%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE022+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 0.45s 0.63s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE022+3 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 18:53:03 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.45/0.63 % SZS status Theorem
% 0.45/0.63 % SZS output start Proof
% 0.45/0.63 tff(addition_type, type, (
% 0.45/0.63 addition: ( $i * $i ) > $i)).
% 0.45/0.63 tff(multiplication_type, type, (
% 0.45/0.63 multiplication: ( $i * $i ) > $i)).
% 0.45/0.63 tff(tptp_fun_X1_0_type, type, (
% 0.45/0.63 tptp_fun_X1_0: $i > $i)).
% 0.45/0.63 tff(tptp_fun_X1_1_type, type, (
% 0.45/0.63 tptp_fun_X1_1: $i)).
% 0.45/0.63 tff(tptp_fun_X0_2_type, type, (
% 0.45/0.63 tptp_fun_X0_2: $i)).
% 0.45/0.63 tff(c_type, type, (
% 0.45/0.63 c: $i > $i)).
% 0.45/0.63 tff(complement_type, type, (
% 0.45/0.63 complement: ( $i * $i ) > $o)).
% 0.45/0.63 tff(test_type, type, (
% 0.45/0.63 test: $i > $o)).
% 0.45/0.63 tff(one_type, type, (
% 0.45/0.63 one: $i)).
% 0.45/0.63 tff(zero_type, type, (
% 0.45/0.63 zero: $i)).
% 0.45/0.63 tff(1,plain,
% 0.45/0.63 ((~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1))))))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(2,plain,
% 0.45/0.63 ((~![X0: $i, X1: $i] : (test(X1) => (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1))))))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(3,axiom,(~![X0: $i, X1: $i] : (test(X1) => (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.45/0.63 tff(4,plain,
% 0.45/0.63 (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.45/0.63 tff(5,plain,
% 0.45/0.63 (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.45/0.63 tff(6,plain,
% 0.45/0.63 (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.45/0.63 tff(7,plain,
% 0.45/0.63 (~![X0: $i, X1: $i] : ((~test(X1)) | (X0 = addition(multiplication(X0, X1), multiplication(X0, c(X1)))))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.45/0.63 tff(8,plain,(
% 0.45/0.63 ~((~test(X1!1)) | (X0!2 = addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1)))))),
% 0.45/0.63 inference(skolemize,[status(sab)],[7])).
% 0.45/0.63 tff(9,plain,
% 0.45/0.63 (test(X1!1)),
% 0.45/0.63 inference(or_elim,[status(thm)],[8])).
% 0.45/0.63 tff(10,plain,
% 0.45/0.63 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.45/0.63 inference(bind,[status(th)],[])).
% 0.45/0.63 tff(11,plain,
% 0.45/0.63 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.45/0.63 inference(quant_intro,[status(thm)],[10])).
% 0.45/0.63 tff(12,plain,
% 0.45/0.63 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.45/0.63 inference(rewrite,[status(thm)],[])).
% 0.45/0.63 tff(13,plain,
% 0.45/0.63 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.45/0.63 inference(bind,[status(th)],[])).
% 0.45/0.63 tff(14,plain,
% 0.45/0.63 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.45/0.63 inference(quant_intro,[status(thm)],[13])).
% 0.45/0.63 tff(15,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_3')).
% 0.45/0.63 tff(16,plain,
% 0.45/0.63 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.45/0.63 tff(17,plain,
% 0.45/0.63 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.45/0.63 tff(18,plain,(
% 0.45/0.63 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.45/0.63 inference(skolemize,[status(sab)],[17])).
% 0.45/0.63 tff(19,plain,
% 0.45/0.63 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.45/0.63 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.45/0.63 tff(20,plain,
% 0.45/0.63 (((~![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))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(21,plain,
% 0.47/0.63 ((~![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))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(22,plain,
% 0.47/0.63 ((~![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)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.47/0.63 tff(23,plain,
% 0.47/0.63 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.47/0.63 tff(24,plain,
% 0.47/0.63 (^[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))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(25,plain,
% 0.47/0.63 (![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)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[24])).
% 0.47/0.63 tff(26,plain,
% 0.47/0.63 (^[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)))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(27,plain,
% 0.47/0.63 (![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)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[26])).
% 0.47/0.63 tff(28,plain,
% 0.47/0.63 (![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)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(29,plain,
% 0.47/0.63 (^[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))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(30,plain,
% 0.47/0.63 (![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)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[29])).
% 0.47/0.63 tff(31,axiom,(![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_2')).
% 0.47/0.63 tff(32,plain,
% 0.47/0.63 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.47/0.63 tff(33,plain,
% 0.47/0.63 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.47/0.63 tff(34,plain,(
% 0.47/0.63 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.47/0.63 inference(skolemize,[status(sab)],[33])).
% 0.47/0.63 tff(35,plain,
% 0.47/0.63 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.47/0.63 tff(36,plain,
% 0.47/0.63 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.47/0.63 tff(37,plain,
% 0.47/0.63 (((~![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)))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(38,plain,
% 0.47/0.63 ((~(((~(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))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(39,plain,
% 0.47/0.63 ((((~(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)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(40,plain,
% 0.47/0.63 ((~(((~(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))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[39])).
% 0.47/0.63 tff(41,plain,
% 0.47/0.63 ((~(((~(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))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[40, 38])).
% 0.47/0.63 tff(42,plain,
% 0.47/0.63 (((~![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)))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[41])).
% 0.47/0.63 tff(43,plain,
% 0.47/0.63 (((~![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)))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[42, 37])).
% 0.47/0.63 tff(44,plain,
% 0.47/0.63 ((~![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))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(45,plain,
% 0.47/0.63 ((~![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))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.47/0.63 tff(46,plain,
% 0.47/0.63 (~(((~(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)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[45, 36])).
% 0.47/0.63 tff(47,plain,
% 0.47/0.63 ((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))),
% 0.47/0.63 inference(commutativity,[status(thm)],[])).
% 0.47/0.63 tff(48,plain,
% 0.47/0.63 ((~![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)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(49,plain,
% 0.47/0.63 (~(((~(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))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[48, 36])).
% 0.47/0.63 tff(50,plain,
% 0.47/0.63 (^[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)))))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(51,plain,
% 0.47/0.63 (![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))))))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[50])).
% 0.47/0.63 tff(52,plain,
% 0.47/0.63 (^[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)))))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(53,plain,
% 0.47/0.63 (![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))))))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[52])).
% 0.47/0.63 tff(54,plain,
% 0.47/0.63 (![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))))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[53, 51])).
% 0.47/0.63 tff(55,plain,
% 0.47/0.63 (^[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))))))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(56,plain,
% 0.47/0.63 (![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))))))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[55])).
% 0.47/0.63 tff(57,plain,
% 0.47/0.63 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(58,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_1')).
% 0.47/0.63 tff(59,plain,
% 0.47/0.63 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.47/0.63 tff(60,plain,(
% 0.47/0.63 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 0.47/0.63 inference(skolemize,[status(sab)],[59])).
% 0.47/0.63 tff(61,plain,
% 0.47/0.63 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.47/0.63 tff(62,plain,
% 0.47/0.63 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.47/0.63 tff(63,plain,
% 0.47/0.63 ((~![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))))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(64,plain,
% 0.47/0.64 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.47/0.64 tff(65,plain,
% 0.47/0.64 (((~((~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))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(66,plain,
% 0.47/0.64 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.47/0.64 tff(67,plain,
% 0.47/0.64 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(68,plain,
% 0.47/0.64 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[67, 9])).
% 0.47/0.64 tff(69,plain,
% 0.47/0.64 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[68, 66])).
% 0.47/0.64 tff(70,plain,
% 0.47/0.64 ((((~(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))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(71,plain,
% 0.47/0.64 ((((~(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))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.47/0.64 tff(72,plain,
% 0.47/0.64 (~((~(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)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[71, 49])).
% 0.47/0.64 tff(73,plain,
% 0.47/0.64 (((~(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)),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(74,plain,
% 0.47/0.64 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.47/0.64 tff(75,plain,
% 0.47/0.64 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 0.47/0.64 inference(symmetry,[status(thm)],[74])).
% 0.47/0.64 tff(76,plain,
% 0.47/0.64 ((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)))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[75])).
% 0.47/0.64 tff(77,plain,
% 0.47/0.64 ((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))),
% 0.47/0.64 inference(transitivity,[status(thm)],[76, 47])).
% 0.47/0.64 tff(78,plain,
% 0.47/0.64 ((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)),
% 0.47/0.64 inference(symmetry,[status(thm)],[77])).
% 0.47/0.64 tff(79,plain,
% 0.47/0.64 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(80,plain,
% 0.47/0.64 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[79])).
% 0.47/0.64 tff(81,plain,
% 0.47/0.64 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(82,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 0.47/0.64 tff(83,plain,
% 0.47/0.64 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.47/0.64 tff(84,plain,(
% 0.47/0.64 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.47/0.64 inference(skolemize,[status(sab)],[83])).
% 0.47/0.64 tff(85,plain,
% 0.47/0.64 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.47/0.64 tff(86,plain,
% 0.47/0.64 ((~![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))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(87,plain,
% 0.47/0.64 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.47/0.64 tff(88,plain,
% 0.47/0.64 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[87, 78])).
% 0.47/0.64 tff(89,plain,
% 0.47/0.64 (((~(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)),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(90,plain,
% 0.47/0.64 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[89, 72])).
% 0.47/0.64 tff(91,plain,
% 0.47/0.64 (((~(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)),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(92,plain,
% 0.47/0.64 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[91, 72])).
% 0.47/0.64 tff(93,plain,
% 0.47/0.64 ((~((~(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))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(94,plain,
% 0.47/0.64 ((~((~(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))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[93, 92, 90])).
% 0.47/0.64 tff(95,plain,
% 0.47/0.64 (~((~(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)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[94, 88])).
% 0.47/0.64 tff(96,plain,
% 0.47/0.64 ((((~(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))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(97,plain,
% 0.47/0.64 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[96, 95, 46])).
% 0.47/0.64 tff(98,plain,
% 0.47/0.64 ((~((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)))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(99,plain,
% 0.47/0.64 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[98, 97, 23])).
% 0.47/0.64 tff(100,plain,
% 0.47/0.64 (tptp_fun_X1_0(X1!1) = c(X1!1)),
% 0.47/0.64 inference(symmetry,[status(thm)],[99])).
% 0.47/0.64 tff(101,plain,
% 0.47/0.64 (multiplication(X0!2, tptp_fun_X1_0(X1!1)) = multiplication(X0!2, c(X1!1))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[100])).
% 0.47/0.64 tff(102,assumption,((~((~test(tptp_fun_X1_0(X1!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))) | (~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))))), introduced(assumption)).
% 0.47/0.64 tff(103,plain,
% 0.47/0.64 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(tptp_fun_X1_0(X1!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))) | (~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(104,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[103, 62, 102])).
% 0.47/0.64 tff(105,plain,(~((~((~test(tptp_fun_X1_0(X1!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))) | (~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(106,plain,
% 0.47/0.64 (((~((~test(tptp_fun_X1_0(X1!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))) | (~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))))) | (test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(107,plain,
% 0.47/0.64 (test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.47/0.64 tff(108,assumption,(![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))), introduced(assumption)).
% 0.47/0.64 tff(109,plain,
% 0.47/0.64 ((~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))) | (~complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(110,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[109, 97, 108])).
% 0.47/0.64 tff(111,plain,(~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(112,plain,
% 0.47/0.64 ((~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))) | test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(113,plain,
% 0.47/0.64 ((~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))) | test(tptp_fun_X1_0(X1!1))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.47/0.64 tff(114,plain,
% 0.47/0.64 (test(tptp_fun_X1_0(X1!1))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[113, 107])).
% 0.47/0.64 tff(115,plain,
% 0.47/0.64 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(116,plain,
% 0.47/0.64 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(117,plain,
% 0.47/0.64 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.47/0.64 tff(118,plain,
% 0.47/0.64 ((~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[117, 19])).
% 0.47/0.64 tff(119,plain,
% 0.47/0.64 ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[118, 114])).
% 0.47/0.64 tff(120,plain,
% 0.47/0.64 ((~((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1))) | (c(tptp_fun_X1_0(X1!1)) = X1!1) | (~complement(tptp_fun_X1_0(X1!1), X1!1))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(121,plain,
% 0.47/0.64 ((~((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1))) | (c(tptp_fun_X1_0(X1!1)) = X1!1)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[120, 69])).
% 0.47/0.64 tff(122,plain,
% 0.47/0.64 (c(tptp_fun_X1_0(X1!1)) = X1!1),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[121, 119])).
% 0.47/0.64 tff(123,plain,
% 0.47/0.64 (multiplication(X0!2, c(tptp_fun_X1_0(X1!1))) = multiplication(X0!2, X1!1)),
% 0.47/0.64 inference(monotonicity,[status(thm)],[122])).
% 0.47/0.64 tff(124,plain,
% 0.47/0.64 (addition(multiplication(X0!2, c(tptp_fun_X1_0(X1!1))), multiplication(X0!2, tptp_fun_X1_0(X1!1))) = addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1)))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[123, 101])).
% 0.47/0.64 tff(125,assumption,(multiplication(X0!2, addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = addition(multiplication(X0!2, c(tptp_fun_X1_0(X1!1))), multiplication(X0!2, tptp_fun_X1_0(X1!1)))), introduced(assumption)).
% 0.47/0.64 tff(126,plain,
% 0.47/0.64 (addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[100])).
% 0.47/0.64 tff(127,plain,
% 0.47/0.64 (addition(c(tptp_fun_X1_0(X1!1)), c(X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 0.47/0.64 inference(symmetry,[status(thm)],[126])).
% 0.47/0.64 tff(128,plain,
% 0.47/0.64 (X1!1 = c(tptp_fun_X1_0(X1!1))),
% 0.47/0.64 inference(symmetry,[status(thm)],[122])).
% 0.47/0.64 tff(129,plain,
% 0.47/0.64 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(c(tptp_fun_X1_0(X1!1)), c(X1!1))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[128, 100])).
% 0.47/0.64 tff(130,plain,
% 0.47/0.64 (one = addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 0.47/0.64 inference(transitivity,[status(thm)],[75, 129, 127])).
% 0.47/0.64 tff(131,plain,
% 0.47/0.64 (multiplication(X0!2, one) = multiplication(X0!2, addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[130])).
% 0.47/0.64 tff(132,plain,
% 0.47/0.64 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(133,plain,
% 0.47/0.64 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.47/0.64 inference(quant_intro,[status(thm)],[132])).
% 0.47/0.64 tff(134,plain,
% 0.47/0.64 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(135,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 0.47/0.64 tff(136,plain,
% 0.47/0.64 (![A: $i] : (multiplication(A, one) = A)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.47/0.64 tff(137,plain,(
% 0.47/0.64 ![A: $i] : (multiplication(A, one) = A)),
% 0.47/0.64 inference(skolemize,[status(sab)],[136])).
% 0.47/0.64 tff(138,plain,
% 0.47/0.64 (![A: $i] : (multiplication(A, one) = A)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.47/0.64 tff(139,plain,
% 0.47/0.64 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X0!2, one) = X0!2)),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(140,plain,
% 0.47/0.64 (multiplication(X0!2, one) = X0!2),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.47/0.64 tff(141,plain,
% 0.47/0.64 (X0!2 = multiplication(X0!2, one)),
% 0.47/0.64 inference(symmetry,[status(thm)],[140])).
% 0.47/0.64 tff(142,plain,
% 0.47/0.64 (X0!2 = addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[141, 131, 125, 124])).
% 0.47/0.64 tff(143,plain,
% 0.47/0.64 (~(X0!2 = addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))))),
% 0.47/0.64 inference(or_elim,[status(thm)],[8])).
% 0.47/0.64 tff(144,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.47/0.64 tff(145,plain,(~(multiplication(X0!2, addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = addition(multiplication(X0!2, c(tptp_fun_X1_0(X1!1))), multiplication(X0!2, tptp_fun_X1_0(X1!1))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(146,plain,
% 0.47/0.64 (^[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))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(147,plain,
% 0.47/0.64 (![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)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[146])).
% 0.47/0.64 tff(148,plain,
% 0.47/0.64 (![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)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(149,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')).
% 0.47/0.64 tff(150,plain,
% 0.47/0.64 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.47/0.64 tff(151,plain,(
% 0.47/0.64 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.47/0.64 inference(skolemize,[status(sab)],[150])).
% 0.47/0.64 tff(152,plain,
% 0.47/0.64 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.47/0.64 tff(153,plain,
% 0.47/0.64 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!2, addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = addition(multiplication(X0!2, c(tptp_fun_X1_0(X1!1))), multiplication(X0!2, tptp_fun_X1_0(X1!1))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(154,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[153, 152, 145])).
% 0.47/0.64 % SZS output end Proof
% 0.47/0.64 % E exiting
%------------------------------------------------------------------------------