TSTP Solution File: KLE025+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE025+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 19.86s 12.91s
% Output : Proof 19.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE025+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 08:15:04 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 19.86/12.91 % SZS status Theorem
% 19.86/12.91 % SZS output start Proof
% 19.86/12.91 tff(test_type, type, (
% 19.86/12.91 test: $i > $o)).
% 19.86/12.91 tff(zero_type, type, (
% 19.86/12.91 zero: $i)).
% 19.86/12.91 tff(tptp_fun_X2_1_type, type, (
% 19.86/12.91 tptp_fun_X2_1: $i)).
% 19.86/12.91 tff(c_type, type, (
% 19.86/12.91 c: $i > $i)).
% 19.86/12.91 tff(tptp_fun_X1_0_type, type, (
% 19.86/12.91 tptp_fun_X1_0: $i > $i)).
% 19.86/12.91 tff(complement_type, type, (
% 19.86/12.91 complement: ( $i * $i ) > $o)).
% 19.86/12.91 tff(one_type, type, (
% 19.86/12.91 one: $i)).
% 19.86/12.91 tff(addition_type, type, (
% 19.86/12.91 addition: ( $i * $i ) > $i)).
% 19.86/12.91 tff(multiplication_type, type, (
% 19.86/12.91 multiplication: ( $i * $i ) > $i)).
% 19.86/12.91 tff(tptp_fun_X1_2_type, type, (
% 19.86/12.91 tptp_fun_X1_2: $i)).
% 19.86/12.91 tff(tptp_fun_X0_3_type, type, (
% 19.86/12.91 tptp_fun_X0_3: $i)).
% 19.86/12.91 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)).
% 19.86/12.91 tff(2,plain,
% 19.86/12.91 (^[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)))))))),
% 19.86/12.91 inference(bind,[status(th)],[])).
% 19.86/12.91 tff(3,plain,
% 19.86/12.91 (![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))))))),
% 19.86/12.91 inference(quant_intro,[status(thm)],[2])).
% 19.86/12.91 tff(4,plain,
% 19.86/12.91 (^[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)))))))),
% 19.86/12.91 inference(bind,[status(th)],[])).
% 19.86/12.91 tff(5,plain,
% 19.86/12.91 (![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))))))),
% 19.86/12.91 inference(quant_intro,[status(thm)],[4])).
% 19.86/12.91 tff(6,plain,
% 19.86/12.91 (![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))))))),
% 19.86/12.91 inference(transitivity,[status(thm)],[5, 3])).
% 19.86/12.91 tff(7,plain,
% 19.86/12.91 (^[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))))))))),
% 19.86/12.91 inference(bind,[status(th)],[])).
% 19.86/12.91 tff(8,plain,
% 19.86/12.91 (![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))))))),
% 19.86/12.91 inference(quant_intro,[status(thm)],[7])).
% 19.86/12.91 tff(9,plain,
% 19.86/12.91 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 19.86/12.91 inference(rewrite,[status(thm)],[])).
% 19.86/12.91 tff(10,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_1')).
% 19.86/12.91 tff(11,plain,
% 19.86/12.91 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[10, 9])).
% 19.86/12.91 tff(12,plain,(
% 19.86/12.91 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 19.86/12.91 inference(skolemize,[status(sab)],[11])).
% 19.86/12.91 tff(13,plain,
% 19.86/12.91 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[12, 8])).
% 19.86/12.91 tff(14,plain,
% 19.86/12.91 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[13, 6])).
% 19.86/12.91 tff(15,plain,
% 19.86/12.91 ((~![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: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))))))),
% 19.86/12.91 inference(quant_inst,[status(thm)],[])).
% 19.86/12.91 tff(16,plain,
% 19.86/12.91 ($false),
% 19.86/12.91 inference(unit_resolution,[status(thm)],[15, 14, 1])).
% 19.86/12.91 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,[]))).
% 19.86/12.91 tff(18,plain,
% 19.86/12.91 (((~((~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))))),
% 19.86/12.91 inference(tautology,[status(thm)],[])).
% 19.86/12.91 tff(19,plain,
% 19.86/12.91 (test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))),
% 19.86/12.91 inference(unit_resolution,[status(thm)],[18, 17])).
% 19.86/12.91 tff(20,assumption,(![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))), introduced(assumption)).
% 19.86/12.91 tff(21,plain,
% 19.86/12.91 (^[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))))))),
% 19.86/12.91 inference(bind,[status(th)],[])).
% 19.86/12.91 tff(22,plain,
% 19.86/12.91 (![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)))))),
% 19.86/12.91 inference(quant_intro,[status(thm)],[21])).
% 19.86/12.91 tff(23,plain,
% 19.86/12.91 (^[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))))))),
% 19.86/12.91 inference(bind,[status(th)],[])).
% 19.86/12.91 tff(24,plain,
% 19.86/12.91 (![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)))))),
% 19.86/12.91 inference(quant_intro,[status(thm)],[23])).
% 19.86/12.91 tff(25,plain,
% 19.86/12.91 (![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)))),
% 19.86/12.91 inference(rewrite,[status(thm)],[])).
% 19.86/12.91 tff(26,plain,
% 19.86/12.91 (^[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))))),
% 19.86/12.91 inference(bind,[status(th)],[])).
% 19.86/12.91 tff(27,plain,
% 19.86/12.91 (![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)))),
% 19.86/12.91 inference(quant_intro,[status(thm)],[26])).
% 19.86/12.91 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')).
% 19.86/12.91 tff(29,plain,
% 19.86/12.91 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[28, 27])).
% 19.86/12.91 tff(30,plain,
% 19.86/12.91 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[29, 25])).
% 19.86/12.91 tff(31,plain,(
% 19.86/12.91 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 19.86/12.91 inference(skolemize,[status(sab)],[30])).
% 19.86/12.91 tff(32,plain,
% 19.86/12.91 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[31, 24])).
% 19.86/12.91 tff(33,plain,
% 19.86/12.91 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[32, 22])).
% 19.86/12.91 tff(34,plain,
% 19.86/12.91 (((~![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))))))),
% 19.86/12.91 inference(rewrite,[status(thm)],[])).
% 19.86/12.91 tff(35,plain,
% 19.86/12.91 ((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)))))),
% 19.86/12.91 inference(rewrite,[status(thm)],[])).
% 19.86/12.91 tff(36,plain,
% 19.86/12.91 (((~![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))))))),
% 19.86/12.91 inference(monotonicity,[status(thm)],[35])).
% 19.86/12.91 tff(37,plain,
% 19.86/12.91 (((~![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))))))),
% 19.86/12.91 inference(transitivity,[status(thm)],[36, 34])).
% 19.86/12.91 tff(38,plain,
% 19.86/12.91 ((~![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)))))),
% 19.86/12.91 inference(quant_inst,[status(thm)],[])).
% 19.86/12.91 tff(39,plain,
% 19.86/12.91 ((~![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)))))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[38, 37])).
% 19.86/12.91 tff(40,plain,
% 19.86/12.91 (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))))),
% 19.86/12.91 inference(unit_resolution,[status(thm)],[39, 33])).
% 19.86/12.91 tff(41,plain,
% 19.86/12.91 ((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))),
% 19.86/12.91 inference(commutativity,[status(thm)],[])).
% 19.86/12.91 tff(42,plain,
% 19.86/12.91 ((~![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)))))),
% 19.86/12.91 inference(quant_inst,[status(thm)],[])).
% 19.86/12.91 tff(43,plain,
% 19.86/12.91 (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))))),
% 19.86/12.91 inference(unit_resolution,[status(thm)],[42, 33])).
% 19.86/12.91 tff(44,plain,
% 19.86/12.91 ((~![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))))))),
% 19.86/12.91 inference(quant_inst,[status(thm)],[])).
% 19.86/12.91 tff(45,plain,
% 19.86/12.91 (~((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | (~(test(X2!1) | ![X1: $i] : (~complement(X1, X2!1)))))),
% 19.86/12.91 inference(unit_resolution,[status(thm)],[44, 14])).
% 19.86/12.91 tff(46,plain,
% 19.86/12.91 (((~((~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))),
% 19.86/12.91 inference(tautology,[status(thm)],[])).
% 19.86/12.91 tff(47,plain,
% 19.86/12.91 ((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1)),
% 19.86/12.91 inference(unit_resolution,[status(thm)],[46, 45])).
% 19.86/12.91 tff(48,plain,
% 19.86/12.91 ((~((multiplication(X1!2, X0!3) = multiplication(multiplication(X1!2, X0!3), X2!1)) | (~(test(X1!2) & test(X2!1))) | (~(multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero)))) <=> (~((multiplication(X1!2, X0!3) = multiplication(multiplication(X1!2, X0!3), X2!1)) | (~(test(X1!2) & test(X2!1))) | (~(multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero))))),
% 19.86/12.91 inference(rewrite,[status(thm)],[])).
% 19.86/12.91 tff(49,plain,
% 19.86/12.91 ((~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(test(X1) & test(X2))) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)))) <=> (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(test(X1) & test(X2))) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero))))),
% 19.86/12.91 inference(rewrite,[status(thm)],[])).
% 19.86/12.91 tff(50,plain,
% 19.86/12.91 ((~![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)) | (~(test(X1) & test(X2))) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero))))),
% 19.86/12.91 inference(rewrite,[status(thm)],[])).
% 19.86/12.91 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')).
% 19.86/12.91 tff(52,plain,
% 19.86/12.91 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(test(X1) & test(X2))) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[51, 50])).
% 19.86/12.91 tff(53,plain,
% 19.86/12.91 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(test(X1) & test(X2))) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[52, 49])).
% 19.86/12.91 tff(54,plain,
% 19.86/12.91 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(test(X1) & test(X2))) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[53, 49])).
% 19.86/12.91 tff(55,plain,
% 19.86/12.91 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(test(X1) & test(X2))) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[54, 49])).
% 19.86/12.91 tff(56,plain,
% 19.86/12.91 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(test(X1) & test(X2))) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[55, 49])).
% 19.86/12.91 tff(57,plain,
% 19.86/12.91 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(test(X1) & test(X2))) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[56, 49])).
% 19.86/12.91 tff(58,plain,
% 19.86/12.91 (~![X0: $i, X1: $i, X2: $i] : ((multiplication(X1, X0) = multiplication(multiplication(X1, X0), X2)) | (~(test(X1) & test(X2))) | (~(multiplication(multiplication(X1, X0), c(X2)) = zero)))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[57, 49])).
% 19.86/12.91 tff(59,plain,(
% 19.86/12.91 ~((multiplication(X1!2, X0!3) = multiplication(multiplication(X1!2, X0!3), X2!1)) | (~(test(X1!2) & test(X2!1))) | (~(multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero)))),
% 19.86/12.91 inference(skolemize,[status(sab)],[58])).
% 19.86/12.91 tff(60,plain,
% 19.86/12.91 (~((multiplication(X1!2, X0!3) = multiplication(multiplication(X1!2, X0!3), X2!1)) | (~(test(X1!2) & test(X2!1))) | (~(multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero)))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[59, 48])).
% 19.86/12.91 tff(61,plain,
% 19.86/12.91 (test(X1!2) & test(X2!1)),
% 19.86/12.91 inference(or_elim,[status(thm)],[60])).
% 19.86/12.91 tff(62,plain,
% 19.86/12.91 (test(X2!1)),
% 19.86/12.91 inference(and_elim,[status(thm)],[61])).
% 19.86/12.91 tff(63,plain,
% 19.86/12.91 ((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | (~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1)),
% 19.86/12.91 inference(tautology,[status(thm)],[])).
% 19.86/12.91 tff(64,plain,
% 19.86/12.91 ((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | complement(tptp_fun_X1_0(X2!1), X2!1)),
% 19.86/12.91 inference(unit_resolution,[status(thm)],[63, 62])).
% 19.86/12.91 tff(65,plain,
% 19.86/12.91 (complement(tptp_fun_X1_0(X2!1), X2!1)),
% 19.86/12.91 inference(unit_resolution,[status(thm)],[64, 47])).
% 19.86/12.91 tff(66,plain,
% 19.86/12.91 ((~(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))))),
% 19.86/12.91 inference(tautology,[status(thm)],[])).
% 19.86/12.91 tff(67,plain,
% 19.86/12.91 ((~(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))))),
% 19.86/12.91 inference(unit_resolution,[status(thm)],[66, 65])).
% 19.86/12.91 tff(68,plain,
% 19.86/12.91 (~((~(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)))),
% 19.86/12.91 inference(unit_resolution,[status(thm)],[67, 43])).
% 19.86/12.91 tff(69,plain,
% 19.86/12.91 (((~(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)),
% 19.86/12.91 inference(tautology,[status(thm)],[])).
% 19.86/12.91 tff(70,plain,
% 19.86/12.91 (addition(X2!1, tptp_fun_X1_0(X2!1)) = one),
% 19.86/12.91 inference(unit_resolution,[status(thm)],[69, 68])).
% 19.86/12.91 tff(71,plain,
% 19.86/12.91 (one = addition(X2!1, tptp_fun_X1_0(X2!1))),
% 19.86/12.91 inference(symmetry,[status(thm)],[70])).
% 19.86/12.91 tff(72,plain,
% 19.86/12.91 ((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)))),
% 19.86/12.91 inference(monotonicity,[status(thm)],[71])).
% 19.86/12.91 tff(73,plain,
% 19.86/12.91 ((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))),
% 19.86/12.91 inference(transitivity,[status(thm)],[72, 41])).
% 19.86/12.91 tff(74,plain,
% 19.86/12.91 ((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)),
% 19.86/12.91 inference(symmetry,[status(thm)],[73])).
% 19.86/12.91 tff(75,plain,
% 19.86/12.91 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 19.86/12.91 inference(bind,[status(th)],[])).
% 19.86/12.91 tff(76,plain,
% 19.86/12.91 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 19.86/12.91 inference(quant_intro,[status(thm)],[75])).
% 19.86/12.91 tff(77,plain,
% 19.86/12.91 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 19.86/12.91 inference(rewrite,[status(thm)],[])).
% 19.86/12.91 tff(78,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 19.86/12.91 tff(79,plain,
% 19.86/12.91 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[78, 77])).
% 19.86/12.91 tff(80,plain,(
% 19.86/12.91 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 19.86/12.91 inference(skolemize,[status(sab)],[79])).
% 19.86/12.91 tff(81,plain,
% 19.86/12.91 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[80, 76])).
% 19.86/12.91 tff(82,plain,
% 19.86/12.91 ((~![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))),
% 19.86/12.91 inference(quant_inst,[status(thm)],[])).
% 19.86/12.91 tff(83,plain,
% 19.86/12.91 (addition(X2!1, tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), X2!1)),
% 19.86/12.91 inference(unit_resolution,[status(thm)],[82, 81])).
% 19.86/12.91 tff(84,plain,
% 19.86/12.91 (addition(tptp_fun_X1_0(X2!1), X2!1) = one),
% 19.86/12.91 inference(modus_ponens,[status(thm)],[83, 74])).
% 19.86/12.91 tff(85,plain,
% 19.86/12.91 (((~(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)),
% 19.86/12.91 inference(tautology,[status(thm)],[])).
% 19.86/12.91 tff(86,plain,
% 19.86/12.91 (multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero),
% 19.86/12.91 inference(unit_resolution,[status(thm)],[85, 68])).
% 19.86/12.91 tff(87,plain,
% 19.86/12.91 (((~(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)),
% 19.86/12.91 inference(tautology,[status(thm)],[])).
% 19.86/12.92 tff(88,plain,
% 19.86/12.92 (multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[87, 68])).
% 19.86/12.92 tff(89,plain,
% 19.86/12.92 ((~((~(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))),
% 19.86/12.92 inference(tautology,[status(thm)],[])).
% 19.86/12.92 tff(90,plain,
% 19.86/12.92 ((~((~(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))),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[89, 88, 86])).
% 19.86/12.92 tff(91,plain,
% 19.86/12.92 (~((~(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)))),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[90, 84])).
% 19.86/12.92 tff(92,plain,
% 19.86/12.92 ((~(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)))),
% 19.86/12.92 inference(tautology,[status(thm)],[])).
% 19.86/12.92 tff(93,plain,
% 19.86/12.92 (complement(X2!1, tptp_fun_X1_0(X2!1))),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[92, 91, 40])).
% 19.86/12.92 tff(94,plain,
% 19.86/12.92 ((~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))) | (~complement(X2!1, tptp_fun_X1_0(X2!1)))),
% 19.86/12.92 inference(quant_inst,[status(thm)],[])).
% 19.86/12.92 tff(95,plain,
% 19.86/12.92 ($false),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[94, 93, 20])).
% 19.86/12.92 tff(96,plain,(~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1)))), inference(lemma,lemma(discharge,[]))).
% 19.86/12.92 tff(97,plain,
% 19.86/12.92 ((~(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)))),
% 19.86/12.92 inference(tautology,[status(thm)],[])).
% 19.86/12.92 tff(98,plain,
% 19.86/12.92 ((~(test(tptp_fun_X1_0(X2!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X2!1))))) | test(tptp_fun_X1_0(X2!1))),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[97, 96])).
% 19.86/12.92 tff(99,plain,
% 19.86/12.92 (test(tptp_fun_X1_0(X2!1))),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[98, 19])).
% 19.86/12.92 tff(100,plain,
% 19.86/12.92 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 19.86/12.92 inference(bind,[status(th)],[])).
% 19.86/12.92 tff(101,plain,
% 19.86/12.92 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 19.86/12.92 inference(quant_intro,[status(thm)],[100])).
% 19.86/12.92 tff(102,plain,
% 19.86/12.92 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 19.86/12.92 inference(rewrite,[status(thm)],[])).
% 19.86/12.92 tff(103,plain,
% 19.86/12.92 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 19.86/12.92 inference(bind,[status(th)],[])).
% 19.86/12.92 tff(104,plain,
% 19.86/12.92 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 19.86/12.92 inference(quant_intro,[status(thm)],[103])).
% 19.86/12.92 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')).
% 19.86/12.92 tff(106,plain,
% 19.86/12.92 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 19.86/12.92 inference(modus_ponens,[status(thm)],[105, 104])).
% 19.86/12.92 tff(107,plain,
% 19.86/12.92 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 19.86/12.92 inference(modus_ponens,[status(thm)],[106, 102])).
% 19.86/12.92 tff(108,plain,(
% 19.86/12.92 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 19.86/12.92 inference(skolemize,[status(sab)],[107])).
% 19.86/12.92 tff(109,plain,
% 19.86/12.92 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 19.86/12.92 inference(modus_ponens,[status(thm)],[108, 101])).
% 19.86/12.92 tff(110,plain,
% 19.86/12.92 (((~![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)))),
% 19.86/12.92 inference(rewrite,[status(thm)],[])).
% 19.86/12.92 tff(111,plain,
% 19.86/12.92 ((~![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)))),
% 19.86/12.92 inference(quant_inst,[status(thm)],[])).
% 19.86/12.92 tff(112,plain,
% 19.86/12.92 ((~![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))),
% 19.86/12.92 inference(modus_ponens,[status(thm)],[111, 110])).
% 19.86/12.92 tff(113,plain,
% 19.86/12.92 ((~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))),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[112, 109])).
% 19.86/12.92 tff(114,plain,
% 19.86/12.92 ((c(tptp_fun_X1_0(X2!1)) = X2!1) <=> complement(tptp_fun_X1_0(X2!1), X2!1)),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[113, 99])).
% 19.86/12.92 tff(115,plain,
% 19.86/12.92 ((~((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))),
% 19.86/12.92 inference(tautology,[status(thm)],[])).
% 19.86/12.92 tff(116,plain,
% 19.86/12.92 ((~((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)),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[115, 65])).
% 19.86/12.92 tff(117,plain,
% 19.86/12.92 (c(tptp_fun_X1_0(X2!1)) = X2!1),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[116, 114])).
% 19.86/12.92 tff(118,plain,
% 19.86/12.92 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 19.86/12.92 inference(bind,[status(th)],[])).
% 19.86/12.92 tff(119,plain,
% 19.86/12.92 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 19.86/12.92 inference(quant_intro,[status(thm)],[118])).
% 19.86/12.92 tff(120,plain,
% 19.86/12.92 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 19.86/12.92 inference(rewrite,[status(thm)],[])).
% 19.86/12.92 tff(121,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 19.86/12.92 tff(122,plain,
% 19.86/12.92 (![A: $i] : (addition(A, zero) = A)),
% 19.86/12.92 inference(modus_ponens,[status(thm)],[121, 120])).
% 19.86/12.92 tff(123,plain,(
% 19.86/12.92 ![A: $i] : (addition(A, zero) = A)),
% 19.86/12.92 inference(skolemize,[status(sab)],[122])).
% 19.86/12.92 tff(124,plain,
% 19.86/12.92 (![A: $i] : (addition(A, zero) = A)),
% 19.86/12.92 inference(modus_ponens,[status(thm)],[123, 119])).
% 19.86/12.92 tff(125,plain,
% 19.86/12.92 ((~![A: $i] : (addition(A, zero) = A)) | (addition(c(tptp_fun_X1_0(X2!1)), zero) = c(tptp_fun_X1_0(X2!1)))),
% 19.86/12.92 inference(quant_inst,[status(thm)],[])).
% 19.86/12.92 tff(126,plain,
% 19.86/12.92 (addition(c(tptp_fun_X1_0(X2!1)), zero) = c(tptp_fun_X1_0(X2!1))),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[125, 124])).
% 19.86/12.92 tff(127,plain,
% 19.86/12.92 (((~![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))))),
% 19.86/12.92 inference(rewrite,[status(thm)],[])).
% 19.86/12.92 tff(128,plain,
% 19.86/12.92 ((~![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))))),
% 19.86/12.92 inference(quant_inst,[status(thm)],[])).
% 19.86/12.92 tff(129,plain,
% 19.86/12.92 ((~![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)))),
% 19.86/12.92 inference(modus_ponens,[status(thm)],[128, 127])).
% 19.86/12.92 tff(130,plain,
% 19.86/12.92 ((c(X2!1) = tptp_fun_X1_0(X2!1)) <=> complement(X2!1, tptp_fun_X1_0(X2!1))),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[129, 109, 62])).
% 19.86/12.92 tff(131,plain,
% 19.86/12.92 ((~((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)))),
% 19.86/12.92 inference(tautology,[status(thm)],[])).
% 19.86/12.92 tff(132,plain,
% 19.86/12.92 (c(X2!1) = tptp_fun_X1_0(X2!1)),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[131, 93, 130])).
% 19.86/12.92 tff(133,plain,
% 19.86/12.92 (tptp_fun_X1_0(X2!1) = c(X2!1)),
% 19.86/12.92 inference(symmetry,[status(thm)],[132])).
% 19.86/12.92 tff(134,plain,
% 19.86/12.92 (addition(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1)) = addition(c(tptp_fun_X1_0(X2!1)), c(X2!1))),
% 19.86/12.92 inference(monotonicity,[status(thm)],[133])).
% 19.86/12.92 tff(135,plain,
% 19.86/12.92 (addition(c(tptp_fun_X1_0(X2!1)), c(X2!1)) = addition(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1))),
% 19.86/12.92 inference(symmetry,[status(thm)],[134])).
% 19.86/12.92 tff(136,plain,
% 19.86/12.92 (^[X0: $i, X1: $i] : refl(((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0))) <=> ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0))))),
% 19.86/12.92 inference(bind,[status(th)],[])).
% 19.86/12.92 tff(137,plain,
% 19.86/12.92 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 19.86/12.92 inference(quant_intro,[status(thm)],[136])).
% 19.86/12.92 tff(138,plain,
% 19.86/12.92 (^[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(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> (((~test(X1)) | (~test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))))), rewrite((((~test(X1)) | (~test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))), (((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))))),
% 19.86/12.92 inference(bind,[status(th)],[])).
% 19.86/12.92 tff(139,plain,
% 19.86/12.92 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 19.86/12.92 inference(quant_intro,[status(thm)],[138])).
% 19.86/12.92 tff(140,plain,
% 19.86/12.92 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 19.86/12.92 inference(rewrite,[status(thm)],[])).
% 19.86/12.92 tff(141,plain,
% 19.86/12.92 (^[X0: $i, X1: $i] : rewrite(((test(X0) & test(X1)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))))),
% 19.86/12.92 inference(bind,[status(th)],[])).
% 19.86/12.92 tff(142,plain,
% 19.86/12.92 (![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 19.86/12.92 inference(quant_intro,[status(thm)],[141])).
% 19.86/12.92 tff(143,axiom,(![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+2.ax','test_deMorgan2')).
% 19.86/12.92 tff(144,plain,
% 19.86/12.92 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 19.86/12.92 inference(modus_ponens,[status(thm)],[143, 142])).
% 19.86/12.92 tff(145,plain,
% 19.86/12.92 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 19.86/12.92 inference(modus_ponens,[status(thm)],[144, 140])).
% 19.86/12.92 tff(146,plain,(
% 19.86/12.92 ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 19.86/12.92 inference(skolemize,[status(sab)],[145])).
% 19.86/12.92 tff(147,plain,
% 19.86/12.92 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 19.86/12.92 inference(modus_ponens,[status(thm)],[146, 139])).
% 19.86/12.92 tff(148,plain,
% 19.86/12.92 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 19.86/12.92 inference(modus_ponens,[status(thm)],[147, 137])).
% 19.86/12.92 tff(149,plain,
% 19.86/12.92 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(tptp_fun_X1_0(X2!1), X2!1)) = addition(c(tptp_fun_X1_0(X2!1)), c(X2!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(tptp_fun_X1_0(X2!1), X2!1)) = addition(c(tptp_fun_X1_0(X2!1)), c(X2!1))))),
% 19.86/12.92 inference(rewrite,[status(thm)],[])).
% 19.86/12.92 tff(150,plain,
% 19.86/12.92 (((~test(X2!1)) | (c(multiplication(tptp_fun_X1_0(X2!1), X2!1)) = addition(c(tptp_fun_X1_0(X2!1)), c(X2!1))) | (~test(tptp_fun_X1_0(X2!1)))) <=> ((~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(tptp_fun_X1_0(X2!1), X2!1)) = addition(c(tptp_fun_X1_0(X2!1)), c(X2!1))))),
% 19.86/12.92 inference(rewrite,[status(thm)],[])).
% 19.86/12.92 tff(151,plain,
% 19.86/12.92 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (c(multiplication(tptp_fun_X1_0(X2!1), X2!1)) = addition(c(tptp_fun_X1_0(X2!1)), c(X2!1))) | (~test(tptp_fun_X1_0(X2!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(tptp_fun_X1_0(X2!1), X2!1)) = addition(c(tptp_fun_X1_0(X2!1)), c(X2!1)))))),
% 19.86/12.92 inference(monotonicity,[status(thm)],[150])).
% 19.86/12.92 tff(152,plain,
% 19.86/12.92 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (c(multiplication(tptp_fun_X1_0(X2!1), X2!1)) = addition(c(tptp_fun_X1_0(X2!1)), c(X2!1))) | (~test(tptp_fun_X1_0(X2!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(tptp_fun_X1_0(X2!1), X2!1)) = addition(c(tptp_fun_X1_0(X2!1)), c(X2!1))))),
% 19.86/12.92 inference(transitivity,[status(thm)],[151, 149])).
% 19.86/12.92 tff(153,plain,
% 19.86/12.92 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (c(multiplication(tptp_fun_X1_0(X2!1), X2!1)) = addition(c(tptp_fun_X1_0(X2!1)), c(X2!1))) | (~test(tptp_fun_X1_0(X2!1))))),
% 19.86/12.92 inference(quant_inst,[status(thm)],[])).
% 19.86/12.92 tff(154,plain,
% 19.86/12.92 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(tptp_fun_X1_0(X2!1), X2!1)) = addition(c(tptp_fun_X1_0(X2!1)), c(X2!1)))),
% 19.86/12.92 inference(modus_ponens,[status(thm)],[153, 152])).
% 19.86/12.92 tff(155,plain,
% 19.86/12.92 ((~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(tptp_fun_X1_0(X2!1), X2!1)) = addition(c(tptp_fun_X1_0(X2!1)), c(X2!1)))),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[154, 148, 62])).
% 19.86/12.92 tff(156,plain,
% 19.86/12.92 (c(multiplication(tptp_fun_X1_0(X2!1), X2!1)) = addition(c(tptp_fun_X1_0(X2!1)), c(X2!1))),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[155, 99])).
% 19.86/12.92 tff(157,plain,
% 19.86/12.92 (multiplication(multiplication(X1!2, X0!3), c(X2!1)) = zero),
% 19.86/12.92 inference(or_elim,[status(thm)],[60])).
% 19.86/12.92 tff(158,plain,
% 19.86/12.92 (zero = multiplication(multiplication(X1!2, X0!3), c(X2!1))),
% 19.86/12.92 inference(symmetry,[status(thm)],[157])).
% 19.86/12.92 tff(159,plain,
% 19.86/12.92 (multiplication(tptp_fun_X1_0(X2!1), X2!1) = multiplication(multiplication(X1!2, X0!3), c(X2!1))),
% 19.86/12.92 inference(transitivity,[status(thm)],[86, 158])).
% 19.86/12.92 tff(160,plain,
% 19.86/12.92 (c(multiplication(tptp_fun_X1_0(X2!1), X2!1)) = c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))),
% 19.86/12.92 inference(monotonicity,[status(thm)],[159])).
% 19.86/12.92 tff(161,plain,
% 19.86/12.92 (c(multiplication(multiplication(X1!2, X0!3), c(X2!1))) = c(multiplication(tptp_fun_X1_0(X2!1), X2!1))),
% 19.86/12.92 inference(symmetry,[status(thm)],[160])).
% 19.86/12.92 tff(162,plain,
% 19.86/12.92 (c(zero) = c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))),
% 19.86/12.92 inference(monotonicity,[status(thm)],[158])).
% 19.86/12.92 tff(163,assumption,((~((~test(zero)) | complement(tptp_fun_X1_0(zero), zero))) | (~(test(zero) | ![X1: $i] : (~complement(X1, zero))))), introduced(assumption)).
% 19.86/12.92 tff(164,plain,
% 19.86/12.92 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(zero)) | complement(tptp_fun_X1_0(zero), zero))) | (~(test(zero) | ![X1: $i] : (~complement(X1, zero))))))),
% 19.86/12.92 inference(quant_inst,[status(thm)],[])).
% 19.86/12.92 tff(165,plain,
% 19.86/12.92 ($false),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[164, 14, 163])).
% 19.86/12.92 tff(166,plain,(~((~((~test(zero)) | complement(tptp_fun_X1_0(zero), zero))) | (~(test(zero) | ![X1: $i] : (~complement(X1, zero)))))), inference(lemma,lemma(discharge,[]))).
% 19.86/12.92 tff(167,plain,
% 19.86/12.92 (((~((~test(zero)) | complement(tptp_fun_X1_0(zero), zero))) | (~(test(zero) | ![X1: $i] : (~complement(X1, zero))))) | ((~test(zero)) | complement(tptp_fun_X1_0(zero), zero))),
% 19.86/12.92 inference(tautology,[status(thm)],[])).
% 19.86/12.92 tff(168,plain,
% 19.86/12.92 ((~test(zero)) | complement(tptp_fun_X1_0(zero), zero)),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[167, 166])).
% 19.86/12.92 tff(169,assumption,(~(complement(tptp_fun_X1_0(zero), zero) <=> (~((~(multiplication(zero, tptp_fun_X1_0(zero)) = zero)) | (~(multiplication(tptp_fun_X1_0(zero), zero) = zero)) | (~(addition(zero, tptp_fun_X1_0(zero)) = one)))))), introduced(assumption)).
% 19.86/12.92 tff(170,plain,
% 19.86/12.92 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(tptp_fun_X1_0(zero), zero) <=> (~((~(multiplication(zero, tptp_fun_X1_0(zero)) = zero)) | (~(multiplication(tptp_fun_X1_0(zero), zero) = zero)) | (~(addition(zero, tptp_fun_X1_0(zero)) = one)))))),
% 19.86/12.92 inference(quant_inst,[status(thm)],[])).
% 19.86/12.92 tff(171,plain,
% 19.86/12.92 ($false),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[170, 33, 169])).
% 19.86/12.92 tff(172,plain,(complement(tptp_fun_X1_0(zero), zero) <=> (~((~(multiplication(zero, tptp_fun_X1_0(zero)) = zero)) | (~(multiplication(tptp_fun_X1_0(zero), zero) = zero)) | (~(addition(zero, tptp_fun_X1_0(zero)) = one))))), inference(lemma,lemma(discharge,[]))).
% 19.86/12.92 tff(173,plain,
% 19.86/12.92 ((~![A: $i] : (addition(A, zero) = A)) | (addition(tptp_fun_X1_0(zero), zero) = tptp_fun_X1_0(zero))),
% 19.86/12.92 inference(quant_inst,[status(thm)],[])).
% 19.86/12.92 tff(174,plain,
% 19.86/12.92 (addition(tptp_fun_X1_0(zero), zero) = tptp_fun_X1_0(zero)),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[173, 124])).
% 19.86/12.92 tff(175,plain,
% 19.86/12.92 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, tptp_fun_X1_0(zero)) = addition(tptp_fun_X1_0(zero), zero))),
% 19.86/12.92 inference(quant_inst,[status(thm)],[])).
% 19.86/12.92 tff(176,plain,
% 19.86/12.92 (addition(zero, tptp_fun_X1_0(zero)) = addition(tptp_fun_X1_0(zero), zero)),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[175, 81])).
% 19.86/12.92 tff(177,assumption,(~((~(multiplication(zero, tptp_fun_X1_0(zero)) = zero)) | (~(multiplication(tptp_fun_X1_0(zero), zero) = zero)) | (~(addition(zero, tptp_fun_X1_0(zero)) = one)))), introduced(assumption)).
% 19.86/12.92 tff(178,plain,
% 19.86/12.92 (((~(multiplication(zero, tptp_fun_X1_0(zero)) = zero)) | (~(multiplication(tptp_fun_X1_0(zero), zero) = zero)) | (~(addition(zero, tptp_fun_X1_0(zero)) = one))) | (addition(zero, tptp_fun_X1_0(zero)) = one)),
% 19.86/12.92 inference(tautology,[status(thm)],[])).
% 19.86/12.92 tff(179,plain,
% 19.86/12.92 (addition(zero, tptp_fun_X1_0(zero)) = one),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[178, 177])).
% 19.86/12.92 tff(180,plain,
% 19.86/12.92 (one = addition(zero, tptp_fun_X1_0(zero))),
% 19.86/12.92 inference(symmetry,[status(thm)],[179])).
% 19.86/12.92 tff(181,plain,
% 19.86/12.92 ((~![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)))))),
% 19.86/12.92 inference(quant_inst,[status(thm)],[])).
% 19.86/12.92 tff(182,plain,
% 19.86/12.92 (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))))),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[181, 33])).
% 19.86/12.92 tff(183,plain,
% 19.86/12.92 ((~![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))))))),
% 19.86/12.92 inference(quant_inst,[status(thm)],[])).
% 19.86/12.92 tff(184,plain,
% 19.86/12.92 (~((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | (~(test(X1!2) | ![X1: $i] : (~complement(X1, X1!2)))))),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[183, 14])).
% 19.86/12.92 tff(185,plain,
% 19.86/12.92 (((~((~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))),
% 19.86/12.92 inference(tautology,[status(thm)],[])).
% 19.86/12.92 tff(186,plain,
% 19.86/12.92 ((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2)),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[185, 184])).
% 19.86/12.92 tff(187,plain,
% 19.86/12.92 (test(X1!2)),
% 19.86/12.92 inference(and_elim,[status(thm)],[61])).
% 19.86/12.92 tff(188,plain,
% 19.86/12.92 ((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | (~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2)),
% 19.86/12.92 inference(tautology,[status(thm)],[])).
% 19.86/12.92 tff(189,plain,
% 19.86/12.92 ((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | complement(tptp_fun_X1_0(X1!2), X1!2)),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[188, 187])).
% 19.86/12.92 tff(190,plain,
% 19.86/12.92 (complement(tptp_fun_X1_0(X1!2), X1!2)),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[189, 186])).
% 19.86/12.92 tff(191,plain,
% 19.86/12.92 ((~(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))))),
% 19.86/12.92 inference(tautology,[status(thm)],[])).
% 19.86/12.92 tff(192,plain,
% 19.86/12.92 ((~(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))))),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[191, 190])).
% 19.86/12.92 tff(193,plain,
% 19.86/12.92 (~((~(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)))),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[192, 182])).
% 19.86/12.92 tff(194,plain,
% 19.86/12.92 (((~(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)),
% 19.86/12.92 inference(tautology,[status(thm)],[])).
% 19.86/12.92 tff(195,plain,
% 19.86/12.92 (addition(X1!2, tptp_fun_X1_0(X1!2)) = one),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[194, 193])).
% 19.86/12.92 tff(196,plain,
% 19.86/12.92 (((~![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))))),
% 19.86/12.92 inference(rewrite,[status(thm)],[])).
% 19.86/12.92 tff(197,plain,
% 19.86/12.92 ((~![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))))),
% 19.86/12.92 inference(quant_inst,[status(thm)],[])).
% 19.86/12.92 tff(198,plain,
% 19.86/12.92 ((~![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)))),
% 19.86/12.92 inference(modus_ponens,[status(thm)],[197, 196])).
% 19.86/12.92 tff(199,plain,
% 19.86/12.92 ((c(X1!2) = tptp_fun_X1_0(X1!2)) <=> complement(X1!2, tptp_fun_X1_0(X1!2))),
% 19.86/12.92 inference(unit_resolution,[status(thm)],[198, 109, 187])).
% 19.86/12.92 tff(200,plain,
% 19.86/12.92 (((~![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))))))),
% 19.86/12.92 inference(rewrite,[status(thm)],[])).
% 19.86/12.92 tff(201,plain,
% 19.86/12.92 ((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)))))),
% 19.86/12.92 inference(rewrite,[status(thm)],[])).
% 19.86/12.92 tff(202,plain,
% 19.86/12.92 (((~![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))))))),
% 19.86/12.92 inference(monotonicity,[status(thm)],[201])).
% 19.86/12.92 tff(203,plain,
% 19.86/12.92 (((~![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))))))),
% 19.86/12.92 inference(transitivity,[status(thm)],[202, 200])).
% 19.86/12.92 tff(204,plain,
% 19.86/12.92 ((~![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)))))),
% 19.86/12.92 inference(quant_inst,[status(thm)],[])).
% 19.86/12.92 tff(205,plain,
% 19.86/12.92 ((~![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)))))),
% 19.86/12.93 inference(modus_ponens,[status(thm)],[204, 203])).
% 19.86/12.93 tff(206,plain,
% 19.86/12.93 (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))))),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[205, 33])).
% 19.86/12.93 tff(207,plain,
% 19.86/12.93 ((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))),
% 19.86/12.93 inference(commutativity,[status(thm)],[])).
% 19.86/12.93 tff(208,plain,
% 19.86/12.93 (one = addition(X1!2, tptp_fun_X1_0(X1!2))),
% 19.86/12.93 inference(symmetry,[status(thm)],[195])).
% 19.86/12.93 tff(209,plain,
% 19.86/12.93 ((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)))),
% 19.86/12.93 inference(monotonicity,[status(thm)],[208])).
% 19.86/12.93 tff(210,plain,
% 19.86/12.93 ((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))),
% 19.86/12.93 inference(transitivity,[status(thm)],[209, 207])).
% 19.86/12.93 tff(211,plain,
% 19.86/12.93 ((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)),
% 19.86/12.93 inference(symmetry,[status(thm)],[210])).
% 19.86/12.93 tff(212,plain,
% 19.86/12.93 ((~![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))),
% 19.86/12.93 inference(quant_inst,[status(thm)],[])).
% 19.86/12.93 tff(213,plain,
% 19.86/12.93 (addition(X1!2, tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), X1!2)),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[212, 81])).
% 19.86/12.93 tff(214,plain,
% 19.86/12.93 (addition(tptp_fun_X1_0(X1!2), X1!2) = one),
% 19.86/12.93 inference(modus_ponens,[status(thm)],[213, 211])).
% 19.86/12.93 tff(215,plain,
% 19.86/12.93 (((~(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)),
% 19.86/12.93 inference(tautology,[status(thm)],[])).
% 19.86/12.93 tff(216,plain,
% 19.86/12.93 (multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[215, 193])).
% 19.86/12.93 tff(217,plain,
% 19.86/12.93 (((~(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)),
% 19.86/12.93 inference(tautology,[status(thm)],[])).
% 19.86/12.93 tff(218,plain,
% 19.86/12.93 (multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[217, 193])).
% 19.86/12.93 tff(219,plain,
% 19.86/12.93 ((~((~(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))),
% 19.86/12.93 inference(tautology,[status(thm)],[])).
% 19.86/12.93 tff(220,plain,
% 19.86/12.93 ((~((~(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))),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[219, 218, 216])).
% 19.86/12.93 tff(221,plain,
% 19.86/12.93 (~((~(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)))),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[220, 214])).
% 19.86/12.93 tff(222,plain,
% 19.86/12.93 ((~(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)))),
% 19.86/12.93 inference(tautology,[status(thm)],[])).
% 19.86/12.93 tff(223,plain,
% 19.86/12.93 (complement(X1!2, tptp_fun_X1_0(X1!2))),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[222, 221, 206])).
% 19.86/12.93 tff(224,plain,
% 19.86/12.93 ((~((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)))),
% 19.86/12.93 inference(tautology,[status(thm)],[])).
% 19.86/12.93 tff(225,plain,
% 19.86/12.93 (c(X1!2) = tptp_fun_X1_0(X1!2)),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[224, 223, 199])).
% 19.86/12.93 tff(226,plain,
% 19.86/12.93 (tptp_fun_X1_0(X1!2) = c(X1!2)),
% 19.86/12.93 inference(symmetry,[status(thm)],[225])).
% 19.86/12.93 tff(227,assumption,((~((~test(tptp_fun_X1_0(X1!2))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X1!2)))) | (~(test(tptp_fun_X1_0(X1!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!2)))))), introduced(assumption)).
% 19.86/12.93 tff(228,plain,
% 19.86/12.93 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(tptp_fun_X1_0(X1!2))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X1!2)))) | (~(test(tptp_fun_X1_0(X1!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!2)))))))),
% 19.86/12.93 inference(quant_inst,[status(thm)],[])).
% 19.86/12.93 tff(229,plain,
% 19.86/12.93 ($false),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[228, 14, 227])).
% 19.86/12.93 tff(230,plain,(~((~((~test(tptp_fun_X1_0(X1!2))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X1!2)))) | (~(test(tptp_fun_X1_0(X1!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!2))))))), inference(lemma,lemma(discharge,[]))).
% 19.86/12.93 tff(231,plain,
% 19.86/12.93 (((~((~test(tptp_fun_X1_0(X1!2))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X1!2)))) | (~(test(tptp_fun_X1_0(X1!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!2)))))) | (test(tptp_fun_X1_0(X1!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!2))))),
% 19.86/12.93 inference(tautology,[status(thm)],[])).
% 19.86/12.93 tff(232,plain,
% 19.86/12.93 (test(tptp_fun_X1_0(X1!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!2)))),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[231, 230])).
% 19.86/12.93 tff(233,assumption,(![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!2)))), introduced(assumption)).
% 19.86/12.93 tff(234,plain,
% 19.86/12.93 ((~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!2)))) | (~complement(X1!2, tptp_fun_X1_0(X1!2)))),
% 19.86/12.93 inference(quant_inst,[status(thm)],[])).
% 19.86/12.93 tff(235,plain,
% 19.86/12.93 ($false),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[234, 223, 233])).
% 19.86/12.93 tff(236,plain,(~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!2)))), inference(lemma,lemma(discharge,[]))).
% 19.86/12.93 tff(237,plain,
% 19.86/12.93 ((~(test(tptp_fun_X1_0(X1!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!2))))) | test(tptp_fun_X1_0(X1!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!2)))),
% 19.86/12.93 inference(tautology,[status(thm)],[])).
% 19.86/12.93 tff(238,plain,
% 19.86/12.93 ((~(test(tptp_fun_X1_0(X1!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!2))))) | test(tptp_fun_X1_0(X1!2))),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[237, 236])).
% 19.86/12.93 tff(239,plain,
% 19.86/12.93 (test(tptp_fun_X1_0(X1!2))),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[238, 232])).
% 19.86/12.93 tff(240,plain,
% 19.86/12.93 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X1!2))) | ((c(tptp_fun_X1_0(X1!2)) = X1!2) <=> complement(tptp_fun_X1_0(X1!2), X1!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X1!2))) | ((c(tptp_fun_X1_0(X1!2)) = X1!2) <=> complement(tptp_fun_X1_0(X1!2), X1!2)))),
% 19.86/12.93 inference(rewrite,[status(thm)],[])).
% 19.86/12.93 tff(241,plain,
% 19.86/12.93 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X1!2))) | ((c(tptp_fun_X1_0(X1!2)) = X1!2) <=> complement(tptp_fun_X1_0(X1!2), X1!2)))),
% 19.86/12.93 inference(quant_inst,[status(thm)],[])).
% 19.86/12.93 tff(242,plain,
% 19.86/12.93 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X1!2))) | ((c(tptp_fun_X1_0(X1!2)) = X1!2) <=> complement(tptp_fun_X1_0(X1!2), X1!2))),
% 19.86/12.93 inference(modus_ponens,[status(thm)],[241, 240])).
% 19.86/12.93 tff(243,plain,
% 19.86/12.93 ((~test(tptp_fun_X1_0(X1!2))) | ((c(tptp_fun_X1_0(X1!2)) = X1!2) <=> complement(tptp_fun_X1_0(X1!2), X1!2))),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[242, 109])).
% 19.86/12.93 tff(244,plain,
% 19.86/12.93 ((c(tptp_fun_X1_0(X1!2)) = X1!2) <=> complement(tptp_fun_X1_0(X1!2), X1!2)),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[243, 239])).
% 19.86/12.93 tff(245,plain,
% 19.86/12.93 ((~((c(tptp_fun_X1_0(X1!2)) = X1!2) <=> complement(tptp_fun_X1_0(X1!2), X1!2))) | (c(tptp_fun_X1_0(X1!2)) = X1!2) | (~complement(tptp_fun_X1_0(X1!2), X1!2))),
% 19.86/12.93 inference(tautology,[status(thm)],[])).
% 19.86/12.93 tff(246,plain,
% 19.86/12.93 ((~((c(tptp_fun_X1_0(X1!2)) = X1!2) <=> complement(tptp_fun_X1_0(X1!2), X1!2))) | (c(tptp_fun_X1_0(X1!2)) = X1!2)),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[245, 190])).
% 19.86/12.93 tff(247,plain,
% 19.86/12.93 (c(tptp_fun_X1_0(X1!2)) = X1!2),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[246, 244])).
% 19.86/12.93 tff(248,plain,
% 19.86/12.93 (X1!2 = c(tptp_fun_X1_0(X1!2))),
% 19.86/12.93 inference(symmetry,[status(thm)],[247])).
% 19.86/12.93 tff(249,plain,
% 19.86/12.93 (addition(X1!2, tptp_fun_X1_0(X1!2)) = addition(c(tptp_fun_X1_0(X1!2)), c(X1!2))),
% 19.86/12.93 inference(monotonicity,[status(thm)],[248, 226])).
% 19.86/12.93 tff(250,plain,
% 19.86/12.93 (addition(c(tptp_fun_X1_0(X1!2)), c(X1!2)) = addition(X1!2, tptp_fun_X1_0(X1!2))),
% 19.86/12.93 inference(symmetry,[status(thm)],[249])).
% 19.86/12.93 tff(251,plain,
% 19.86/12.93 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!2)) | (~test(tptp_fun_X1_0(X1!2))) | (c(multiplication(tptp_fun_X1_0(X1!2), X1!2)) = addition(c(tptp_fun_X1_0(X1!2)), c(X1!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!2)) | (~test(tptp_fun_X1_0(X1!2))) | (c(multiplication(tptp_fun_X1_0(X1!2), X1!2)) = addition(c(tptp_fun_X1_0(X1!2)), c(X1!2))))),
% 19.86/12.93 inference(rewrite,[status(thm)],[])).
% 19.86/12.93 tff(252,plain,
% 19.86/12.93 (((~test(X1!2)) | (c(multiplication(tptp_fun_X1_0(X1!2), X1!2)) = addition(c(tptp_fun_X1_0(X1!2)), c(X1!2))) | (~test(tptp_fun_X1_0(X1!2)))) <=> ((~test(X1!2)) | (~test(tptp_fun_X1_0(X1!2))) | (c(multiplication(tptp_fun_X1_0(X1!2), X1!2)) = addition(c(tptp_fun_X1_0(X1!2)), c(X1!2))))),
% 19.86/12.93 inference(rewrite,[status(thm)],[])).
% 19.86/12.93 tff(253,plain,
% 19.86/12.93 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!2)) | (c(multiplication(tptp_fun_X1_0(X1!2), X1!2)) = addition(c(tptp_fun_X1_0(X1!2)), c(X1!2))) | (~test(tptp_fun_X1_0(X1!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!2)) | (~test(tptp_fun_X1_0(X1!2))) | (c(multiplication(tptp_fun_X1_0(X1!2), X1!2)) = addition(c(tptp_fun_X1_0(X1!2)), c(X1!2)))))),
% 19.86/12.93 inference(monotonicity,[status(thm)],[252])).
% 19.86/12.93 tff(254,plain,
% 19.86/12.93 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!2)) | (c(multiplication(tptp_fun_X1_0(X1!2), X1!2)) = addition(c(tptp_fun_X1_0(X1!2)), c(X1!2))) | (~test(tptp_fun_X1_0(X1!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!2)) | (~test(tptp_fun_X1_0(X1!2))) | (c(multiplication(tptp_fun_X1_0(X1!2), X1!2)) = addition(c(tptp_fun_X1_0(X1!2)), c(X1!2))))),
% 19.86/12.93 inference(transitivity,[status(thm)],[253, 251])).
% 19.86/12.93 tff(255,plain,
% 19.86/12.93 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!2)) | (c(multiplication(tptp_fun_X1_0(X1!2), X1!2)) = addition(c(tptp_fun_X1_0(X1!2)), c(X1!2))) | (~test(tptp_fun_X1_0(X1!2))))),
% 19.86/12.93 inference(quant_inst,[status(thm)],[])).
% 19.86/12.93 tff(256,plain,
% 19.86/12.93 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!2)) | (~test(tptp_fun_X1_0(X1!2))) | (c(multiplication(tptp_fun_X1_0(X1!2), X1!2)) = addition(c(tptp_fun_X1_0(X1!2)), c(X1!2)))),
% 19.86/12.93 inference(modus_ponens,[status(thm)],[255, 254])).
% 19.86/12.93 tff(257,plain,
% 19.86/12.93 ((~test(tptp_fun_X1_0(X1!2))) | (c(multiplication(tptp_fun_X1_0(X1!2), X1!2)) = addition(c(tptp_fun_X1_0(X1!2)), c(X1!2)))),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[256, 148, 187])).
% 19.86/12.93 tff(258,plain,
% 19.86/12.93 (c(multiplication(tptp_fun_X1_0(X1!2), X1!2)) = addition(c(tptp_fun_X1_0(X1!2)), c(X1!2))),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[257, 239])).
% 19.86/12.93 tff(259,plain,
% 19.86/12.93 (multiplication(tptp_fun_X1_0(X1!2), X1!2) = multiplication(multiplication(X1!2, X0!3), c(X2!1))),
% 19.86/12.93 inference(transitivity,[status(thm)],[216, 158])).
% 19.86/12.93 tff(260,plain,
% 19.86/12.93 (c(multiplication(tptp_fun_X1_0(X1!2), X1!2)) = c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))),
% 19.86/12.93 inference(monotonicity,[status(thm)],[259])).
% 19.86/12.93 tff(261,plain,
% 19.86/12.93 (c(multiplication(multiplication(X1!2, X0!3), c(X2!1))) = c(multiplication(tptp_fun_X1_0(X1!2), X1!2))),
% 19.86/12.93 inference(symmetry,[status(thm)],[260])).
% 19.86/12.93 tff(262,plain,
% 19.86/12.93 (c(multiplication(multiplication(X1!2, X0!3), c(X2!1))) = tptp_fun_X1_0(zero)),
% 19.86/12.93 inference(transitivity,[status(thm)],[261, 258, 250, 195, 180, 176, 174])).
% 19.86/12.93 tff(263,plain,
% 19.86/12.93 (multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))) = multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), tptp_fun_X1_0(zero))),
% 19.86/12.93 inference(monotonicity,[status(thm)],[262])).
% 19.86/12.93 tff(264,plain,
% 19.86/12.93 (multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), tptp_fun_X1_0(zero)) = multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), c(multiplication(multiplication(X1!2, X0!3), c(X2!1))))),
% 19.86/12.93 inference(symmetry,[status(thm)],[263])).
% 19.86/12.93 tff(265,plain,
% 19.86/12.93 (addition(tptp_fun_X1_0(zero), zero) = addition(zero, tptp_fun_X1_0(zero))),
% 19.86/12.93 inference(symmetry,[status(thm)],[176])).
% 19.86/12.93 tff(266,plain,
% 19.86/12.93 (tptp_fun_X1_0(zero) = addition(tptp_fun_X1_0(zero), zero)),
% 19.86/12.93 inference(symmetry,[status(thm)],[174])).
% 19.86/12.93 tff(267,plain,
% 19.86/12.93 (tptp_fun_X1_0(zero) = one),
% 19.86/12.93 inference(transitivity,[status(thm)],[266, 265, 179])).
% 19.86/12.93 tff(268,plain,
% 19.86/12.93 (multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), tptp_fun_X1_0(zero)) = multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), one)),
% 19.86/12.93 inference(monotonicity,[status(thm)],[267])).
% 19.86/12.93 tff(269,plain,
% 19.86/12.93 (multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), one) = multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), tptp_fun_X1_0(zero))),
% 19.86/12.93 inference(symmetry,[status(thm)],[268])).
% 19.86/12.93 tff(270,plain,
% 19.86/12.93 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 19.86/12.93 inference(bind,[status(th)],[])).
% 19.86/12.93 tff(271,plain,
% 19.86/12.93 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 19.86/12.93 inference(quant_intro,[status(thm)],[270])).
% 19.86/12.93 tff(272,plain,
% 19.86/12.93 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 19.86/12.93 inference(rewrite,[status(thm)],[])).
% 19.86/12.93 tff(273,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 19.86/12.93 tff(274,plain,
% 19.86/12.93 (![A: $i] : (multiplication(A, one) = A)),
% 19.86/12.93 inference(modus_ponens,[status(thm)],[273, 272])).
% 19.86/12.93 tff(275,plain,(
% 19.86/12.93 ![A: $i] : (multiplication(A, one) = A)),
% 19.86/12.93 inference(skolemize,[status(sab)],[274])).
% 19.86/12.93 tff(276,plain,
% 19.86/12.93 (![A: $i] : (multiplication(A, one) = A)),
% 19.86/12.93 inference(modus_ponens,[status(thm)],[275, 271])).
% 19.86/12.93 tff(277,plain,
% 19.86/12.93 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), one) = multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)))),
% 19.86/12.93 inference(quant_inst,[status(thm)],[])).
% 19.86/12.93 tff(278,plain,
% 19.86/12.93 (multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), one) = multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero))),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[277, 276])).
% 19.86/12.93 tff(279,plain,
% 19.86/12.93 (multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)) = multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), one)),
% 19.86/12.93 inference(symmetry,[status(thm)],[278])).
% 19.86/12.93 tff(280,plain,
% 19.86/12.93 (multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)) = multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), c(multiplication(multiplication(X1!2, X0!3), c(X2!1))))),
% 19.86/12.93 inference(transitivity,[status(thm)],[279, 269, 264])).
% 19.86/12.93 tff(281,plain,
% 19.86/12.93 (addition(multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero))) = addition(multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero), multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))))),
% 19.86/12.93 inference(monotonicity,[status(thm)],[280])).
% 19.86/12.93 tff(282,plain,
% 19.86/12.93 (addition(multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero), multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), c(multiplication(multiplication(X1!2, X0!3), c(X2!1))))) = addition(multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)))),
% 19.86/12.93 inference(symmetry,[status(thm)],[281])).
% 19.86/12.93 tff(283,plain,
% 19.86/12.93 (^[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))))),
% 19.86/12.93 inference(bind,[status(th)],[])).
% 19.86/12.93 tff(284,plain,
% 19.86/12.93 (![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)))),
% 19.86/12.93 inference(quant_intro,[status(thm)],[283])).
% 19.86/12.93 tff(285,plain,
% 19.86/12.93 (![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)))),
% 19.86/12.93 inference(rewrite,[status(thm)],[])).
% 19.86/12.93 tff(286,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')).
% 19.86/12.93 tff(287,plain,
% 19.86/12.93 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 19.86/12.93 inference(modus_ponens,[status(thm)],[286, 285])).
% 19.86/12.93 tff(288,plain,(
% 19.86/12.93 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 19.86/12.93 inference(skolemize,[status(sab)],[287])).
% 19.86/12.93 tff(289,plain,
% 19.86/12.93 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 19.86/12.93 inference(modus_ponens,[status(thm)],[288, 284])).
% 19.86/12.93 tff(290,plain,
% 19.86/12.93 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), addition(zero, c(multiplication(multiplication(X1!2, X0!3), c(X2!1))))) = addition(multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero), multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), c(multiplication(multiplication(X1!2, X0!3), c(X2!1))))))),
% 19.86/12.93 inference(quant_inst,[status(thm)],[])).
% 19.86/12.93 tff(291,plain,
% 19.86/12.93 (multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), addition(zero, c(multiplication(multiplication(X1!2, X0!3), c(X2!1))))) = addition(multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero), multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))))),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[290, 289])).
% 19.86/12.93 tff(292,plain,
% 19.86/12.93 (addition(zero, c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))) = addition(zero, tptp_fun_X1_0(zero))),
% 19.86/12.93 inference(monotonicity,[status(thm)],[262])).
% 19.86/12.93 tff(293,plain,
% 19.86/12.93 (addition(zero, c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))) = tptp_fun_X1_0(zero)),
% 19.86/12.93 inference(transitivity,[status(thm)],[292, 176, 174])).
% 19.86/12.93 tff(294,plain,
% 19.86/12.93 (multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), addition(zero, c(multiplication(multiplication(X1!2, X0!3), c(X2!1))))) = multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), tptp_fun_X1_0(zero))),
% 19.86/12.93 inference(monotonicity,[status(thm)],[293])).
% 19.86/12.93 tff(295,plain,
% 19.86/12.93 (multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), tptp_fun_X1_0(zero)) = multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), addition(zero, c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))))),
% 19.86/12.93 inference(symmetry,[status(thm)],[294])).
% 19.86/12.93 tff(296,plain,
% 19.86/12.93 (one = tptp_fun_X1_0(zero)),
% 19.86/12.93 inference(transitivity,[status(thm)],[180, 176, 174])).
% 19.86/12.93 tff(297,plain,
% 19.86/12.93 (multiplication(c(tptp_fun_X1_0(X2!1)), one) = multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero))),
% 19.86/12.93 inference(monotonicity,[status(thm)],[296])).
% 19.86/12.93 tff(298,plain,
% 19.86/12.93 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(c(tptp_fun_X1_0(X2!1)), one) = c(tptp_fun_X1_0(X2!1)))),
% 19.86/12.93 inference(quant_inst,[status(thm)],[])).
% 19.86/12.93 tff(299,plain,
% 19.86/12.93 (multiplication(c(tptp_fun_X1_0(X2!1)), one) = c(tptp_fun_X1_0(X2!1))),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[298, 276])).
% 19.86/12.93 tff(300,plain,
% 19.86/12.93 (c(tptp_fun_X1_0(X2!1)) = multiplication(c(tptp_fun_X1_0(X2!1)), one)),
% 19.86/12.93 inference(symmetry,[status(thm)],[299])).
% 19.86/12.93 tff(301,plain,
% 19.86/12.93 (X2!1 = c(tptp_fun_X1_0(X2!1))),
% 19.86/12.93 inference(symmetry,[status(thm)],[117])).
% 19.86/12.93 tff(302,plain,
% 19.86/12.93 (X2!1 = addition(multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)))),
% 19.86/12.93 inference(transitivity,[status(thm)],[301, 300, 297, 279, 269, 295, 291, 282])).
% 19.86/12.93 tff(303,plain,
% 19.86/12.93 (^[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)))),
% 19.86/12.93 inference(bind,[status(th)],[])).
% 19.86/12.93 tff(304,plain,
% 19.86/12.93 (![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))),
% 19.86/12.93 inference(quant_intro,[status(thm)],[303])).
% 19.86/12.93 tff(305,plain,
% 19.86/12.93 (![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))),
% 19.86/12.93 inference(rewrite,[status(thm)],[])).
% 19.86/12.93 tff(306,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_associativity')).
% 19.86/12.93 tff(307,plain,
% 19.86/12.93 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 19.86/12.93 inference(modus_ponens,[status(thm)],[306, 305])).
% 19.86/12.93 tff(308,plain,(
% 19.86/12.93 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 19.86/12.93 inference(skolemize,[status(sab)],[307])).
% 19.86/12.93 tff(309,plain,
% 19.86/12.93 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 19.86/12.93 inference(modus_ponens,[status(thm)],[308, 304])).
% 19.86/12.93 tff(310,plain,
% 19.86/12.93 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3)) = multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3))),
% 19.86/12.93 inference(quant_inst,[status(thm)],[])).
% 19.86/12.93 tff(311,plain,
% 19.86/12.93 (multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3)) = multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3)),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[310, 309])).
% 19.86/12.93 tff(312,plain,
% 19.86/12.93 (multiplication(one, multiplication(X1!2, X0!3)) = multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3))),
% 19.86/12.93 inference(monotonicity,[status(thm)],[296])).
% 19.86/12.93 tff(313,plain,
% 19.86/12.93 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 19.86/12.93 inference(bind,[status(th)],[])).
% 19.86/12.93 tff(314,plain,
% 19.86/12.93 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 19.86/12.93 inference(quant_intro,[status(thm)],[313])).
% 19.86/12.93 tff(315,plain,
% 19.86/12.93 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 19.86/12.93 inference(rewrite,[status(thm)],[])).
% 19.86/12.93 tff(316,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 19.86/12.93 tff(317,plain,
% 19.86/12.93 (![A: $i] : (multiplication(one, A) = A)),
% 19.86/12.93 inference(modus_ponens,[status(thm)],[316, 315])).
% 19.86/12.93 tff(318,plain,(
% 19.86/12.93 ![A: $i] : (multiplication(one, A) = A)),
% 19.86/12.93 inference(skolemize,[status(sab)],[317])).
% 19.86/12.93 tff(319,plain,
% 19.86/12.93 (![A: $i] : (multiplication(one, A) = A)),
% 19.86/12.93 inference(modus_ponens,[status(thm)],[318, 314])).
% 19.86/12.93 tff(320,plain,
% 19.86/12.93 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, multiplication(X1!2, X0!3)) = multiplication(X1!2, X0!3))),
% 19.86/12.93 inference(quant_inst,[status(thm)],[])).
% 19.86/12.93 tff(321,plain,
% 19.86/12.93 (multiplication(one, multiplication(X1!2, X0!3)) = multiplication(X1!2, X0!3)),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[320, 319])).
% 19.86/12.93 tff(322,plain,
% 19.86/12.93 (multiplication(X1!2, X0!3) = multiplication(one, multiplication(X1!2, X0!3))),
% 19.86/12.93 inference(symmetry,[status(thm)],[321])).
% 19.86/12.93 tff(323,plain,
% 19.86/12.93 (multiplication(X1!2, X0!3) = multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3)),
% 19.86/12.93 inference(transitivity,[status(thm)],[322, 312, 311])).
% 19.86/12.93 tff(324,plain,
% 19.86/12.93 (multiplication(multiplication(X1!2, X0!3), X2!1) = multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), addition(multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero))))),
% 19.86/12.93 inference(monotonicity,[status(thm)],[323, 302])).
% 19.86/12.93 tff(325,plain,
% 19.86/12.93 (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), addition(multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)))) = multiplication(multiplication(X1!2, X0!3), X2!1)),
% 19.86/12.93 inference(symmetry,[status(thm)],[324])).
% 19.86/12.93 tff(326,plain,
% 19.86/12.93 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), addition(multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)))) = addition(multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero)), multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)))))),
% 19.86/12.93 inference(quant_inst,[status(thm)],[])).
% 19.86/12.93 tff(327,plain,
% 19.86/12.93 (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), addition(multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)))) = addition(multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero)), multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero))))),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[326, 289])).
% 19.86/12.93 tff(328,plain,
% 19.86/12.93 (addition(multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero)), multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)))) = multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), addition(multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero))))),
% 19.86/12.93 inference(symmetry,[status(thm)],[327])).
% 19.86/12.93 tff(329,plain,
% 19.86/12.93 (multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3) = multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3))),
% 19.86/12.93 inference(symmetry,[status(thm)],[311])).
% 19.86/12.93 tff(330,plain,
% 19.86/12.93 (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero))) = multiplication(multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3)), multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)))),
% 19.86/12.93 inference(monotonicity,[status(thm)],[329])).
% 19.86/12.93 tff(331,plain,
% 19.86/12.93 (multiplication(multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3)), multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero))) = multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)))),
% 19.86/12.93 inference(symmetry,[status(thm)],[330])).
% 19.86/12.93 tff(332,plain,
% 19.86/12.93 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3)), multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero))) = multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3)), tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)))),
% 19.86/12.93 inference(quant_inst,[status(thm)],[])).
% 19.86/12.93 tff(333,plain,
% 19.86/12.93 (multiplication(multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3)), multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero))) = multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3)), tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero))),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[332, 309])).
% 19.86/12.93 tff(334,plain,
% 19.86/12.93 (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3)), tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)) = multiplication(multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3)), multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)))),
% 19.86/12.93 inference(symmetry,[status(thm)],[333])).
% 19.86/12.93 tff(335,plain,
% 19.86/12.93 (((~(multiplication(zero, tptp_fun_X1_0(zero)) = zero)) | (~(multiplication(tptp_fun_X1_0(zero), zero) = zero)) | (~(addition(zero, tptp_fun_X1_0(zero)) = one))) | (multiplication(tptp_fun_X1_0(zero), zero) = zero)),
% 19.86/12.93 inference(tautology,[status(thm)],[])).
% 19.86/12.93 tff(336,plain,
% 19.86/12.93 (multiplication(tptp_fun_X1_0(zero), zero) = zero),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[335, 177])).
% 19.86/12.93 tff(337,plain,
% 19.86/12.93 (multiplication(multiplication(X1!2, X0!3), tptp_fun_X1_0(X2!1)) = multiplication(multiplication(X1!2, X0!3), c(X2!1))),
% 19.86/12.93 inference(monotonicity,[status(thm)],[133])).
% 19.86/12.93 tff(338,plain,
% 19.86/12.93 (multiplication(multiplication(X1!2, X0!3), tptp_fun_X1_0(X2!1)) = zero),
% 19.86/12.93 inference(transitivity,[status(thm)],[337, 157])).
% 19.86/12.93 tff(339,plain,
% 19.86/12.93 (multiplication(tptp_fun_X1_0(zero), multiplication(multiplication(X1!2, X0!3), tptp_fun_X1_0(X2!1))) = multiplication(tptp_fun_X1_0(zero), zero)),
% 19.86/12.93 inference(monotonicity,[status(thm)],[338])).
% 19.86/12.93 tff(340,plain,
% 19.86/12.93 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(zero), multiplication(multiplication(X1!2, X0!3), tptp_fun_X1_0(X2!1))) = multiplication(multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3)), tptp_fun_X1_0(X2!1)))),
% 19.86/12.93 inference(quant_inst,[status(thm)],[])).
% 19.86/12.93 tff(341,plain,
% 19.86/12.93 (multiplication(tptp_fun_X1_0(zero), multiplication(multiplication(X1!2, X0!3), tptp_fun_X1_0(X2!1))) = multiplication(multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3)), tptp_fun_X1_0(X2!1))),
% 19.86/12.93 inference(unit_resolution,[status(thm)],[340, 309])).
% 19.86/12.93 tff(342,plain,
% 19.86/12.93 (multiplication(multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3)), tptp_fun_X1_0(X2!1)) = multiplication(tptp_fun_X1_0(zero), multiplication(multiplication(X1!2, X0!3), tptp_fun_X1_0(X2!1)))),
% 19.86/12.94 inference(symmetry,[status(thm)],[341])).
% 19.86/12.94 tff(343,plain,
% 19.86/12.94 (multiplication(multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3)), tptp_fun_X1_0(X2!1)) = zero),
% 19.86/12.94 inference(transitivity,[status(thm)],[342, 339, 336])).
% 19.86/12.94 tff(344,plain,
% 19.86/12.94 (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3)), tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)) = multiplication(zero, tptp_fun_X1_0(zero))),
% 19.86/12.94 inference(monotonicity,[status(thm)],[343])).
% 19.86/12.94 tff(345,plain,
% 19.86/12.94 (multiplication(zero, tptp_fun_X1_0(zero)) = multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), multiplication(X1!2, X0!3)), tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero))),
% 19.86/12.94 inference(symmetry,[status(thm)],[344])).
% 19.86/12.94 tff(346,plain,
% 19.86/12.94 (((~(multiplication(zero, tptp_fun_X1_0(zero)) = zero)) | (~(multiplication(tptp_fun_X1_0(zero), zero) = zero)) | (~(addition(zero, tptp_fun_X1_0(zero)) = one))) | (multiplication(zero, tptp_fun_X1_0(zero)) = zero)),
% 19.86/12.94 inference(tautology,[status(thm)],[])).
% 19.86/12.94 tff(347,plain,
% 19.86/12.94 (multiplication(zero, tptp_fun_X1_0(zero)) = zero),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[346, 177])).
% 19.86/12.94 tff(348,plain,
% 19.86/12.94 (zero = multiplication(zero, tptp_fun_X1_0(zero))),
% 19.86/12.94 inference(symmetry,[status(thm)],[347])).
% 19.86/12.94 tff(349,plain,
% 19.86/12.94 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 19.86/12.94 inference(bind,[status(th)],[])).
% 19.86/12.94 tff(350,plain,
% 19.86/12.94 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 19.86/12.94 inference(quant_intro,[status(thm)],[349])).
% 19.86/12.94 tff(351,plain,
% 19.86/12.94 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 19.86/12.94 inference(rewrite,[status(thm)],[])).
% 19.86/12.94 tff(352,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 19.86/12.94 tff(353,plain,
% 19.86/12.94 (![A: $i] : (multiplication(zero, A) = zero)),
% 19.86/12.94 inference(modus_ponens,[status(thm)],[352, 351])).
% 19.86/12.94 tff(354,plain,(
% 19.86/12.94 ![A: $i] : (multiplication(zero, A) = zero)),
% 19.86/12.94 inference(skolemize,[status(sab)],[353])).
% 19.86/12.94 tff(355,plain,
% 19.86/12.94 (![A: $i] : (multiplication(zero, A) = zero)),
% 19.86/12.94 inference(modus_ponens,[status(thm)],[354, 350])).
% 19.86/12.94 tff(356,plain,
% 19.86/12.94 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, zero) = zero)),
% 19.86/12.94 inference(quant_inst,[status(thm)],[])).
% 19.86/12.94 tff(357,plain,
% 19.86/12.94 (multiplication(zero, zero) = zero),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[356, 355])).
% 19.86/12.94 tff(358,plain,
% 19.86/12.94 (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero))) = zero),
% 19.86/12.94 inference(transitivity,[status(thm)],[330, 333, 344, 347])).
% 19.86/12.94 tff(359,plain,
% 19.86/12.94 (multiplication(multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero))), zero) = multiplication(zero, zero)),
% 19.86/12.94 inference(monotonicity,[status(thm)],[358])).
% 19.86/12.94 tff(360,plain,
% 19.86/12.94 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)), zero)) = multiplication(multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero))), zero))),
% 19.86/12.94 inference(quant_inst,[status(thm)],[])).
% 19.86/12.94 tff(361,plain,
% 19.86/12.94 (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)), zero)) = multiplication(multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero))), zero)),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[360, 309])).
% 19.86/12.94 tff(362,plain,
% 19.86/12.94 (^[A: $i] : refl((multiplication(A, zero) = zero) <=> (multiplication(A, zero) = zero))),
% 19.86/12.94 inference(bind,[status(th)],[])).
% 19.86/12.94 tff(363,plain,
% 19.86/12.94 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 19.86/12.94 inference(quant_intro,[status(thm)],[362])).
% 19.86/12.94 tff(364,plain,
% 19.86/12.94 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 19.86/12.94 inference(rewrite,[status(thm)],[])).
% 19.86/12.94 tff(365,axiom,(![A: $i] : (multiplication(A, zero) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','right_annihilation')).
% 19.86/12.94 tff(366,plain,
% 19.86/12.94 (![A: $i] : (multiplication(A, zero) = zero)),
% 19.86/12.94 inference(modus_ponens,[status(thm)],[365, 364])).
% 19.86/12.94 tff(367,plain,(
% 19.86/12.94 ![A: $i] : (multiplication(A, zero) = zero)),
% 19.86/12.94 inference(skolemize,[status(sab)],[366])).
% 19.86/12.94 tff(368,plain,
% 19.86/12.94 (![A: $i] : (multiplication(A, zero) = zero)),
% 19.86/12.94 inference(modus_ponens,[status(thm)],[367, 363])).
% 19.86/12.94 tff(369,plain,
% 19.86/12.94 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)), zero) = zero)),
% 19.86/12.94 inference(quant_inst,[status(thm)],[])).
% 19.86/12.94 tff(370,plain,
% 19.86/12.94 (multiplication(multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)), zero) = zero),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[369, 368])).
% 19.86/12.94 tff(371,plain,
% 19.86/12.94 (zero = multiplication(multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)), zero)),
% 19.86/12.94 inference(symmetry,[status(thm)],[370])).
% 19.86/12.94 tff(372,plain,
% 19.86/12.94 (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), zero) = multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)), zero))),
% 19.86/12.94 inference(monotonicity,[status(thm)],[371])).
% 19.86/12.94 tff(373,plain,
% 19.86/12.94 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero) = zero)),
% 19.86/12.94 inference(quant_inst,[status(thm)],[])).
% 19.86/12.94 tff(374,plain,
% 19.86/12.94 (multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero) = zero),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[373, 368])).
% 19.86/12.94 tff(375,plain,
% 19.86/12.94 (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero)) = multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), zero)),
% 19.86/12.94 inference(monotonicity,[status(thm)],[374])).
% 19.86/12.94 tff(376,plain,
% 19.86/12.94 (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero)) = multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)))),
% 19.86/12.94 inference(transitivity,[status(thm)],[375, 372, 361, 359, 357, 348, 345, 334, 331])).
% 19.86/12.94 tff(377,plain,
% 19.86/12.94 (addition(multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero)), multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)))) = addition(multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero))), multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero))))),
% 19.86/12.94 inference(monotonicity,[status(thm)],[376])).
% 19.86/12.94 tff(378,plain,
% 19.86/12.94 (addition(multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero))), multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)))) = addition(multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)), zero)), multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero))))),
% 19.86/12.94 inference(symmetry,[status(thm)],[377])).
% 19.86/12.94 tff(379,plain,
% 19.86/12.94 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), addition(multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)))) = addition(multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero))), multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)))))),
% 19.86/12.94 inference(quant_inst,[status(thm)],[])).
% 19.86/12.94 tff(380,plain,
% 19.86/12.94 (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), addition(multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)))) = addition(multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero))), multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero))))),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[379, 289])).
% 19.86/12.94 tff(381,plain,
% 19.86/12.94 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(c(multiplication(multiplication(X1!2, X0!3), c(X2!1))), one) = c(multiplication(multiplication(X1!2, X0!3), c(X2!1))))),
% 19.86/12.94 inference(quant_inst,[status(thm)],[])).
% 19.86/12.94 tff(382,plain,
% 19.86/12.94 (multiplication(c(multiplication(multiplication(X1!2, X0!3), c(X2!1))), one) = c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[381, 276])).
% 19.86/12.94 tff(383,plain,
% 19.86/12.94 (addition(c(tptp_fun_X1_0(X1!2)), c(X1!2)) = c(multiplication(tptp_fun_X1_0(X1!2), X1!2))),
% 19.86/12.94 inference(symmetry,[status(thm)],[258])).
% 19.86/12.94 tff(384,plain,
% 19.86/12.94 (tptp_fun_X1_0(zero) = c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))),
% 19.86/12.94 inference(transitivity,[status(thm)],[266, 265, 179, 208, 249, 383, 260])).
% 19.86/12.94 tff(385,plain,
% 19.86/12.94 (multiplication(tptp_fun_X1_0(zero), tptp_fun_X1_0(zero)) = multiplication(c(multiplication(multiplication(X1!2, X0!3), c(X2!1))), one)),
% 19.86/12.94 inference(monotonicity,[status(thm)],[384, 267])).
% 19.86/12.94 tff(386,plain,
% 19.86/12.94 (multiplication(X2!1, tptp_fun_X1_0(X2!1)) = multiplication(multiplication(X1!2, X0!3), c(X2!1))),
% 19.86/12.94 inference(transitivity,[status(thm)],[88, 158])).
% 19.86/12.94 tff(387,plain,
% 19.86/12.94 (c(multiplication(X2!1, tptp_fun_X1_0(X2!1))) = c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))),
% 19.86/12.94 inference(monotonicity,[status(thm)],[386])).
% 19.86/12.94 tff(388,plain,
% 19.86/12.94 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(X2!1, tptp_fun_X1_0(X2!1))) = addition(c(X2!1), c(tptp_fun_X1_0(X2!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(X2!1, tptp_fun_X1_0(X2!1))) = addition(c(X2!1), c(tptp_fun_X1_0(X2!1)))))),
% 19.86/12.94 inference(rewrite,[status(thm)],[])).
% 19.86/12.94 tff(389,plain,
% 19.86/12.94 (((~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(X2!1, tptp_fun_X1_0(X2!1))) = addition(c(X2!1), c(tptp_fun_X1_0(X2!1)))) | (~test(X2!1))) <=> ((~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(X2!1, tptp_fun_X1_0(X2!1))) = addition(c(X2!1), c(tptp_fun_X1_0(X2!1)))))),
% 19.86/12.94 inference(rewrite,[status(thm)],[])).
% 19.86/12.94 tff(390,plain,
% 19.86/12.94 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(X2!1, tptp_fun_X1_0(X2!1))) = addition(c(X2!1), c(tptp_fun_X1_0(X2!1)))) | (~test(X2!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(X2!1, tptp_fun_X1_0(X2!1))) = addition(c(X2!1), c(tptp_fun_X1_0(X2!1))))))),
% 19.86/12.94 inference(monotonicity,[status(thm)],[389])).
% 19.86/12.94 tff(391,plain,
% 19.86/12.94 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(X2!1, tptp_fun_X1_0(X2!1))) = addition(c(X2!1), c(tptp_fun_X1_0(X2!1)))) | (~test(X2!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(X2!1, tptp_fun_X1_0(X2!1))) = addition(c(X2!1), c(tptp_fun_X1_0(X2!1)))))),
% 19.86/12.94 inference(transitivity,[status(thm)],[390, 388])).
% 19.86/12.94 tff(392,plain,
% 19.86/12.94 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(X2!1, tptp_fun_X1_0(X2!1))) = addition(c(X2!1), c(tptp_fun_X1_0(X2!1)))) | (~test(X2!1)))),
% 19.86/12.94 inference(quant_inst,[status(thm)],[])).
% 19.86/12.94 tff(393,plain,
% 19.86/12.94 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X2!1)) | (~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(X2!1, tptp_fun_X1_0(X2!1))) = addition(c(X2!1), c(tptp_fun_X1_0(X2!1))))),
% 19.86/12.94 inference(modus_ponens,[status(thm)],[392, 391])).
% 19.86/12.94 tff(394,plain,
% 19.86/12.94 ((~test(tptp_fun_X1_0(X2!1))) | (c(multiplication(X2!1, tptp_fun_X1_0(X2!1))) = addition(c(X2!1), c(tptp_fun_X1_0(X2!1))))),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[393, 148, 62])).
% 19.86/12.94 tff(395,plain,
% 19.86/12.94 (c(multiplication(X2!1, tptp_fun_X1_0(X2!1))) = addition(c(X2!1), c(tptp_fun_X1_0(X2!1)))),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[394, 99])).
% 19.86/12.94 tff(396,plain,
% 19.86/12.94 (addition(c(X2!1), c(tptp_fun_X1_0(X2!1))) = c(multiplication(X2!1, tptp_fun_X1_0(X2!1)))),
% 19.86/12.94 inference(symmetry,[status(thm)],[395])).
% 19.86/12.94 tff(397,plain,
% 19.86/12.94 (addition(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))) = addition(c(X2!1), c(tptp_fun_X1_0(X2!1)))),
% 19.86/12.94 inference(monotonicity,[status(thm)],[133])).
% 19.86/12.94 tff(398,plain,
% 19.86/12.94 (addition(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))) = tptp_fun_X1_0(zero)),
% 19.86/12.94 inference(transitivity,[status(thm)],[397, 396, 387, 261, 258, 250, 195, 180, 176, 174])).
% 19.86/12.94 tff(399,plain,
% 19.86/12.94 (multiplication(addition(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))), c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))) = multiplication(tptp_fun_X1_0(zero), tptp_fun_X1_0(zero))),
% 19.86/12.94 inference(monotonicity,[status(thm)],[398, 262])).
% 19.86/12.94 tff(400,plain,
% 19.86/12.94 (^[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))))),
% 19.86/12.94 inference(bind,[status(th)],[])).
% 19.86/12.94 tff(401,plain,
% 19.86/12.94 (![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)))),
% 19.86/12.94 inference(quant_intro,[status(thm)],[400])).
% 19.86/12.94 tff(402,plain,
% 19.86/12.94 (![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)))),
% 19.86/12.94 inference(rewrite,[status(thm)],[])).
% 19.86/12.94 tff(403,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')).
% 19.86/12.94 tff(404,plain,
% 19.86/12.94 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 19.86/12.94 inference(modus_ponens,[status(thm)],[403, 402])).
% 19.86/12.94 tff(405,plain,(
% 19.86/12.94 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 19.86/12.94 inference(skolemize,[status(sab)],[404])).
% 19.86/12.94 tff(406,plain,
% 19.86/12.94 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 19.86/12.94 inference(modus_ponens,[status(thm)],[405, 401])).
% 19.86/12.94 tff(407,plain,
% 19.86/12.94 ((~![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(multiplication(multiplication(X1!2, X0!3), c(X2!1)))) = addition(multiplication(tptp_fun_X1_0(X2!1), c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))), multiplication(c(tptp_fun_X1_0(X2!1)), c(multiplication(multiplication(X1!2, X0!3), c(X2!1))))))),
% 19.86/12.94 inference(quant_inst,[status(thm)],[])).
% 19.86/12.94 tff(408,plain,
% 19.86/12.94 (multiplication(addition(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))), c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))) = addition(multiplication(tptp_fun_X1_0(X2!1), c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))), multiplication(c(tptp_fun_X1_0(X2!1)), c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))))),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[407, 406])).
% 19.86/12.94 tff(409,plain,
% 19.86/12.94 (addition(multiplication(tptp_fun_X1_0(X2!1), c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))), multiplication(c(tptp_fun_X1_0(X2!1)), c(multiplication(multiplication(X1!2, X0!3), c(X2!1))))) = multiplication(addition(tptp_fun_X1_0(X2!1), c(tptp_fun_X1_0(X2!1))), c(multiplication(multiplication(X1!2, X0!3), c(X2!1))))),
% 19.86/12.94 inference(symmetry,[status(thm)],[408])).
% 19.86/12.94 tff(410,plain,
% 19.86/12.94 (multiplication(c(tptp_fun_X1_0(X2!1)), c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))) = multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero))),
% 19.86/12.94 inference(monotonicity,[status(thm)],[262])).
% 19.86/12.94 tff(411,plain,
% 19.86/12.94 (multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)) = multiplication(c(tptp_fun_X1_0(X2!1)), c(multiplication(multiplication(X1!2, X0!3), c(X2!1))))),
% 19.86/12.94 inference(symmetry,[status(thm)],[410])).
% 19.86/12.94 tff(412,plain,
% 19.86/12.94 (multiplication(tptp_fun_X1_0(X2!1), c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))) = multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero))),
% 19.86/12.94 inference(monotonicity,[status(thm)],[262])).
% 19.86/12.94 tff(413,plain,
% 19.86/12.94 (multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)) = multiplication(tptp_fun_X1_0(X2!1), c(multiplication(multiplication(X1!2, X0!3), c(X2!1))))),
% 19.86/12.94 inference(symmetry,[status(thm)],[412])).
% 19.86/12.94 tff(414,plain,
% 19.86/12.94 (addition(multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero))) = addition(multiplication(tptp_fun_X1_0(X2!1), c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))), multiplication(c(tptp_fun_X1_0(X2!1)), c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))))),
% 19.86/12.94 inference(monotonicity,[status(thm)],[413, 411])).
% 19.86/12.94 tff(415,plain,
% 19.86/12.94 (addition(multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero))) = c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))),
% 19.86/12.94 inference(transitivity,[status(thm)],[414, 409, 399, 385, 382])).
% 19.86/12.94 tff(416,plain,
% 19.86/12.94 (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), addition(multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero)))) = multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), c(multiplication(multiplication(X1!2, X0!3), c(X2!1))))),
% 19.86/12.94 inference(monotonicity,[status(thm)],[415])).
% 19.86/12.94 tff(417,plain,
% 19.86/12.94 (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))) = multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), addition(multiplication(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(zero)), multiplication(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(zero))))),
% 19.86/12.94 inference(symmetry,[status(thm)],[416])).
% 19.86/12.94 tff(418,plain,
% 19.86/12.94 (c(multiplication(multiplication(X1!2, X0!3), c(X2!1))) = one),
% 19.86/12.94 inference(transitivity,[status(thm)],[261, 258, 250, 195])).
% 19.86/12.94 tff(419,plain,
% 19.86/12.94 (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), c(multiplication(multiplication(X1!2, X0!3), c(X2!1)))) = multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), one)),
% 19.86/12.94 inference(monotonicity,[status(thm)],[418])).
% 19.86/12.94 tff(420,plain,
% 19.86/12.94 (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), one) = multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), c(multiplication(multiplication(X1!2, X0!3), c(X2!1))))),
% 19.86/12.94 inference(symmetry,[status(thm)],[419])).
% 19.86/12.94 tff(421,plain,
% 19.86/12.94 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), one) = multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3))),
% 19.86/12.94 inference(quant_inst,[status(thm)],[])).
% 19.86/12.94 tff(422,plain,
% 19.86/12.94 (multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), one) = multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3)),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[421, 276])).
% 19.86/12.94 tff(423,plain,
% 19.86/12.94 (multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3) = multiplication(multiplication(multiplication(tptp_fun_X1_0(zero), X1!2), X0!3), one)),
% 19.86/12.94 inference(symmetry,[status(thm)],[422])).
% 19.86/12.94 tff(424,plain,
% 19.86/12.94 (multiplication(X1!2, X0!3) = multiplication(multiplication(X1!2, X0!3), X2!1)),
% 19.86/12.94 inference(transitivity,[status(thm)],[322, 312, 311, 423, 420, 417, 380, 378, 328, 325])).
% 19.86/12.94 tff(425,plain,
% 19.86/12.94 (~(multiplication(X1!2, X0!3) = multiplication(multiplication(X1!2, X0!3), X2!1))),
% 19.86/12.94 inference(or_elim,[status(thm)],[60])).
% 19.86/12.94 tff(426,plain,
% 19.86/12.94 ($false),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[425, 424])).
% 19.86/12.94 tff(427,plain,((~(multiplication(zero, tptp_fun_X1_0(zero)) = zero)) | (~(multiplication(tptp_fun_X1_0(zero), zero) = zero)) | (~(addition(zero, tptp_fun_X1_0(zero)) = one))), inference(lemma,lemma(discharge,[]))).
% 19.86/12.94 tff(428,plain,
% 19.86/12.94 ((~(complement(tptp_fun_X1_0(zero), zero) <=> (~((~(multiplication(zero, tptp_fun_X1_0(zero)) = zero)) | (~(multiplication(tptp_fun_X1_0(zero), zero) = zero)) | (~(addition(zero, tptp_fun_X1_0(zero)) = one)))))) | (~complement(tptp_fun_X1_0(zero), zero)) | (~((~(multiplication(zero, tptp_fun_X1_0(zero)) = zero)) | (~(multiplication(tptp_fun_X1_0(zero), zero) = zero)) | (~(addition(zero, tptp_fun_X1_0(zero)) = one))))),
% 19.86/12.94 inference(tautology,[status(thm)],[])).
% 19.86/12.94 tff(429,plain,
% 19.86/12.94 ((~(complement(tptp_fun_X1_0(zero), zero) <=> (~((~(multiplication(zero, tptp_fun_X1_0(zero)) = zero)) | (~(multiplication(tptp_fun_X1_0(zero), zero) = zero)) | (~(addition(zero, tptp_fun_X1_0(zero)) = one)))))) | (~complement(tptp_fun_X1_0(zero), zero))),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[428, 427])).
% 19.86/12.94 tff(430,plain,
% 19.86/12.94 (~complement(tptp_fun_X1_0(zero), zero)),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[429, 172])).
% 19.86/12.94 tff(431,plain,
% 19.86/12.94 ((~((~test(zero)) | complement(tptp_fun_X1_0(zero), zero))) | (~test(zero)) | complement(tptp_fun_X1_0(zero), zero)),
% 19.86/12.94 inference(tautology,[status(thm)],[])).
% 19.86/12.94 tff(432,plain,
% 19.86/12.94 ((~((~test(zero)) | complement(tptp_fun_X1_0(zero), zero))) | (~test(zero))),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[431, 430])).
% 19.86/12.94 tff(433,plain,
% 19.86/12.94 (~test(zero)),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[432, 168])).
% 19.86/12.94 tff(434,plain,
% 19.86/12.94 (^[X0: $i] : refl((test(X0) | (c(X0) = zero)) <=> (test(X0) | (c(X0) = zero)))),
% 19.86/12.94 inference(bind,[status(th)],[])).
% 19.86/12.94 tff(435,plain,
% 19.86/12.94 (![X0: $i] : (test(X0) | (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 19.86/12.94 inference(quant_intro,[status(thm)],[434])).
% 19.86/12.94 tff(436,plain,
% 19.86/12.94 (![X0: $i] : (test(X0) | (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 19.86/12.94 inference(rewrite,[status(thm)],[])).
% 19.86/12.94 tff(437,plain,
% 19.86/12.94 (^[X0: $i] : rewrite(((~test(X0)) => (c(X0) = zero)) <=> (test(X0) | (c(X0) = zero)))),
% 19.86/12.94 inference(bind,[status(th)],[])).
% 19.86/12.94 tff(438,plain,
% 19.86/12.94 (![X0: $i] : ((~test(X0)) => (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 19.86/12.94 inference(quant_intro,[status(thm)],[437])).
% 19.86/12.94 tff(439,axiom,(![X0: $i] : ((~test(X0)) => (c(X0) = zero))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_4')).
% 19.86/12.94 tff(440,plain,
% 19.86/12.94 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 19.86/12.94 inference(modus_ponens,[status(thm)],[439, 438])).
% 19.86/12.94 tff(441,plain,
% 19.86/12.94 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 19.86/12.94 inference(modus_ponens,[status(thm)],[440, 436])).
% 19.86/12.94 tff(442,plain,(
% 19.86/12.94 ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 19.86/12.94 inference(skolemize,[status(sab)],[441])).
% 19.86/12.94 tff(443,plain,
% 19.86/12.94 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 19.86/12.94 inference(modus_ponens,[status(thm)],[442, 435])).
% 19.86/12.94 tff(444,plain,
% 19.86/12.94 (((~![X0: $i] : (test(X0) | (c(X0) = zero))) | (test(zero) | (c(zero) = zero))) <=> ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | test(zero) | (c(zero) = zero))),
% 19.86/12.94 inference(rewrite,[status(thm)],[])).
% 19.86/12.94 tff(445,plain,
% 19.86/12.94 ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | (test(zero) | (c(zero) = zero))),
% 19.86/12.94 inference(quant_inst,[status(thm)],[])).
% 19.86/12.94 tff(446,plain,
% 19.86/12.94 ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | test(zero) | (c(zero) = zero)),
% 19.86/12.94 inference(modus_ponens,[status(thm)],[445, 444])).
% 19.86/12.94 tff(447,plain,
% 19.86/12.94 (test(zero) | (c(zero) = zero)),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[446, 443])).
% 19.86/12.94 tff(448,plain,
% 19.86/12.94 (c(zero) = zero),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[447, 433])).
% 19.86/12.94 tff(449,plain,
% 19.86/12.94 (zero = c(zero)),
% 19.86/12.94 inference(symmetry,[status(thm)],[448])).
% 19.86/12.94 tff(450,plain,
% 19.86/12.94 (zero = addition(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1))),
% 19.86/12.94 inference(transitivity,[status(thm)],[449, 162, 161, 156, 135])).
% 19.86/12.94 tff(451,plain,
% 19.86/12.94 (addition(c(tptp_fun_X1_0(X2!1)), zero) = addition(c(tptp_fun_X1_0(X2!1)), addition(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1)))),
% 19.86/12.94 inference(monotonicity,[status(thm)],[450])).
% 19.86/12.94 tff(452,plain,
% 19.86/12.94 (addition(c(tptp_fun_X1_0(X2!1)), addition(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1))) = addition(c(tptp_fun_X1_0(X2!1)), zero)),
% 19.86/12.94 inference(symmetry,[status(thm)],[451])).
% 19.86/12.94 tff(453,plain,
% 19.86/12.94 (^[C: $i, B: $i, A: $i] : refl((addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> (addition(A, addition(B, C)) = addition(addition(A, B), C)))),
% 19.86/12.94 inference(bind,[status(th)],[])).
% 19.86/12.94 tff(454,plain,
% 19.86/12.94 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 19.86/12.94 inference(quant_intro,[status(thm)],[453])).
% 19.86/12.94 tff(455,plain,
% 19.86/12.94 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 19.86/12.94 inference(rewrite,[status(thm)],[])).
% 19.86/12.94 tff(456,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_associativity')).
% 19.86/12.94 tff(457,plain,
% 19.86/12.94 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 19.86/12.94 inference(modus_ponens,[status(thm)],[456, 455])).
% 19.86/12.94 tff(458,plain,(
% 19.86/12.94 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 19.86/12.94 inference(skolemize,[status(sab)],[457])).
% 19.86/12.94 tff(459,plain,
% 19.86/12.94 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 19.86/12.94 inference(modus_ponens,[status(thm)],[458, 454])).
% 19.86/12.94 tff(460,plain,
% 19.86/12.94 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(c(tptp_fun_X1_0(X2!1)), addition(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1))) = addition(addition(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))), tptp_fun_X1_0(X2!1)))),
% 19.86/12.94 inference(quant_inst,[status(thm)],[])).
% 19.86/12.94 tff(461,plain,
% 19.86/12.94 (addition(c(tptp_fun_X1_0(X2!1)), addition(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1))) = addition(addition(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))), tptp_fun_X1_0(X2!1))),
% 19.86/12.94 inference(unit_resolution,[status(thm)],[460, 459])).
% 19.86/12.94 tff(462,plain,
% 19.86/12.94 (addition(addition(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))), tptp_fun_X1_0(X2!1)) = addition(c(tptp_fun_X1_0(X2!1)), addition(c(tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1)))),
% 19.86/12.94 inference(symmetry,[status(thm)],[461])).
% 19.86/12.94 tff(463,assumption,(~(addition(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))) = c(tptp_fun_X1_0(X2!1)))), introduced(assumption)).
% 19.86/12.94 tff(464,plain,
% 19.86/12.94 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 19.86/12.95 inference(bind,[status(th)],[])).
% 19.86/12.95 tff(465,plain,
% 19.86/12.95 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 19.86/12.95 inference(quant_intro,[status(thm)],[464])).
% 19.86/12.95 tff(466,plain,
% 19.86/12.95 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 19.86/12.95 inference(rewrite,[status(thm)],[])).
% 19.86/12.95 tff(467,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 19.86/12.95 tff(468,plain,
% 19.86/12.95 (![A: $i] : (addition(A, A) = A)),
% 19.86/12.95 inference(modus_ponens,[status(thm)],[467, 466])).
% 19.86/12.95 tff(469,plain,(
% 19.86/12.95 ![A: $i] : (addition(A, A) = A)),
% 19.86/12.95 inference(skolemize,[status(sab)],[468])).
% 19.86/12.95 tff(470,plain,
% 19.86/12.95 (![A: $i] : (addition(A, A) = A)),
% 19.86/12.95 inference(modus_ponens,[status(thm)],[469, 465])).
% 19.86/12.95 tff(471,plain,
% 19.86/12.95 ((~![A: $i] : (addition(A, A) = A)) | (addition(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))) = c(tptp_fun_X1_0(X2!1)))),
% 19.86/12.95 inference(quant_inst,[status(thm)],[])).
% 19.86/12.95 tff(472,plain,
% 19.86/12.95 ($false),
% 19.86/12.95 inference(unit_resolution,[status(thm)],[471, 470, 463])).
% 19.86/12.95 tff(473,plain,(addition(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))) = c(tptp_fun_X1_0(X2!1))), inference(lemma,lemma(discharge,[]))).
% 19.86/12.95 tff(474,plain,
% 19.86/12.95 (addition(addition(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))), tptp_fun_X1_0(X2!1)) = addition(c(tptp_fun_X1_0(X2!1)), c(X2!1))),
% 19.86/12.95 inference(monotonicity,[status(thm)],[473, 133])).
% 19.86/12.95 tff(475,plain,
% 19.86/12.95 (addition(c(tptp_fun_X1_0(X2!1)), c(X2!1)) = addition(addition(c(tptp_fun_X1_0(X2!1)), c(tptp_fun_X1_0(X2!1))), tptp_fun_X1_0(X2!1))),
% 19.86/12.95 inference(symmetry,[status(thm)],[474])).
% 19.86/12.95 tff(476,plain,
% 19.86/12.95 (zero = X2!1),
% 19.86/12.95 inference(transitivity,[status(thm)],[449, 162, 161, 156, 475, 462, 452, 126, 117])).
% 19.86/12.95 tff(477,plain,
% 19.86/12.95 (test(zero) <=> test(X2!1)),
% 19.86/12.95 inference(monotonicity,[status(thm)],[476])).
% 19.86/12.95 tff(478,plain,
% 19.86/12.95 (test(X2!1) <=> test(zero)),
% 19.86/12.95 inference(symmetry,[status(thm)],[477])).
% 19.86/12.95 tff(479,plain,
% 19.86/12.95 (test(zero)),
% 19.86/12.95 inference(modus_ponens,[status(thm)],[62, 478])).
% 19.86/12.95 tff(480,plain,
% 19.86/12.95 ($false),
% 19.86/12.95 inference(unit_resolution,[status(thm)],[433, 479])).
% 19.86/12.95 % SZS output end Proof
%------------------------------------------------------------------------------