%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE007+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:12:50 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE007+2 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 18:52:11 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(leq_type, type, (
% 0.11/0.37 leq: ( $i * $i ) > $o)).
% 0.11/0.37 tff(one_type, type, (
% 0.11/0.37 one: $i)).
% 0.11/0.37 tff(addition_type, type, (
% 0.11/0.37 addition: ( $i * $i ) > $i)).
% 0.11/0.37 tff(multiplication_type, type, (
% 0.11/0.37 multiplication: ( $i * $i ) > $i)).
% 0.11/0.37 tff(c_type, type, (
% 0.11/0.37 c: $i > $i)).
% 0.11/0.37 tff(tptp_fun_X1_1_type, type, (
% 0.11/0.37 tptp_fun_X1_1: $i)).
% 0.11/0.37 tff(tptp_fun_X0_2_type, type, (
% 0.11/0.37 tptp_fun_X0_2: $i)).
% 0.11/0.37 tff(tptp_fun_X1_0_type, type, (
% 0.11/0.37 tptp_fun_X1_0: $i > $i)).
% 0.11/0.37 tff(complement_type, type, (
% 0.11/0.37 complement: ( $i * $i ) > $o)).
% 0.11/0.37 tff(test_type, type, (
% 0.11/0.37 test: $i > $o)).
% 0.11/0.37 tff(zero_type, type, (
% 0.11/0.37 zero: $i)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.11/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(4,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (![A: $i] : (multiplication(one, A) = A)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.37 tff(6,plain,(
% 0.11/0.37 ![A: $i] : (multiplication(one, A) = A)),
% 0.11/0.37 inference(skolemize,[status(sab)],[5])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![A: $i] : (multiplication(one, A) = A)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, tptp_fun_X1_0(X1!1)) = tptp_fun_X1_0(X1!1))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (multiplication(one, tptp_fun_X1_0(X1!1)) = tptp_fun_X1_0(X1!1)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 ((~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1)))) & leq(addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1))), one)))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1)))) & leq(addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1))), one))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 ((~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (leq(one, addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1)))) & leq(addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1))), one)))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1)))) & leq(addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1))), one))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(12,axiom,(~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (leq(one, addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1)))) & leq(addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1))), one)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1)))) & leq(addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1))), one)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1)))) & leq(addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1))), one)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1)))) & leq(addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1))), one)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1)))) & leq(addition(multiplication(addition(X0, c(X0)), X1), multiplication(addition(X0, c(X0)), c(X1))), one)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.11/0.37 tff(17,plain,(
% 0.11/0.37 ~((~(test(X1!1) & test(X0!2))) | (leq(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1)))) & leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[16])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (test(X1!1) & test(X0!2)),
% 0.11/0.37 inference(or_elim,[status(thm)],[17])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (test(X1!1)),
% 0.11/0.37 inference(and_elim,[status(thm)],[18])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[20])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.11/0.37 tff(25,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_3')).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.11/0.37 tff(28,plain,(
% 0.11/0.37 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[27])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (((~![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))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 ((~![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))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 ((~![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)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[32, 29, 19])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (^[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))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))) <=> ![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 (^[X0: $i, X1: $i] : trans(trans(monotonicity(rewrite(((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))), ((complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))))), rewrite((complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))), ((complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))))), rewrite((~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))), ((complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(37,plain,
% 0.11/0.38 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[36])).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (^[X0: $i, X1: $i] : rewrite((complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one))) <=> (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[39])).
% 0.11/0.38 tff(41,axiom,(![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_2')).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.11/0.38 tff(44,plain,(
% 0.11/0.38 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[43])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (((~![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)))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 ((~(((~(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))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(49,plain,
% 0.11/0.38 ((((~(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)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 ((~(((~(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))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[49])).
% 0.11/0.38 tff(51,plain,
% 0.11/0.38 ((~(((~(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))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[50, 48])).
% 0.11/0.38 tff(52,plain,
% 0.11/0.38 (((~![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)))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[51])).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 (((~![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)))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[52, 47])).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 ((~![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))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 ((~![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))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 (~(((~(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)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[55, 46])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 ((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))),
% 0.11/0.38 inference(commutativity,[status(thm)],[])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 ((~![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)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 (~(((~(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))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[58, 46])).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 (^[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)))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 (![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))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[60])).
% 0.11/0.38 tff(62,plain,
% 0.11/0.38 (^[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)))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 (![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))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[62])).
% 0.11/0.38 tff(64,plain,
% 0.11/0.38 (![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))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[63, 61])).
% 0.11/0.38 tff(65,plain,
% 0.11/0.38 (^[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))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 (![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))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[65])).
% 0.11/0.38 tff(67,plain,
% 0.11/0.38 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(68,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_1')).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.11/0.38 tff(70,plain,(
% 0.11/0.38 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[69])).
% 0.11/0.38 tff(71,plain,
% 0.11/0.38 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.11/0.38 tff(72,plain,
% 0.11/0.38 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.11/0.38 tff(73,plain,
% 0.11/0.38 ((~![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))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(74,plain,
% 0.11/0.38 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.11/0.38 tff(75,plain,
% 0.11/0.38 (((~((~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))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(76,plain,
% 0.11/0.38 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.11/0.38 tff(77,plain,
% 0.11/0.38 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(78,plain,
% 0.11/0.38 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[77, 19])).
% 0.11/0.39 tff(79,plain,
% 0.11/0.39 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[78, 76])).
% 0.11/0.39 tff(80,plain,
% 0.11/0.39 ((((~(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))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(81,plain,
% 0.11/0.39 ((((~(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))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.11/0.39 tff(82,plain,
% 0.11/0.39 (~((~(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)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[81, 59])).
% 0.11/0.39 tff(83,plain,
% 0.11/0.39 (((~(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)),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(84,plain,
% 0.11/0.39 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.11/0.39 tff(85,plain,
% 0.11/0.39 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 0.11/0.39 inference(symmetry,[status(thm)],[84])).
% 0.11/0.39 tff(86,plain,
% 0.11/0.39 ((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)))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[85])).
% 0.11/0.39 tff(87,plain,
% 0.11/0.39 ((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))),
% 0.11/0.39 inference(transitivity,[status(thm)],[86, 57])).
% 0.11/0.39 tff(88,plain,
% 0.11/0.39 ((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)),
% 0.11/0.39 inference(symmetry,[status(thm)],[87])).
% 0.11/0.39 tff(89,plain,
% 0.11/0.39 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(90,plain,
% 0.11/0.39 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[89])).
% 0.11/0.39 tff(91,plain,
% 0.11/0.39 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(92,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 0.11/0.39 tff(93,plain,
% 0.11/0.39 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.11/0.39 tff(94,plain,(
% 0.11/0.39 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.11/0.39 inference(skolemize,[status(sab)],[93])).
% 0.11/0.39 tff(95,plain,
% 0.11/0.39 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.11/0.39 tff(96,plain,
% 0.11/0.39 ((~![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))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(97,plain,
% 0.11/0.39 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.11/0.39 tff(98,plain,
% 0.11/0.39 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[97, 88])).
% 0.11/0.39 tff(99,plain,
% 0.11/0.39 (((~(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)),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(100,plain,
% 0.11/0.39 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[99, 82])).
% 0.11/0.39 tff(101,plain,
% 0.11/0.39 (((~(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)),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(102,plain,
% 0.11/0.39 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[101, 82])).
% 0.11/0.39 tff(103,plain,
% 0.11/0.39 ((~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))) | (~(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))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(104,plain,
% 0.11/0.39 ((~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[103, 102, 100])).
% 0.11/0.39 tff(105,plain,
% 0.11/0.39 (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[104, 98])).
% 0.11/0.39 tff(106,plain,
% 0.11/0.39 ((((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))) | ((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))) | complement(X1!1, tptp_fun_X1_0(X1!1))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(107,plain,
% 0.11/0.39 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[106, 105, 56])).
% 0.11/0.39 tff(108,plain,
% 0.11/0.39 ((~((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)))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(109,plain,
% 0.11/0.39 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[108, 107, 33])).
% 0.11/0.39 tff(110,plain,
% 0.11/0.39 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) <=> complement(tptp_fun_X1_0(X0!2), X0!2)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(111,plain,
% 0.11/0.39 (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) <=> complement(tptp_fun_X1_0(X0!2), X0!2))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[110, 46])).
% 0.11/0.39 tff(112,plain,
% 0.11/0.39 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2))))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(113,plain,
% 0.11/0.39 (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2)))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[112, 72])).
% 0.11/0.39 tff(114,plain,
% 0.11/0.39 (((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2))))) | ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(115,plain,
% 0.11/0.39 ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.11/0.39 tff(116,plain,
% 0.11/0.39 (test(X0!2)),
% 0.11/0.39 inference(and_elim,[status(thm)],[18])).
% 0.11/0.39 tff(117,plain,
% 0.11/0.39 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(118,plain,
% 0.11/0.39 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.11/0.39 tff(119,plain,
% 0.11/0.39 (complement(tptp_fun_X1_0(X0!2), X0!2)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[118, 115])).
% 0.11/0.39 tff(120,plain,
% 0.11/0.39 ((((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) <=> complement(tptp_fun_X1_0(X0!2), X0!2)) | (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one)))) | (~complement(tptp_fun_X1_0(X0!2), X0!2))),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(121,plain,
% 0.11/0.39 ((((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) <=> complement(tptp_fun_X1_0(X0!2), X0!2)) | (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.11/0.39 tff(122,plain,
% 0.11/0.39 (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[121, 111])).
% 0.11/0.39 tff(123,plain,
% 0.11/0.39 (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) | (addition(X0!2, tptp_fun_X1_0(X0!2)) = one)),
% 0.11/0.39 inference(tautology,[status(thm)],[])).
% 0.11/0.39 tff(124,plain,
% 0.11/0.39 (addition(X0!2, tptp_fun_X1_0(X0!2)) = one),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.11/0.39 tff(125,plain,
% 0.11/0.39 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(126,plain,
% 0.11/0.39 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(127,plain,
% 0.11/0.39 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.11/0.39 tff(128,plain,
% 0.11/0.39 ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[127, 29, 116])).
% 0.11/0.39 tff(129,plain,
% 0.11/0.39 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(130,plain,
% 0.11/0.39 ((~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))) <=> (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(131,plain,
% 0.19/0.40 ((((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))) <=> (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(132,plain,
% 0.19/0.40 ((~(((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))) <=> (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[131])).
% 0.19/0.40 tff(133,plain,
% 0.19/0.40 ((~(((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))) <=> (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[132, 130])).
% 0.19/0.40 tff(134,plain,
% 0.19/0.40 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[133])).
% 0.19/0.40 tff(135,plain,
% 0.19/0.40 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[134, 129])).
% 0.19/0.40 tff(136,plain,
% 0.19/0.40 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(137,plain,
% 0.19/0.40 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.40 tff(138,plain,
% 0.19/0.40 (~(((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[137, 46])).
% 0.19/0.40 tff(139,plain,
% 0.19/0.40 ((addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2))) <=> (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2))),
% 0.19/0.40 inference(commutativity,[status(thm)],[])).
% 0.19/0.40 tff(140,plain,
% 0.19/0.40 (one = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 0.19/0.40 inference(symmetry,[status(thm)],[124])).
% 0.19/0.40 tff(141,plain,
% 0.19/0.40 ((addition(tptp_fun_X1_0(X0!2), X0!2) = one) <=> (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[140])).
% 0.19/0.40 tff(142,plain,
% 0.19/0.40 ((addition(tptp_fun_X1_0(X0!2), X0!2) = one) <=> (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2))),
% 0.19/0.40 inference(transitivity,[status(thm)],[141, 139])).
% 0.19/0.40 tff(143,plain,
% 0.19/0.40 ((addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)) <=> (addition(tptp_fun_X1_0(X0!2), X0!2) = one)),
% 0.19/0.40 inference(symmetry,[status(thm)],[142])).
% 0.19/0.40 tff(144,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(145,plain,
% 0.19/0.40 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[144, 95])).
% 0.19/0.40 tff(146,plain,
% 0.19/0.40 (addition(tptp_fun_X1_0(X0!2), X0!2) = one),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[145, 143])).
% 0.19/0.40 tff(147,plain,
% 0.19/0.40 (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) | (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(148,plain,
% 0.19/0.40 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[147, 122])).
% 0.19/0.40 tff(149,plain,
% 0.19/0.40 (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) | (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(150,plain,
% 0.19/0.40 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[149, 122])).
% 0.19/0.40 tff(151,plain,
% 0.19/0.40 ((~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(152,plain,
% 0.19/0.40 ((~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[151, 150, 148])).
% 0.19/0.40 tff(153,plain,
% 0.19/0.40 (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[152, 146])).
% 0.19/0.40 tff(154,plain,
% 0.19/0.40 ((((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))) | ((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))) | complement(X0!2, tptp_fun_X1_0(X0!2))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(155,plain,
% 0.19/0.40 (complement(X0!2, tptp_fun_X1_0(X0!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[154, 153, 138])).
% 0.19/0.40 tff(156,plain,
% 0.19/0.40 ((~((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))) | (c(X0!2) = tptp_fun_X1_0(X0!2)) | (~complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(157,plain,
% 0.19/0.40 (c(X0!2) = tptp_fun_X1_0(X0!2)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[156, 155, 128])).
% 0.19/0.40 tff(158,plain,
% 0.19/0.40 (addition(X0!2, c(X0!2)) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[157])).
% 0.19/0.40 tff(159,plain,
% 0.19/0.40 (addition(X0!2, c(X0!2)) = one),
% 0.19/0.40 inference(transitivity,[status(thm)],[158, 124])).
% 0.19/0.40 tff(160,plain,
% 0.19/0.40 (multiplication(addition(X0!2, c(X0!2)), c(X1!1)) = multiplication(one, tptp_fun_X1_0(X1!1))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[159, 109])).
% 0.19/0.40 tff(161,plain,
% 0.19/0.40 (multiplication(addition(X0!2, c(X0!2)), c(X1!1)) = tptp_fun_X1_0(X1!1)),
% 0.19/0.40 inference(transitivity,[status(thm)],[160, 9])).
% 0.19/0.40 tff(162,plain,
% 0.19/0.40 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X1!1) = X1!1)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(163,plain,
% 0.19/0.40 (multiplication(one, X1!1) = X1!1),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[162, 7])).
% 0.19/0.40 tff(164,plain,
% 0.19/0.40 (multiplication(addition(X0!2, c(X0!2)), X1!1) = multiplication(one, X1!1)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[159])).
% 0.19/0.40 tff(165,plain,
% 0.19/0.40 (multiplication(addition(X0!2, c(X0!2)), X1!1) = X1!1),
% 0.19/0.40 inference(transitivity,[status(thm)],[164, 163])).
% 0.19/0.40 tff(166,plain,
% 0.19/0.40 (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[165, 161])).
% 0.19/0.40 tff(167,plain,
% 0.19/0.40 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1)))),
% 0.19/0.40 inference(symmetry,[status(thm)],[166])).
% 0.19/0.40 tff(168,plain,
% 0.19/0.40 (one = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[85, 167])).
% 0.19/0.40 tff(169,plain,
% 0.19/0.40 (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))) = one),
% 0.19/0.40 inference(transitivity,[status(thm)],[166, 84])).
% 0.19/0.40 tff(170,plain,
% 0.19/0.40 (leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one) <=> leq(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[169, 168])).
% 0.19/0.40 tff(171,plain,
% 0.19/0.40 (leq(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1)))) <=> leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one)),
% 0.19/0.40 inference(symmetry,[status(thm)],[170])).
% 0.19/0.40 tff(172,plain,
% 0.19/0.40 ((~leq(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))))) <=> (~leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[171])).
% 0.19/0.40 tff(173,plain,
% 0.19/0.40 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(174,plain,
% 0.19/0.40 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.19/0.40 inference(quant_intro,[status(thm)],[173])).
% 0.19/0.40 tff(175,plain,
% 0.19/0.40 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(176,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 0.19/0.40 tff(177,plain,
% 0.19/0.40 (![A: $i] : (addition(A, A) = A)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.19/0.40 tff(178,plain,(
% 0.19/0.40 ![A: $i] : (addition(A, A) = A)),
% 0.19/0.40 inference(skolemize,[status(sab)],[177])).
% 0.19/0.40 tff(179,plain,
% 0.19/0.40 (![A: $i] : (addition(A, A) = A)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.19/0.40 tff(180,plain,
% 0.19/0.40 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(181,plain,
% 0.19/0.40 (addition(one, one) = one),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.19/0.40 tff(182,plain,
% 0.19/0.40 (addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one) = addition(one, one)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[169])).
% 0.19/0.40 tff(183,plain,
% 0.19/0.40 (addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one) = one),
% 0.19/0.40 inference(transitivity,[status(thm)],[182, 181])).
% 0.19/0.40 tff(184,plain,
% 0.19/0.40 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(185,plain,
% 0.19/0.40 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[184])).
% 0.19/0.40 tff(186,plain,
% 0.19/0.40 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(187,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','order')).
% 0.19/0.40 tff(188,plain,
% 0.19/0.40 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.40 tff(189,plain,(
% 0.19/0.40 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.40 inference(skolemize,[status(sab)],[188])).
% 0.19/0.40 tff(190,plain,
% 0.19/0.40 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.19/0.40 tff(191,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one) <=> (addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one) = one))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(192,plain,
% 0.19/0.40 (leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one) <=> (addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one) = one)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.19/0.40 tff(193,assumption,(~leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one)), introduced(assumption)).
% 0.19/0.40 tff(194,plain,
% 0.19/0.40 ((~(leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one) <=> (addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one) = one))) | leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one) | (~(addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one) = one))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(195,plain,
% 0.19/0.40 ((~(leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one) <=> (addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one) = one))) | (~(addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one) = one))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.19/0.40 tff(196,plain,
% 0.19/0.40 (~(addition(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one) = one)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[195, 192])).
% 0.19/0.40 tff(197,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[196, 183])).
% 0.19/0.40 tff(198,plain,(leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(199,plain,
% 0.19/0.41 ((~(~((~leq(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))))) | (~leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one))))) <=> ((~leq(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))))) | (~leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(200,plain,
% 0.19/0.41 ((leq(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1)))) & leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one)) <=> (~((~leq(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))))) | (~leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(201,plain,
% 0.19/0.41 ((~(leq(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1)))) & leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one))) <=> (~(~((~leq(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))))) | (~leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[200])).
% 0.19/0.41 tff(202,plain,
% 0.19/0.41 ((~(leq(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1)))) & leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one))) <=> ((~leq(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))))) | (~leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[201, 199])).
% 0.19/0.41 tff(203,plain,
% 0.19/0.41 (~(leq(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1)))) & leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one))),
% 0.19/0.41 inference(or_elim,[status(thm)],[17])).
% 0.19/0.41 tff(204,plain,
% 0.19/0.41 ((~leq(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))))) | (~leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.19/0.41 tff(205,plain,
% 0.19/0.41 (~leq(one, addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[204, 198])).
% 0.19/0.41 tff(206,plain,
% 0.19/0.41 (~leq(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X0!2, c(X0!2)), c(X1!1))), one)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[205, 172])).
% 0.19/0.41 tff(207,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[198, 206])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------