TSTP Solution File: KLE025+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE025+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:23:54 EDT 2022
% Result : Theorem 0.52s 0.56s
% Output : Proof 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : KLE025+1 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 07:37:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.52/0.56 % SZS status Theorem
% 0.52/0.56 % SZS output start Proof
% 0.52/0.56 tff(multiplication_type, type, (
% 0.52/0.56 multiplication: ( $i * $i ) > $i)).
% 0.52/0.56 tff(tptp_fun_X2_1_type, type, (
% 0.52/0.56 tptp_fun_X2_1: $i)).
% 0.52/0.56 tff(tptp_fun_X0_3_type, type, (
% 0.52/0.56 tptp_fun_X0_3: $i)).
% 0.52/0.56 tff(tptp_fun_X1_2_type, type, (
% 0.52/0.56 tptp_fun_X1_2: $i)).
% 0.52/0.56 tff(addition_type, type, (
% 0.52/0.56 addition: ( $i * $i ) > $i)).
% 0.52/0.56 tff(c_type, type, (
% 0.52/0.56 c: $i > $i)).
% 0.52/0.56 tff(tptp_fun_X1_0_type, type, (
% 0.52/0.56 tptp_fun_X1_0: $i > $i)).
% 0.52/0.56 tff(zero_type, type, (
% 0.52/0.56 zero: $i)).
% 0.52/0.56 tff(complement_type, type, (
% 0.52/0.56 complement: ( $i * $i ) > $o)).
% 0.52/0.56 tff(test_type, type, (
% 0.52/0.56 test: $i > $o)).
% 0.52/0.56 tff(one_type, type, (
% 0.52/0.56 one: $i)).
% 0.52/0.56 tff(1,assumption,((~((~test(tptp_fun_X1_0(X2!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1)))) | (~(test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))))), introduced(assumption)).
% 0.52/0.56 tff(2,plain,
% 0.52/0.56 (^[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)))))))),
% 0.52/0.56 inference(bind,[status(th)],[])).
% 0.52/0.56 tff(3,plain,
% 0.52/0.56 (![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))))))),
% 0.52/0.56 inference(quant_intro,[status(thm)],[2])).
% 0.52/0.56 tff(4,plain,
% 0.52/0.56 (^[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)))))))),
% 0.52/0.56 inference(bind,[status(th)],[])).
% 0.52/0.56 tff(5,plain,
% 0.52/0.56 (![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))))))),
% 0.52/0.56 inference(quant_intro,[status(thm)],[4])).
% 0.52/0.56 tff(6,plain,
% 0.52/0.56 (![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))))))),
% 0.52/0.56 inference(transitivity,[status(thm)],[5, 3])).
% 0.52/0.56 tff(7,plain,
% 0.52/0.56 (^[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))))))))),
% 0.52/0.56 inference(bind,[status(th)],[])).
% 0.52/0.56 tff(8,plain,
% 0.52/0.56 (![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))))))),
% 0.52/0.56 inference(quant_intro,[status(thm)],[7])).
% 0.52/0.56 tff(9,plain,
% 0.52/0.56 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 0.52/0.56 inference(rewrite,[status(thm)],[])).
% 0.52/0.56 tff(10,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_1')).
% 0.52/0.56 tff(11,plain,
% 0.52/0.56 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 0.52/0.56 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.52/0.56 tff(12,plain,(
% 0.52/0.56 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 0.52/0.56 inference(skolemize,[status(sab)],[11])).
% 0.52/0.56 tff(13,plain,
% 0.52/0.56 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.52/0.56 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.52/0.56 tff(14,plain,
% 0.52/0.56 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.52/0.56 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.52/0.56 tff(15,plain,
% 0.52/0.56 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(tptp_fun_X1_0(X2!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1)))) | (~(test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))))))),
% 0.52/0.56 inference(quant_inst,[status(thm)],[])).
% 0.52/0.56 tff(16,plain,
% 0.52/0.56 ($false),
% 0.52/0.56 inference(unit_resolution,[status(thm)],[15, 14, 1])).
% 0.52/0.56 tff(17,plain,(~((~((~test(tptp_fun_X1_0(X2!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1)))) | (~(test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1))))))), inference(lemma,lemma(discharge,[]))).
% 0.52/0.56 tff(18,plain,
% 0.52/0.56 (((~((~test(tptp_fun_X1_0(X2!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1)))) | (~(test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))))) | (test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1))))),
% 0.52/0.56 inference(tautology,[status(thm)],[])).
% 0.52/0.56 tff(19,plain,
% 0.52/0.56 (test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))),
% 0.52/0.56 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.52/0.56 tff(20,assumption,(![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))), introduced(assumption)).
% 0.52/0.56 tff(21,plain,
% 0.52/0.56 (^[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))))))),
% 0.52/0.56 inference(bind,[status(th)],[])).
% 0.52/0.56 tff(22,plain,
% 0.52/0.56 (![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)))))),
% 0.52/0.56 inference(quant_intro,[status(thm)],[21])).
% 0.52/0.56 tff(23,plain,
% 0.52/0.56 (^[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))))))),
% 0.52/0.56 inference(bind,[status(th)],[])).
% 0.52/0.56 tff(24,plain,
% 0.52/0.56 (![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)))))),
% 0.52/0.56 inference(quant_intro,[status(thm)],[23])).
% 0.52/0.56 tff(25,plain,
% 0.52/0.56 (![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)))),
% 0.52/0.56 inference(rewrite,[status(thm)],[])).
% 0.52/0.56 tff(26,plain,
% 0.52/0.56 (^[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))))),
% 0.52/0.56 inference(bind,[status(th)],[])).
% 0.52/0.56 tff(27,plain,
% 0.52/0.56 (![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)))),
% 0.52/0.56 inference(quant_intro,[status(thm)],[26])).
% 0.52/0.56 tff(28,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')).
% 0.52/0.56 tff(29,plain,
% 0.52/0.56 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.52/0.56 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.52/0.56 tff(30,plain,
% 0.52/0.56 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.52/0.56 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.52/0.56 tff(31,plain,(
% 0.52/0.56 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.52/0.56 inference(skolemize,[status(sab)],[30])).
% 0.52/0.56 tff(32,plain,
% 0.52/0.56 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 0.52/0.56 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.52/0.56 tff(33,plain,
% 0.52/0.56 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 0.52/0.56 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.52/0.56 tff(34,plain,
% 0.52/0.56 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X2!1, tptp_fun_X1_0(X2!1)) <=> (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X2!1, tptp_fun_X1_0(X2!1)) <=> (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))))))),
% 0.52/0.56 inference(rewrite,[status(thm)],[])).
% 0.52/0.56 tff(35,plain,
% 0.52/0.56 ((complement(X2!1, tptp_fun_X1_0(X2!1)) <=> (~((~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))))) <=> (complement(X2!1, tptp_fun_X1_0(X2!1)) <=> (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one)))))),
% 0.52/0.56 inference(rewrite,[status(thm)],[])).
% 0.52/0.56 tff(36,plain,
% 0.52/0.56 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X2!1, tptp_fun_X1_0(X2!1)) <=> (~((~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X2!1, tptp_fun_X1_0(X2!1)) <=> (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))))))),
% 0.52/0.56 inference(monotonicity,[status(thm)],[35])).
% 0.52/0.56 tff(37,plain,
% 0.52/0.56 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X2!1, tptp_fun_X1_0(X2!1)) <=> (~((~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X2!1, tptp_fun_X1_0(X2!1)) <=> (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))))))),
% 0.52/0.57 inference(transitivity,[status(thm)],[36, 34])).
% 0.52/0.57 tff(38,plain,
% 0.52/0.57 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X2!1, tptp_fun_X1_0(X2!1)) <=> (~((~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one)))))),
% 0.52/0.57 inference(quant_inst,[status(thm)],[])).
% 0.52/0.57 tff(39,plain,
% 0.52/0.57 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X2!1, tptp_fun_X1_0(X2!1)) <=> (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one)))))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.52/0.57 tff(40,plain,
% 0.52/0.57 (complement(X2!1, tptp_fun_X1_0(X2!1)) <=> (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[39, 33])).
% 0.52/0.57 tff(41,plain,
% 0.52/0.57 ((addition(tptp_fun_X1_0(X2!1), X2!1) = addition(X2!1, tptp_fun_X1_0(X2!1))) <=> (addition(X2!1, tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), X2!1))),
% 0.52/0.57 inference(commutativity,[status(thm)],[])).
% 0.52/0.57 tff(42,plain,
% 0.52/0.57 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(tptp_fun_X1_0(X2!1), X2!1) <=> (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one)))))),
% 0.52/0.57 inference(quant_inst,[status(thm)],[])).
% 0.52/0.57 tff(43,plain,
% 0.52/0.57 (complement(tptp_fun_X1_0(X2!1), X2!1) <=> (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[42, 33])).
% 0.52/0.57 tff(44,plain,
% 0.52/0.57 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | (~(test(X2!1) | ![X1: $i] : (~complement(X1, X2!1))))))),
% 0.52/0.57 inference(quant_inst,[status(thm)],[])).
% 0.52/0.57 tff(45,plain,
% 0.52/0.57 (~((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | (~(test(X2!1) | ![X1: $i] : (~complement(X1, X2!1)))))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[44, 14])).
% 0.52/0.57 tff(46,plain,
% 0.52/0.57 (((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | (~(test(X2!1) | ![X1: $i] : (~complement(X1, X2!1))))) | ((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))),
% 0.52/0.57 inference(tautology,[status(thm)],[])).
% 0.52/0.57 tff(47,plain,
% 0.52/0.57 ((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1)),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.52/0.57 tff(48,plain,
% 0.52/0.57 ((~((multiplication(X1!2, X0!3) = multiplication(multiplication(X1!2, X0!3), X2!1)) | (~(multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero)) | (~(test(X1!2) & test(X2!1))))) <=> (~((multiplication(X1!2, X0!3) = multiplication(multiplication(X1!2, X0!3), X2!1)) | (~(multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero)) | (~(test(X1!2) & test(X2!1)))))),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(49,plain,
% 0.52/0.57 ((~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)) | (~(test(X1) & test(X2))))) <=> (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)) | (~(test(X1) & test(X2)))))),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(50,plain,
% 0.52/0.57 ((~![X0: $i, X1: $i, X2: $i] : ((test(X1) & test(X2)) => ((multiplication(multiplication(X1, X0), c(X2)) = zero) => (multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2))))) <=> (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)) | (~(test(X1) & test(X2)))))),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(51,axiom,(~![X0: $i, X1: $i, X2: $i] : ((test(X1) & test(X2)) => ((multiplication(multiplication(X1, X0), c(X2)) = zero) => (multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.52/0.57 tff(52,plain,
% 0.52/0.57 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)) | (~(test(X1) & test(X2))))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.52/0.57 tff(53,plain,
% 0.52/0.57 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)) | (~(test(X1) & test(X2))))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[52, 49])).
% 0.52/0.57 tff(54,plain,
% 0.52/0.57 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)) | (~(test(X1) & test(X2))))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.52/0.57 tff(55,plain,
% 0.52/0.57 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)) | (~(test(X1) & test(X2))))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[54, 49])).
% 0.52/0.57 tff(56,plain,
% 0.52/0.57 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)) | (~(test(X1) & test(X2))))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[55, 49])).
% 0.52/0.57 tff(57,plain,
% 0.52/0.57 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)) | (~(test(X1) & test(X2))))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.52/0.57 tff(58,plain,
% 0.52/0.57 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)) | (~(test(X1) & test(X2))))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[57, 49])).
% 0.52/0.57 tff(59,plain,(
% 0.52/0.57 ~((multiplication(X1!2, X0!3) = multiplication(multiplication(X1!2, X0!3), X2!1)) | (~(multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero)) | (~(test(X1!2) & test(X2!1))))),
% 0.52/0.57 inference(skolemize,[status(sab)],[58])).
% 0.52/0.57 tff(60,plain,
% 0.52/0.57 (~((multiplication(X1!2, X0!3) = multiplication(multiplication(X1!2, X0!3), X2!1)) | (~(multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero)) | (~(test(X1!2) & test(X2!1))))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[59, 48])).
% 0.52/0.57 tff(61,plain,
% 0.52/0.57 (test(X1!2) & test(X2!1)),
% 0.52/0.57 inference(or_elim,[status(thm)],[60])).
% 0.52/0.57 tff(62,plain,
% 0.52/0.57 (test(X2!1)),
% 0.52/0.57 inference(and_elim,[status(thm)],[61])).
% 0.52/0.57 tff(63,plain,
% 0.52/0.57 ((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | (~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1)),
% 0.52/0.57 inference(tautology,[status(thm)],[])).
% 0.52/0.57 tff(64,plain,
% 0.52/0.57 ((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | complement(tptp_fun_X1_0(X2!1), X2!1)),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.52/0.57 tff(65,plain,
% 0.52/0.57 (complement(tptp_fun_X1_0(X2!1), X2!1)),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[64, 47])).
% 0.52/0.57 tff(66,plain,
% 0.52/0.57 ((~(complement(tptp_fun_X1_0(X2!1), X2!1) <=> (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one)))))) | (~complement(tptp_fun_X1_0(X2!1), X2!1)) | (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))))),
% 0.52/0.57 inference(tautology,[status(thm)],[])).
% 0.52/0.57 tff(67,plain,
% 0.52/0.57 ((~(complement(tptp_fun_X1_0(X2!1), X2!1) <=> (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one)))))) | (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.52/0.57 tff(68,plain,
% 0.52/0.57 (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one)))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[67, 43])).
% 0.52/0.57 tff(69,plain,
% 0.52/0.57 (((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))) | (addition(X2!1, tptp_fun_X1_0(X2!1)) = one)),
% 0.52/0.57 inference(tautology,[status(thm)],[])).
% 0.52/0.57 tff(70,plain,
% 0.52/0.57 (addition(X2!1, tptp_fun_X1_0(X2!1)) = one),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.52/0.57 tff(71,plain,
% 0.52/0.57 (one = addition(X2!1, tptp_fun_X1_0(X2!1))),
% 0.52/0.57 inference(symmetry,[status(thm)],[70])).
% 0.52/0.57 tff(72,plain,
% 0.52/0.57 ((addition(tptp_fun_X1_0(X2!1), X2!1) = one) <=> (addition(tptp_fun_X1_0(X2!1), X2!1) = addition(X2!1, tptp_fun_X1_0(X2!1)))),
% 0.52/0.57 inference(monotonicity,[status(thm)],[71])).
% 0.52/0.57 tff(73,plain,
% 0.52/0.57 ((addition(tptp_fun_X1_0(X2!1), X2!1) = one) <=> (addition(X2!1, tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), X2!1))),
% 0.52/0.57 inference(transitivity,[status(thm)],[72, 41])).
% 0.52/0.57 tff(74,plain,
% 0.52/0.57 ((addition(X2!1, tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), X2!1)) <=> (addition(tptp_fun_X1_0(X2!1), X2!1) = one)),
% 0.52/0.57 inference(symmetry,[status(thm)],[73])).
% 0.52/0.57 tff(75,plain,
% 0.52/0.57 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.52/0.57 inference(bind,[status(th)],[])).
% 0.52/0.57 tff(76,plain,
% 0.52/0.57 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.52/0.57 inference(quant_intro,[status(thm)],[75])).
% 0.52/0.57 tff(77,plain,
% 0.52/0.57 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(78,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 0.52/0.57 tff(79,plain,
% 0.52/0.57 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.52/0.57 tff(80,plain,(
% 0.52/0.57 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.52/0.57 inference(skolemize,[status(sab)],[79])).
% 0.52/0.57 tff(81,plain,
% 0.52/0.57 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.52/0.57 tff(82,plain,
% 0.52/0.57 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X2!1, tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), X2!1))),
% 0.52/0.57 inference(quant_inst,[status(thm)],[])).
% 0.52/0.57 tff(83,plain,
% 0.52/0.57 (addition(X2!1, tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), X2!1)),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.52/0.57 tff(84,plain,
% 0.52/0.57 (addition(tptp_fun_X1_0(X2!1), X2!1) = one),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[83, 74])).
% 0.52/0.57 tff(85,plain,
% 0.52/0.57 (((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))) | (multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)),
% 0.52/0.57 inference(tautology,[status(thm)],[])).
% 0.52/0.57 tff(86,plain,
% 0.52/0.57 (multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[85, 68])).
% 0.52/0.57 tff(87,plain,
% 0.52/0.57 (((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))) | (multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)),
% 0.52/0.57 inference(tautology,[status(thm)],[])).
% 0.52/0.57 tff(88,plain,
% 0.52/0.57 (multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[87, 68])).
% 0.52/0.57 tff(89,plain,
% 0.52/0.57 ((~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one)))) | (~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))),
% 0.52/0.57 inference(tautology,[status(thm)],[])).
% 0.52/0.57 tff(90,plain,
% 0.52/0.57 ((~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one)))) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[89, 88, 86])).
% 0.52/0.57 tff(91,plain,
% 0.52/0.57 (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one)))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[90, 84])).
% 0.52/0.57 tff(92,plain,
% 0.52/0.57 ((~(complement(X2!1, tptp_fun_X1_0(X2!1)) <=> (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one)))))) | complement(X2!1, tptp_fun_X1_0(X2!1)) | ((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(tptp_fun_X1_0(X2!1), X2!1) = one)))),
% 0.52/0.57 inference(tautology,[status(thm)],[])).
% 0.52/0.57 tff(93,plain,
% 0.52/0.57 (complement(X2!1, tptp_fun_X1_0(X2!1))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[92, 91, 40])).
% 0.52/0.57 tff(94,plain,
% 0.52/0.57 ((~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))) | (~complement(X2!1, tptp_fun_X1_0(X2!1)))),
% 0.52/0.57 inference(quant_inst,[status(thm)],[])).
% 0.52/0.57 tff(95,plain,
% 0.52/0.57 ($false),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[94, 93, 20])).
% 0.52/0.57 tff(96,plain,(~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))), inference(lemma,lemma(discharge,[]))).
% 0.52/0.57 tff(97,plain,
% 0.52/0.57 ((~(test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1))))) | test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))),
% 0.52/0.57 inference(tautology,[status(thm)],[])).
% 0.52/0.57 tff(98,plain,
% 0.52/0.57 ((~(test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1))))) | test(tptp_fun_X1_0(X2!1))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.52/0.57 tff(99,plain,
% 0.52/0.57 (test(tptp_fun_X1_0(X2!1))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[98, 19])).
% 0.52/0.57 tff(100,plain,
% 0.52/0.57 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.52/0.57 inference(bind,[status(th)],[])).
% 0.52/0.57 tff(101,plain,
% 0.52/0.57 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.52/0.57 inference(quant_intro,[status(thm)],[100])).
% 0.52/0.57 tff(102,plain,
% 0.52/0.57 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(103,plain,
% 0.52/0.57 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.52/0.57 inference(bind,[status(th)],[])).
% 0.52/0.57 tff(104,plain,
% 0.52/0.57 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.52/0.57 inference(quant_intro,[status(thm)],[103])).
% 0.52/0.57 tff(105,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_3')).
% 0.52/0.57 tff(106,plain,
% 0.52/0.57 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.52/0.57 tff(107,plain,
% 0.52/0.57 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.52/0.57 tff(108,plain,(
% 0.52/0.57 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.52/0.57 inference(skolemize,[status(sab)],[107])).
% 0.52/0.57 tff(109,plain,
% 0.52/0.57 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.52/0.57 tff(110,plain,
% 0.52/0.57 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X2!1))) | ((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X2!1))) | ((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1)))),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(111,plain,
% 0.52/0.57 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X2!1))) | ((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1)))),
% 0.52/0.57 inference(quant_inst,[status(thm)],[])).
% 0.52/0.57 tff(112,plain,
% 0.52/0.57 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X2!1))) | ((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.52/0.57 tff(113,plain,
% 0.52/0.57 ((~test(tptp_fun_X1_0(X2!1))) | ((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[112, 109])).
% 0.52/0.57 tff(114,plain,
% 0.52/0.57 ((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1)),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[113, 99])).
% 0.52/0.57 tff(115,plain,
% 0.52/0.57 ((~((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1))) | (c(tptp_fun_X1_0(X2!1)) = X2!1) | (~complement(tptp_fun_X1_0(X2!1), X2!1))),
% 0.52/0.57 inference(tautology,[status(thm)],[])).
% 0.52/0.57 tff(116,plain,
% 0.52/0.57 ((~((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1))) | (c(tptp_fun_X1_0(X2!1)) = X2!1)),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[115, 65])).
% 0.52/0.57 tff(117,plain,
% 0.52/0.57 (c(tptp_fun_X1_0(X2!1)) = X2!1),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[116, 114])).
% 0.52/0.57 tff(118,plain,
% 0.52/0.57 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 0.52/0.57 inference(bind,[status(th)],[])).
% 0.52/0.57 tff(119,plain,
% 0.52/0.57 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.52/0.57 inference(quant_intro,[status(thm)],[118])).
% 0.52/0.57 tff(120,plain,
% 0.52/0.57 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(121,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 0.52/0.57 tff(122,plain,
% 0.52/0.57 (![A: $i] : (multiplication(one, A) = A)),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.52/0.57 tff(123,plain,(
% 0.52/0.57 ![A: $i] : (multiplication(one, A) = A)),
% 0.52/0.57 inference(skolemize,[status(sab)],[122])).
% 0.52/0.57 tff(124,plain,
% 0.52/0.57 (![A: $i] : (multiplication(one, A) = A)),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.52/0.57 tff(125,plain,
% 0.52/0.57 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, c(tptp_fun_X1_0(X2!1))) = c(tptp_fun_X1_0(X2!1)))),
% 0.52/0.57 inference(quant_inst,[status(thm)],[])).
% 0.52/0.57 tff(126,plain,
% 0.52/0.57 (multiplication(one, c(tptp_fun_X1_0(X2!1))) = c(tptp_fun_X1_0(X2!1))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.52/0.57 tff(127,plain,
% 0.52/0.57 (addition(tptp_fun_X1_0(X2!1), X2!1) = addition(X2!1, tptp_fun_X1_0(X2!1))),
% 0.52/0.57 inference(symmetry,[status(thm)],[83])).
% 0.52/0.57 tff(128,plain,
% 0.52/0.57 (addition(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))) = addition(tptp_fun_X1_0(X2!1), X2!1)),
% 0.52/0.57 inference(monotonicity,[status(thm)],[117])).
% 0.52/0.57 tff(129,plain,
% 0.52/0.57 (addition(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))) = one),
% 0.52/0.57 inference(transitivity,[status(thm)],[128, 127, 70])).
% 0.52/0.57 tff(130,plain,
% 0.52/0.57 (multiplication(addition(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))), c(tptp_fun_X1_0(X2!1))) = multiplication(one, c(tptp_fun_X1_0(X2!1)))),
% 0.52/0.57 inference(monotonicity,[status(thm)],[129])).
% 0.52/0.57 tff(131,plain,
% 0.52/0.57 (^[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))))),
% 0.52/0.57 inference(bind,[status(th)],[])).
% 0.52/0.57 tff(132,plain,
% 0.52/0.57 (![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)))),
% 0.52/0.57 inference(quant_intro,[status(thm)],[131])).
% 0.52/0.57 tff(133,plain,
% 0.52/0.57 (![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)))),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(134,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_distributivity')).
% 0.52/0.57 tff(135,plain,
% 0.52/0.57 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.52/0.57 tff(136,plain,(
% 0.52/0.57 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.52/0.57 inference(skolemize,[status(sab)],[135])).
% 0.52/0.57 tff(137,plain,
% 0.52/0.57 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.52/0.57 tff(138,plain,
% 0.52/0.57 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))), c(tptp_fun_X1_0(X2!1))) = addition(multiplication(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))), multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1)))))),
% 0.52/0.57 inference(quant_inst,[status(thm)],[])).
% 0.52/0.57 tff(139,plain,
% 0.52/0.57 (multiplication(addition(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))), c(tptp_fun_X1_0(X2!1))) = addition(multiplication(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))), multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.52/0.57 tff(140,plain,
% 0.52/0.57 (addition(multiplication(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))), multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1)))) = multiplication(addition(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))), c(tptp_fun_X1_0(X2!1)))),
% 0.52/0.57 inference(symmetry,[status(thm)],[139])).
% 0.52/0.57 tff(141,plain,
% 0.52/0.57 (multiplication(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))) = multiplication(tptp_fun_X1_0(X2!1), X2!1)),
% 0.52/0.57 inference(monotonicity,[status(thm)],[117])).
% 0.52/0.57 tff(142,plain,
% 0.52/0.57 (multiplication(tptp_fun_X1_0(X2!1), X2!1) = multiplication(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1)))),
% 0.52/0.57 inference(symmetry,[status(thm)],[141])).
% 0.52/0.57 tff(143,plain,
% 0.52/0.57 (zero = multiplication(tptp_fun_X1_0(X2!1), X2!1)),
% 0.52/0.57 inference(symmetry,[status(thm)],[86])).
% 0.52/0.57 tff(144,plain,
% 0.52/0.57 (zero = multiplication(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1)))),
% 0.52/0.57 inference(transitivity,[status(thm)],[143, 142])).
% 0.52/0.57 tff(145,plain,
% 0.52/0.57 (addition(zero, multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1)))) = addition(multiplication(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))), multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))))),
% 0.52/0.57 inference(monotonicity,[status(thm)],[144])).
% 0.52/0.57 tff(146,plain,
% 0.52/0.57 (addition(zero, multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1)))) = X2!1),
% 0.52/0.57 inference(transitivity,[status(thm)],[145, 140, 130, 126, 117])).
% 0.52/0.57 tff(147,plain,
% 0.52/0.57 (multiplication(multiplication(X1!2, X0!3), addition(zero, multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))))) = multiplication(multiplication(X1!2, X0!3), X2!1)),
% 0.52/0.57 inference(monotonicity,[status(thm)],[146])).
% 0.52/0.57 tff(148,plain,
% 0.52/0.57 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))))),
% 0.52/0.57 inference(bind,[status(th)],[])).
% 0.52/0.57 tff(149,plain,
% 0.52/0.57 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.52/0.57 inference(quant_intro,[status(thm)],[148])).
% 0.52/0.57 tff(150,plain,
% 0.52/0.57 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(151,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','right_distributivity')).
% 0.52/0.57 tff(152,plain,
% 0.52/0.57 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.52/0.57 tff(153,plain,(
% 0.52/0.57 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.52/0.57 inference(skolemize,[status(sab)],[152])).
% 0.52/0.57 tff(154,plain,
% 0.52/0.57 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.52/0.57 tff(155,plain,
% 0.52/0.57 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(multiplication(X1!2, X0!3), addition(zero, multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))))) = addition(multiplication(multiplication(X1!2, X0!3), zero), multiplication(multiplication(X1!2, X0!3), multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))))))),
% 0.52/0.57 inference(quant_inst,[status(thm)],[])).
% 0.52/0.57 tff(156,plain,
% 0.52/0.57 (multiplication(multiplication(X1!2, X0!3), addition(zero, multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))))) = addition(multiplication(multiplication(X1!2, X0!3), zero), multiplication(multiplication(X1!2, X0!3), multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1)))))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.52/0.57 tff(157,plain,
% 0.52/0.57 (addition(multiplication(multiplication(X1!2, X0!3), zero), multiplication(multiplication(X1!2, X0!3), multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))))) = multiplication(multiplication(X1!2, X0!3), addition(zero, multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1)))))),
% 0.52/0.57 inference(symmetry,[status(thm)],[156])).
% 0.52/0.57 tff(158,plain,
% 0.52/0.57 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1)))) = addition(multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))), zero))),
% 0.52/0.57 inference(quant_inst,[status(thm)],[])).
% 0.52/0.57 tff(159,plain,
% 0.52/0.57 (addition(zero, multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1)))) = addition(multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))), zero)),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[158, 81])).
% 0.52/0.57 tff(160,plain,
% 0.52/0.57 (addition(multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))), zero) = addition(zero, multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))))),
% 0.52/0.57 inference(symmetry,[status(thm)],[159])).
% 0.52/0.57 tff(161,plain,
% 0.52/0.57 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 0.52/0.57 inference(bind,[status(th)],[])).
% 0.52/0.57 tff(162,plain,
% 0.52/0.57 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.52/0.57 inference(quant_intro,[status(thm)],[161])).
% 0.52/0.57 tff(163,plain,
% 0.52/0.57 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(164,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 0.52/0.57 tff(165,plain,
% 0.52/0.57 (![A: $i] : (addition(A, zero) = A)),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.52/0.57 tff(166,plain,(
% 0.52/0.57 ![A: $i] : (addition(A, zero) = A)),
% 0.52/0.57 inference(skolemize,[status(sab)],[165])).
% 0.52/0.57 tff(167,plain,
% 0.52/0.57 (![A: $i] : (addition(A, zero) = A)),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.52/0.57 tff(168,plain,
% 0.52/0.57 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))), zero) = multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))))),
% 0.52/0.57 inference(quant_inst,[status(thm)],[])).
% 0.52/0.57 tff(169,plain,
% 0.52/0.57 (addition(multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))), zero) = multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1)))),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.52/0.57 tff(170,plain,
% 0.52/0.57 (multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))) = addition(multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))), zero)),
% 0.52/0.57 inference(symmetry,[status(thm)],[169])).
% 0.52/0.57 tff(171,plain,
% 0.52/0.57 (multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))) = X2!1),
% 0.52/0.57 inference(transitivity,[status(thm)],[170, 160, 145, 140, 130, 126, 117])).
% 0.52/0.57 tff(172,plain,
% 0.52/0.57 (multiplication(multiplication(X1!2, X0!3), multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1)))) = multiplication(multiplication(X1!2, X0!3), X2!1)),
% 0.52/0.57 inference(monotonicity,[status(thm)],[171])).
% 0.52/0.57 tff(173,plain,
% 0.52/0.57 (multiplication(multiplication(X1!2, X0!3), X2!1) = multiplication(multiplication(X1!2, X0!3), multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))))),
% 0.52/0.57 inference(symmetry,[status(thm)],[172])).
% 0.52/0.57 tff(174,plain,
% 0.52/0.57 (multiplication(multiplication(X1!2, X0!3), c(tptp_fun_X1_0(X2!1))) = multiplication(multiplication(X1!2, X0!3), X2!1)),
% 0.52/0.57 inference(monotonicity,[status(thm)],[117])).
% 0.52/0.57 tff(175,plain,
% 0.52/0.57 (multiplication(multiplication(X1!2, X0!3), c(tptp_fun_X1_0(X2!1))) = multiplication(multiplication(X1!2, X0!3), multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))))),
% 0.52/0.57 inference(transitivity,[status(thm)],[174, 173])).
% 0.52/0.57 tff(176,plain,
% 0.52/0.57 (^[A: $i] : refl((multiplication(A, zero) = zero) <=> (multiplication(A, zero) = zero))),
% 0.52/0.57 inference(bind,[status(th)],[])).
% 0.52/0.57 tff(177,plain,
% 0.52/0.57 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 0.52/0.57 inference(quant_intro,[status(thm)],[176])).
% 0.52/0.57 tff(178,plain,
% 0.52/0.57 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(179,axiom,(![A: $i] : (multiplication(A, zero) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','right_annihilation')).
% 0.52/0.57 tff(180,plain,
% 0.52/0.57 (![A: $i] : (multiplication(A, zero) = zero)),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.52/0.57 tff(181,plain,(
% 0.52/0.57 ![A: $i] : (multiplication(A, zero) = zero)),
% 0.52/0.57 inference(skolemize,[status(sab)],[180])).
% 0.52/0.57 tff(182,plain,
% 0.52/0.57 (![A: $i] : (multiplication(A, zero) = zero)),
% 0.52/0.57 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.52/0.57 tff(183,plain,
% 0.52/0.57 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(multiplication(X1!2, X0!3), zero) = zero)),
% 0.52/0.57 inference(quant_inst,[status(thm)],[])).
% 0.52/0.57 tff(184,plain,
% 0.52/0.57 (multiplication(multiplication(X1!2, X0!3), zero) = zero),
% 0.52/0.57 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.52/0.57 tff(185,plain,
% 0.52/0.57 (zero = multiplication(multiplication(X1!2, X0!3), zero)),
% 0.52/0.57 inference(symmetry,[status(thm)],[184])).
% 0.52/0.57 tff(186,plain,
% 0.52/0.57 (multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero),
% 0.52/0.57 inference(or_elim,[status(thm)],[60])).
% 0.52/0.57 tff(187,plain,
% 0.52/0.57 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X2!1)) | ((c(X2!1) = tptp_fun_X1_0(X2!1)) <=> complement(X2!1, tptp_fun_X1_0(X2!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X2!1)) | ((c(X2!1) = tptp_fun_X1_0(X2!1)) <=> complement(X2!1, tptp_fun_X1_0(X2!1))))),
% 0.52/0.57 inference(rewrite,[status(thm)],[])).
% 0.52/0.57 tff(188,plain,
% 0.52/0.57 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X2!1)) | ((c(X2!1) = tptp_fun_X1_0(X2!1)) <=> complement(X2!1, tptp_fun_X1_0(X2!1))))),
% 0.52/0.58 inference(quant_inst,[status(thm)],[])).
% 0.52/0.58 tff(189,plain,
% 0.52/0.58 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X2!1)) | ((c(X2!1) = tptp_fun_X1_0(X2!1)) <=> complement(X2!1, tptp_fun_X1_0(X2!1)))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.52/0.58 tff(190,plain,
% 0.52/0.58 ((c(X2!1) = tptp_fun_X1_0(X2!1)) <=> complement(X2!1, tptp_fun_X1_0(X2!1))),
% 0.52/0.58 inference(unit_resolution,[status(thm)],[189, 109, 62])).
% 0.52/0.58 tff(191,plain,
% 0.52/0.58 ((~((c(X2!1) = tptp_fun_X1_0(X2!1)) <=> complement(X2!1, tptp_fun_X1_0(X2!1)))) | (c(X2!1) = tptp_fun_X1_0(X2!1)) | (~complement(X2!1, tptp_fun_X1_0(X2!1)))),
% 0.52/0.58 inference(tautology,[status(thm)],[])).
% 0.52/0.58 tff(192,plain,
% 0.52/0.58 (c(X2!1) = tptp_fun_X1_0(X2!1)),
% 0.52/0.58 inference(unit_resolution,[status(thm)],[191, 93, 190])).
% 0.52/0.58 tff(193,plain,
% 0.52/0.58 (tptp_fun_X1_0(X2!1) = c(X2!1)),
% 0.52/0.58 inference(symmetry,[status(thm)],[192])).
% 0.52/0.58 tff(194,plain,
% 0.52/0.58 (multiplication(multiplication(X1!2, X0!3), tptp_fun_X1_0(X2!1)) = multiplication(multiplication(X1!2, X0!3), c(X2!1))),
% 0.52/0.58 inference(monotonicity,[status(thm)],[193])).
% 0.52/0.58 tff(195,plain,
% 0.52/0.58 (multiplication(multiplication(X1!2, X0!3), tptp_fun_X1_0(X2!1)) = multiplication(multiplication(X1!2, X0!3), zero)),
% 0.52/0.58 inference(transitivity,[status(thm)],[194, 186, 185])).
% 0.52/0.58 tff(196,plain,
% 0.52/0.58 (addition(multiplication(multiplication(X1!2, X0!3), tptp_fun_X1_0(X2!1)), multiplication(multiplication(X1!2, X0!3), c(tptp_fun_X1_0(X2!1)))) = addition(multiplication(multiplication(X1!2, X0!3), zero), multiplication(multiplication(X1!2, X0!3), multiplication(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1)))))),
% 0.52/0.58 inference(monotonicity,[status(thm)],[195, 175])).
% 0.52/0.58 tff(197,plain,
% 0.52/0.58 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(multiplication(X1!2, X0!3), addition(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1)))) = addition(multiplication(multiplication(X1!2, X0!3), tptp_fun_X1_0(X2!1)), multiplication(multiplication(X1!2, X0!3), c(tptp_fun_X1_0(X2!1)))))),
% 0.52/0.58 inference(quant_inst,[status(thm)],[])).
% 0.52/0.58 tff(198,plain,
% 0.52/0.58 (multiplication(multiplication(X1!2, X0!3), addition(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1)))) = addition(multiplication(multiplication(X1!2, X0!3), tptp_fun_X1_0(X2!1)), multiplication(multiplication(X1!2, X0!3), c(tptp_fun_X1_0(X2!1))))),
% 0.52/0.58 inference(unit_resolution,[status(thm)],[197, 154])).
% 0.52/0.58 tff(199,plain,
% 0.52/0.58 (addition(tptp_fun_X1_0(X2!1), X2!1) = addition(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1)))),
% 0.52/0.58 inference(symmetry,[status(thm)],[128])).
% 0.52/0.58 tff(200,plain,
% 0.52/0.58 (one = addition(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1)))),
% 0.52/0.58 inference(transitivity,[status(thm)],[71, 83, 199])).
% 0.52/0.58 tff(201,plain,
% 0.52/0.58 (multiplication(multiplication(X1!2, X0!3), one) = multiplication(multiplication(X1!2, X0!3), addition(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))))),
% 0.52/0.58 inference(monotonicity,[status(thm)],[200])).
% 0.52/0.58 tff(202,plain,
% 0.52/0.58 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.52/0.58 inference(bind,[status(th)],[])).
% 0.52/0.58 tff(203,plain,
% 0.52/0.58 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.52/0.58 inference(quant_intro,[status(thm)],[202])).
% 0.52/0.58 tff(204,plain,
% 0.52/0.58 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.52/0.58 inference(rewrite,[status(thm)],[])).
% 0.52/0.58 tff(205,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 0.52/0.58 tff(206,plain,
% 0.52/0.58 (![A: $i] : (multiplication(A, one) = A)),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.52/0.58 tff(207,plain,(
% 0.52/0.58 ![A: $i] : (multiplication(A, one) = A)),
% 0.52/0.58 inference(skolemize,[status(sab)],[206])).
% 0.52/0.58 tff(208,plain,
% 0.52/0.58 (![A: $i] : (multiplication(A, one) = A)),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[207, 203])).
% 0.52/0.58 tff(209,plain,
% 0.52/0.58 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(multiplication(X1!2, X0!3), one) = multiplication(X1!2, X0!3))),
% 0.52/0.58 inference(quant_inst,[status(thm)],[])).
% 0.52/0.58 tff(210,plain,
% 0.52/0.58 (multiplication(multiplication(X1!2, X0!3), one) = multiplication(X1!2, X0!3)),
% 0.52/0.58 inference(unit_resolution,[status(thm)],[209, 208])).
% 0.52/0.58 tff(211,plain,
% 0.52/0.58 (multiplication(X1!2, X0!3) = multiplication(multiplication(X1!2, X0!3), one)),
% 0.52/0.58 inference(symmetry,[status(thm)],[210])).
% 0.52/0.58 tff(212,plain,
% 0.52/0.58 (multiplication(X1!2, X0!3) = multiplication(multiplication(X1!2, X0!3), X2!1)),
% 0.52/0.58 inference(transitivity,[status(thm)],[211, 201, 198, 196, 157, 147])).
% 0.52/0.58 tff(213,plain,
% 0.52/0.58 (~(multiplication(X1!2, X0!3) = multiplication(multiplication(X1!2, X0!3), X2!1))),
% 0.52/0.58 inference(or_elim,[status(thm)],[60])).
% 0.52/0.58 tff(214,plain,
% 0.52/0.58 ($false),
% 0.52/0.58 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.52/0.58 % SZS output end Proof
%------------------------------------------------------------------------------