TSTP Solution File: KLE009+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE009+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 17:23:47 EDT 2022
% Result : Theorem 0.13s 0.49s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : KLE009+4 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.08/0.28 % Computer : n011.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Thu Sep 1 07:40:56 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.08/0.29 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.08/0.29 Usage: tptp [options] [-file:]file
% 0.08/0.29 -h, -? prints this message.
% 0.08/0.29 -smt2 print SMT-LIB2 benchmark.
% 0.08/0.29 -m, -model generate model.
% 0.08/0.29 -p, -proof generate proof.
% 0.08/0.29 -c, -core generate unsat core of named formulas.
% 0.08/0.29 -st, -statistics display statistics.
% 0.08/0.29 -t:timeout set timeout (in second).
% 0.08/0.29 -smt2status display status in smt2 format instead of SZS.
% 0.08/0.29 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.08/0.29 -<param>:<value> configuration parameter and value.
% 0.08/0.29 -o:<output-file> file to place output in.
% 0.13/0.49 % SZS status Theorem
% 0.13/0.49 % SZS output start Proof
% 0.13/0.49 tff(one_type, type, (
% 0.13/0.49 one: $i)).
% 0.13/0.49 tff(addition_type, type, (
% 0.13/0.49 addition: ( $i * $i ) > $i)).
% 0.13/0.49 tff(multiplication_type, type, (
% 0.13/0.49 multiplication: ( $i * $i ) > $i)).
% 0.13/0.49 tff(c_type, type, (
% 0.13/0.49 c: $i > $i)).
% 0.13/0.49 tff(tptp_fun_X1_1_type, type, (
% 0.13/0.49 tptp_fun_X1_1: $i)).
% 0.13/0.49 tff(tptp_fun_X0_2_type, type, (
% 0.13/0.49 tptp_fun_X0_2: $i)).
% 0.13/0.49 tff(tptp_fun_X1_0_type, type, (
% 0.13/0.49 tptp_fun_X1_0: $i > $i)).
% 0.13/0.49 tff(zero_type, type, (
% 0.13/0.49 zero: $i)).
% 0.13/0.49 tff(complement_type, type, (
% 0.13/0.49 complement: ( $i * $i ) > $o)).
% 0.13/0.49 tff(test_type, type, (
% 0.13/0.49 test: $i > $o)).
% 0.13/0.49 tff(leq_type, type, (
% 0.13/0.49 leq: ( $i * $i ) > $o)).
% 0.13/0.49 tff(1,plain,
% 0.13/0.49 (^[X0: $i, X1: $i] : refl((complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))) <=> (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))))),
% 0.13/0.49 inference(bind,[status(th)],[])).
% 0.13/0.49 tff(2,plain,
% 0.13/0.49 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))) <=> ![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 0.13/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.49 tff(3,plain,
% 0.13/0.49 (^[X0: $i, X1: $i] : rewrite((complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))))),
% 0.13/0.49 inference(bind,[status(th)],[])).
% 0.13/0.49 tff(4,plain,
% 0.13/0.49 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 0.13/0.49 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.49 tff(5,plain,
% 0.13/0.49 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.13/0.49 inference(rewrite,[status(thm)],[])).
% 0.13/0.49 tff(6,plain,
% 0.13/0.49 (^[X0: $i, X1: $i] : rewrite((complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one))) <=> (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))))),
% 0.13/0.49 inference(bind,[status(th)],[])).
% 0.13/0.49 tff(7,plain,
% 0.13/0.49 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.13/0.49 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.49 tff(8,axiom,(![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_2')).
% 0.13/0.49 tff(9,plain,
% 0.13/0.49 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.13/0.49 tff(10,plain,
% 0.13/0.49 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.13/0.49 tff(11,plain,(
% 0.13/0.49 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.13/0.49 inference(skolemize,[status(sab)],[10])).
% 0.13/0.49 tff(12,plain,
% 0.13/0.49 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.13/0.49 tff(13,plain,
% 0.13/0.49 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.13/0.49 tff(14,plain,
% 0.13/0.49 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(tptp_fun_X1_0(X0!2), X0!2) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one)))))),
% 0.13/0.49 inference(quant_inst,[status(thm)],[])).
% 0.13/0.49 tff(15,plain,
% 0.13/0.49 (complement(tptp_fun_X1_0(X0!2), X0!2) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))))),
% 0.13/0.49 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.13/0.49 tff(16,plain,
% 0.13/0.49 (^[X0: $i] : refl((~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))))),
% 0.13/0.49 inference(bind,[status(th)],[])).
% 0.13/0.49 tff(17,plain,
% 0.13/0.49 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> ![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.13/0.49 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.49 tff(18,plain,
% 0.13/0.49 (^[X0: $i] : rewrite((~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))))),
% 0.13/0.49 inference(bind,[status(th)],[])).
% 0.13/0.49 tff(19,plain,
% 0.13/0.49 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> ![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.13/0.49 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.49 tff(20,plain,
% 0.13/0.49 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0)))))) <=> ![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.13/0.49 inference(transitivity,[status(thm)],[19, 17])).
% 0.13/0.49 tff(21,plain,
% 0.13/0.49 (^[X0: $i] : trans(monotonicity(rewrite((test(X0) | ![X1: $i] : (~complement(X1, X0))) <=> (test(X0) | ![X1: $i] : (~complement(X1, X0)))), ((((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))) <=> (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))))), rewrite((((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))) <=> (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))), ((((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))) <=> (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))))),
% 0.13/0.49 inference(bind,[status(th)],[])).
% 0.13/0.49 tff(22,plain,
% 0.13/0.49 (![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0)))) <=> ![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.13/0.49 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.49 tff(23,plain,
% 0.13/0.49 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 0.13/0.49 inference(rewrite,[status(thm)],[])).
% 0.13/0.49 tff(24,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_1')).
% 0.13/0.49 tff(25,plain,
% 0.13/0.49 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.13/0.49 tff(26,plain,(
% 0.13/0.49 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 0.13/0.49 inference(skolemize,[status(sab)],[25])).
% 0.13/0.49 tff(27,plain,
% 0.13/0.49 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.13/0.49 tff(28,plain,
% 0.13/0.49 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.13/0.49 tff(29,plain,
% 0.13/0.49 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2))))))),
% 0.13/0.49 inference(quant_inst,[status(thm)],[])).
% 0.13/0.49 tff(30,plain,
% 0.13/0.49 (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2)))))),
% 0.13/0.49 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.13/0.49 tff(31,plain,
% 0.13/0.49 (((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2))))) | ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))),
% 0.13/0.49 inference(tautology,[status(thm)],[])).
% 0.13/0.49 tff(32,plain,
% 0.13/0.49 ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 0.13/0.49 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.13/0.49 tff(33,plain,
% 0.13/0.49 ((~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one))))),
% 0.13/0.49 inference(rewrite,[status(thm)],[])).
% 0.13/0.49 tff(34,plain,
% 0.13/0.49 ((~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one))))),
% 0.13/0.49 inference(rewrite,[status(thm)],[])).
% 0.13/0.49 tff(35,axiom,(~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.13/0.49 tff(36,plain,
% 0.13/0.49 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.49 tff(37,plain,
% 0.13/0.49 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.13/0.49 tff(38,plain,
% 0.13/0.49 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.13/0.49 tff(39,plain,
% 0.13/0.49 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[38, 33])).
% 0.13/0.49 tff(40,plain,
% 0.13/0.49 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[39, 33])).
% 0.13/0.49 tff(41,plain,
% 0.13/0.49 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.13/0.49 tff(42,plain,
% 0.13/0.49 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 0.13/0.49 inference(modus_ponens,[status(thm)],[41, 33])).
% 0.13/0.49 tff(43,plain,(
% 0.13/0.49 ~((~(test(X1!1) & test(X0!2))) | (leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) & leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)))),
% 0.13/0.49 inference(skolemize,[status(sab)],[42])).
% 0.13/0.49 tff(44,plain,
% 0.13/0.49 (test(X1!1) & test(X0!2)),
% 0.13/0.49 inference(or_elim,[status(thm)],[43])).
% 0.13/0.49 tff(45,plain,
% 0.13/0.49 (test(X0!2)),
% 0.13/0.49 inference(and_elim,[status(thm)],[44])).
% 0.13/0.49 tff(46,plain,
% 0.13/0.49 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 0.13/0.49 inference(tautology,[status(thm)],[])).
% 0.13/0.49 tff(47,plain,
% 0.13/0.49 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 0.13/0.49 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.13/0.49 tff(48,plain,
% 0.13/0.49 (complement(tptp_fun_X1_0(X0!2), X0!2)),
% 0.13/0.49 inference(unit_resolution,[status(thm)],[47, 32])).
% 0.13/0.49 tff(49,plain,
% 0.13/0.49 ((~(complement(tptp_fun_X1_0(X0!2), X0!2) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one)))))) | (~complement(tptp_fun_X1_0(X0!2), X0!2)) | (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))))),
% 0.13/0.49 inference(tautology,[status(thm)],[])).
% 0.13/0.49 tff(50,plain,
% 0.13/0.49 ((~(complement(tptp_fun_X1_0(X0!2), X0!2) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one)))))) | (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.13/0.50 tff(51,plain,
% 0.13/0.50 (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one)))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[50, 15])).
% 0.13/0.50 tff(52,plain,
% 0.13/0.50 (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) | (addition(X0!2, tptp_fun_X1_0(X0!2)) = one)),
% 0.13/0.50 inference(tautology,[status(thm)],[])).
% 0.13/0.50 tff(53,plain,
% 0.13/0.50 (addition(X0!2, tptp_fun_X1_0(X0!2)) = one),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.13/0.50 tff(54,plain,
% 0.13/0.50 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.13/0.50 inference(bind,[status(th)],[])).
% 0.13/0.50 tff(55,plain,
% 0.13/0.50 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.13/0.50 inference(quant_intro,[status(thm)],[54])).
% 0.13/0.50 tff(56,plain,
% 0.13/0.50 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.13/0.50 inference(rewrite,[status(thm)],[])).
% 0.13/0.50 tff(57,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 0.13/0.50 tff(58,plain,
% 0.13/0.50 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.13/0.50 tff(59,plain,(
% 0.13/0.50 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.13/0.50 inference(skolemize,[status(sab)],[58])).
% 0.13/0.50 tff(60,plain,
% 0.13/0.50 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.13/0.50 tff(61,plain,
% 0.13/0.50 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2))),
% 0.13/0.50 inference(quant_inst,[status(thm)],[])).
% 0.13/0.50 tff(62,plain,
% 0.13/0.50 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.13/0.50 tff(63,plain,
% 0.13/0.50 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 0.13/0.50 inference(symmetry,[status(thm)],[62])).
% 0.13/0.50 tff(64,plain,
% 0.13/0.50 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.13/0.50 inference(bind,[status(th)],[])).
% 0.13/0.50 tff(65,plain,
% 0.13/0.50 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.13/0.50 inference(quant_intro,[status(thm)],[64])).
% 0.13/0.50 tff(66,plain,
% 0.13/0.50 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.13/0.50 inference(rewrite,[status(thm)],[])).
% 0.13/0.50 tff(67,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 0.13/0.50 tff(68,plain,
% 0.13/0.50 (![A: $i] : (multiplication(A, one) = A)),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.13/0.50 tff(69,plain,(
% 0.13/0.50 ![A: $i] : (multiplication(A, one) = A)),
% 0.13/0.50 inference(skolemize,[status(sab)],[68])).
% 0.13/0.50 tff(70,plain,
% 0.13/0.50 (![A: $i] : (multiplication(A, one) = A)),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.13/0.50 tff(71,plain,
% 0.13/0.50 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X0!2, one) = X0!2)),
% 0.13/0.50 inference(quant_inst,[status(thm)],[])).
% 0.13/0.50 tff(72,plain,
% 0.13/0.50 (multiplication(X0!2, one) = X0!2),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.13/0.50 tff(73,plain,
% 0.13/0.50 ((~![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!1), X1!1) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one)))))),
% 0.13/0.50 inference(quant_inst,[status(thm)],[])).
% 0.13/0.50 tff(74,plain,
% 0.13/0.50 (complement(tptp_fun_X1_0(X1!1), X1!1) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[73, 13])).
% 0.13/0.50 tff(75,plain,
% 0.13/0.50 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1))))))),
% 0.13/0.50 inference(quant_inst,[status(thm)],[])).
% 0.13/0.50 tff(76,plain,
% 0.13/0.50 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[75, 28])).
% 0.13/0.50 tff(77,plain,
% 0.13/0.50 (((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1))))) | ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))),
% 0.13/0.50 inference(tautology,[status(thm)],[])).
% 0.13/0.50 tff(78,plain,
% 0.13/0.50 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.13/0.50 tff(79,plain,
% 0.13/0.50 (test(X1!1)),
% 0.13/0.50 inference(and_elim,[status(thm)],[44])).
% 0.13/0.50 tff(80,plain,
% 0.13/0.50 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.13/0.50 inference(tautology,[status(thm)],[])).
% 0.13/0.50 tff(81,plain,
% 0.13/0.50 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.13/0.50 tff(82,plain,
% 0.13/0.50 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[81, 78])).
% 0.13/0.50 tff(83,plain,
% 0.13/0.50 ((~(complement(tptp_fun_X1_0(X1!1), X1!1) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one)))))) | (~complement(tptp_fun_X1_0(X1!1), X1!1)) | (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))))),
% 0.13/0.50 inference(tautology,[status(thm)],[])).
% 0.13/0.50 tff(84,plain,
% 0.13/0.50 ((~(complement(tptp_fun_X1_0(X1!1), X1!1) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one)))))) | (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.13/0.50 tff(85,plain,
% 0.13/0.50 (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one)))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[84, 74])).
% 0.13/0.50 tff(86,plain,
% 0.13/0.50 (((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))) | (addition(X1!1, tptp_fun_X1_0(X1!1)) = one)),
% 0.13/0.50 inference(tautology,[status(thm)],[])).
% 0.13/0.50 tff(87,plain,
% 0.13/0.50 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.13/0.50 tff(88,plain,
% 0.13/0.50 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 0.13/0.50 inference(symmetry,[status(thm)],[87])).
% 0.13/0.50 tff(89,plain,
% 0.13/0.50 (multiplication(X0!2, one) = multiplication(X0!2, addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 0.13/0.50 inference(monotonicity,[status(thm)],[88])).
% 0.13/0.50 tff(90,plain,
% 0.13/0.50 (multiplication(X0!2, addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(X0!2, one)),
% 0.13/0.50 inference(symmetry,[status(thm)],[89])).
% 0.13/0.50 tff(91,plain,
% 0.13/0.50 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))))),
% 0.13/0.50 inference(bind,[status(th)],[])).
% 0.13/0.50 tff(92,plain,
% 0.13/0.50 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.13/0.50 inference(quant_intro,[status(thm)],[91])).
% 0.13/0.50 tff(93,plain,
% 0.13/0.50 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.13/0.50 inference(rewrite,[status(thm)],[])).
% 0.13/0.50 tff(94,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','right_distributivity')).
% 0.13/0.50 tff(95,plain,
% 0.13/0.50 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.13/0.50 tff(96,plain,(
% 0.13/0.50 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.13/0.50 inference(skolemize,[status(sab)],[95])).
% 0.13/0.50 tff(97,plain,
% 0.13/0.50 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.13/0.50 tff(98,plain,
% 0.13/0.50 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!2, addition(X1!1, tptp_fun_X1_0(X1!1))) = addition(multiplication(X0!2, X1!1), multiplication(X0!2, tptp_fun_X1_0(X1!1))))),
% 0.13/0.50 inference(quant_inst,[status(thm)],[])).
% 0.13/0.50 tff(99,plain,
% 0.13/0.50 (multiplication(X0!2, addition(X1!1, tptp_fun_X1_0(X1!1))) = addition(multiplication(X0!2, X1!1), multiplication(X0!2, tptp_fun_X1_0(X1!1)))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.13/0.50 tff(100,plain,
% 0.13/0.50 (addition(multiplication(X0!2, X1!1), multiplication(X0!2, tptp_fun_X1_0(X1!1))) = multiplication(X0!2, addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 0.13/0.50 inference(symmetry,[status(thm)],[99])).
% 0.13/0.50 tff(101,plain,
% 0.13/0.50 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.13/0.50 inference(bind,[status(th)],[])).
% 0.13/0.50 tff(102,plain,
% 0.13/0.50 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.13/0.50 inference(quant_intro,[status(thm)],[101])).
% 0.13/0.50 tff(103,plain,
% 0.13/0.50 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.13/0.50 inference(rewrite,[status(thm)],[])).
% 0.13/0.50 tff(104,plain,
% 0.13/0.50 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.13/0.50 inference(bind,[status(th)],[])).
% 0.13/0.50 tff(105,plain,
% 0.13/0.50 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.13/0.50 inference(quant_intro,[status(thm)],[104])).
% 0.13/0.50 tff(106,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_3')).
% 0.13/0.50 tff(107,plain,
% 0.13/0.50 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.13/0.50 tff(108,plain,
% 0.13/0.50 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.13/0.50 tff(109,plain,(
% 0.13/0.50 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.13/0.50 inference(skolemize,[status(sab)],[108])).
% 0.13/0.50 tff(110,plain,
% 0.13/0.50 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.13/0.50 tff(111,plain,
% 0.13/0.50 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 0.13/0.50 inference(rewrite,[status(thm)],[])).
% 0.13/0.50 tff(112,plain,
% 0.13/0.50 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 0.13/0.50 inference(quant_inst,[status(thm)],[])).
% 0.13/0.50 tff(113,plain,
% 0.13/0.50 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 0.13/0.50 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.13/0.50 tff(114,plain,
% 0.13/0.50 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 0.13/0.50 inference(unit_resolution,[status(thm)],[113, 110, 79])).
% 0.13/0.50 tff(115,plain,
% 0.13/0.50 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))))))),
% 0.13/0.50 inference(rewrite,[status(thm)],[])).
% 0.13/0.50 tff(116,plain,
% 0.13/0.50 ((complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))))) <=> (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))),
% 0.13/0.50 inference(rewrite,[status(thm)],[])).
% 0.13/0.50 tff(117,plain,
% 0.13/0.50 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))))))),
% 0.13/0.50 inference(monotonicity,[status(thm)],[116])).
% 0.13/0.50 tff(118,plain,
% 0.13/0.50 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))))))),
% 0.13/0.50 inference(transitivity,[status(thm)],[117, 115])).
% 0.13/0.50 tff(119,plain,
% 0.13/0.50 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))),
% 0.13/0.50 inference(quant_inst,[status(thm)],[])).
% 0.13/0.50 tff(120,plain,
% 0.13/0.51 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))),
% 0.13/0.51 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.13/0.51 tff(121,plain,
% 0.13/0.51 (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))))),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[120, 13])).
% 0.13/0.51 tff(122,plain,
% 0.13/0.51 ((addition(tptp_fun_X1_0(X1!1), X1!1) = addition(X1!1, tptp_fun_X1_0(X1!1))) <=> (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1))),
% 0.13/0.51 inference(commutativity,[status(thm)],[])).
% 0.13/0.51 tff(123,plain,
% 0.13/0.51 ((addition(tptp_fun_X1_0(X1!1), X1!1) = one) <=> (addition(tptp_fun_X1_0(X1!1), X1!1) = addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 0.13/0.51 inference(monotonicity,[status(thm)],[88])).
% 0.13/0.51 tff(124,plain,
% 0.13/0.51 ((addition(tptp_fun_X1_0(X1!1), X1!1) = one) <=> (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1))),
% 0.13/0.51 inference(transitivity,[status(thm)],[123, 122])).
% 0.13/0.51 tff(125,plain,
% 0.13/0.51 ((addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)) <=> (addition(tptp_fun_X1_0(X1!1), X1!1) = one)),
% 0.13/0.51 inference(symmetry,[status(thm)],[124])).
% 0.13/0.51 tff(126,plain,
% 0.13/0.51 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1))),
% 0.13/0.51 inference(quant_inst,[status(thm)],[])).
% 0.13/0.51 tff(127,plain,
% 0.13/0.51 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[126, 60])).
% 0.13/0.51 tff(128,plain,
% 0.13/0.51 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 0.13/0.51 inference(modus_ponens,[status(thm)],[127, 125])).
% 0.13/0.51 tff(129,plain,
% 0.13/0.51 (((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))) | (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)),
% 0.13/0.51 inference(tautology,[status(thm)],[])).
% 0.13/0.51 tff(130,plain,
% 0.13/0.51 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[129, 85])).
% 0.13/0.51 tff(131,plain,
% 0.13/0.51 (((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))) | (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)),
% 0.13/0.51 inference(tautology,[status(thm)],[])).
% 0.13/0.51 tff(132,plain,
% 0.13/0.51 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[131, 85])).
% 0.13/0.51 tff(133,plain,
% 0.13/0.51 ((~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))),
% 0.13/0.51 inference(tautology,[status(thm)],[])).
% 0.13/0.51 tff(134,plain,
% 0.13/0.51 ((~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[133, 132, 130])).
% 0.13/0.51 tff(135,plain,
% 0.13/0.51 (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[134, 128])).
% 0.13/0.51 tff(136,plain,
% 0.13/0.51 ((~(complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))) | complement(X1!1, tptp_fun_X1_0(X1!1)) | ((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))),
% 0.13/0.51 inference(tautology,[status(thm)],[])).
% 0.13/0.51 tff(137,plain,
% 0.13/0.51 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[136, 135, 121])).
% 0.13/0.51 tff(138,plain,
% 0.13/0.51 ((~((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))) | (c(X1!1) = tptp_fun_X1_0(X1!1)) | (~complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 0.13/0.51 inference(tautology,[status(thm)],[])).
% 0.13/0.51 tff(139,plain,
% 0.13/0.51 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[138, 137, 114])).
% 0.13/0.51 tff(140,plain,
% 0.13/0.51 (tptp_fun_X1_0(X1!1) = c(X1!1)),
% 0.13/0.51 inference(symmetry,[status(thm)],[139])).
% 0.13/0.51 tff(141,plain,
% 0.13/0.51 (multiplication(X0!2, tptp_fun_X1_0(X1!1)) = multiplication(X0!2, c(X1!1))),
% 0.13/0.51 inference(monotonicity,[status(thm)],[140])).
% 0.13/0.51 tff(142,plain,
% 0.13/0.51 (addition(multiplication(X0!2, X1!1), multiplication(X0!2, tptp_fun_X1_0(X1!1))) = addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1)))),
% 0.13/0.51 inference(monotonicity,[status(thm)],[141])).
% 0.13/0.51 tff(143,plain,
% 0.13/0.51 (addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))) = addition(multiplication(X0!2, X1!1), multiplication(X0!2, tptp_fun_X1_0(X1!1)))),
% 0.13/0.51 inference(symmetry,[status(thm)],[142])).
% 0.13/0.51 tff(144,plain,
% 0.13/0.51 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))) = addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 0.13/0.51 inference(quant_inst,[status(thm)],[])).
% 0.13/0.51 tff(145,plain,
% 0.13/0.51 (addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))) = addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[144, 60])).
% 0.13/0.51 tff(146,plain,
% 0.13/0.51 (addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1)))),
% 0.13/0.51 inference(symmetry,[status(thm)],[145])).
% 0.13/0.51 tff(147,plain,
% 0.13/0.51 (addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)) = X0!2),
% 0.13/0.51 inference(transitivity,[status(thm)],[146, 143, 100, 90, 72])).
% 0.13/0.51 tff(148,plain,
% 0.13/0.51 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(tptp_fun_X1_0(X0!2), one) = tptp_fun_X1_0(X0!2))),
% 0.13/0.51 inference(quant_inst,[status(thm)],[])).
% 0.13/0.51 tff(149,plain,
% 0.13/0.51 (multiplication(tptp_fun_X1_0(X0!2), one) = tptp_fun_X1_0(X0!2)),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[148, 70])).
% 0.13/0.51 tff(150,plain,
% 0.13/0.51 (multiplication(tptp_fun_X1_0(X0!2), addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), one)),
% 0.13/0.51 inference(monotonicity,[status(thm)],[87])).
% 0.13/0.51 tff(151,plain,
% 0.13/0.51 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(tptp_fun_X1_0(X0!2), addition(X1!1, tptp_fun_X1_0(X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))))),
% 0.13/0.51 inference(quant_inst,[status(thm)],[])).
% 0.13/0.51 tff(152,plain,
% 0.13/0.51 (multiplication(tptp_fun_X1_0(X0!2), addition(X1!1, tptp_fun_X1_0(X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[151, 97])).
% 0.13/0.51 tff(153,plain,
% 0.13/0.51 (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 0.13/0.51 inference(symmetry,[status(thm)],[152])).
% 0.13/0.51 tff(154,plain,
% 0.13/0.51 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 0.13/0.51 inference(rewrite,[status(thm)],[])).
% 0.13/0.51 tff(155,plain,
% 0.13/0.51 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 0.13/0.51 inference(quant_inst,[status(thm)],[])).
% 0.13/0.51 tff(156,plain,
% 0.13/0.51 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 0.13/0.51 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.13/0.51 tff(157,plain,
% 0.13/0.51 ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[156, 110, 45])).
% 0.13/0.51 tff(158,plain,
% 0.13/0.51 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))))))),
% 0.13/0.51 inference(rewrite,[status(thm)],[])).
% 0.13/0.51 tff(159,plain,
% 0.13/0.51 ((complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))))) <=> (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))))),
% 0.13/0.51 inference(rewrite,[status(thm)],[])).
% 0.13/0.51 tff(160,plain,
% 0.13/0.51 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))))))),
% 0.13/0.51 inference(monotonicity,[status(thm)],[159])).
% 0.13/0.51 tff(161,plain,
% 0.13/0.51 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))))))),
% 0.13/0.51 inference(transitivity,[status(thm)],[160, 158])).
% 0.13/0.51 tff(162,plain,
% 0.13/0.51 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))))),
% 0.13/0.51 inference(quant_inst,[status(thm)],[])).
% 0.13/0.51 tff(163,plain,
% 0.13/0.51 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))))),
% 0.13/0.51 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.13/0.51 tff(164,plain,
% 0.13/0.51 (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))))),
% 0.13/0.51 inference(unit_resolution,[status(thm)],[163, 13])).
% 0.13/0.51 tff(165,plain,
% 0.13/0.51 ((addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2))) <=> (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2))),
% 0.13/0.51 inference(commutativity,[status(thm)],[])).
% 0.13/0.51 tff(166,plain,
% 0.13/0.51 (one = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 0.13/0.51 inference(symmetry,[status(thm)],[53])).
% 0.13/0.51 tff(167,plain,
% 0.13/0.51 ((addition(tptp_fun_X1_0(X0!2), X0!2) = one) <=> (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2)))),
% 0.13/0.51 inference(monotonicity,[status(thm)],[166])).
% 0.13/0.51 tff(168,plain,
% 0.13/0.51 ((addition(tptp_fun_X1_0(X0!2), X0!2) = one) <=> (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2))),
% 0.13/0.52 inference(transitivity,[status(thm)],[167, 165])).
% 0.13/0.52 tff(169,plain,
% 0.13/0.52 ((addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)) <=> (addition(tptp_fun_X1_0(X0!2), X0!2) = one)),
% 0.13/0.52 inference(symmetry,[status(thm)],[168])).
% 0.13/0.52 tff(170,plain,
% 0.13/0.52 (addition(tptp_fun_X1_0(X0!2), X0!2) = one),
% 0.13/0.52 inference(modus_ponens,[status(thm)],[62, 169])).
% 0.13/0.52 tff(171,plain,
% 0.13/0.52 (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) | (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)),
% 0.13/0.52 inference(tautology,[status(thm)],[])).
% 0.13/0.52 tff(172,plain,
% 0.13/0.52 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero),
% 0.13/0.52 inference(unit_resolution,[status(thm)],[171, 51])).
% 0.13/0.52 tff(173,plain,
% 0.13/0.52 (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) | (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)),
% 0.13/0.52 inference(tautology,[status(thm)],[])).
% 0.13/0.52 tff(174,plain,
% 0.13/0.52 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero),
% 0.13/0.52 inference(unit_resolution,[status(thm)],[173, 51])).
% 0.13/0.52 tff(175,plain,
% 0.13/0.52 ((~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))),
% 0.13/0.52 inference(tautology,[status(thm)],[])).
% 0.13/0.52 tff(176,plain,
% 0.13/0.52 ((~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))),
% 0.13/0.52 inference(unit_resolution,[status(thm)],[175, 174, 172])).
% 0.13/0.52 tff(177,plain,
% 0.13/0.52 (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))),
% 0.13/0.52 inference(unit_resolution,[status(thm)],[176, 170])).
% 0.13/0.52 tff(178,plain,
% 0.13/0.52 ((~(complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))))) | complement(X0!2, tptp_fun_X1_0(X0!2)) | ((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))),
% 0.13/0.52 inference(tautology,[status(thm)],[])).
% 0.13/0.52 tff(179,plain,
% 0.13/0.52 (complement(X0!2, tptp_fun_X1_0(X0!2))),
% 0.13/0.52 inference(unit_resolution,[status(thm)],[178, 177, 164])).
% 0.13/0.52 tff(180,plain,
% 0.13/0.52 ((~((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))) | (c(X0!2) = tptp_fun_X1_0(X0!2)) | (~complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 0.13/0.52 inference(tautology,[status(thm)],[])).
% 0.13/0.52 tff(181,plain,
% 0.13/0.52 (c(X0!2) = tptp_fun_X1_0(X0!2)),
% 0.13/0.52 inference(unit_resolution,[status(thm)],[180, 179, 157])).
% 0.13/0.52 tff(182,plain,
% 0.13/0.52 (tptp_fun_X1_0(X0!2) = c(X0!2)),
% 0.13/0.52 inference(symmetry,[status(thm)],[181])).
% 0.13/0.52 tff(183,plain,
% 0.13/0.52 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)) = multiplication(c(X0!2), c(X1!1))),
% 0.13/0.52 inference(monotonicity,[status(thm)],[182, 140])).
% 0.13/0.52 tff(184,plain,
% 0.13/0.52 (multiplication(c(X0!2), c(X1!1)) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 0.13/0.52 inference(symmetry,[status(thm)],[183])).
% 0.13/0.52 tff(185,plain,
% 0.13/0.52 (multiplication(tptp_fun_X1_0(X0!2), X1!1) = multiplication(c(X0!2), X1!1)),
% 0.13/0.52 inference(monotonicity,[status(thm)],[182])).
% 0.13/0.52 tff(186,plain,
% 0.13/0.52 (multiplication(c(X0!2), X1!1) = multiplication(tptp_fun_X1_0(X0!2), X1!1)),
% 0.13/0.52 inference(symmetry,[status(thm)],[185])).
% 0.13/0.52 tff(187,plain,
% 0.13/0.52 (addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 0.13/0.52 inference(monotonicity,[status(thm)],[186, 184])).
% 0.13/0.52 tff(188,plain,
% 0.13/0.52 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))),
% 0.13/0.52 inference(quant_inst,[status(thm)],[])).
% 0.13/0.52 tff(189,plain,
% 0.13/0.52 (addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))),
% 0.13/0.52 inference(unit_resolution,[status(thm)],[188, 60])).
% 0.13/0.52 tff(190,plain,
% 0.13/0.52 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 0.13/0.52 inference(symmetry,[status(thm)],[189])).
% 0.13/0.52 tff(191,plain,
% 0.13/0.52 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)) = tptp_fun_X1_0(X0!2)),
% 0.13/0.52 inference(transitivity,[status(thm)],[190, 187, 153, 150, 149])).
% 0.13/0.52 tff(192,plain,
% 0.13/0.52 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 0.13/0.52 inference(monotonicity,[status(thm)],[191, 147])).
% 0.13/0.52 tff(193,plain,
% 0.13/0.52 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 0.13/0.52 inference(monotonicity,[status(thm)],[189])).
% 0.13/0.52 tff(194,plain,
% 0.13/0.52 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))))),
% 0.13/0.52 inference(quant_inst,[status(thm)],[])).
% 0.13/0.52 tff(195,plain,
% 0.13/0.52 (addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 0.13/0.52 inference(unit_resolution,[status(thm)],[194, 60])).
% 0.13/0.52 tff(196,plain,
% 0.13/0.52 (addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 0.13/0.52 inference(monotonicity,[status(thm)],[145])).
% 0.13/0.52 tff(197,plain,
% 0.13/0.52 (^[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)))),
% 0.13/0.52 inference(bind,[status(th)],[])).
% 0.13/0.52 tff(198,plain,
% 0.13/0.52 (![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))),
% 0.13/0.52 inference(quant_intro,[status(thm)],[197])).
% 0.13/0.52 tff(199,plain,
% 0.13/0.52 (![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))),
% 0.13/0.52 inference(rewrite,[status(thm)],[])).
% 0.13/0.52 tff(200,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')).
% 0.13/0.52 tff(201,plain,
% 0.13/0.52 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.13/0.52 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.13/0.52 tff(202,plain,(
% 0.13/0.52 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.13/0.52 inference(skolemize,[status(sab)],[201])).
% 0.13/0.52 tff(203,plain,
% 0.13/0.52 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.13/0.52 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.13/0.52 tff(204,plain,
% 0.13/0.52 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 0.13/0.52 inference(quant_inst,[status(thm)],[])).
% 0.13/0.52 tff(205,plain,
% 0.13/0.52 (addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 0.13/0.52 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.13/0.52 tff(206,plain,
% 0.13/0.52 (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 0.13/0.52 inference(symmetry,[status(thm)],[205])).
% 0.13/0.52 tff(207,plain,
% 0.13/0.52 (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = one),
% 0.13/0.52 inference(transitivity,[status(thm)],[206, 196, 195, 193, 192, 63, 53])).
% 0.13/0.52 tff(208,plain,
% 0.13/0.52 ((one = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = one)),
% 0.13/0.52 inference(commutativity,[status(thm)],[])).
% 0.13/0.52 tff(209,plain,
% 0.13/0.52 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 0.13/0.52 inference(bind,[status(th)],[])).
% 0.13/0.52 tff(210,plain,
% 0.13/0.52 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.13/0.52 inference(quant_intro,[status(thm)],[209])).
% 0.13/0.52 tff(211,plain,
% 0.13/0.52 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.13/0.52 inference(rewrite,[status(thm)],[])).
% 0.13/0.52 tff(212,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','order')).
% 0.13/0.52 tff(213,plain,
% 0.13/0.52 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.13/0.52 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.13/0.52 tff(214,plain,(
% 0.13/0.52 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.13/0.52 inference(skolemize,[status(sab)],[213])).
% 0.13/0.52 tff(215,plain,
% 0.13/0.52 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 0.13/0.52 inference(modus_ponens,[status(thm)],[214, 210])).
% 0.13/0.52 tff(216,plain,
% 0.13/0.52 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) <=> (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one))),
% 0.13/0.52 inference(quant_inst,[status(thm)],[])).
% 0.13/0.52 tff(217,plain,
% 0.13/0.52 (leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) <=> (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one)),
% 0.13/0.52 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.13/0.52 tff(218,plain,
% 0.13/0.52 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.13/0.52 inference(bind,[status(th)],[])).
% 0.13/0.52 tff(219,plain,
% 0.13/0.52 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.13/0.52 inference(quant_intro,[status(thm)],[218])).
% 0.13/0.52 tff(220,plain,
% 0.13/0.52 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.13/0.52 inference(rewrite,[status(thm)],[])).
% 0.13/0.52 tff(221,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 0.13/0.52 tff(222,plain,
% 0.13/0.52 (![A: $i] : (addition(A, A) = A)),
% 0.13/0.52 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.13/0.52 tff(223,plain,(
% 0.13/0.52 ![A: $i] : (addition(A, A) = A)),
% 0.13/0.52 inference(skolemize,[status(sab)],[222])).
% 0.13/0.52 tff(224,plain,
% 0.13/0.52 (![A: $i] : (addition(A, A) = A)),
% 0.13/0.52 inference(modus_ponens,[status(thm)],[223, 219])).
% 0.13/0.52 tff(225,plain,
% 0.13/0.52 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 0.13/0.52 inference(quant_inst,[status(thm)],[])).
% 0.13/0.52 tff(226,plain,
% 0.13/0.52 (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 0.13/0.52 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.13/0.52 tff(227,plain,
% 0.13/0.52 (X0!2 = multiplication(X0!2, one)),
% 0.13/0.52 inference(symmetry,[status(thm)],[72])).
% 0.13/0.52 tff(228,plain,
% 0.13/0.52 (X0!2 = addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))),
% 0.13/0.52 inference(transitivity,[status(thm)],[227, 89, 99, 142, 145])).
% 0.13/0.52 tff(229,plain,
% 0.13/0.52 (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 0.13/0.52 inference(symmetry,[status(thm)],[187])).
% 0.13/0.52 tff(230,plain,
% 0.13/0.52 (multiplication(tptp_fun_X1_0(X0!2), one) = multiplication(tptp_fun_X1_0(X0!2), addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 0.13/0.52 inference(symmetry,[status(thm)],[150])).
% 0.13/0.52 tff(231,plain,
% 0.13/0.52 (tptp_fun_X1_0(X0!2) = multiplication(tptp_fun_X1_0(X0!2), one)),
% 0.13/0.52 inference(symmetry,[status(thm)],[149])).
% 0.13/0.52 tff(232,plain,
% 0.13/0.52 (tptp_fun_X1_0(X0!2) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))),
% 0.13/0.52 inference(transitivity,[status(thm)],[231, 230, 152, 229, 189])).
% 0.13/0.52 tff(233,plain,
% 0.13/0.52 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 0.13/0.52 inference(monotonicity,[status(thm)],[232, 228])).
% 0.13/0.53 tff(234,plain,
% 0.13/0.53 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 0.13/0.53 inference(symmetry,[status(thm)],[233])).
% 0.13/0.53 tff(235,plain,
% 0.13/0.53 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 0.13/0.53 inference(monotonicity,[status(thm)],[190])).
% 0.13/0.53 tff(236,plain,
% 0.13/0.53 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 0.13/0.53 inference(symmetry,[status(thm)],[235])).
% 0.13/0.53 tff(237,plain,
% 0.13/0.53 (addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 0.13/0.53 inference(monotonicity,[status(thm)],[146])).
% 0.13/0.53 tff(238,plain,
% 0.13/0.53 (addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 0.13/0.53 inference(symmetry,[status(thm)],[237])).
% 0.13/0.53 tff(239,plain,
% 0.13/0.53 (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = one),
% 0.13/0.53 inference(transitivity,[status(thm)],[206, 238, 195, 236, 234, 63, 53])).
% 0.13/0.53 tff(240,plain,
% 0.13/0.53 (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)),
% 0.13/0.53 inference(monotonicity,[status(thm)],[239])).
% 0.13/0.53 tff(241,plain,
% 0.13/0.53 (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 0.13/0.53 inference(symmetry,[status(thm)],[240])).
% 0.13/0.53 tff(242,plain,
% 0.13/0.53 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 0.13/0.53 inference(quant_inst,[status(thm)],[])).
% 0.13/0.53 tff(243,plain,
% 0.13/0.53 (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 0.13/0.53 inference(unit_resolution,[status(thm)],[242, 60])).
% 0.13/0.53 tff(244,plain,
% 0.13/0.53 (addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)),
% 0.13/0.53 inference(symmetry,[status(thm)],[243])).
% 0.13/0.53 tff(245,plain,
% 0.13/0.53 (addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 0.13/0.53 inference(transitivity,[status(thm)],[244, 241, 226])).
% 0.13/0.53 tff(246,plain,
% 0.13/0.53 ((addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one)),
% 0.13/0.53 inference(monotonicity,[status(thm)],[244, 239])).
% 0.13/0.53 tff(247,plain,
% 0.13/0.53 ((addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one) <=> (addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 0.13/0.53 inference(symmetry,[status(thm)],[246])).
% 0.13/0.53 tff(248,plain,
% 0.13/0.53 ((~(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one)) <=> (~(addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 0.13/0.53 inference(monotonicity,[status(thm)],[247])).
% 0.13/0.53 tff(249,assumption,(~leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)), introduced(assumption)).
% 0.13/0.53 tff(250,plain,
% 0.13/0.53 ((~(leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) <=> (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one))) | leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) | (~(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one))),
% 0.13/0.53 inference(tautology,[status(thm)],[])).
% 0.13/0.53 tff(251,plain,
% 0.13/0.53 ((~(leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) <=> (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one))) | (~(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one))),
% 0.13/0.53 inference(unit_resolution,[status(thm)],[250, 249])).
% 0.13/0.53 tff(252,plain,
% 0.13/0.53 (~(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one)),
% 0.13/0.53 inference(unit_resolution,[status(thm)],[251, 217])).
% 0.13/0.53 tff(253,plain,
% 0.13/0.53 (~(addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 0.13/0.53 inference(modus_ponens,[status(thm)],[252, 248])).
% 0.13/0.53 tff(254,plain,
% 0.13/0.53 ($false),
% 0.13/0.53 inference(unit_resolution,[status(thm)],[253, 245])).
% 0.13/0.53 tff(255,plain,(leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.53 tff(256,plain,
% 0.13/0.53 ((~(leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) <=> (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one))) | (~leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)) | (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one)),
% 0.13/0.53 inference(tautology,[status(thm)],[])).
% 0.13/0.53 tff(257,plain,
% 0.13/0.53 ((~(leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) <=> (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one))) | (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one)),
% 0.13/0.53 inference(unit_resolution,[status(thm)],[256, 255])).
% 0.13/0.53 tff(258,plain,
% 0.13/0.53 (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one),
% 0.13/0.53 inference(unit_resolution,[status(thm)],[257, 217])).
% 0.13/0.53 tff(259,plain,
% 0.13/0.53 (addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = one),
% 0.13/0.53 inference(transitivity,[status(thm)],[244, 258])).
% 0.13/0.53 tff(260,plain,
% 0.13/0.53 ((addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (one = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 0.13/0.53 inference(monotonicity,[status(thm)],[259])).
% 0.13/0.53 tff(261,plain,
% 0.13/0.53 ((addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = one)),
% 0.13/0.53 inference(transitivity,[status(thm)],[260, 208])).
% 0.13/0.53 tff(262,plain,
% 0.13/0.53 ((~(addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) <=> (~(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = one))),
% 0.13/0.54 inference(monotonicity,[status(thm)],[261])).
% 0.13/0.54 tff(263,plain,
% 0.13/0.54 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 0.13/0.54 inference(quant_inst,[status(thm)],[])).
% 0.13/0.54 tff(264,plain,
% 0.13/0.54 (leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 0.13/0.54 inference(unit_resolution,[status(thm)],[263, 215])).
% 0.13/0.54 tff(265,plain,
% 0.13/0.54 ((~(~((~leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))))) <=> ((~leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)))),
% 0.13/0.54 inference(rewrite,[status(thm)],[])).
% 0.13/0.54 tff(266,plain,
% 0.13/0.54 ((leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) & leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)) <=> (~((~leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))))),
% 0.13/0.54 inference(rewrite,[status(thm)],[])).
% 0.13/0.54 tff(267,plain,
% 0.13/0.54 ((~(leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) & leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))) <=> (~(~((~leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)))))),
% 0.13/0.54 inference(monotonicity,[status(thm)],[266])).
% 0.13/0.54 tff(268,plain,
% 0.13/0.54 ((~(leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) & leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))) <=> ((~leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)))),
% 0.13/0.54 inference(transitivity,[status(thm)],[267, 265])).
% 0.13/0.54 tff(269,plain,
% 0.13/0.54 (~(leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) & leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))),
% 0.13/0.54 inference(or_elim,[status(thm)],[43])).
% 0.13/0.54 tff(270,plain,
% 0.13/0.54 ((~leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))),
% 0.13/0.54 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.13/0.54 tff(271,plain,
% 0.13/0.54 (~leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 0.13/0.54 inference(unit_resolution,[status(thm)],[270, 255])).
% 0.13/0.54 tff(272,plain,
% 0.13/0.54 ((~(leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))) | leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) | (~(addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 0.13/0.54 inference(tautology,[status(thm)],[])).
% 0.13/0.54 tff(273,plain,
% 0.13/0.54 ((~(leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))) | (~(addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 0.13/0.54 inference(unit_resolution,[status(thm)],[272, 271])).
% 0.13/0.54 tff(274,plain,
% 0.13/0.54 (~(addition(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 0.13/0.54 inference(unit_resolution,[status(thm)],[273, 264])).
% 0.13/0.54 tff(275,plain,
% 0.13/0.54 (~(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = one)),
% 0.13/0.55 inference(modus_ponens,[status(thm)],[274, 262])).
% 0.13/0.55 tff(276,plain,
% 0.13/0.55 ($false),
% 0.13/0.55 inference(unit_resolution,[status(thm)],[275, 207])).
% 0.13/0.55 % SZS output end Proof
%------------------------------------------------------------------------------