TSTP Solution File: KLE024+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE024+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 Sep 17 17:23:53 EDT 2022
% Result : Theorem 201.25s 129.72s
% Output : Proof 201.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE024+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.32 % Computer : n005.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 07:51:48 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 201.25/129.72 % SZS status Theorem
% 201.25/129.72 % SZS output start Proof
% 201.25/129.72 tff(zero_type, type, (
% 201.25/129.72 zero: $i)).
% 201.25/129.72 tff(multiplication_type, type, (
% 201.25/129.72 multiplication: ( $i * $i ) > $i)).
% 201.25/129.72 tff(c_type, type, (
% 201.25/129.72 c: $i > $i)).
% 201.25/129.72 tff(tptp_fun_X2_1_type, type, (
% 201.25/129.72 tptp_fun_X2_1: $i)).
% 201.25/129.72 tff(tptp_fun_X0_3_type, type, (
% 201.25/129.72 tptp_fun_X0_3: $i)).
% 201.25/129.72 tff(tptp_fun_X1_2_type, type, (
% 201.25/129.72 tptp_fun_X1_2: $i)).
% 201.25/129.72 tff(tptp_fun_X1_0_type, type, (
% 201.25/129.72 tptp_fun_X1_0: $i > $i)).
% 201.25/129.72 tff(one_type, type, (
% 201.25/129.72 one: $i)).
% 201.25/129.72 tff(addition_type, type, (
% 201.25/129.72 addition: ( $i * $i ) > $i)).
% 201.25/129.72 tff(complement_type, type, (
% 201.25/129.72 complement: ( $i * $i ) > $o)).
% 201.25/129.72 tff(test_type, type, (
% 201.25/129.72 test: $i > $o)).
% 201.25/129.72 tff(1,plain,
% 201.25/129.72 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 201.25/129.72 inference(bind,[status(th)],[])).
% 201.25/129.72 tff(2,plain,
% 201.25/129.72 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 201.25/129.72 inference(quant_intro,[status(thm)],[1])).
% 201.25/129.72 tff(3,plain,
% 201.25/129.72 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 201.25/129.72 inference(rewrite,[status(thm)],[])).
% 201.25/129.72 tff(4,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 201.25/129.72 tff(5,plain,
% 201.25/129.72 (![A: $i] : (multiplication(zero, A) = zero)),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[4, 3])).
% 201.25/129.72 tff(6,plain,(
% 201.25/129.72 ![A: $i] : (multiplication(zero, A) = zero)),
% 201.25/129.72 inference(skolemize,[status(sab)],[5])).
% 201.25/129.72 tff(7,plain,
% 201.25/129.72 (![A: $i] : (multiplication(zero, A) = zero)),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[6, 2])).
% 201.25/129.72 tff(8,plain,
% 201.25/129.72 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, multiplication(X0!3, c(X2!1))) = zero)),
% 201.25/129.72 inference(quant_inst,[status(thm)],[])).
% 201.25/129.72 tff(9,plain,
% 201.25/129.72 (multiplication(zero, multiplication(X0!3, c(X2!1))) = zero),
% 201.25/129.72 inference(unit_resolution,[status(thm)],[8, 7])).
% 201.25/129.72 tff(10,plain,
% 201.25/129.72 (^[X0: $i, X1: $i] : refl((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))))))),
% 201.25/129.72 inference(bind,[status(th)],[])).
% 201.25/129.72 tff(11,plain,
% 201.25/129.72 (![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)))))),
% 201.25/129.72 inference(quant_intro,[status(thm)],[10])).
% 201.25/129.72 tff(12,plain,
% 201.25/129.72 (^[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))))))),
% 201.25/129.72 inference(bind,[status(th)],[])).
% 201.25/129.72 tff(13,plain,
% 201.25/129.72 (![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)))))),
% 201.25/129.72 inference(quant_intro,[status(thm)],[12])).
% 201.25/129.72 tff(14,plain,
% 201.25/129.72 (![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)))),
% 201.25/129.72 inference(rewrite,[status(thm)],[])).
% 201.25/129.72 tff(15,plain,
% 201.25/129.72 (^[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))))),
% 201.25/129.72 inference(bind,[status(th)],[])).
% 201.25/129.72 tff(16,plain,
% 201.25/129.72 (![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)))),
% 201.25/129.72 inference(quant_intro,[status(thm)],[15])).
% 201.25/129.72 tff(17,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')).
% 201.25/129.72 tff(18,plain,
% 201.25/129.72 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[17, 16])).
% 201.25/129.72 tff(19,plain,
% 201.25/129.72 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[18, 14])).
% 201.25/129.72 tff(20,plain,(
% 201.25/129.72 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 201.25/129.72 inference(skolemize,[status(sab)],[19])).
% 201.25/129.72 tff(21,plain,
% 201.25/129.72 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[20, 13])).
% 201.25/129.72 tff(22,plain,
% 201.25/129.72 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[21, 11])).
% 201.25/129.72 tff(23,plain,
% 201.25/129.72 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(tptp_fun_X1_0(X1!2), X1!2) <=> (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one)))))),
% 201.25/129.72 inference(quant_inst,[status(thm)],[])).
% 201.25/129.72 tff(24,plain,
% 201.25/129.72 (complement(tptp_fun_X1_0(X1!2), X1!2) <=> (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))))),
% 201.25/129.72 inference(unit_resolution,[status(thm)],[23, 22])).
% 201.25/129.72 tff(25,plain,
% 201.25/129.72 (^[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)))))))),
% 201.25/129.72 inference(bind,[status(th)],[])).
% 201.25/129.72 tff(26,plain,
% 201.25/129.72 (![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))))))),
% 201.25/129.72 inference(quant_intro,[status(thm)],[25])).
% 201.25/129.72 tff(27,plain,
% 201.25/129.72 (^[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)))))))),
% 201.25/129.72 inference(bind,[status(th)],[])).
% 201.25/129.72 tff(28,plain,
% 201.25/129.72 (![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))))))),
% 201.25/129.72 inference(quant_intro,[status(thm)],[27])).
% 201.25/129.72 tff(29,plain,
% 201.25/129.72 (![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))))))),
% 201.25/129.72 inference(transitivity,[status(thm)],[28, 26])).
% 201.25/129.72 tff(30,plain,
% 201.25/129.72 (^[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))))))))),
% 201.25/129.72 inference(bind,[status(th)],[])).
% 201.25/129.72 tff(31,plain,
% 201.25/129.72 (![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))))))),
% 201.25/129.72 inference(quant_intro,[status(thm)],[30])).
% 201.25/129.72 tff(32,plain,
% 201.25/129.72 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 201.25/129.72 inference(rewrite,[status(thm)],[])).
% 201.25/129.72 tff(33,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_1')).
% 201.25/129.72 tff(34,plain,
% 201.25/129.72 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[33, 32])).
% 201.25/129.72 tff(35,plain,(
% 201.25/129.72 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 201.25/129.72 inference(skolemize,[status(sab)],[34])).
% 201.25/129.72 tff(36,plain,
% 201.25/129.72 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[35, 31])).
% 201.25/129.72 tff(37,plain,
% 201.25/129.72 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[36, 29])).
% 201.25/129.72 tff(38,plain,
% 201.25/129.72 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | (~(test(X1!2) | ![X1: $i] : (~complement(X1, X1!2))))))),
% 201.25/129.72 inference(quant_inst,[status(thm)],[])).
% 201.25/129.72 tff(39,plain,
% 201.25/129.72 (~((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | (~(test(X1!2) | ![X1: $i] : (~complement(X1, X1!2)))))),
% 201.25/129.72 inference(unit_resolution,[status(thm)],[38, 37])).
% 201.25/129.72 tff(40,plain,
% 201.25/129.72 (((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | (~(test(X1!2) | ![X1: $i] : (~complement(X1, X1!2))))) | ((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))),
% 201.25/129.72 inference(tautology,[status(thm)],[])).
% 201.25/129.72 tff(41,plain,
% 201.25/129.72 ((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2)),
% 201.25/129.72 inference(unit_resolution,[status(thm)],[40, 39])).
% 201.25/129.72 tff(42,plain,
% 201.25/129.72 ((~((multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero) | (~(test(X1!2) & test(X2!1))) | (~(addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3)) = multiplication(c(X1!2), X0!3))))) <=> (~((multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero) | (~(test(X1!2) & test(X2!1))) | (~(addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3)) = multiplication(c(X1!2), X0!3)))))),
% 201.25/129.72 inference(rewrite,[status(thm)],[])).
% 201.25/129.72 tff(43,plain,
% 201.25/129.72 ((~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0))))) <=> (~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0)))))),
% 201.25/129.72 inference(rewrite,[status(thm)],[])).
% 201.25/129.72 tff(44,plain,
% 201.25/129.72 ((~![X0: $i, X1: $i, X2: $i] : ((test(X1) & test(X2)) => ((addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0)) => (multiplication(multiplication(X1, X0), c(X2)) = zero)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0)))))),
% 201.25/129.72 inference(rewrite,[status(thm)],[])).
% 201.25/129.72 tff(45,axiom,(~![X0: $i, X1: $i, X2: $i] : ((test(X1) & test(X2)) => ((addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0)) => (multiplication(multiplication(X1, X0), c(X2)) = zero)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 201.25/129.72 tff(46,plain,
% 201.25/129.72 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0))))),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[45, 44])).
% 201.25/129.72 tff(47,plain,
% 201.25/129.72 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0))))),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[46, 43])).
% 201.25/129.72 tff(48,plain,
% 201.25/129.72 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0))))),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[47, 43])).
% 201.25/129.72 tff(49,plain,
% 201.25/129.72 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0))))),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[48, 43])).
% 201.25/129.72 tff(50,plain,
% 201.25/129.72 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0))))),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[49, 43])).
% 201.25/129.72 tff(51,plain,
% 201.25/129.72 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0))))),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[50, 43])).
% 201.25/129.72 tff(52,plain,
% 201.25/129.72 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(multiplication(X1, X0), c(X2)) = zero) | (~(test(X1) & test(X2))) | (~(addition(multiplication(X0, c(X2)), multiplication(c(X1), X0)) = multiplication(c(X1), X0))))),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[51, 43])).
% 201.25/129.72 tff(53,plain,(
% 201.25/129.72 ~((multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero) | (~(test(X1!2) & test(X2!1))) | (~(addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3)) = multiplication(c(X1!2), X0!3))))),
% 201.25/129.72 inference(skolemize,[status(sab)],[52])).
% 201.25/129.72 tff(54,plain,
% 201.25/129.72 (~((multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero) | (~(test(X1!2) & test(X2!1))) | (~(addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3)) = multiplication(c(X1!2), X0!3))))),
% 201.25/129.72 inference(modus_ponens,[status(thm)],[53, 42])).
% 201.25/129.72 tff(55,plain,
% 201.25/129.72 (test(X1!2) & test(X2!1)),
% 201.25/129.72 inference(or_elim,[status(thm)],[54])).
% 201.25/129.72 tff(56,plain,
% 201.25/129.72 (test(X1!2)),
% 201.25/129.72 inference(and_elim,[status(thm)],[55])).
% 201.25/129.72 tff(57,plain,
% 201.25/129.72 ((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | (~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2)),
% 201.25/129.72 inference(tautology,[status(thm)],[])).
% 201.25/129.72 tff(58,plain,
% 201.25/129.72 ((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | complement(tptp_fun_X1_0(X1!2), X1!2)),
% 201.25/129.72 inference(unit_resolution,[status(thm)],[57, 56])).
% 201.25/129.72 tff(59,plain,
% 201.25/129.72 (complement(tptp_fun_X1_0(X1!2), X1!2)),
% 201.25/129.72 inference(unit_resolution,[status(thm)],[58, 41])).
% 201.25/129.72 tff(60,plain,
% 201.25/129.72 ((~(complement(tptp_fun_X1_0(X1!2), X1!2) <=> (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one)))))) | (~complement(tptp_fun_X1_0(X1!2), X1!2)) | (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))))),
% 201.25/129.73 inference(tautology,[status(thm)],[])).
% 201.25/129.73 tff(61,plain,
% 201.25/129.73 ((~(complement(tptp_fun_X1_0(X1!2), X1!2) <=> (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one)))))) | (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))))),
% 201.25/129.73 inference(unit_resolution,[status(thm)],[60, 59])).
% 201.25/129.73 tff(62,plain,
% 201.25/129.73 (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one)))),
% 201.25/129.73 inference(unit_resolution,[status(thm)],[61, 24])).
% 201.25/129.73 tff(63,plain,
% 201.25/129.73 (((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))) | (multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)),
% 201.25/129.73 inference(tautology,[status(thm)],[])).
% 201.25/129.73 tff(64,plain,
% 201.25/129.73 (multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero),
% 201.25/129.73 inference(unit_resolution,[status(thm)],[63, 62])).
% 201.25/129.73 tff(65,plain,
% 201.25/129.73 (multiplication(multiplication(X1!2, tptp_fun_X1_0(X1!2)), multiplication(X0!3, c(X2!1))) = multiplication(zero, multiplication(X0!3, c(X2!1)))),
% 201.25/129.73 inference(monotonicity,[status(thm)],[64])).
% 201.25/129.73 tff(66,plain,
% 201.25/129.73 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)))),
% 201.25/129.73 inference(bind,[status(th)],[])).
% 201.25/129.73 tff(67,plain,
% 201.25/129.73 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 201.25/129.73 inference(quant_intro,[status(thm)],[66])).
% 201.25/129.73 tff(68,plain,
% 201.25/129.73 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 201.25/129.73 inference(rewrite,[status(thm)],[])).
% 201.25/129.73 tff(69,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_associativity')).
% 201.25/129.73 tff(70,plain,
% 201.25/129.73 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 201.25/129.73 inference(modus_ponens,[status(thm)],[69, 68])).
% 201.25/129.73 tff(71,plain,(
% 201.25/129.73 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 201.25/129.73 inference(skolemize,[status(sab)],[70])).
% 201.25/129.73 tff(72,plain,
% 201.25/129.73 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 201.25/129.73 inference(modus_ponens,[status(thm)],[71, 67])).
% 201.25/129.73 tff(73,plain,
% 201.25/129.73 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X1!2, multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))) = multiplication(multiplication(X1!2, tptp_fun_X1_0(X1!2)), multiplication(X0!3, c(X2!1))))),
% 201.25/129.73 inference(quant_inst,[status(thm)],[])).
% 201.25/129.73 tff(74,plain,
% 201.25/129.73 (multiplication(X1!2, multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))) = multiplication(multiplication(X1!2, tptp_fun_X1_0(X1!2)), multiplication(X0!3, c(X2!1)))),
% 201.25/129.73 inference(unit_resolution,[status(thm)],[73, 72])).
% 201.25/129.73 tff(75,plain,
% 201.25/129.73 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))) = multiplication(multiplication(tptp_fun_X1_0(X1!2), X0!3), c(X2!1)))),
% 201.25/129.73 inference(quant_inst,[status(thm)],[])).
% 201.25/129.73 tff(76,plain,
% 201.25/129.73 (multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))) = multiplication(multiplication(tptp_fun_X1_0(X1!2), X0!3), c(X2!1))),
% 201.25/129.73 inference(unit_resolution,[status(thm)],[75, 72])).
% 201.29/129.73 tff(77,plain,
% 201.29/129.73 (multiplication(multiplication(tptp_fun_X1_0(X1!2), X0!3), c(X2!1)) = multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))),
% 201.29/129.73 inference(symmetry,[status(thm)],[76])).
% 201.29/129.73 tff(78,plain,
% 201.29/129.73 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 201.29/129.73 inference(bind,[status(th)],[])).
% 201.29/129.73 tff(79,plain,
% 201.29/129.73 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 201.29/129.73 inference(quant_intro,[status(thm)],[78])).
% 201.29/129.73 tff(80,plain,
% 201.29/129.73 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 201.29/129.73 inference(rewrite,[status(thm)],[])).
% 201.29/129.73 tff(81,plain,
% 201.29/129.73 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 201.29/129.73 inference(bind,[status(th)],[])).
% 201.29/129.73 tff(82,plain,
% 201.29/129.73 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 201.29/129.73 inference(quant_intro,[status(thm)],[81])).
% 201.29/129.73 tff(83,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_3')).
% 201.29/129.73 tff(84,plain,
% 201.29/129.73 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[83, 82])).
% 201.29/129.73 tff(85,plain,
% 201.29/129.73 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[84, 80])).
% 201.29/129.73 tff(86,plain,(
% 201.29/129.73 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 201.29/129.73 inference(skolemize,[status(sab)],[85])).
% 201.29/129.73 tff(87,plain,
% 201.29/129.73 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[86, 79])).
% 201.29/129.73 tff(88,plain,
% 201.29/129.73 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!2)) | ((c(X1!2) = tptp_fun_X1_0(X1!2)) <=> complement(X1!2, tptp_fun_X1_0(X1!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!2)) | ((c(X1!2) = tptp_fun_X1_0(X1!2)) <=> complement(X1!2, tptp_fun_X1_0(X1!2))))),
% 201.29/129.73 inference(rewrite,[status(thm)],[])).
% 201.29/129.73 tff(89,plain,
% 201.29/129.73 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!2)) | ((c(X1!2) = tptp_fun_X1_0(X1!2)) <=> complement(X1!2, tptp_fun_X1_0(X1!2))))),
% 201.29/129.73 inference(quant_inst,[status(thm)],[])).
% 201.29/129.73 tff(90,plain,
% 201.29/129.73 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!2)) | ((c(X1!2) = tptp_fun_X1_0(X1!2)) <=> complement(X1!2, tptp_fun_X1_0(X1!2)))),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[89, 88])).
% 201.29/129.73 tff(91,plain,
% 201.29/129.73 ((c(X1!2) = tptp_fun_X1_0(X1!2)) <=> complement(X1!2, tptp_fun_X1_0(X1!2))),
% 201.29/129.73 inference(unit_resolution,[status(thm)],[90, 87, 56])).
% 201.29/129.73 tff(92,plain,
% 201.29/129.73 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!2, tptp_fun_X1_0(X1!2)) <=> (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!2, tptp_fun_X1_0(X1!2)) <=> (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))))))),
% 201.29/129.73 inference(rewrite,[status(thm)],[])).
% 201.29/129.73 tff(93,plain,
% 201.29/129.73 ((complement(X1!2, tptp_fun_X1_0(X1!2)) <=> (~((~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))))) <=> (complement(X1!2, tptp_fun_X1_0(X1!2)) <=> (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one)))))),
% 201.29/129.73 inference(rewrite,[status(thm)],[])).
% 201.29/129.73 tff(94,plain,
% 201.29/129.73 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!2, tptp_fun_X1_0(X1!2)) <=> (~((~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!2, tptp_fun_X1_0(X1!2)) <=> (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))))))),
% 201.29/129.73 inference(monotonicity,[status(thm)],[93])).
% 201.29/129.73 tff(95,plain,
% 201.29/129.73 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!2, tptp_fun_X1_0(X1!2)) <=> (~((~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!2, tptp_fun_X1_0(X1!2)) <=> (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))))))),
% 201.29/129.73 inference(transitivity,[status(thm)],[94, 92])).
% 201.29/129.73 tff(96,plain,
% 201.29/129.73 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!2, tptp_fun_X1_0(X1!2)) <=> (~((~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one)))))),
% 201.29/129.73 inference(quant_inst,[status(thm)],[])).
% 201.29/129.73 tff(97,plain,
% 201.29/129.73 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!2, tptp_fun_X1_0(X1!2)) <=> (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one)))))),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[96, 95])).
% 201.29/129.73 tff(98,plain,
% 201.29/129.73 (complement(X1!2, tptp_fun_X1_0(X1!2)) <=> (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))))),
% 201.29/129.73 inference(unit_resolution,[status(thm)],[97, 22])).
% 201.29/129.73 tff(99,plain,
% 201.29/129.73 ((addition(tptp_fun_X1_0(X1!2), X1!2) = addition(X1!2, tptp_fun_X1_0(X1!2))) <=> (addition(X1!2, tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), X1!2))),
% 201.29/129.73 inference(commutativity,[status(thm)],[])).
% 201.29/129.73 tff(100,plain,
% 201.29/129.73 (((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))) | (addition(X1!2, tptp_fun_X1_0(X1!2)) = one)),
% 201.29/129.73 inference(tautology,[status(thm)],[])).
% 201.29/129.73 tff(101,plain,
% 201.29/129.73 (addition(X1!2, tptp_fun_X1_0(X1!2)) = one),
% 201.29/129.73 inference(unit_resolution,[status(thm)],[100, 62])).
% 201.29/129.73 tff(102,plain,
% 201.29/129.73 (one = addition(X1!2, tptp_fun_X1_0(X1!2))),
% 201.29/129.73 inference(symmetry,[status(thm)],[101])).
% 201.29/129.73 tff(103,plain,
% 201.29/129.73 ((addition(tptp_fun_X1_0(X1!2), X1!2) = one) <=> (addition(tptp_fun_X1_0(X1!2), X1!2) = addition(X1!2, tptp_fun_X1_0(X1!2)))),
% 201.29/129.73 inference(monotonicity,[status(thm)],[102])).
% 201.29/129.73 tff(104,plain,
% 201.29/129.73 ((addition(tptp_fun_X1_0(X1!2), X1!2) = one) <=> (addition(X1!2, tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), X1!2))),
% 201.29/129.73 inference(transitivity,[status(thm)],[103, 99])).
% 201.29/129.73 tff(105,plain,
% 201.29/129.73 ((addition(X1!2, tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), X1!2)) <=> (addition(tptp_fun_X1_0(X1!2), X1!2) = one)),
% 201.29/129.73 inference(symmetry,[status(thm)],[104])).
% 201.29/129.73 tff(106,plain,
% 201.29/129.73 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 201.29/129.73 inference(bind,[status(th)],[])).
% 201.29/129.73 tff(107,plain,
% 201.29/129.73 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 201.29/129.73 inference(quant_intro,[status(thm)],[106])).
% 201.29/129.73 tff(108,plain,
% 201.29/129.73 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 201.29/129.73 inference(rewrite,[status(thm)],[])).
% 201.29/129.73 tff(109,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 201.29/129.73 tff(110,plain,
% 201.29/129.73 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[109, 108])).
% 201.29/129.73 tff(111,plain,(
% 201.29/129.73 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 201.29/129.73 inference(skolemize,[status(sab)],[110])).
% 201.29/129.73 tff(112,plain,
% 201.29/129.73 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[111, 107])).
% 201.29/129.73 tff(113,plain,
% 201.29/129.73 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!2, tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), X1!2))),
% 201.29/129.73 inference(quant_inst,[status(thm)],[])).
% 201.29/129.73 tff(114,plain,
% 201.29/129.73 (addition(X1!2, tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), X1!2)),
% 201.29/129.73 inference(unit_resolution,[status(thm)],[113, 112])).
% 201.29/129.73 tff(115,plain,
% 201.29/129.73 (addition(tptp_fun_X1_0(X1!2), X1!2) = one),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[114, 105])).
% 201.29/129.73 tff(116,plain,
% 201.29/129.73 (((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))) | (multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)),
% 201.29/129.73 inference(tautology,[status(thm)],[])).
% 201.29/129.73 tff(117,plain,
% 201.29/129.73 (multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero),
% 201.29/129.73 inference(unit_resolution,[status(thm)],[116, 62])).
% 201.29/129.73 tff(118,plain,
% 201.29/129.73 ((~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one)))) | (~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))),
% 201.29/129.73 inference(tautology,[status(thm)],[])).
% 201.29/129.73 tff(119,plain,
% 201.29/129.73 ((~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one)))) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one))),
% 201.29/129.73 inference(unit_resolution,[status(thm)],[118, 64, 117])).
% 201.29/129.73 tff(120,plain,
% 201.29/129.73 (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one)))),
% 201.29/129.73 inference(unit_resolution,[status(thm)],[119, 115])).
% 201.29/129.73 tff(121,plain,
% 201.29/129.73 ((~(complement(X1!2, tptp_fun_X1_0(X1!2)) <=> (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one)))))) | complement(X1!2, tptp_fun_X1_0(X1!2)) | ((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(tptp_fun_X1_0(X1!2), X1!2) = one)))),
% 201.29/129.73 inference(tautology,[status(thm)],[])).
% 201.29/129.73 tff(122,plain,
% 201.29/129.73 (complement(X1!2, tptp_fun_X1_0(X1!2))),
% 201.29/129.73 inference(unit_resolution,[status(thm)],[121, 120, 98])).
% 201.29/129.73 tff(123,plain,
% 201.29/129.73 ((~((c(X1!2) = tptp_fun_X1_0(X1!2)) <=> complement(X1!2, tptp_fun_X1_0(X1!2)))) | (c(X1!2) = tptp_fun_X1_0(X1!2)) | (~complement(X1!2, tptp_fun_X1_0(X1!2)))),
% 201.29/129.73 inference(tautology,[status(thm)],[])).
% 201.29/129.73 tff(124,plain,
% 201.29/129.73 (c(X1!2) = tptp_fun_X1_0(X1!2)),
% 201.29/129.73 inference(unit_resolution,[status(thm)],[123, 122, 91])).
% 201.29/129.73 tff(125,plain,
% 201.29/129.73 (tptp_fun_X1_0(X1!2) = c(X1!2)),
% 201.29/129.73 inference(symmetry,[status(thm)],[124])).
% 201.29/129.73 tff(126,plain,
% 201.29/129.73 (multiplication(tptp_fun_X1_0(X1!2), X0!3) = multiplication(c(X1!2), X0!3)),
% 201.29/129.73 inference(monotonicity,[status(thm)],[125])).
% 201.29/129.73 tff(127,plain,
% 201.29/129.73 (multiplication(c(X1!2), X0!3) = multiplication(tptp_fun_X1_0(X1!2), X0!3)),
% 201.29/129.73 inference(symmetry,[status(thm)],[126])).
% 201.29/129.73 tff(128,plain,
% 201.29/129.73 (addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3)) = multiplication(c(X1!2), X0!3)),
% 201.29/129.73 inference(or_elim,[status(thm)],[54])).
% 201.29/129.73 tff(129,plain,
% 201.29/129.73 (addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3)) = multiplication(tptp_fun_X1_0(X1!2), X0!3)),
% 201.29/129.73 inference(transitivity,[status(thm)],[128, 127])).
% 201.29/129.73 tff(130,plain,
% 201.29/129.73 (multiplication(addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3)), c(X2!1)) = multiplication(multiplication(tptp_fun_X1_0(X1!2), X0!3), c(X2!1))),
% 201.29/129.73 inference(monotonicity,[status(thm)],[129])).
% 201.29/129.73 tff(131,plain,
% 201.29/129.73 (^[A: $i, B: $i, C: $i] : refl((multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))))),
% 201.29/129.73 inference(bind,[status(th)],[])).
% 201.29/129.73 tff(132,plain,
% 201.29/129.73 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 201.29/129.73 inference(quant_intro,[status(thm)],[131])).
% 201.29/129.73 tff(133,plain,
% 201.29/129.73 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 201.29/129.73 inference(rewrite,[status(thm)],[])).
% 201.29/129.73 tff(134,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','left_distributivity')).
% 201.29/129.73 tff(135,plain,
% 201.29/129.73 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[134, 133])).
% 201.29/129.73 tff(136,plain,(
% 201.29/129.73 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 201.29/129.73 inference(skolemize,[status(sab)],[135])).
% 201.29/129.73 tff(137,plain,
% 201.29/129.73 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[136, 132])).
% 201.29/129.73 tff(138,plain,
% 201.29/129.73 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3)), c(X2!1)) = addition(multiplication(multiplication(X0!3, c(X2!1)), c(X2!1)), multiplication(multiplication(c(X1!2), X0!3), c(X2!1))))),
% 201.29/129.73 inference(quant_inst,[status(thm)],[])).
% 201.29/129.73 tff(139,plain,
% 201.29/129.73 (multiplication(addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3)), c(X2!1)) = addition(multiplication(multiplication(X0!3, c(X2!1)), c(X2!1)), multiplication(multiplication(c(X1!2), X0!3), c(X2!1)))),
% 201.29/129.73 inference(unit_resolution,[status(thm)],[138, 137])).
% 201.29/129.73 tff(140,plain,
% 201.29/129.73 (addition(multiplication(multiplication(X0!3, c(X2!1)), c(X2!1)), multiplication(multiplication(c(X1!2), X0!3), c(X2!1))) = multiplication(addition(multiplication(X0!3, c(X2!1)), multiplication(c(X1!2), X0!3)), c(X2!1))),
% 201.29/129.73 inference(symmetry,[status(thm)],[139])).
% 201.29/129.73 tff(141,plain,
% 201.29/129.73 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!3, multiplication(c(X2!1), c(X2!1))) = multiplication(multiplication(X0!3, c(X2!1)), c(X2!1)))),
% 201.29/129.73 inference(quant_inst,[status(thm)],[])).
% 201.29/129.73 tff(142,plain,
% 201.29/129.73 (multiplication(X0!3, multiplication(c(X2!1), c(X2!1))) = multiplication(multiplication(X0!3, c(X2!1)), c(X2!1))),
% 201.29/129.73 inference(unit_resolution,[status(thm)],[141, 72])).
% 201.29/129.73 tff(143,plain,
% 201.29/129.73 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 201.29/129.73 inference(bind,[status(th)],[])).
% 201.29/129.73 tff(144,plain,
% 201.29/129.73 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 201.29/129.73 inference(quant_intro,[status(thm)],[143])).
% 201.29/129.73 tff(145,plain,
% 201.29/129.73 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 201.29/129.73 inference(rewrite,[status(thm)],[])).
% 201.29/129.73 tff(146,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 201.29/129.73 tff(147,plain,
% 201.29/129.73 (![A: $i] : (addition(A, A) = A)),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[146, 145])).
% 201.29/129.73 tff(148,plain,(
% 201.29/129.73 ![A: $i] : (addition(A, A) = A)),
% 201.29/129.73 inference(skolemize,[status(sab)],[147])).
% 201.29/129.73 tff(149,plain,
% 201.29/129.73 (![A: $i] : (addition(A, A) = A)),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[148, 144])).
% 201.29/129.73 tff(150,plain,
% 201.29/129.73 ((~![A: $i] : (addition(A, A) = A)) | (addition(X2!1, X2!1) = X2!1)),
% 201.29/129.73 inference(quant_inst,[status(thm)],[])).
% 201.29/129.73 tff(151,plain,
% 201.29/129.73 (addition(X2!1, X2!1) = X2!1),
% 201.29/129.73 inference(unit_resolution,[status(thm)],[150, 149])).
% 201.29/129.73 tff(152,plain,
% 201.29/129.73 (c(addition(X2!1, X2!1)) = c(X2!1)),
% 201.29/129.73 inference(monotonicity,[status(thm)],[151])).
% 201.29/129.73 tff(153,plain,
% 201.29/129.73 (test(X2!1)),
% 201.29/129.73 inference(and_elim,[status(thm)],[55])).
% 201.29/129.73 tff(154,plain,
% 201.29/129.73 (^[X0: $i, X1: $i] : refl(((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))))),
% 201.29/129.73 inference(bind,[status(th)],[])).
% 201.29/129.73 tff(155,plain,
% 201.29/129.73 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 201.29/129.73 inference(quant_intro,[status(thm)],[154])).
% 201.29/129.73 tff(156,plain,
% 201.29/129.73 (^[X0: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((test(X0) & test(X1)) <=> (~((~test(X1)) | (~test(X0))))), ((~(test(X0) & test(X1))) <=> (~(~((~test(X1)) | (~test(X0))))))), rewrite((~(~((~test(X1)) | (~test(X0))))) <=> ((~test(X1)) | (~test(X0)))), ((~(test(X0) & test(X1))) <=> ((~test(X1)) | (~test(X0))))), (((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> (((~test(X1)) | (~test(X0))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))))), rewrite((((~test(X1)) | (~test(X0))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))), (((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))))),
% 201.29/129.73 inference(bind,[status(th)],[])).
% 201.29/129.73 tff(157,plain,
% 201.29/129.73 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 201.29/129.73 inference(quant_intro,[status(thm)],[156])).
% 201.29/129.73 tff(158,plain,
% 201.29/129.73 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 201.29/129.73 inference(rewrite,[status(thm)],[])).
% 201.29/129.73 tff(159,plain,
% 201.29/129.73 (^[X0: $i, X1: $i] : rewrite(((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))))),
% 201.29/129.73 inference(bind,[status(th)],[])).
% 201.29/129.73 tff(160,plain,
% 201.29/129.73 (![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 201.29/129.73 inference(quant_intro,[status(thm)],[159])).
% 201.29/129.73 tff(161,axiom,(![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax','test_deMorgan1')).
% 201.29/129.73 tff(162,plain,
% 201.29/129.73 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[161, 160])).
% 201.29/129.73 tff(163,plain,
% 201.29/129.73 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[162, 158])).
% 201.29/129.73 tff(164,plain,(
% 201.29/129.73 ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 201.29/129.73 inference(skolemize,[status(sab)],[163])).
% 201.29/129.73 tff(165,plain,
% 201.29/129.73 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[164, 157])).
% 201.29/129.73 tff(166,plain,
% 201.29/129.73 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[165, 155])).
% 201.29/129.73 tff(167,plain,
% 201.29/129.73 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (c(addition(X2!1, X2!1)) = multiplication(c(X2!1), c(X2!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X2!1)) | (c(addition(X2!1, X2!1)) = multiplication(c(X2!1), c(X2!1))))),
% 201.29/129.73 inference(rewrite,[status(thm)],[])).
% 201.29/129.73 tff(168,plain,
% 201.29/129.73 (((~test(X2!1)) | (c(addition(X2!1, X2!1)) = multiplication(c(X2!1), c(X2!1))) | (~test(X2!1))) <=> ((~test(X2!1)) | (c(addition(X2!1, X2!1)) = multiplication(c(X2!1), c(X2!1))))),
% 201.29/129.73 inference(rewrite,[status(thm)],[])).
% 201.29/129.73 tff(169,plain,
% 201.29/129.73 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (c(addition(X2!1, X2!1)) = multiplication(c(X2!1), c(X2!1))) | (~test(X2!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (c(addition(X2!1, X2!1)) = multiplication(c(X2!1), c(X2!1)))))),
% 201.29/129.73 inference(monotonicity,[status(thm)],[168])).
% 201.29/129.73 tff(170,plain,
% 201.29/129.73 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (c(addition(X2!1, X2!1)) = multiplication(c(X2!1), c(X2!1))) | (~test(X2!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X2!1)) | (c(addition(X2!1, X2!1)) = multiplication(c(X2!1), c(X2!1))))),
% 201.29/129.73 inference(transitivity,[status(thm)],[169, 167])).
% 201.29/129.73 tff(171,plain,
% 201.29/129.73 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (c(addition(X2!1, X2!1)) = multiplication(c(X2!1), c(X2!1))) | (~test(X2!1)))),
% 201.29/129.73 inference(quant_inst,[status(thm)],[])).
% 201.29/129.73 tff(172,plain,
% 201.29/129.73 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X2!1)) | (c(addition(X2!1, X2!1)) = multiplication(c(X2!1), c(X2!1)))),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[171, 170])).
% 201.29/129.73 tff(173,plain,
% 201.29/129.73 (c(addition(X2!1, X2!1)) = multiplication(c(X2!1), c(X2!1))),
% 201.29/129.73 inference(unit_resolution,[status(thm)],[172, 166, 153])).
% 201.29/129.73 tff(174,plain,
% 201.29/129.73 (multiplication(c(X2!1), c(X2!1)) = c(addition(X2!1, X2!1))),
% 201.29/129.73 inference(symmetry,[status(thm)],[173])).
% 201.29/129.73 tff(175,plain,
% 201.29/129.73 (multiplication(c(X2!1), c(X2!1)) = c(X2!1)),
% 201.29/129.73 inference(transitivity,[status(thm)],[174, 152])).
% 201.29/129.73 tff(176,plain,
% 201.29/129.73 (multiplication(X0!3, multiplication(c(X2!1), c(X2!1))) = multiplication(X0!3, c(X2!1))),
% 201.29/129.73 inference(monotonicity,[status(thm)],[175])).
% 201.29/129.73 tff(177,plain,
% 201.29/129.73 (multiplication(X0!3, c(X2!1)) = multiplication(X0!3, multiplication(c(X2!1), c(X2!1)))),
% 201.29/129.73 inference(symmetry,[status(thm)],[176])).
% 201.29/129.73 tff(178,plain,
% 201.29/129.73 (multiplication(X0!3, c(X2!1)) = multiplication(multiplication(X0!3, c(X2!1)), c(X2!1))),
% 201.29/129.73 inference(transitivity,[status(thm)],[177, 142])).
% 201.29/129.73 tff(179,plain,
% 201.29/129.73 (addition(multiplication(X0!3, c(X2!1)), multiplication(multiplication(c(X1!2), X0!3), c(X2!1))) = addition(multiplication(multiplication(X0!3, c(X2!1)), c(X2!1)), multiplication(multiplication(c(X1!2), X0!3), c(X2!1)))),
% 201.29/129.73 inference(monotonicity,[status(thm)],[178])).
% 201.29/129.73 tff(180,plain,
% 201.29/129.73 (multiplication(multiplication(c(X1!2), X0!3), c(X2!1)) = multiplication(multiplication(tptp_fun_X1_0(X1!2), X0!3), c(X2!1))),
% 201.29/129.73 inference(monotonicity,[status(thm)],[127])).
% 201.29/129.73 tff(181,plain,
% 201.29/129.73 (multiplication(multiplication(tptp_fun_X1_0(X1!2), X0!3), c(X2!1)) = multiplication(multiplication(c(X1!2), X0!3), c(X2!1))),
% 201.29/129.73 inference(symmetry,[status(thm)],[180])).
% 201.29/129.73 tff(182,plain,
% 201.29/129.73 (multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))) = multiplication(multiplication(c(X1!2), X0!3), c(X2!1))),
% 201.29/129.73 inference(transitivity,[status(thm)],[76, 181])).
% 201.29/129.73 tff(183,plain,
% 201.29/129.73 (addition(multiplication(X0!3, c(X2!1)), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))) = addition(multiplication(X0!3, c(X2!1)), multiplication(multiplication(c(X1!2), X0!3), c(X2!1)))),
% 201.29/129.73 inference(monotonicity,[status(thm)],[182])).
% 201.29/129.73 tff(184,plain,
% 201.29/129.73 ((~![A: $i] : (addition(A, A) = A)) | (addition(multiplication(X0!3, c(X2!1)), multiplication(X0!3, c(X2!1))) = multiplication(X0!3, c(X2!1)))),
% 201.29/129.73 inference(quant_inst,[status(thm)],[])).
% 201.29/129.73 tff(185,plain,
% 201.29/129.73 (addition(multiplication(X0!3, c(X2!1)), multiplication(X0!3, c(X2!1))) = multiplication(X0!3, c(X2!1))),
% 201.29/129.73 inference(unit_resolution,[status(thm)],[184, 149])).
% 201.29/129.73 tff(186,plain,
% 201.29/129.73 (multiplication(X0!3, c(X2!1)) = addition(multiplication(X0!3, c(X2!1)), multiplication(X0!3, c(X2!1)))),
% 201.29/129.73 inference(symmetry,[status(thm)],[185])).
% 201.29/129.73 tff(187,plain,
% 201.29/129.73 (multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))) = multiplication(tptp_fun_X1_0(X1!2), addition(multiplication(X0!3, c(X2!1)), multiplication(X0!3, c(X2!1))))),
% 201.29/129.73 inference(monotonicity,[status(thm)],[186])).
% 201.29/129.73 tff(188,plain,
% 201.29/129.73 (multiplication(tptp_fun_X1_0(X1!2), addition(multiplication(X0!3, c(X2!1)), multiplication(X0!3, c(X2!1)))) = multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))),
% 201.29/129.73 inference(symmetry,[status(thm)],[187])).
% 201.29/129.73 tff(189,plain,
% 201.29/129.73 (^[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))))),
% 201.29/129.73 inference(bind,[status(th)],[])).
% 201.29/129.73 tff(190,plain,
% 201.29/129.73 (![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)))),
% 201.29/129.73 inference(quant_intro,[status(thm)],[189])).
% 201.29/129.73 tff(191,plain,
% 201.29/129.73 (![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)))),
% 201.29/129.73 inference(rewrite,[status(thm)],[])).
% 201.29/129.73 tff(192,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')).
% 201.29/129.73 tff(193,plain,
% 201.29/129.73 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[192, 191])).
% 201.29/129.73 tff(194,plain,(
% 201.29/129.73 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 201.29/129.73 inference(skolemize,[status(sab)],[193])).
% 201.29/129.73 tff(195,plain,
% 201.29/129.73 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 201.29/129.73 inference(modus_ponens,[status(thm)],[194, 190])).
% 201.29/129.73 tff(196,plain,
% 201.29/129.73 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(tptp_fun_X1_0(X1!2), addition(multiplication(X0!3, c(X2!1)), multiplication(X0!3, c(X2!1)))) = addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))))),
% 201.29/129.73 inference(quant_inst,[status(thm)],[])).
% 201.29/129.73 tff(197,plain,
% 201.29/129.73 (multiplication(tptp_fun_X1_0(X1!2), addition(multiplication(X0!3, c(X2!1)), multiplication(X0!3, c(X2!1)))) = addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))))),
% 201.29/129.74 inference(unit_resolution,[status(thm)],[196, 195])).
% 201.29/129.74 tff(198,plain,
% 201.29/129.74 (addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))) = multiplication(tptp_fun_X1_0(X1!2), addition(multiplication(X0!3, c(X2!1)), multiplication(X0!3, c(X2!1))))),
% 201.29/129.74 inference(symmetry,[status(thm)],[197])).
% 201.29/129.74 tff(199,plain,
% 201.29/129.74 (addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))) = multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))),
% 201.29/129.74 inference(transitivity,[status(thm)],[198, 188])).
% 201.29/129.74 tff(200,plain,
% 201.29/129.74 (addition(multiplication(X0!3, c(X2!1)), addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))))) = addition(multiplication(X0!3, c(X2!1)), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))))),
% 201.29/129.74 inference(monotonicity,[status(thm)],[199])).
% 201.29/129.74 tff(201,plain,
% 201.29/129.74 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!3, c(X2!1)), addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))))) = addition(addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))), multiplication(X0!3, c(X2!1))))),
% 201.29/129.74 inference(quant_inst,[status(thm)],[])).
% 201.29/129.74 tff(202,plain,
% 201.29/129.74 (addition(multiplication(X0!3, c(X2!1)), addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))))) = addition(addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))), multiplication(X0!3, c(X2!1)))),
% 201.29/129.74 inference(unit_resolution,[status(thm)],[201, 112])).
% 201.29/129.74 tff(203,plain,
% 201.29/129.74 (addition(addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))), multiplication(X0!3, c(X2!1))) = addition(multiplication(X0!3, c(X2!1)), addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))))),
% 201.29/129.74 inference(symmetry,[status(thm)],[202])).
% 201.29/129.74 tff(204,plain,
% 201.29/129.74 (addition(addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))), multiplication(X0!3, c(X2!1))) = multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))),
% 201.29/129.74 inference(transitivity,[status(thm)],[203, 200, 183, 179, 140, 130, 77])).
% 201.29/129.74 tff(205,plain,
% 201.29/129.74 (multiplication(X1!2, addition(addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))), multiplication(X0!3, c(X2!1)))) = multiplication(X1!2, multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))))),
% 201.29/129.74 inference(monotonicity,[status(thm)],[204])).
% 201.29/129.74 tff(206,plain,
% 201.29/129.74 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X1!2, addition(addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))), multiplication(X0!3, c(X2!1)))) = addition(multiplication(X1!2, addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))))), multiplication(X1!2, multiplication(X0!3, c(X2!1)))))),
% 201.29/129.74 inference(quant_inst,[status(thm)],[])).
% 201.29/129.74 tff(207,plain,
% 201.29/129.74 (multiplication(X1!2, addition(addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))), multiplication(X0!3, c(X2!1)))) = addition(multiplication(X1!2, addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))))), multiplication(X1!2, multiplication(X0!3, c(X2!1))))),
% 201.29/129.74 inference(unit_resolution,[status(thm)],[206, 195])).
% 201.29/129.74 tff(208,plain,
% 201.29/129.74 (addition(multiplication(X1!2, addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))))), multiplication(X1!2, multiplication(X0!3, c(X2!1)))) = multiplication(X1!2, addition(addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))), multiplication(X0!3, c(X2!1))))),
% 201.29/129.74 inference(symmetry,[status(thm)],[207])).
% 201.29/129.74 tff(209,plain,
% 201.29/129.74 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X1!2, multiplication(X0!3, c(X2!1))) = multiplication(multiplication(X1!2, X0!3), c(X2!1)))),
% 201.29/129.74 inference(quant_inst,[status(thm)],[])).
% 201.29/129.74 tff(210,plain,
% 201.29/129.74 (multiplication(X1!2, multiplication(X0!3, c(X2!1))) = multiplication(multiplication(X1!2, X0!3), c(X2!1))),
% 201.29/129.74 inference(unit_resolution,[status(thm)],[209, 72])).
% 201.29/129.74 tff(211,plain,
% 201.29/129.74 (multiplication(multiplication(X1!2, X0!3), c(X2!1)) = multiplication(X1!2, multiplication(X0!3, c(X2!1)))),
% 201.29/129.74 inference(symmetry,[status(thm)],[210])).
% 201.29/129.74 tff(212,plain,
% 201.29/129.74 (multiplication(X1!2, addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))))) = multiplication(X1!2, multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))))),
% 201.29/129.74 inference(monotonicity,[status(thm)],[199])).
% 201.29/129.74 tff(213,plain,
% 201.29/129.74 (multiplication(X1!2, multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))) = multiplication(X1!2, addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))))),
% 201.29/129.74 inference(symmetry,[status(thm)],[212])).
% 201.29/129.74 tff(214,plain,
% 201.29/129.74 (multiplication(multiplication(X1!2, tptp_fun_X1_0(X1!2)), multiplication(X0!3, c(X2!1))) = multiplication(X1!2, multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))))),
% 201.29/129.74 inference(symmetry,[status(thm)],[74])).
% 201.29/129.74 tff(215,plain,
% 201.29/129.74 (multiplication(zero, multiplication(X0!3, c(X2!1))) = multiplication(multiplication(X1!2, tptp_fun_X1_0(X1!2)), multiplication(X0!3, c(X2!1)))),
% 201.29/129.74 inference(symmetry,[status(thm)],[65])).
% 201.29/129.74 tff(216,plain,
% 201.29/129.74 (zero = multiplication(zero, multiplication(X0!3, c(X2!1)))),
% 201.29/129.74 inference(symmetry,[status(thm)],[9])).
% 201.29/129.74 tff(217,plain,
% 201.29/129.74 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, X0!3) = zero)),
% 201.29/129.74 inference(quant_inst,[status(thm)],[])).
% 201.29/129.74 tff(218,plain,
% 201.29/129.74 (multiplication(zero, X0!3) = zero),
% 201.29/129.74 inference(unit_resolution,[status(thm)],[217, 7])).
% 201.29/129.74 tff(219,plain,
% 201.29/129.74 (multiplication(zero, X0!3) = multiplication(X1!2, addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1)))))),
% 201.29/129.74 inference(transitivity,[status(thm)],[218, 216, 215, 214, 213])).
% 201.29/129.74 tff(220,plain,
% 201.29/129.74 (addition(multiplication(zero, X0!3), multiplication(multiplication(X1!2, X0!3), c(X2!1))) = addition(multiplication(X1!2, addition(multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))), multiplication(tptp_fun_X1_0(X1!2), multiplication(X0!3, c(X2!1))))), multiplication(X1!2, multiplication(X0!3, c(X2!1))))),
% 201.29/129.74 inference(monotonicity,[status(thm)],[219, 211])).
% 201.29/129.74 tff(221,plain,
% 201.29/129.74 (zero = multiplication(zero, X0!3)),
% 201.29/129.74 inference(symmetry,[status(thm)],[218])).
% 201.29/129.74 tff(222,plain,
% 201.29/129.74 (multiplication(zero, multiplication(X0!3, c(X2!1))) = multiplication(zero, X0!3)),
% 201.29/129.74 inference(transitivity,[status(thm)],[9, 221])).
% 201.29/129.74 tff(223,plain,
% 201.29/129.74 (addition(multiplication(zero, multiplication(X0!3, c(X2!1))), multiplication(X1!2, multiplication(X0!3, c(X2!1)))) = addition(multiplication(zero, X0!3), multiplication(multiplication(X1!2, X0!3), c(X2!1)))),
% 201.29/129.74 inference(monotonicity,[status(thm)],[222, 210])).
% 201.29/129.74 tff(224,plain,
% 201.29/129.74 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(zero, X1!2), multiplication(X0!3, c(X2!1))) = addition(multiplication(zero, multiplication(X0!3, c(X2!1))), multiplication(X1!2, multiplication(X0!3, c(X2!1)))))),
% 201.29/129.74 inference(quant_inst,[status(thm)],[])).
% 201.29/129.74 tff(225,plain,
% 201.29/129.74 (multiplication(addition(zero, X1!2), multiplication(X0!3, c(X2!1))) = addition(multiplication(zero, multiplication(X0!3, c(X2!1))), multiplication(X1!2, multiplication(X0!3, c(X2!1))))),
% 201.29/129.74 inference(unit_resolution,[status(thm)],[224, 137])).
% 201.29/129.74 tff(226,plain,
% 201.29/129.74 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!2, zero) = addition(zero, X1!2))),
% 201.29/129.74 inference(quant_inst,[status(thm)],[])).
% 201.29/129.74 tff(227,plain,
% 201.29/129.74 (addition(X1!2, zero) = addition(zero, X1!2)),
% 201.29/129.74 inference(unit_resolution,[status(thm)],[226, 112])).
% 201.29/129.74 tff(228,plain,
% 201.29/129.74 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 201.29/129.74 inference(bind,[status(th)],[])).
% 201.29/129.74 tff(229,plain,
% 201.29/129.74 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 201.29/129.74 inference(quant_intro,[status(thm)],[228])).
% 201.29/129.74 tff(230,plain,
% 201.29/129.74 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 201.29/129.74 inference(rewrite,[status(thm)],[])).
% 201.29/129.74 tff(231,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 201.29/129.74 tff(232,plain,
% 201.29/129.74 (![A: $i] : (addition(A, zero) = A)),
% 201.29/129.74 inference(modus_ponens,[status(thm)],[231, 230])).
% 201.29/129.74 tff(233,plain,(
% 201.29/129.74 ![A: $i] : (addition(A, zero) = A)),
% 201.29/129.74 inference(skolemize,[status(sab)],[232])).
% 201.29/129.74 tff(234,plain,
% 201.29/129.74 (![A: $i] : (addition(A, zero) = A)),
% 201.29/129.74 inference(modus_ponens,[status(thm)],[233, 229])).
% 201.29/129.74 tff(235,plain,
% 201.29/129.74 ((~![A: $i] : (addition(A, zero) = A)) | (addition(X1!2, zero) = X1!2)),
% 201.29/129.74 inference(quant_inst,[status(thm)],[])).
% 201.29/129.74 tff(236,plain,
% 201.29/129.74 (addition(X1!2, zero) = X1!2),
% 201.29/129.74 inference(unit_resolution,[status(thm)],[235, 234])).
% 201.29/129.74 tff(237,plain,
% 201.29/129.74 (X1!2 = addition(X1!2, zero)),
% 201.29/129.74 inference(symmetry,[status(thm)],[236])).
% 201.29/129.74 tff(238,plain,
% 201.29/129.74 (X1!2 = addition(zero, X1!2)),
% 201.29/129.74 inference(transitivity,[status(thm)],[237, 227])).
% 201.29/129.74 tff(239,plain,
% 201.29/129.74 (multiplication(X1!2, multiplication(X0!3, c(X2!1))) = multiplication(addition(zero, X1!2), multiplication(X0!3, c(X2!1)))),
% 201.29/129.74 inference(monotonicity,[status(thm)],[238])).
% 201.29/129.74 tff(240,plain,
% 201.29/129.74 (multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero),
% 201.29/129.74 inference(transitivity,[status(thm)],[211, 239, 225, 223, 220, 208, 205, 74, 65, 9])).
% 201.29/129.74 tff(241,plain,
% 201.29/129.74 (~(multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero)),
% 201.29/129.74 inference(or_elim,[status(thm)],[54])).
% 201.29/129.74 tff(242,plain,
% 201.29/129.74 ($false),
% 201.29/129.74 inference(unit_resolution,[status(thm)],[241, 240])).
% 201.29/129.74 % SZS output end Proof
%------------------------------------------------------------------------------