff(163,plain,
% 4.12/4.36 (c(X2!1) = tptp_fun_X1_0(X2!1)),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[162, 161, 134])).
% 4.12/4.36 tff(164,plain,
% 4.12/4.36 (tptp_fun_X1_0(X2!1) = c(X2!1)),
% 4.12/4.36 inference(symmetry,[status(thm)],[163])).
% 4.12/4.36 tff(165,assumption,((~((~test(tptp_fun_X1_0(X2!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1)))) | (~(test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))))), introduced(assumption)).
% 4.12/4.36 tff(166,plain,
% 4.12/4.36 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(tptp_fun_X1_0(X2!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1)))) | (~(test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))))))),
% 4.12/4.36 inference(quant_inst,[status(thm)],[])).
% 4.12/4.36 tff(167,plain,
% 4.12/4.36 ($false),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[166, 76, 165])).
% 4.12/4.36 tff(168,plain,(~((~((~test(tptp_fun_X1_0(X2!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1)))) | (~(test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1))))))), inference(lemma,lemma(discharge,[]))).
% 4.12/4.36 tff(169,plain,
% 4.12/4.36 (((~((~test(tptp_fun_X1_0(X2!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1)))) | (~(test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))))) | (test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1))))),
% 4.12/4.36 inference(tautology,[status(thm)],[])).
% 4.12/4.36 tff(170,plain,
% 4.12/4.36 (test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[169, 168])).
% 4.12/4.36 tff(171,assumption,(![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))), introduced(assumption)).
% 4.12/4.36 tff(172,plain,
% 4.12/4.36 ((~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))) | (~complement(X2!1, tptp_fun_X1_0(X2!1)))),
% 4.12/4.36 inference(quant_inst,[status(thm)],[])).
% 4.12/4.36 tff(173,plain,
% 4.12/4.36 ($false),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[172, 161, 171])).
% 4.12/4.36 tff(174,plain,(~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))), inference(lemma,lemma(discharge,[]))).
% 4.12/4.36 tff(175,plain,
% 4.12/4.36 ((~(test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1))))) | test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))),
% 4.12/4.36 inference(tautology,[status(thm)],[])).
% 4.12/4.36 tff(176,plain,
% 4.12/4.36 ((~(test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1))))) | test(tptp_fun_X1_0(X2!1))),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[175, 174])).
% 4.12/4.36 tff(177,plain,
% 4.12/4.36 (test(tptp_fun_X1_0(X2!1))),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[176, 170])).
% 4.12/4.36 tff(178,plain,
% 4.12/4.36 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X2!1))) | ((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X2!1))) | ((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1)))),
% 4.12/4.36 inference(rewrite,[status(thm)],[])).
% 4.12/4.36 tff(179,plain,
% 4.12/4.36 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X2!1))) | ((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1)))),
% 4.12/4.36 inference(quant_inst,[status(thm)],[])).
% 4.12/4.36 tff(180,plain,
% 4.12/4.36 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X2!1))) | ((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1))),
% 4.12/4.36 inference(modus_ponens,[status(thm)],[179, 178])).
% 4.12/4.36 tff(181,plain,
% 4.12/4.36 ((~test(tptp_fun_X1_0(X2!1))) | ((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1))),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[180, 33])).
% 4.12/4.36 tff(182,plain,
% 4.12/4.36 ((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1)),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[181, 177])).
% 4.12/4.36 tff(183,plain,
% 4.12/4.36 ((~((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1))) | (c(tptp_fun_X1_0(X2!1)) = X2!1) | (~complement(tptp_fun_X1_0(X2!1), X2!1))),
% 4.12/4.36 inference(tautology,[status(thm)],[])).
% 4.12/4.36 tff(184,plain,
% 4.12/4.36 ((~((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1))) | (c(tptp_fun_X1_0(X2!1)) = X2!1)),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[183, 125])).
% 4.12/4.36 tff(185,plain,
% 4.12/4.36 (c(tptp_fun_X1_0(X2!1)) = X2!1),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[184, 182])).
% 4.12/4.36 tff(186,plain,
% 4.12/4.36 (X2!1 = c(tptp_fun_X1_0(X2!1))),
% 4.12/4.36 inference(symmetry,[status(thm)],[185])).
% 4.12/4.36 tff(187,plain,
% 4.12/4.36 (multiplication(X2!1, tptp_fun_X1_0(X2!1)) = multiplication(c(tptp_fun_X1_0(X2!1)), c(X2!1))),
% 4.12/4.36 inference(monotonicity,[status(thm)],[186, 164])).
% 4.12/4.36 tff(188,plain,
% 4.12/4.36 (multiplication(c(tptp_fun_X1_0(X2!1)), c(X2!1)) = multiplication(X2!1, tptp_fun_X1_0(X2!1))),
% 4.12/4.36 inference(symmetry,[status(thm)],[187])).
% 4.12/4.36 tff(189,plain,
% 4.12/4.36 (^[X0: $i, X1: $i] : refl(((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))))),
% 4.12/4.36 inference(bind,[status(th)],[])).
% 4.12/4.36 tff(190,plain,
% 4.12/4.36 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 4.12/4.36 inference(quant_intro,[status(thm)],[189])).
% 4.12/4.36 tff(191,plain,
% 4.12/4.36 (^[X0: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((test(X0) & test(X1)) <=> (~((~test(X1)) | (~test(X0))))), ((~(test(X0) & test(X1))) <=> (~(~((~test(X1)) | (~test(X0))))))), rewrite((~(~((~test(X1)) | (~test(X0))))) <=> ((~test(X1)) | (~test(X0)))), ((~(test(X0) & test(X1))) <=> ((~test(X1)) | (~test(X0))))), (((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> (((~test(X1)) | (~test(X0))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))))), rewrite((((~test(X1)) | (~test(X0))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))), (((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))))),
% 4.12/4.36 inference(bind,[status(th)],[])).
% 4.12/4.36 tff(192,plain,
% 4.12/4.36 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 4.12/4.36 inference(quant_intro,[status(thm)],[191])).
% 4.12/4.36 tff(193,plain,
% 4.12/4.36 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 4.12/4.36 inference(rewrite,[status(thm)],[])).
% 4.12/4.36 tff(194,plain,
% 4.12/4.36 (^[X0: $i, X1: $i] : rewrite(((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))))),
% 4.12/4.36 inference(bind,[status(th)],[])).
% 4.12/4.36 tff(195,plain,
% 4.12/4.36 (![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 4.12/4.36 inference(quant_intro,[status(thm)],[194])).
% 4.12/4.36 tff(196,axiom,(![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax','test_deMorgan1')).
% 4.12/4.36 tff(197,plain,
% 4.12/4.36 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 4.12/4.36 inference(modus_ponens,[status(thm)],[196, 195])).
% 4.12/4.36 tff(198,plain,
% 4.12/4.36 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 4.12/4.36 inference(modus_ponens,[status(thm)],[197, 193])).
% 4.12/4.36 tff(199,plain,(
% 4.12/4.36 ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 4.12/4.36 inference(skolemize,[status(sab)],[198])).
% 4.12/4.36 tff(200,plain,
% 4.12/4.36 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 4.12/4.36 inference(modus_ponens,[status(thm)],[199, 192])).
% 4.12/4.36 tff(201,plain,
% 4.12/4.36 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 4.12/4.36 inference(modus_ponens,[status(thm)],[200, 190])).
% 4.12/4.36 tff(202,plain,
% 4.12/4.36 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(addition(tptp_fun_X1_0(X2!1), X2!1)) = multiplication(c(tptp_fun_X1_0(X2!1)), c(X2!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(addition(tptp_fun_X1_0(X2!1), X2!1)) = multiplication(c(tptp_fun_X1_0(X2!1)), c(X2!1))))),
% 4.12/4.36 inference(rewrite,[status(thm)],[])).
% 4.12/4.36 tff(203,plain,
% 4.12/4.36 (((~test(X2!1)) | (c(addition(tptp_fun_X1_0(X2!1), X2!1)) = multiplication(c(tptp_fun_X1_0(X2!1)), c(X2!1))) | (~test(tptp_fun_X1_0(X2!1)))) <=> ((~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(addition(tptp_fun_X1_0(X2!1), X2!1)) = multiplication(c(tptp_fun_X1_0(X2!1)), c(X2!1))))),
% 4.12/4.36 inference(rewrite,[status(thm)],[])).
% 4.12/4.36 tff(204,plain,
% 4.12/4.36 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (c(addition(tptp_fun_X1_0(X2!1), X2!1)) = multiplication(c(tptp_fun_X1_0(X2!1)), c(X2!1))) | (~test(tptp_fun_X1_0(X2!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(addition(tptp_fun_X1_0(X2!1), X2!1)) = multiplication(c(tptp_fun_X1_0(X2!1)), c(X2!1)))))),
% 4.12/4.36 inference(monotonicity,[status(thm)],[203])).
% 4.12/4.36 tff(205,plain,
% 4.12/4.36 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (c(addition(tptp_fun_X1_0(X2!1), X2!1)) = multiplication(c(tptp_fun_X1_0(X2!1)), c(X2!1))) | (~test(tptp_fun_X1_0(X2!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(addition(tptp_fun_X1_0(X2!1), X2!1)) = multiplication(c(tptp_fun_X1_0(X2!1)), c(X2!1))))),
% 4.12/4.36 inference(transitivity,[status(thm)],[204, 202])).
% 4.12/4.36 tff(206,plain,
% 4.12/4.36 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (c(addition(tptp_fun_X1_0(X2!1), X2!1)) = multiplication(c(tptp_fun_X1_0(X2!1)), c(X2!1))) | (~test(tptp_fun_X1_0(X2!1))))),
% 4.12/4.36 inference(quant_inst,[status(thm)],[])).
% 4.12/4.36 tff(207,plain,
% 4.12/4.36 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(addition(tptp_fun_X1_0(X2!1), X2!1)) = multiplication(c(tptp_fun_X1_0(X2!1)), c(X2!1)))),
% 4.12/4.36 inference(modus_ponens,[status(thm)],[206, 205])).
% 4.12/4.36 tff(208,plain,
% 4.12/4.36 ((~test(tptp_fun_X1_0(X2!1))) | (c(addition(tptp_fun_X1_0(X2!1), X2!1)) = multiplication(c(tptp_fun_X1_0(X2!1)), c(X2!1)))),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[207, 201, 122])).
% 4.12/4.36 tff(209,plain,
% 4.12/4.36 (c(addition(tptp_fun_X1_0(X2!1), X2!1)) = multiplication(c(tptp_fun_X1_0(X2!1)), c(X2!1))),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[208, 177])).
% 4.12/4.36 tff(210,plain,
% 4.12/4.36 (addition(tptp_fun_X1_0(X2!1), X2!1) = addition(X2!1, tptp_fun_X1_0(X2!1))),
% 4.12/4.36 inference(symmetry,[status(thm)],[153])).
% 4.12/4.36 tff(211,plain,
% 4.12/4.36 (addition(tptp_fun_X1_0(X2!1), X2!1) = addition(X1!2, tptp_fun_X1_0(X1!2))),
% 4.12/4.36 inference(transitivity,[status(thm)],[210, 147, 89])).
% 4.12/4.36 tff(212,plain,
% 4.12/4.36 (c(addition(tptp_fun_X1_0(X2!1), X2!1)) = c(addition(X1!2, tptp_fun_X1_0(X1!2)))),
% 4.12/4.36 inference(monotonicity,[status(thm)],[211])).
% 4.12/4.36 tff(213,plain,
% 4.12/4.36 (c(addition(X1!2, tptp_fun_X1_0(X1!2))) = c(addition(tptp_fun_X1_0(X2!1), X2!1))),
% 4.12/4.36 inference(symmetry,[status(thm)],[212])).
% 4.12/4.36 tff(214,plain,
% 4.12/4.36 (c(addition(X1!2, tptp_fun_X1_0(X1!2))) = zero),
% 4.12/4.36 inference(transitivity,[status(thm)],[213, 209, 188, 130])).
% 4.12/4.36 tff(215,plain,
% 4.12/4.36 (multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), multiplication(tptp_fun_X1_0(X1!2), X0!3)) = multiplication(zero, multiplication(c(X1!2), X0!3))),
% 4.12/4.36 inference(monotonicity,[status(thm)],[214, 115])).
% 4.12/4.36 tff(216,plain,
% 4.12/4.36 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)))),
% 4.12/4.36 inference(bind,[status(th)],[])).
% 4.12/4.36 tff(217,plain,
% 4.12/4.36 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 4.12/4.36 inference(quant_intro,[status(thm)],[216])).
% 4.12/4.36 tff(218,plain,
% 4.12/4.36 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 4.12/4.36 inference(rewrite,[status(thm)],[])).
% 4.12/4.36 tff(219,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_associativity')).
% 4.12/4.36 tff(220,plain,
% 4.12/4.36 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 4.12/4.36 inference(modus_ponens,[status(thm)],[219, 218])).
% 4.12/4.36 tff(221,plain,(
% 4.12/4.36 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 4.12/4.36 inference(skolemize,[status(sab)],[220])).
% 4.12/4.36 tff(222,plain,
% 4.12/4.36 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 4.12/4.36 inference(modus_ponens,[status(thm)],[221, 217])).
% 4.12/4.36 tff(223,plain,
% 4.12/4.36 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), multiplication(tptp_fun_X1_0(X1!2), X0!3)) = multiplication(multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), tptp_fun_X1_0(X1!2)), X0!3))),
% 4.12/4.36 inference(quant_inst,[status(thm)],[])).
% 4.12/4.36 tff(224,plain,
% 4.12/4.36 (multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), multiplication(tptp_fun_X1_0(X1!2), X0!3)) = multiplication(multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), tptp_fun_X1_0(X1!2)), X0!3)),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[223, 222])).
% 4.12/4.36 tff(225,plain,
% 4.12/4.36 (multiplication(multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), tptp_fun_X1_0(X1!2)), X0!3) = multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), multiplication(tptp_fun_X1_0(X1!2), X0!3))),
% 4.12/4.36 inference(symmetry,[status(thm)],[224])).
% 4.12/4.36 tff(226,plain,
% 4.12/4.36 (multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), tptp_fun_X1_0(X1!2)) = multiplication(zero, tptp_fun_X1_0(X1!2))),
% 4.12/4.36 inference(monotonicity,[status(thm)],[214])).
% 4.12/4.36 tff(227,plain,
% 4.12/4.36 (multiplication(zero, tptp_fun_X1_0(X1!2)) = multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), tptp_fun_X1_0(X1!2))),
% 4.12/4.36 inference(symmetry,[status(thm)],[226])).
% 4.12/4.36 tff(228,plain,
% 4.12/4.36 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, tptp_fun_X1_0(X1!2)) = zero)),
% 4.12/4.36 inference(quant_inst,[status(thm)],[])).
% 4.12/4.36 tff(229,plain,
% 4.12/4.36 (multiplication(zero, tptp_fun_X1_0(X1!2)) = zero),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[228, 8])).
% 4.12/4.36 tff(230,plain,
% 4.12/4.36 (zero = multiplication(zero, tptp_fun_X1_0(X1!2))),
% 4.12/4.36 inference(symmetry,[status(thm)],[229])).
% 4.12/4.36 tff(231,plain,
% 4.12/4.36 (c(addition(X1!2, tptp_fun_X1_0(X1!2))) = multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), tptp_fun_X1_0(X1!2))),
% 4.12/4.36 inference(transitivity,[status(thm)],[213, 209, 188, 130, 230, 227])).
% 4.12/4.36 tff(232,plain,
% 4.12/4.36 (multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), X0!3) = multiplication(multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), tptp_fun_X1_0(X1!2)), X0!3)),
% 4.12/4.36 inference(monotonicity,[status(thm)],[231])).
% 4.12/4.36 tff(233,plain,
% 4.12/4.36 (multiplication(c(tptp_fun_X1_0(X2!1)), c(X2!1)) = c(addition(tptp_fun_X1_0(X2!1), X2!1))),
% 4.12/4.36 inference(symmetry,[status(thm)],[209])).
% 4.12/4.36 tff(234,plain,
% 4.12/4.36 (zero = multiplication(X2!1, tptp_fun_X1_0(X2!1))),
% 4.12/4.36 inference(symmetry,[status(thm)],[130])).
% 4.12/4.36 tff(235,plain,
% 4.12/4.36 (multiplication(X1!2, tptp_fun_X1_0(X1!2)) = c(addition(X1!2, tptp_fun_X1_0(X1!2)))),
% 4.12/4.36 inference(transitivity,[status(thm)],[106, 234, 187, 233, 212])).
% 4.12/4.36 tff(236,plain,
% 4.12/4.36 (multiplication(multiplication(X1!2, tptp_fun_X1_0(X1!2)), X0!3) = multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), X0!3)),
% 4.12/4.36 inference(monotonicity,[status(thm)],[235])).
% 4.12/4.36 tff(237,plain,
% 4.12/4.36 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X1!2, multiplication(tptp_fun_X1_0(X1!2), X0!3)) = multiplication(multiplication(X1!2, tptp_fun_X1_0(X1!2)), X0!3))),
% 4.12/4.36 inference(quant_inst,[status(thm)],[])).
% 4.12/4.36 tff(238,plain,
% 4.12/4.36 (multiplication(X1!2, multiplication(tptp_fun_X1_0(X1!2), X0!3)) = multiplication(multiplication(X1!2, tptp_fun_X1_0(X1!2)), X0!3)),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[237, 222])).
% 4.12/4.36 tff(239,plain,
% 4.12/4.36 (multiplication(c(X1!2), X0!3) = multiplication(tptp_fun_X1_0(X1!2), X0!3)),
% 4.12/4.36 inference(symmetry,[status(thm)],[115])).
% 4.12/4.36 tff(240,plain,
% 4.12/4.36 (multiplication(X1!2, multiplication(c(X1!2), X0!3)) = multiplication(X1!2, multiplication(tptp_fun_X1_0(X1!2), X0!3))),
% 4.12/4.36 inference(monotonicity,[status(thm)],[239])).
% 4.12/4.36 tff(241,plain,
% 4.12/4.36 (addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3)) = multiplication(c(X1!2), X0!3)),
% 4.12/4.36 inference(or_elim,[status(thm)],[21])).
% 4.12/4.36 tff(242,plain,
% 4.12/4.36 (multiplication(X1!2, addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3))) = multiplication(X1!2, multiplication(c(X1!2), X0!3))),
% 4.12/4.36 inference(monotonicity,[status(thm)],[241])).
% 4.12/4.36 tff(243,plain,
% 4.12/4.36 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))))),
% 4.12/4.36 inference(bind,[status(th)],[])).
% 4.12/4.36 tff(244,plain,
% 4.12/4.36 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 4.12/4.36 inference(quant_intro,[status(thm)],[243])).
% 4.12/4.36 tff(245,plain,
% 4.12/4.36 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 4.12/4.36 inference(rewrite,[status(thm)],[])).
% 4.12/4.36 tff(246,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','right_distributivity')).
% 4.12/4.36 tff(247,plain,
% 4.12/4.36 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 4.12/4.36 inference(modus_ponens,[status(thm)],[246, 245])).
% 4.12/4.36 tff(248,plain,(
% 4.12/4.36 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 4.12/4.36 inference(skolemize,[status(sab)],[247])).
% 4.12/4.36 tff(249,plain,
% 4.12/4.36 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 4.12/4.36 inference(modus_ponens,[status(thm)],[248, 244])).
% 4.12/4.36 tff(250,plain,
% 4.12/4.36 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X1!2, addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3))) = addition(multiplication(X1!2, multiplication(X0!3, c(X2!1))), multiplication(X1!2, multiplication(c(X1!2), X0!3))))),
% 4.12/4.36 inference(quant_inst,[status(thm)],[])).
% 4.12/4.36 tff(251,plain,
% 4.12/4.36 (multiplication(X1!2, addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3))) = addition(multiplication(X1!2, multiplication(X0!3, c(X2!1))), multiplication(X1!2, multiplication(c(X1!2), X0!3)))),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[250, 249])).
% 4.12/4.36 tff(252,plain,
% 4.12/4.36 (addition(multiplication(X1!2, multiplication(X0!3, c(X2!1))), multiplication(X1!2, multiplication(c(X1!2), X0!3))) = multiplication(X1!2, addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3)))),
% 4.12/4.36 inference(symmetry,[status(thm)],[251])).
% 4.12/4.36 tff(253,plain,
% 4.12/4.36 (multiplication(X1!2, multiplication(tptp_fun_X1_0(X1!2), X0!3)) = multiplication(X1!2, multiplication(c(X1!2), X0!3))),
% 4.12/4.36 inference(symmetry,[status(thm)],[240])).
% 4.12/4.36 tff(254,plain,
% 4.12/4.36 (multiplication(multiplication(X1!2, tptp_fun_X1_0(X1!2)), X0!3) = multiplication(X1!2, multiplication(tptp_fun_X1_0(X1!2), X0!3))),
% 4.12/4.36 inference(symmetry,[status(thm)],[238])).
% 4.12/4.36 tff(255,plain,
% 4.12/4.36 (multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), X0!3) = multiplication(multiplication(X1!2, tptp_fun_X1_0(X1!2)), X0!3)),
% 4.12/4.36 inference(symmetry,[status(thm)],[236])).
% 4.12/4.36 tff(256,plain,
% 4.12/4.36 (multiplication(multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), tptp_fun_X1_0(X1!2)), X0!3) = multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), X0!3)),
% 4.12/4.36 inference(symmetry,[status(thm)],[232])).
% 4.12/4.36 tff(257,plain,
% 4.12/4.36 (multiplication(zero, multiplication(c(X1!2), X0!3)) = multiplication(c(addition(X1!2, tptp_fun_X1_0(X1!2))), multiplication(tptp_fun_X1_0(X1!2), X0!3))),
% 4.12/4.36 inference(symmetry,[status(thm)],[215])).
% 4.12/4.36 tff(258,plain,
% 4.12/4.36 (zero = multiplication(zero, multiplication(c(X1!2), X0!3))),
% 4.12/4.36 inference(symmetry,[status(thm)],[11])).
% 4.12/4.36 tff(259,plain,
% 4.12/4.36 (zero = multiplication(X1!2, multiplication(c(X1!2), X0!3))),
% 4.12/4.36 inference(transitivity,[status(thm)],[258, 257, 224, 256, 255, 254, 253])).
% 4.12/4.36 tff(260,plain,
% 4.12/4.36 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X1!2, multiplication(X0!3, c(X2!1))) = multiplication(multiplication(X1!2, X0!3), c(X2!1)))),
% 4.12/4.36 inference(quant_inst,[status(thm)],[])).
% 4.12/4.36 tff(261,plain,
% 4.12/4.36 (multiplication(X1!2, multiplication(X0!3, c(X2!1))) = multiplication(multiplication(X1!2, X0!3), c(X2!1))),
% 4.12/4.36 inference(unit_resolution,[status(thm)],[260, 222])).
% 4.12/4.36 tff(262,plain,
% 4.12/4.36 (multiplication(multiplication(X1!2, X0!3), c(X2!1)) = multiplication(X1!2, multiplication(X0!3, c(X2!1)))),
% 4.12/4.36 inference(symmetry,[status(thm)],[261])).
% 4.12/4.36 tff(263,plain,
% 4.12/4.36 (addition(multiplication(multiplication(X1!2, X0!3), c(X2!1)), zero) = addition(multiplication(X1!2, multiplication(X0!3, c(X2!1))), multiplication(X1!2, multiplication(c(X1!2), X0!3)))),
% 4.12/4.36 inference(monotonicity,[status(thm)],[262, 259])).
% 4.12/4.36 tff(264,plain,
% 4.12/4.36 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 4.12/4.36 inference(bind,[status(th)],[])).
% 4.12/4.36 tff(265,plain,
% 4.12/4.36 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 4.12/4.36 inference(quant_intro,[status(thm)],[264])).
% 4.12/4.36 tff(266,plain,
% 4.12/4.36 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 4.22/4.37 inference(rewrite,[status(thm)],[])).
% 4.22/4.37 tff(267,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 4.22/4.37 tff(268,plain,
% 4.22/4.37 (![A: $i] : (addition(A, zero) = A)),
% 4.22/4.37 inference(modus_ponens,[status(thm)],[267, 266])).
% 4.22/4.37 tff(269,plain,(
% 4.22/4.37 ![A: $i] : (addition(A, zero) = A)),
% 4.22/4.37 inference(skolemize,[status(sab)],[268])).
% 4.22/4.37 tff(270,plain,
% 4.22/4.37 (![A: $i] : (addition(A, zero) = A)),
% 4.22/4.37 inference(modus_ponens,[status(thm)],[269, 265])).
% 4.22/4.37 tff(271,plain,
% 4.22/4.37 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(multiplication(X1!2, X0!3), c(X2!1)), zero) = multiplication(multiplication(X1!2, X0!3), c(X2!1)))),
% 4.22/4.37 inference(quant_inst,[status(thm)],[])).
% 4.22/4.37 tff(272,plain,
% 4.22/4.37 (addition(multiplication(multiplication(X1!2, X0!3), c(X2!1)), zero) = multiplication(multiplication(X1!2, X0!3), c(X2!1))),
% 4.22/4.37 inference(unit_resolution,[status(thm)],[271, 270])).
% 4.22/4.37 tff(273,plain,
% 4.22/4.37 (multiplication(multiplication(X1!2, X0!3), c(X2!1)) = addition(multiplication(multiplication(X1!2, X0!3), c(X2!1)), zero)),
% 4.22/4.37 inference(symmetry,[status(thm)],[272])).
% 4.22/4.37 tff(274,plain,
% 4.22/4.37 (multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero),
% 4.22/4.37 inference(transitivity,[status(thm)],[273, 263, 252, 242, 240, 238, 236, 232, 225, 215, 11])).
% 4.22/4.37 tff(275,plain,
% 4.22/4.37 (~(multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero)),
% 4.22/4.37 inference(or_elim,[status(thm)],[21])).
% 4.22/4.37 tff(276,plain,
% 4.22/4.37 ($false),
% 4.22/4.37 inference(unit_resolution,[status(thm)],[275, 274])).
% 4.22/4.37 % SZS output end Proof
% 4.22/4.37 % E exiting
%------------------------------------------------------------------------------