TSTP Solution File: KLE010+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE010+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:23:47 EDT 2022
% Result : Theorem 4.10s 2.88s
% Output : Proof 4.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE010+2 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Sep 1 07:36:58 EDT 2022
% 0.20/0.35 % CPUTime :
% 0.20/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.35 Usage: tptp [options] [-file:]file
% 0.20/0.35 -h, -? prints this message.
% 0.20/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.35 -m, -model generate model.
% 0.20/0.35 -p, -proof generate proof.
% 0.20/0.35 -c, -core generate unsat core of named formulas.
% 0.20/0.35 -st, -statistics display statistics.
% 0.20/0.35 -t:timeout set timeout (in second).
% 0.20/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.35 -<param>:<value> configuration parameter and value.
% 0.20/0.35 -o:<output-file> file to place output in.
% 4.10/2.88 % SZS status Theorem
% 4.10/2.88 % SZS output start Proof
% 4.10/2.88 tff(one_type, type, (
% 4.10/2.88 one: $i)).
% 4.10/2.88 tff(addition_type, type, (
% 4.10/2.88 addition: ( $i * $i ) > $i)).
% 4.10/2.88 tff(multiplication_type, type, (
% 4.10/2.88 multiplication: ( $i * $i ) > $i)).
% 4.10/2.88 tff(c_type, type, (
% 4.10/2.88 c: $i > $i)).
% 4.10/2.88 tff(tptp_fun_X1_1_type, type, (
% 4.10/2.88 tptp_fun_X1_1: $i)).
% 4.10/2.88 tff(tptp_fun_X0_2_type, type, (
% 4.10/2.88 tptp_fun_X0_2: $i)).
% 4.10/2.88 tff(tptp_fun_X1_0_type, type, (
% 4.10/2.88 tptp_fun_X1_0: $i > $i)).
% 4.10/2.88 tff(zero_type, type, (
% 4.10/2.88 zero: $i)).
% 4.10/2.88 tff(complement_type, type, (
% 4.10/2.88 complement: ( $i * $i ) > $o)).
% 4.10/2.88 tff(test_type, type, (
% 4.10/2.88 test: $i > $o)).
% 4.10/2.88 tff(leq_type, type, (
% 4.10/2.88 leq: ( $i * $i ) > $o)).
% 4.10/2.88 tff(1,plain,
% 4.10/2.88 (^[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))))))),
% 4.10/2.88 inference(bind,[status(th)],[])).
% 4.10/2.88 tff(2,plain,
% 4.10/2.88 (![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)))))),
% 4.10/2.88 inference(quant_intro,[status(thm)],[1])).
% 4.10/2.88 tff(3,plain,
% 4.10/2.88 (^[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))))))),
% 4.10/2.88 inference(bind,[status(th)],[])).
% 4.10/2.88 tff(4,plain,
% 4.10/2.88 (![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)))))),
% 4.10/2.88 inference(quant_intro,[status(thm)],[3])).
% 4.10/2.88 tff(5,plain,
% 4.10/2.88 (![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)))),
% 4.10/2.88 inference(rewrite,[status(thm)],[])).
% 4.10/2.88 tff(6,plain,
% 4.10/2.88 (^[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))))),
% 4.10/2.88 inference(bind,[status(th)],[])).
% 4.10/2.88 tff(7,plain,
% 4.10/2.88 (![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)))),
% 4.10/2.88 inference(quant_intro,[status(thm)],[6])).
% 4.10/2.88 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')).
% 4.10/2.88 tff(9,plain,
% 4.10/2.88 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 4.10/2.88 inference(modus_ponens,[status(thm)],[8, 7])).
% 4.10/2.88 tff(10,plain,
% 4.10/2.88 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 4.10/2.88 inference(modus_ponens,[status(thm)],[9, 5])).
% 4.10/2.88 tff(11,plain,(
% 4.10/2.88 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 4.10/2.88 inference(skolemize,[status(sab)],[10])).
% 4.10/2.88 tff(12,plain,
% 4.10/2.88 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 4.10/2.88 inference(modus_ponens,[status(thm)],[11, 4])).
% 4.10/2.88 tff(13,plain,
% 4.10/2.88 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 4.10/2.88 inference(modus_ponens,[status(thm)],[12, 2])).
% 4.10/2.88 tff(14,plain,
% 4.10/2.88 ((~![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)))))),
% 4.10/2.88 inference(quant_inst,[status(thm)],[])).
% 4.10/2.88 tff(15,plain,
% 4.10/2.88 (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))))),
% 4.10/2.88 inference(unit_resolution,[status(thm)],[14, 13])).
% 4.10/2.88 tff(16,plain,
% 4.10/2.88 (^[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)))))))),
% 4.10/2.88 inference(bind,[status(th)],[])).
% 4.10/2.88 tff(17,plain,
% 4.10/2.88 (![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))))))),
% 4.10/2.88 inference(quant_intro,[status(thm)],[16])).
% 4.10/2.88 tff(18,plain,
% 4.10/2.88 (^[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)))))))),
% 4.10/2.88 inference(bind,[status(th)],[])).
% 4.10/2.88 tff(19,plain,
% 4.10/2.88 (![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))))))),
% 4.10/2.88 inference(quant_intro,[status(thm)],[18])).
% 4.10/2.88 tff(20,plain,
% 4.10/2.88 (![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))))))),
% 4.10/2.88 inference(transitivity,[status(thm)],[19, 17])).
% 4.10/2.88 tff(21,plain,
% 4.10/2.88 (^[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))))))))),
% 4.10/2.88 inference(bind,[status(th)],[])).
% 4.10/2.88 tff(22,plain,
% 4.10/2.88 (![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))))))),
% 4.10/2.88 inference(quant_intro,[status(thm)],[21])).
% 4.10/2.88 tff(23,plain,
% 4.10/2.88 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 4.10/2.88 inference(rewrite,[status(thm)],[])).
% 4.10/2.88 tff(24,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_1')).
% 4.10/2.88 tff(25,plain,
% 4.10/2.88 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 4.10/2.88 inference(modus_ponens,[status(thm)],[24, 23])).
% 4.10/2.88 tff(26,plain,(
% 4.10/2.88 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 4.10/2.88 inference(skolemize,[status(sab)],[25])).
% 4.10/2.88 tff(27,plain,
% 4.10/2.88 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 4.10/2.88 inference(modus_ponens,[status(thm)],[26, 22])).
% 4.10/2.88 tff(28,plain,
% 4.10/2.88 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 4.10/2.88 inference(modus_ponens,[status(thm)],[27, 20])).
% 4.10/2.88 tff(29,plain,
% 4.10/2.88 ((~![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))))))),
% 4.10/2.88 inference(quant_inst,[status(thm)],[])).
% 4.10/2.88 tff(30,plain,
% 4.10/2.88 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 4.10/2.88 inference(unit_resolution,[status(thm)],[29, 28])).
% 4.10/2.88 tff(31,plain,
% 4.10/2.88 (((~((~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))),
% 4.10/2.88 inference(tautology,[status(thm)],[])).
% 4.10/2.88 tff(32,plain,
% 4.10/2.88 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 4.10/2.88 inference(unit_resolution,[status(thm)],[31, 30])).
% 4.10/2.88 tff(33,plain,
% 4.10/2.88 ((~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one))))),
% 4.10/2.88 inference(rewrite,[status(thm)],[])).
% 4.10/2.88 tff(34,plain,
% 4.10/2.88 ((~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (leq(one, addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one))))),
% 4.10/2.88 inference(rewrite,[status(thm)],[])).
% 4.10/2.88 tff(35,axiom,(~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (leq(one, addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 4.10/2.88 tff(36,plain,
% 4.10/2.88 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 4.10/2.88 inference(modus_ponens,[status(thm)],[35, 34])).
% 4.10/2.88 tff(37,plain,
% 4.10/2.88 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 4.10/2.88 inference(modus_ponens,[status(thm)],[36, 33])).
% 4.10/2.88 tff(38,plain,
% 4.10/2.88 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 4.10/2.88 inference(modus_ponens,[status(thm)],[37, 33])).
% 4.10/2.88 tff(39,plain,
% 4.10/2.88 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 4.10/2.88 inference(modus_ponens,[status(thm)],[38, 33])).
% 4.10/2.88 tff(40,plain,
% 4.10/2.88 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 4.10/2.88 inference(modus_ponens,[status(thm)],[39, 33])).
% 4.10/2.88 tff(41,plain,
% 4.10/2.88 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 4.10/2.88 inference(modus_ponens,[status(thm)],[40, 33])).
% 4.10/2.88 tff(42,plain,
% 4.10/2.88 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 4.10/2.88 inference(modus_ponens,[status(thm)],[41, 33])).
% 4.10/2.88 tff(43,plain,(
% 4.10/2.88 ~((~(test(X1!1) & test(X0!2))) | (leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) & leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)))),
% 4.10/2.88 inference(skolemize,[status(sab)],[42])).
% 4.10/2.88 tff(44,plain,
% 4.10/2.88 (test(X1!1) & test(X0!2)),
% 4.10/2.88 inference(or_elim,[status(thm)],[43])).
% 4.10/2.88 tff(45,plain,
% 4.10/2.88 (test(X1!1)),
% 4.10/2.88 inference(and_elim,[status(thm)],[44])).
% 4.10/2.88 tff(46,plain,
% 4.10/2.88 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 4.10/2.88 inference(tautology,[status(thm)],[])).
% 4.10/2.88 tff(47,plain,
% 4.10/2.88 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 4.10/2.88 inference(unit_resolution,[status(thm)],[46, 45])).
% 4.10/2.88 tff(48,plain,
% 4.10/2.88 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 4.10/2.88 inference(unit_resolution,[status(thm)],[47, 32])).
% 4.10/2.88 tff(49,plain,
% 4.10/2.88 ((~(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))))),
% 4.10/2.88 inference(tautology,[status(thm)],[])).
% 4.10/2.88 tff(50,plain,
% 4.10/2.88 ((~(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))))),
% 4.10/2.88 inference(unit_resolution,[status(thm)],[49, 48])).
% 4.10/2.88 tff(51,plain,
% 4.10/2.88 (~((~(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)))),
% 4.10/2.88 inference(unit_resolution,[status(thm)],[50, 15])).
% 4.10/2.88 tff(52,plain,
% 4.10/2.88 (((~(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)),
% 4.10/2.88 inference(tautology,[status(thm)],[])).
% 4.10/2.88 tff(53,plain,
% 4.10/2.88 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 4.10/2.88 inference(unit_resolution,[status(thm)],[52, 51])).
% 4.10/2.88 tff(54,plain,
% 4.10/2.88 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 4.10/2.88 inference(bind,[status(th)],[])).
% 4.10/2.88 tff(55,plain,
% 4.10/2.88 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 4.10/2.88 inference(quant_intro,[status(thm)],[54])).
% 4.10/2.88 tff(56,plain,
% 4.10/2.88 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 4.10/2.88 inference(rewrite,[status(thm)],[])).
% 4.10/2.88 tff(57,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 4.10/2.88 tff(58,plain,
% 4.10/2.88 (![A: $i] : (multiplication(one, A) = A)),
% 4.10/2.88 inference(modus_ponens,[status(thm)],[57, 56])).
% 4.10/2.88 tff(59,plain,(
% 4.10/2.88 ![A: $i] : (multiplication(one, A) = A)),
% 4.10/2.88 inference(skolemize,[status(sab)],[58])).
% 4.10/2.88 tff(60,plain,
% 4.10/2.88 (![A: $i] : (multiplication(one, A) = A)),
% 4.10/2.88 inference(modus_ponens,[status(thm)],[59, 55])).
% 4.10/2.88 tff(61,plain,
% 4.10/2.88 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X1!1) = X1!1)),
% 4.10/2.88 inference(quant_inst,[status(thm)],[])).
% 4.10/2.88 tff(62,plain,
% 4.10/2.88 (multiplication(one, X1!1) = X1!1),
% 4.10/2.88 inference(unit_resolution,[status(thm)],[61, 60])).
% 4.10/2.88 tff(63,plain,
% 4.10/2.88 ((~![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)))))),
% 4.10/2.88 inference(quant_inst,[status(thm)],[])).
% 4.10/2.88 tff(64,plain,
% 4.10/2.88 (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))))),
% 4.10/2.88 inference(unit_resolution,[status(thm)],[63, 13])).
% 4.10/2.88 tff(65,plain,
% 4.10/2.88 ((~![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))))))),
% 4.10/2.88 inference(quant_inst,[status(thm)],[])).
% 4.10/2.88 tff(66,plain,
% 4.10/2.88 (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2)))))),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[65, 28])).
% 4.10/2.89 tff(67,plain,
% 4.10/2.89 (((~((~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))),
% 4.10/2.89 inference(tautology,[status(thm)],[])).
% 4.10/2.89 tff(68,plain,
% 4.10/2.89 ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[67, 66])).
% 4.10/2.89 tff(69,plain,
% 4.10/2.89 (test(X0!2)),
% 4.10/2.89 inference(and_elim,[status(thm)],[44])).
% 4.10/2.89 tff(70,plain,
% 4.10/2.89 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 4.10/2.89 inference(tautology,[status(thm)],[])).
% 4.10/2.89 tff(71,plain,
% 4.10/2.89 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[70, 69])).
% 4.10/2.89 tff(72,plain,
% 4.10/2.89 (complement(tptp_fun_X1_0(X0!2), X0!2)),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[71, 68])).
% 4.10/2.89 tff(73,plain,
% 4.10/2.89 ((~(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))))),
% 4.10/2.89 inference(tautology,[status(thm)],[])).
% 4.10/2.89 tff(74,plain,
% 4.10/2.89 ((~(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))))),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[73, 72])).
% 4.10/2.89 tff(75,plain,
% 4.10/2.89 (~((~(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)))),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[74, 64])).
% 4.10/2.89 tff(76,plain,
% 4.10/2.89 (((~(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)),
% 4.10/2.89 inference(tautology,[status(thm)],[])).
% 4.10/2.89 tff(77,plain,
% 4.10/2.89 (addition(X0!2, tptp_fun_X1_0(X0!2)) = one),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[76, 75])).
% 4.10/2.89 tff(78,plain,
% 4.10/2.89 (one = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 4.10/2.89 inference(symmetry,[status(thm)],[77])).
% 4.10/2.89 tff(79,plain,
% 4.10/2.89 (multiplication(one, X1!1) = multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1)),
% 4.10/2.89 inference(monotonicity,[status(thm)],[78])).
% 4.10/2.89 tff(80,plain,
% 4.10/2.89 (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1) = multiplication(one, X1!1)),
% 4.10/2.89 inference(symmetry,[status(thm)],[79])).
% 4.10/2.89 tff(81,plain,
% 4.10/2.89 (^[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))))),
% 4.10/2.89 inference(bind,[status(th)],[])).
% 4.10/2.89 tff(82,plain,
% 4.10/2.89 (![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)))),
% 4.10/2.89 inference(quant_intro,[status(thm)],[81])).
% 4.10/2.89 tff(83,plain,
% 4.10/2.89 (![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)))),
% 4.10/2.89 inference(rewrite,[status(thm)],[])).
% 4.10/2.89 tff(84,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')).
% 4.10/2.89 tff(85,plain,
% 4.10/2.89 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 4.10/2.89 inference(modus_ponens,[status(thm)],[84, 83])).
% 4.10/2.89 tff(86,plain,(
% 4.10/2.89 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 4.10/2.89 inference(skolemize,[status(sab)],[85])).
% 4.10/2.89 tff(87,plain,
% 4.10/2.89 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 4.10/2.89 inference(modus_ponens,[status(thm)],[86, 82])).
% 4.10/2.89 tff(88,plain,
% 4.10/2.89 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1) = addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)))),
% 4.10/2.89 inference(quant_inst,[status(thm)],[])).
% 4.10/2.89 tff(89,plain,
% 4.10/2.89 (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1) = addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[88, 87])).
% 4.10/2.89 tff(90,plain,
% 4.10/2.89 (addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1)),
% 4.10/2.89 inference(symmetry,[status(thm)],[89])).
% 4.10/2.89 tff(91,plain,
% 4.10/2.89 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 4.10/2.89 inference(bind,[status(th)],[])).
% 4.10/2.89 tff(92,plain,
% 4.10/2.89 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.10/2.89 inference(quant_intro,[status(thm)],[91])).
% 4.10/2.89 tff(93,plain,
% 4.10/2.89 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.10/2.89 inference(rewrite,[status(thm)],[])).
% 4.10/2.89 tff(94,plain,
% 4.10/2.89 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 4.10/2.89 inference(bind,[status(th)],[])).
% 4.10/2.89 tff(95,plain,
% 4.10/2.89 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.10/2.89 inference(quant_intro,[status(thm)],[94])).
% 4.10/2.89 tff(96,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_3')).
% 4.10/2.89 tff(97,plain,
% 4.10/2.89 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.10/2.89 inference(modus_ponens,[status(thm)],[96, 95])).
% 4.10/2.89 tff(98,plain,
% 4.10/2.89 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.10/2.89 inference(modus_ponens,[status(thm)],[97, 93])).
% 4.10/2.89 tff(99,plain,(
% 4.10/2.89 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.10/2.89 inference(skolemize,[status(sab)],[98])).
% 4.10/2.89 tff(100,plain,
% 4.10/2.89 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.10/2.89 inference(modus_ponens,[status(thm)],[99, 92])).
% 4.10/2.89 tff(101,plain,
% 4.10/2.89 (((~![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))))),
% 4.10/2.89 inference(rewrite,[status(thm)],[])).
% 4.10/2.89 tff(102,plain,
% 4.10/2.89 ((~![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))))),
% 4.10/2.89 inference(quant_inst,[status(thm)],[])).
% 4.10/2.89 tff(103,plain,
% 4.10/2.89 ((~![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)))),
% 4.10/2.89 inference(modus_ponens,[status(thm)],[102, 101])).
% 4.10/2.89 tff(104,plain,
% 4.10/2.89 ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[103, 100, 69])).
% 4.10/2.89 tff(105,plain,
% 4.10/2.89 (((~![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))))))),
% 4.10/2.89 inference(rewrite,[status(thm)],[])).
% 4.10/2.89 tff(106,plain,
% 4.10/2.89 ((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)))))),
% 4.10/2.89 inference(rewrite,[status(thm)],[])).
% 4.10/2.89 tff(107,plain,
% 4.10/2.89 (((~![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))))))),
% 4.10/2.89 inference(monotonicity,[status(thm)],[106])).
% 4.10/2.89 tff(108,plain,
% 4.10/2.89 (((~![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))))))),
% 4.10/2.89 inference(transitivity,[status(thm)],[107, 105])).
% 4.10/2.89 tff(109,plain,
% 4.10/2.89 ((~![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)))))),
% 4.10/2.89 inference(quant_inst,[status(thm)],[])).
% 4.10/2.89 tff(110,plain,
% 4.10/2.89 ((~![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)))))),
% 4.10/2.89 inference(modus_ponens,[status(thm)],[109, 108])).
% 4.10/2.89 tff(111,plain,
% 4.10/2.89 (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))))),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[110, 13])).
% 4.10/2.89 tff(112,plain,
% 4.10/2.89 ((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))),
% 4.10/2.89 inference(commutativity,[status(thm)],[])).
% 4.10/2.89 tff(113,plain,
% 4.10/2.89 ((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)))),
% 4.10/2.89 inference(monotonicity,[status(thm)],[78])).
% 4.10/2.89 tff(114,plain,
% 4.10/2.89 ((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))),
% 4.10/2.89 inference(transitivity,[status(thm)],[113, 112])).
% 4.10/2.89 tff(115,plain,
% 4.10/2.89 ((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)),
% 4.10/2.89 inference(symmetry,[status(thm)],[114])).
% 4.10/2.89 tff(116,plain,
% 4.10/2.89 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 4.10/2.89 inference(bind,[status(th)],[])).
% 4.10/2.89 tff(117,plain,
% 4.10/2.89 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 4.10/2.89 inference(quant_intro,[status(thm)],[116])).
% 4.10/2.89 tff(118,plain,
% 4.10/2.89 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 4.10/2.89 inference(rewrite,[status(thm)],[])).
% 4.10/2.89 tff(119,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 4.10/2.89 tff(120,plain,
% 4.10/2.89 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 4.10/2.89 inference(modus_ponens,[status(thm)],[119, 118])).
% 4.10/2.89 tff(121,plain,(
% 4.10/2.89 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 4.10/2.89 inference(skolemize,[status(sab)],[120])).
% 4.10/2.89 tff(122,plain,
% 4.10/2.89 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 4.10/2.89 inference(modus_ponens,[status(thm)],[121, 117])).
% 4.10/2.89 tff(123,plain,
% 4.10/2.89 ((~![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))),
% 4.10/2.89 inference(quant_inst,[status(thm)],[])).
% 4.10/2.89 tff(124,plain,
% 4.10/2.89 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[123, 122])).
% 4.10/2.89 tff(125,plain,
% 4.10/2.89 (addition(tptp_fun_X1_0(X0!2), X0!2) = one),
% 4.10/2.89 inference(modus_ponens,[status(thm)],[124, 115])).
% 4.10/2.89 tff(126,plain,
% 4.10/2.89 (((~(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)),
% 4.10/2.89 inference(tautology,[status(thm)],[])).
% 4.10/2.89 tff(127,plain,
% 4.10/2.89 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[126, 75])).
% 4.10/2.89 tff(128,plain,
% 4.10/2.89 (((~(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)),
% 4.10/2.89 inference(tautology,[status(thm)],[])).
% 4.10/2.89 tff(129,plain,
% 4.10/2.89 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[128, 75])).
% 4.10/2.89 tff(130,plain,
% 4.10/2.89 ((~((~(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))),
% 4.10/2.89 inference(tautology,[status(thm)],[])).
% 4.10/2.89 tff(131,plain,
% 4.10/2.89 ((~((~(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))),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[130, 129, 127])).
% 4.10/2.89 tff(132,plain,
% 4.10/2.89 (~((~(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)))),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[131, 125])).
% 4.10/2.89 tff(133,plain,
% 4.10/2.89 ((~(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)))),
% 4.10/2.89 inference(tautology,[status(thm)],[])).
% 4.10/2.89 tff(134,plain,
% 4.10/2.89 (complement(X0!2, tptp_fun_X1_0(X0!2))),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[133, 132, 111])).
% 4.10/2.89 tff(135,plain,
% 4.10/2.89 ((~((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)))),
% 4.10/2.89 inference(tautology,[status(thm)],[])).
% 4.10/2.89 tff(136,plain,
% 4.10/2.89 (c(X0!2) = tptp_fun_X1_0(X0!2)),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[135, 134, 104])).
% 4.10/2.89 tff(137,plain,
% 4.10/2.89 (tptp_fun_X1_0(X0!2) = c(X0!2)),
% 4.10/2.89 inference(symmetry,[status(thm)],[136])).
% 4.10/2.89 tff(138,plain,
% 4.10/2.89 (multiplication(tptp_fun_X1_0(X0!2), X1!1) = multiplication(c(X0!2), X1!1)),
% 4.10/2.89 inference(monotonicity,[status(thm)],[137])).
% 4.10/2.89 tff(139,plain,
% 4.10/2.89 (addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))),
% 4.10/2.89 inference(monotonicity,[status(thm)],[138])).
% 4.10/2.89 tff(140,plain,
% 4.10/2.89 (addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 4.10/2.89 inference(symmetry,[status(thm)],[139])).
% 4.10/2.89 tff(141,plain,
% 4.10/2.89 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.89 inference(quant_inst,[status(thm)],[])).
% 4.10/2.89 tff(142,plain,
% 4.10/2.89 (addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[141, 122])).
% 4.10/2.89 tff(143,plain,
% 4.10/2.89 (addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))),
% 4.10/2.89 inference(symmetry,[status(thm)],[142])).
% 4.10/2.89 tff(144,plain,
% 4.10/2.89 (addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)) = X1!1),
% 4.10/2.89 inference(transitivity,[status(thm)],[143, 140, 90, 80, 62])).
% 4.10/2.89 tff(145,plain,
% 4.10/2.89 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1)) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 4.10/2.89 inference(monotonicity,[status(thm)],[144])).
% 4.10/2.89 tff(146,plain,
% 4.10/2.89 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 4.10/2.89 inference(bind,[status(th)],[])).
% 4.10/2.89 tff(147,plain,
% 4.10/2.89 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 4.10/2.89 inference(quant_intro,[status(thm)],[146])).
% 4.10/2.89 tff(148,plain,
% 4.10/2.89 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 4.10/2.89 inference(rewrite,[status(thm)],[])).
% 4.10/2.89 tff(149,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 4.10/2.89 tff(150,plain,
% 4.10/2.89 (![A: $i] : (addition(A, A) = A)),
% 4.10/2.89 inference(modus_ponens,[status(thm)],[149, 148])).
% 4.10/2.89 tff(151,plain,(
% 4.10/2.89 ![A: $i] : (addition(A, A) = A)),
% 4.10/2.89 inference(skolemize,[status(sab)],[150])).
% 4.10/2.89 tff(152,plain,
% 4.10/2.89 (![A: $i] : (addition(A, A) = A)),
% 4.10/2.89 inference(modus_ponens,[status(thm)],[151, 147])).
% 4.10/2.89 tff(153,plain,
% 4.10/2.89 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.89 inference(quant_inst,[status(thm)],[])).
% 4.10/2.89 tff(154,plain,
% 4.10/2.89 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[153, 152])).
% 4.10/2.89 tff(155,plain,
% 4.10/2.89 (addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))), tptp_fun_X1_0(X1!1)) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1))),
% 4.10/2.89 inference(monotonicity,[status(thm)],[154])).
% 4.10/2.89 tff(156,plain,
% 4.10/2.89 (^[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)))),
% 4.10/2.89 inference(bind,[status(th)],[])).
% 4.10/2.89 tff(157,plain,
% 4.10/2.89 (![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))),
% 4.10/2.89 inference(quant_intro,[status(thm)],[156])).
% 4.10/2.89 tff(158,plain,
% 4.10/2.89 (![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))),
% 4.10/2.89 inference(rewrite,[status(thm)],[])).
% 4.10/2.89 tff(159,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')).
% 4.10/2.89 tff(160,plain,
% 4.10/2.89 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 4.10/2.89 inference(modus_ponens,[status(thm)],[159, 158])).
% 4.10/2.89 tff(161,plain,(
% 4.10/2.89 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 4.10/2.89 inference(skolemize,[status(sab)],[160])).
% 4.10/2.89 tff(162,plain,
% 4.10/2.89 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 4.10/2.89 inference(modus_ponens,[status(thm)],[161, 157])).
% 4.10/2.89 tff(163,plain,
% 4.10/2.89 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1))) = addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))), tptp_fun_X1_0(X1!1)))),
% 4.10/2.89 inference(quant_inst,[status(thm)],[])).
% 4.10/2.89 tff(164,plain,
% 4.10/2.89 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1))) = addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))), tptp_fun_X1_0(X1!1))),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[163, 162])).
% 4.10/2.89 tff(165,plain,
% 4.10/2.89 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1))),
% 4.10/2.89 inference(symmetry,[status(thm)],[145])).
% 4.10/2.89 tff(166,plain,
% 4.10/2.89 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 4.10/2.89 inference(symmetry,[status(thm)],[53])).
% 4.10/2.89 tff(167,plain,
% 4.10/2.89 (one = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1))),
% 4.10/2.89 inference(transitivity,[status(thm)],[166, 165])).
% 4.10/2.89 tff(168,plain,
% 4.10/2.89 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), one) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1)))),
% 4.10/2.89 inference(monotonicity,[status(thm)],[167])).
% 4.10/2.89 tff(169,plain,
% 4.10/2.89 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), one) = addition(one, addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))))),
% 4.10/2.89 inference(quant_inst,[status(thm)],[])).
% 4.10/2.89 tff(170,plain,
% 4.10/2.89 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), one) = addition(one, addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[169, 122])).
% 4.10/2.89 tff(171,plain,
% 4.10/2.89 (addition(one, addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), one)),
% 4.10/2.89 inference(symmetry,[status(thm)],[170])).
% 4.10/2.89 tff(172,plain,
% 4.10/2.89 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 4.10/2.89 inference(bind,[status(th)],[])).
% 4.10/2.89 tff(173,plain,
% 4.10/2.89 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 4.10/2.89 inference(quant_intro,[status(thm)],[172])).
% 4.10/2.89 tff(174,plain,
% 4.10/2.89 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 4.10/2.89 inference(rewrite,[status(thm)],[])).
% 4.10/2.89 tff(175,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','order')).
% 4.10/2.89 tff(176,plain,
% 4.10/2.89 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 4.10/2.89 inference(modus_ponens,[status(thm)],[175, 174])).
% 4.10/2.89 tff(177,plain,(
% 4.10/2.89 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 4.10/2.89 inference(skolemize,[status(sab)],[176])).
% 4.10/2.89 tff(178,plain,
% 4.10/2.89 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 4.10/2.89 inference(modus_ponens,[status(thm)],[177, 173])).
% 4.10/2.89 tff(179,plain,
% 4.10/2.89 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) <=> (addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one))),
% 4.10/2.89 inference(quant_inst,[status(thm)],[])).
% 4.10/2.89 tff(180,plain,
% 4.10/2.89 (leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) <=> (addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one)),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[179, 178])).
% 4.10/2.89 tff(181,plain,
% 4.10/2.89 (X1!1 = multiplication(one, X1!1)),
% 4.10/2.89 inference(symmetry,[status(thm)],[62])).
% 4.10/2.89 tff(182,plain,
% 4.10/2.89 (X1!1 = addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))),
% 4.10/2.89 inference(transitivity,[status(thm)],[181, 79, 89, 139, 142])).
% 4.10/2.89 tff(183,plain,
% 4.10/2.89 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1))),
% 4.10/2.89 inference(monotonicity,[status(thm)],[182])).
% 4.10/2.89 tff(184,plain,
% 4.10/2.89 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1)) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 4.10/2.89 inference(symmetry,[status(thm)],[183])).
% 4.10/2.89 tff(185,plain,
% 4.10/2.89 (addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.89 inference(symmetry,[status(thm)],[154])).
% 4.10/2.89 tff(186,plain,
% 4.10/2.89 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1)) = addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))), tptp_fun_X1_0(X1!1))),
% 4.10/2.89 inference(monotonicity,[status(thm)],[185])).
% 4.10/2.89 tff(187,plain,
% 4.10/2.89 (addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))), tptp_fun_X1_0(X1!1)) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1))),
% 4.10/2.89 inference(symmetry,[status(thm)],[186])).
% 4.10/2.89 tff(188,plain,
% 4.10/2.89 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1)) = one),
% 4.10/2.89 inference(transitivity,[status(thm)],[184, 53])).
% 4.10/2.89 tff(189,plain,
% 4.10/2.89 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), one)),
% 4.10/2.89 inference(monotonicity,[status(thm)],[188])).
% 4.10/2.89 tff(190,plain,
% 4.10/2.89 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), one) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1)))),
% 4.10/2.89 inference(symmetry,[status(thm)],[189])).
% 4.10/2.89 tff(191,plain,
% 4.10/2.89 (addition(one, addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = addition(one, X1!1)),
% 4.10/2.89 inference(monotonicity,[status(thm)],[144])).
% 4.10/2.89 tff(192,plain,
% 4.10/2.89 (addition(one, X1!1) = addition(one, addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.89 inference(symmetry,[status(thm)],[191])).
% 4.10/2.89 tff(193,plain,
% 4.10/2.89 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)))),
% 4.10/2.89 inference(quant_inst,[status(thm)],[])).
% 4.10/2.89 tff(194,plain,
% 4.10/2.89 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2))),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[193, 162])).
% 4.10/2.89 tff(195,plain,
% 4.10/2.89 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.10/2.89 inference(symmetry,[status(thm)],[194])).
% 4.10/2.89 tff(196,plain,
% 4.10/2.89 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), multiplication(c(X0!2), X1!1)) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), multiplication(c(X0!2), X1!1))),
% 4.10/2.89 inference(monotonicity,[status(thm)],[195])).
% 4.10/2.89 tff(197,plain,
% 4.10/2.89 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), multiplication(c(X0!2), X1!1)) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), multiplication(c(X0!2), X1!1))),
% 4.10/2.89 inference(symmetry,[status(thm)],[196])).
% 4.10/2.89 tff(198,plain,
% 4.10/2.89 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(c(X0!2), c(X1!1))))),
% 4.10/2.89 inference(quant_inst,[status(thm)],[])).
% 4.10/2.89 tff(199,plain,
% 4.10/2.89 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(c(X0!2), c(X1!1)))),
% 4.10/2.89 inference(unit_resolution,[status(thm)],[198, 122])).
% 4.10/2.89 tff(200,plain,
% 4.10/2.89 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), multiplication(c(X0!2), X1!1)) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X0!2), X1!1))),
% 4.10/2.89 inference(monotonicity,[status(thm)],[199])).
% 4.10/2.89 tff(201,plain,
% 4.10/2.89 (addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X0!2), X1!1)) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), multiplication(c(X0!2), X1!1))),
% 4.10/2.90 inference(symmetry,[status(thm)],[200])).
% 4.10/2.90 tff(202,plain,
% 4.10/2.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X0!2), X1!1)))),
% 4.10/2.90 inference(quant_inst,[status(thm)],[])).
% 4.10/2.90 tff(203,plain,
% 4.10/2.90 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X0!2), X1!1))),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[202, 162])).
% 4.10/2.90 tff(204,plain,
% 4.10/2.90 ((~![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)))),
% 4.10/2.90 inference(quant_inst,[status(thm)],[])).
% 4.10/2.90 tff(205,plain,
% 4.10/2.90 (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))),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[204, 122])).
% 4.10/2.90 tff(206,plain,
% 4.10/2.90 (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)))),
% 4.10/2.90 inference(symmetry,[status(thm)],[205])).
% 4.10/2.90 tff(207,plain,
% 4.10/2.90 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 4.10/2.90 inference(monotonicity,[status(thm)],[206])).
% 4.10/2.90 tff(208,plain,
% 4.10/2.90 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))),
% 4.10/2.90 inference(symmetry,[status(thm)],[207])).
% 4.10/2.90 tff(209,plain,
% 4.10/2.90 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 4.10/2.90 inference(bind,[status(th)],[])).
% 4.10/2.90 tff(210,plain,
% 4.10/2.90 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 4.10/2.90 inference(quant_intro,[status(thm)],[209])).
% 4.10/2.90 tff(211,plain,
% 4.10/2.90 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 4.10/2.90 inference(rewrite,[status(thm)],[])).
% 4.10/2.90 tff(212,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 4.10/2.90 tff(213,plain,
% 4.10/2.90 (![A: $i] : (multiplication(A, one) = A)),
% 4.10/2.90 inference(modus_ponens,[status(thm)],[212, 211])).
% 4.10/2.90 tff(214,plain,(
% 4.10/2.90 ![A: $i] : (multiplication(A, one) = A)),
% 4.10/2.90 inference(skolemize,[status(sab)],[213])).
% 4.10/2.90 tff(215,plain,
% 4.10/2.90 (![A: $i] : (multiplication(A, one) = A)),
% 4.10/2.90 inference(modus_ponens,[status(thm)],[214, 210])).
% 4.10/2.90 tff(216,plain,
% 4.10/2.90 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(tptp_fun_X1_0(X0!2), one) = tptp_fun_X1_0(X0!2))),
% 4.10/2.90 inference(quant_inst,[status(thm)],[])).
% 4.10/2.90 tff(217,plain,
% 4.10/2.90 (multiplication(tptp_fun_X1_0(X0!2), one) = tptp_fun_X1_0(X0!2)),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[216, 215])).
% 4.10/2.90 tff(218,plain,
% 4.10/2.90 (multiplication(tptp_fun_X1_0(X0!2), one) = multiplication(tptp_fun_X1_0(X0!2), addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 4.10/2.90 inference(monotonicity,[status(thm)],[166])).
% 4.10/2.90 tff(219,plain,
% 4.10/2.90 (multiplication(tptp_fun_X1_0(X0!2), addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), one)),
% 4.10/2.90 inference(symmetry,[status(thm)],[218])).
% 4.10/2.90 tff(220,plain,
% 4.10/2.90 (^[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))))),
% 4.10/2.90 inference(bind,[status(th)],[])).
% 4.10/2.90 tff(221,plain,
% 4.10/2.90 (![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)))),
% 4.10/2.90 inference(quant_intro,[status(thm)],[220])).
% 4.10/2.90 tff(222,plain,
% 4.10/2.90 (![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)))),
% 4.10/2.90 inference(rewrite,[status(thm)],[])).
% 4.10/2.90 tff(223,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')).
% 4.10/2.90 tff(224,plain,
% 4.10/2.90 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 4.10/2.90 inference(modus_ponens,[status(thm)],[223, 222])).
% 4.10/2.90 tff(225,plain,(
% 4.10/2.90 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 4.10/2.90 inference(skolemize,[status(sab)],[224])).
% 4.10/2.90 tff(226,plain,
% 4.10/2.90 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 4.10/2.90 inference(modus_ponens,[status(thm)],[225, 221])).
% 4.10/2.90 tff(227,plain,
% 4.10/2.90 ((~![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))))),
% 4.10/2.90 inference(quant_inst,[status(thm)],[])).
% 4.10/2.90 tff(228,plain,
% 4.10/2.90 (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)))),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[227, 226])).
% 4.10/2.90 tff(229,plain,
% 4.10/2.90 (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)))),
% 4.10/2.90 inference(symmetry,[status(thm)],[228])).
% 4.10/2.90 tff(230,plain,
% 4.10/2.90 (((~![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))))),
% 4.10/2.90 inference(rewrite,[status(thm)],[])).
% 4.10/2.90 tff(231,plain,
% 4.10/2.90 ((~![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))))),
% 4.10/2.90 inference(quant_inst,[status(thm)],[])).
% 4.10/2.90 tff(232,plain,
% 4.10/2.90 ((~![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)))),
% 4.10/2.90 inference(modus_ponens,[status(thm)],[231, 230])).
% 4.10/2.90 tff(233,plain,
% 4.10/2.90 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[232, 100, 45])).
% 4.10/2.90 tff(234,plain,
% 4.10/2.90 (((~![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))))))),
% 4.10/2.90 inference(rewrite,[status(thm)],[])).
% 4.10/2.90 tff(235,plain,
% 4.10/2.90 ((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)))))),
% 4.10/2.90 inference(rewrite,[status(thm)],[])).
% 4.10/2.90 tff(236,plain,
% 4.10/2.90 (((~![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))))))),
% 4.10/2.90 inference(monotonicity,[status(thm)],[235])).
% 4.10/2.90 tff(237,plain,
% 4.10/2.90 (((~![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))))))),
% 4.10/2.90 inference(transitivity,[status(thm)],[236, 234])).
% 4.10/2.90 tff(238,plain,
% 4.10/2.90 ((~![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)))))),
% 4.10/2.90 inference(quant_inst,[status(thm)],[])).
% 4.10/2.90 tff(239,plain,
% 4.10/2.90 ((~![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)))))),
% 4.10/2.90 inference(modus_ponens,[status(thm)],[238, 237])).
% 4.10/2.90 tff(240,plain,
% 4.10/2.90 (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))))),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[239, 13])).
% 4.10/2.90 tff(241,plain,
% 4.10/2.90 ((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))),
% 4.10/2.90 inference(commutativity,[status(thm)],[])).
% 4.10/2.90 tff(242,plain,
% 4.10/2.90 ((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)))),
% 4.10/2.90 inference(monotonicity,[status(thm)],[166])).
% 4.10/2.90 tff(243,plain,
% 4.10/2.90 ((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))),
% 4.10/2.90 inference(transitivity,[status(thm)],[242, 241])).
% 4.10/2.90 tff(244,plain,
% 4.10/2.90 ((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)),
% 4.10/2.90 inference(symmetry,[status(thm)],[243])).
% 4.10/2.90 tff(245,plain,
% 4.10/2.90 ((~![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))),
% 4.10/2.90 inference(quant_inst,[status(thm)],[])).
% 4.10/2.90 tff(246,plain,
% 4.10/2.90 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[245, 122])).
% 4.10/2.90 tff(247,plain,
% 4.10/2.90 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 4.10/2.90 inference(modus_ponens,[status(thm)],[246, 244])).
% 4.10/2.90 tff(248,plain,
% 4.10/2.90 (((~(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)),
% 4.10/2.90 inference(tautology,[status(thm)],[])).
% 4.10/2.90 tff(249,plain,
% 4.10/2.90 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[248, 51])).
% 4.10/2.90 tff(250,plain,
% 4.10/2.90 (((~(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)),
% 4.10/2.90 inference(tautology,[status(thm)],[])).
% 4.10/2.90 tff(251,plain,
% 4.10/2.90 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[250, 51])).
% 4.10/2.90 tff(252,plain,
% 4.10/2.90 ((~((~(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))),
% 4.10/2.90 inference(tautology,[status(thm)],[])).
% 4.10/2.90 tff(253,plain,
% 4.10/2.90 ((~((~(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))),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[252, 251, 249])).
% 4.10/2.90 tff(254,plain,
% 4.10/2.90 (~((~(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)))),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[253, 247])).
% 4.10/2.90 tff(255,plain,
% 4.10/2.90 ((~(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)))),
% 4.10/2.90 inference(tautology,[status(thm)],[])).
% 4.10/2.90 tff(256,plain,
% 4.10/2.90 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[255, 254, 240])).
% 4.10/2.90 tff(257,plain,
% 4.10/2.90 ((~((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)))),
% 4.10/2.90 inference(tautology,[status(thm)],[])).
% 4.10/2.90 tff(258,plain,
% 4.10/2.90 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[257, 256, 233])).
% 4.10/2.90 tff(259,plain,
% 4.10/2.90 (tptp_fun_X1_0(X1!1) = c(X1!1)),
% 4.10/2.90 inference(symmetry,[status(thm)],[258])).
% 4.10/2.90 tff(260,plain,
% 4.10/2.90 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)) = multiplication(c(X0!2), c(X1!1))),
% 4.10/2.90 inference(monotonicity,[status(thm)],[137, 259])).
% 4.10/2.90 tff(261,plain,
% 4.10/2.90 (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)))),
% 4.10/2.90 inference(monotonicity,[status(thm)],[138, 260])).
% 4.10/2.90 tff(262,plain,
% 4.10/2.90 (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)))),
% 4.10/2.90 inference(symmetry,[status(thm)],[261])).
% 4.10/2.90 tff(263,plain,
% 4.10/2.90 (addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = tptp_fun_X1_0(X0!2)),
% 4.10/2.90 inference(transitivity,[status(thm)],[262, 229, 219, 217])).
% 4.10/2.90 tff(264,plain,
% 4.10/2.90 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!2) = X0!2)),
% 4.10/2.90 inference(quant_inst,[status(thm)],[])).
% 4.10/2.90 tff(265,plain,
% 4.10/2.90 (multiplication(one, X0!2) = X0!2),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[264, 60])).
% 4.10/2.90 tff(266,plain,
% 4.10/2.90 (multiplication(one, X0!2) = multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2)),
% 4.10/2.90 inference(monotonicity,[status(thm)],[166])).
% 4.10/2.90 tff(267,plain,
% 4.10/2.90 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = multiplication(one, X0!2)),
% 4.10/2.90 inference(symmetry,[status(thm)],[266])).
% 4.10/2.90 tff(268,plain,
% 4.10/2.90 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)))),
% 4.10/2.90 inference(quant_inst,[status(thm)],[])).
% 4.10/2.90 tff(269,plain,
% 4.10/2.90 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[268, 87])).
% 4.10/2.90 tff(270,plain,
% 4.10/2.90 (addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2)),
% 4.10/2.90 inference(symmetry,[status(thm)],[269])).
% 4.10/2.90 tff(271,plain,
% 4.10/2.90 (multiplication(tptp_fun_X1_0(X1!1), X0!2) = multiplication(c(X1!1), X0!2)),
% 4.10/2.90 inference(monotonicity,[status(thm)],[259])).
% 4.10/2.90 tff(272,plain,
% 4.10/2.90 (addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 4.10/2.90 inference(monotonicity,[status(thm)],[271])).
% 4.10/2.90 tff(273,plain,
% 4.10/2.90 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 4.10/2.90 inference(symmetry,[status(thm)],[272])).
% 4.10/2.90 tff(274,plain,
% 4.10/2.90 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.10/2.90 inference(quant_inst,[status(thm)],[])).
% 4.10/2.90 tff(275,plain,
% 4.10/2.90 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[274, 122])).
% 4.10/2.90 tff(276,plain,
% 4.10/2.90 (addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 4.10/2.90 inference(symmetry,[status(thm)],[275])).
% 4.10/2.90 tff(277,plain,
% 4.10/2.90 (addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)) = X0!2),
% 4.10/2.90 inference(transitivity,[status(thm)],[276, 273, 270, 267, 265])).
% 4.10/2.90 tff(278,plain,
% 4.10/2.90 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 4.10/2.90 inference(monotonicity,[status(thm)],[277, 263])).
% 4.10/2.90 tff(279,plain,
% 4.10/2.90 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 4.10/2.90 inference(symmetry,[status(thm)],[278])).
% 4.10/2.90 tff(280,plain,
% 4.10/2.90 (one = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), multiplication(c(X0!2), X1!1))),
% 4.10/2.90 inference(transitivity,[status(thm)],[78, 279, 208, 203, 201, 197])).
% 4.10/2.90 tff(281,plain,
% 4.10/2.90 (addition(one, X1!1) = addition(addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.90 inference(monotonicity,[status(thm)],[280, 182])).
% 4.10/2.90 tff(282,plain,
% 4.10/2.90 (addition(addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = addition(one, X1!1)),
% 4.10/2.90 inference(symmetry,[status(thm)],[281])).
% 4.10/2.90 tff(283,plain,
% 4.10/2.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))) = addition(addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))))),
% 4.10/2.90 inference(quant_inst,[status(thm)],[])).
% 4.10/2.90 tff(284,plain,
% 4.10/2.90 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))) = addition(addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[283, 162])).
% 4.10/2.90 tff(285,plain,
% 4.10/2.90 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))),
% 4.10/2.90 inference(quant_inst,[status(thm)],[])).
% 4.10/2.90 tff(286,plain,
% 4.10/2.90 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[285, 152])).
% 4.10/2.90 tff(287,plain,
% 4.10/2.90 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), 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)))),
% 4.10/2.90 inference(transitivity,[status(thm)],[286, 206])).
% 4.10/2.90 tff(288,plain,
% 4.10/2.90 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 4.10/2.90 inference(monotonicity,[status(thm)],[287])).
% 4.10/2.90 tff(289,plain,
% 4.10/2.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))))),
% 4.10/2.90 inference(quant_inst,[status(thm)],[])).
% 4.10/2.90 tff(290,plain,
% 4.10/2.90 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[289, 162])).
% 4.10/2.90 tff(291,plain,
% 4.10/2.90 (addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))))),
% 4.10/2.90 inference(symmetry,[status(thm)],[290])).
% 4.10/2.90 tff(292,plain,
% 4.10/2.90 (one = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))),
% 4.10/2.90 inference(transitivity,[status(thm)],[78, 279, 208])).
% 4.10/2.90 tff(293,plain,
% 4.10/2.90 (addition(one, addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))),
% 4.10/2.90 inference(monotonicity,[status(thm)],[292])).
% 4.10/2.90 tff(294,plain,
% 4.10/2.90 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), one) = addition(one, addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))))),
% 4.10/2.90 inference(quant_inst,[status(thm)],[])).
% 4.10/2.90 tff(295,plain,
% 4.10/2.90 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), one) = addition(one, addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[294, 122])).
% 4.10/2.90 tff(296,plain,
% 4.10/2.90 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), one) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 4.10/2.90 inference(transitivity,[status(thm)],[295, 293, 291, 288, 278])).
% 4.10/2.90 tff(297,plain,
% 4.10/2.90 (multiplication(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), one), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1)),
% 4.10/2.90 inference(monotonicity,[status(thm)],[296, 144])).
% 4.10/2.90 tff(298,plain,
% 4.10/2.90 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), one), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = addition(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))), multiplication(one, addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))))),
% 4.10/2.90 inference(quant_inst,[status(thm)],[])).
% 4.10/2.90 tff(299,plain,
% 4.10/2.90 (multiplication(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), one), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = addition(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))), multiplication(one, addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))))),
% 4.10/2.90 inference(unit_resolution,[status(thm)],[298, 87])).
% 4.10/2.90 tff(300,plain,
% 4.10/2.90 (addition(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))), multiplication(one, addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))) = multiplication(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), one), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.90 inference(symmetry,[status(thm)],[299])).
% 4.10/2.90 tff(301,plain,
% 4.10/2.90 (multiplication(one, addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1)),
% 4.10/2.90 inference(monotonicity,[status(thm)],[78, 144])).
% 4.10/2.90 tff(302,plain,
% 4.10/2.90 (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1) = multiplication(one, addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.90 inference(symmetry,[status(thm)],[301])).
% 4.10/2.90 tff(303,plain,
% 4.10/2.90 (X1!1 = multiplication(one, addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.90 inference(transitivity,[status(thm)],[181, 79, 302])).
% 4.10/2.90 tff(304,plain,
% 4.10/2.90 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)) = c(X0!2)),
% 4.10/2.90 inference(transitivity,[status(thm)],[206, 262, 229, 219, 217, 137])).
% 4.10/2.90 tff(305,plain,
% 4.10/2.90 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = multiplication(c(X0!2), X1!1)),
% 4.10/2.90 inference(monotonicity,[status(thm)],[304, 144])).
% 4.10/2.90 tff(306,plain,
% 4.10/2.90 (multiplication(c(X0!2), X1!1) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.90 inference(symmetry,[status(thm)],[305])).
% 4.10/2.90 tff(307,plain,
% 4.10/2.90 (addition(multiplication(c(X0!2), X1!1), X1!1) = addition(multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))), multiplication(one, addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))))),
% 4.10/2.90 inference(monotonicity,[status(thm)],[306, 303])).
% 4.10/2.90 tff(308,plain,
% 4.10/2.90 (addition(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = addition(multiplication(c(X0!2), X1!1), X1!1)),
% 4.10/2.90 inference(monotonicity,[status(thm)],[144])).
% 4.10/2.90 tff(309,plain,
% 4.10/2.90 (addition(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))),
% 4.10/2.90 inference(transitivity,[status(thm)],[308, 307, 300, 297, 89, 139])).
% 4.10/2.90 tff(310,plain,
% 4.10/2.90 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 4.10/2.90 inference(monotonicity,[status(thm)],[195, 309])).
% 4.10/2.90 tff(311,plain,
% 4.10/2.90 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))))),
% 4.10/2.90 inference(symmetry,[status(thm)],[310])).
% 4.10/2.90 tff(312,plain,
% 4.10/2.90 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 4.10/2.90 inference(quant_inst,[status(thm)],[])).
% 4.10/2.90 tff(313,plain,
% 4.10/2.90 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 4.10/2.91 inference(unit_resolution,[status(thm)],[312, 162])).
% 4.10/2.91 tff(314,plain,
% 4.10/2.91 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)))),
% 4.10/2.91 inference(quant_inst,[status(thm)],[])).
% 4.10/2.91 tff(315,plain,
% 4.10/2.91 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))),
% 4.10/2.91 inference(unit_resolution,[status(thm)],[314, 162])).
% 4.10/2.91 tff(316,plain,
% 4.10/2.91 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 4.10/2.91 inference(monotonicity,[status(thm)],[276])).
% 4.10/2.91 tff(317,plain,
% 4.10/2.91 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))),
% 4.10/2.91 inference(transitivity,[status(thm)],[316, 315])).
% 4.10/2.91 tff(318,plain,
% 4.10/2.91 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)))),
% 4.10/2.91 inference(monotonicity,[status(thm)],[317])).
% 4.10/2.91 tff(319,plain,
% 4.10/2.91 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 4.10/2.91 inference(symmetry,[status(thm)],[318])).
% 4.10/2.91 tff(320,plain,
% 4.10/2.91 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))))),
% 4.10/2.91 inference(quant_inst,[status(thm)],[])).
% 4.10/2.91 tff(321,plain,
% 4.10/2.91 (addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))),
% 4.10/2.91 inference(unit_resolution,[status(thm)],[320, 122])).
% 4.10/2.91 tff(322,plain,
% 4.10/2.91 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))))),
% 4.10/2.91 inference(monotonicity,[status(thm)],[321])).
% 4.10/2.91 tff(323,plain,
% 4.10/2.91 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)))),
% 4.10/2.91 inference(symmetry,[status(thm)],[322])).
% 4.10/2.91 tff(324,plain,
% 4.10/2.91 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))))),
% 4.10/2.91 inference(quant_inst,[status(thm)],[])).
% 4.10/2.91 tff(325,plain,
% 4.10/2.91 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))),
% 4.10/2.91 inference(unit_resolution,[status(thm)],[324, 162])).
% 4.10/2.91 tff(326,plain,
% 4.10/2.91 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))))),
% 4.10/2.91 inference(symmetry,[status(thm)],[325])).
% 4.10/2.91 tff(327,plain,
% 4.10/2.91 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(X0!2, X1!1)) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))),
% 4.10/2.91 inference(monotonicity,[status(thm)],[276])).
% 4.10/2.91 tff(328,plain,
% 4.10/2.91 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(X0!2, X1!1))),
% 4.10/2.91 inference(symmetry,[status(thm)],[327])).
% 4.10/2.91 tff(329,plain,
% 4.10/2.91 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(X0!2, X1!1)))),
% 4.10/2.91 inference(monotonicity,[status(thm)],[328])).
% 4.10/2.91 tff(330,plain,
% 4.10/2.91 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(X0!2, X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))),
% 4.10/2.91 inference(symmetry,[status(thm)],[329])).
% 4.10/2.91 tff(331,plain,
% 4.10/2.91 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(X0!2, X1!1))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), multiplication(X0!2, X1!1)))),
% 4.10/2.91 inference(quant_inst,[status(thm)],[])).
% 4.10/2.91 tff(332,plain,
% 4.10/2.91 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(X0!2, X1!1))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), multiplication(X0!2, X1!1))),
% 4.10/2.91 inference(unit_resolution,[status(thm)],[331, 162])).
% 4.10/2.91 tff(333,plain,
% 4.10/2.91 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), multiplication(X0!2, X1!1)) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(X0!2, X1!1)))),
% 4.10/2.91 inference(symmetry,[status(thm)],[332])).
% 4.10/2.91 tff(334,plain,
% 4.10/2.91 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))),
% 4.10/2.91 inference(quant_inst,[status(thm)],[])).
% 4.10/2.91 tff(335,plain,
% 4.10/2.91 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.10/2.91 inference(unit_resolution,[status(thm)],[334, 122])).
% 4.10/2.91 tff(336,plain,
% 4.10/2.91 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))),
% 4.10/2.91 inference(symmetry,[status(thm)],[335])).
% 4.10/2.91 tff(337,plain,
% 4.10/2.91 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = one),
% 4.10/2.91 inference(transitivity,[status(thm)],[336, 207, 278, 77])).
% 4.10/2.91 tff(338,plain,
% 4.10/2.91 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), multiplication(X0!2, X1!1)) = addition(one, multiplication(X0!2, X1!1))),
% 4.10/2.91 inference(monotonicity,[status(thm)],[337])).
% 4.10/2.91 tff(339,plain,
% 4.10/2.91 (addition(one, multiplication(X0!2, X1!1)) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), multiplication(X0!2, X1!1))),
% 4.10/2.91 inference(symmetry,[status(thm)],[338])).
% 4.10/2.91 tff(340,plain,
% 4.10/2.91 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), X1!1) = addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1)))),
% 4.10/2.91 inference(quant_inst,[status(thm)],[])).
% 4.10/2.91 tff(341,plain,
% 4.10/2.91 (multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), X1!1) = addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1))),
% 4.10/2.91 inference(unit_resolution,[status(thm)],[340, 87])).
% 4.10/2.91 tff(342,plain,
% 4.10/2.91 (X0!2 = multiplication(one, X0!2)),
% 4.10/2.91 inference(symmetry,[status(thm)],[265])).
% 4.10/2.91 tff(343,plain,
% 4.10/2.91 (X0!2 = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 4.10/2.91 inference(transitivity,[status(thm)],[342, 266, 269, 272, 275])).
% 4.10/2.91 tff(344,plain,
% 4.10/2.91 (multiplication(X0!2, X1!1) = multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), X1!1)),
% 4.10/2.91 inference(monotonicity,[status(thm)],[343])).
% 4.10/2.91 tff(345,plain,
% 4.10/2.91 (multiplication(X0!2, X1!1) = addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1))),
% 4.10/2.91 inference(transitivity,[status(thm)],[344, 341])).
% 4.10/2.91 tff(346,plain,
% 4.10/2.91 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 4.10/2.91 inference(quant_inst,[status(thm)],[])).
% 4.10/2.91 tff(347,plain,
% 4.10/2.91 (addition(one, one) = one),
% 4.10/2.91 inference(unit_resolution,[status(thm)],[346, 152])).
% 4.10/2.91 tff(348,plain,
% 4.10/2.91 (one = addition(one, one)),
% 4.10/2.91 inference(symmetry,[status(thm)],[347])).
% 4.10/2.91 tff(349,plain,
% 4.10/2.91 (addition(one, multiplication(X0!2, X1!1)) = addition(addition(one, one), addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1)))),
% 4.10/2.91 inference(monotonicity,[status(thm)],[348, 345])).
% 4.10/2.91 tff(350,plain,
% 4.10/2.91 (addition(addition(one, one), addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1))) = addition(one, multiplication(X0!2, X1!1))),
% 4.10/2.91 inference(symmetry,[status(thm)],[349])).
% 4.10/2.91 tff(351,plain,
% 4.10/2.91 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(one, addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1)))) = addition(addition(one, one), addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1))))),
% 4.10/2.91 inference(quant_inst,[status(thm)],[])).
% 4.10/2.91 tff(352,plain,
% 4.10/2.91 (addition(one, addition(one, addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1)))) = addition(addition(one, one), addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1)))),
% 4.10/2.91 inference(unit_resolution,[status(thm)],[351, 162])).
% 4.10/2.91 tff(353,plain,
% 4.10/2.91 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))))),
% 4.10/2.91 inference(quant_inst,[status(thm)],[])).
% 4.10/2.91 tff(354,plain,
% 4.10/2.91 (addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)))),
% 4.10/2.91 inference(unit_resolution,[status(thm)],[353, 122])).
% 4.10/2.91 tff(355,plain,
% 4.10/2.91 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 4.10/2.91 inference(symmetry,[status(thm)],[354])).
% 4.10/2.91 tff(356,plain,
% 4.10/2.91 (multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), X1!1) = multiplication(X0!2, X1!1)),
% 4.10/2.91 inference(symmetry,[status(thm)],[344])).
% 4.10/2.91 tff(357,plain,
% 4.10/2.91 (addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1)) = multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), X1!1)),
% 4.10/2.91 inference(symmetry,[status(thm)],[341])).
% 4.10/2.91 tff(358,plain,
% 4.10/2.91 (addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1)) = multiplication(X0!2, X1!1)),
% 4.10/2.91 inference(transitivity,[status(thm)],[357, 356])).
% 4.10/2.91 tff(359,plain,
% 4.10/2.91 (addition(one, addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1))) = addition(one, multiplication(X0!2, X1!1))),
% 4.10/2.91 inference(monotonicity,[status(thm)],[358])).
% 4.10/2.91 tff(360,plain,
% 4.10/2.91 (addition(one, addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 4.10/2.91 inference(transitivity,[status(thm)],[359, 339, 333, 330, 326, 323, 355])).
% 4.10/2.91 tff(361,plain,
% 4.10/2.91 (addition(one, addition(one, addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1)))) = addition(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 4.10/2.91 inference(monotonicity,[status(thm)],[360])).
% 4.10/2.91 tff(362,plain,
% 4.10/2.91 (addition(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(one, addition(one, addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1))))),
% 4.10/2.91 inference(symmetry,[status(thm)],[361])).
% 4.10/2.91 tff(363,plain,
% 4.10/2.91 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = addition(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 4.10/2.91 inference(quant_inst,[status(thm)],[])).
% 4.10/2.91 tff(364,plain,
% 4.10/2.91 (addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = addition(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 4.10/2.91 inference(unit_resolution,[status(thm)],[363, 122])).
% 4.10/2.91 tff(365,plain,
% 4.10/2.91 (addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one),
% 4.10/2.91 inference(transitivity,[status(thm)],[364, 362, 352, 350, 339, 333, 330, 326, 323, 319, 313, 311, 284, 282, 192, 171, 190, 164, 187, 184, 53])).
% 4.10/2.91 tff(366,assumption,(~leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)), introduced(assumption)).
% 4.10/2.91 tff(367,plain,
% 4.10/2.91 ((~(leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) <=> (addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one))) | leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) | (~(addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one))),
% 4.10/2.91 inference(tautology,[status(thm)],[])).
% 4.10/2.91 tff(368,plain,
% 4.10/2.91 ((~(leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) <=> (addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one))) | (~(addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one))),
% 4.10/2.91 inference(unit_resolution,[status(thm)],[367, 366])).
% 4.10/2.91 tff(369,plain,
% 4.10/2.91 (~(addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one)),
% 4.10/2.91 inference(unit_resolution,[status(thm)],[368, 180])).
% 4.10/2.91 tff(370,plain,
% 4.10/2.91 ($false),
% 4.10/2.91 inference(unit_resolution,[status(thm)],[369, 365])).
% 4.10/2.91 tff(371,plain,(leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)), inference(lemma,lemma(discharge,[]))).
% 4.10/2.91 tff(372,plain,
% 4.10/2.91 ((~(leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) <=> (addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one))) | (~leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)) | (addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one)),
% 4.10/2.91 inference(tautology,[status(thm)],[])).
% 4.10/2.91 tff(373,plain,
% 4.10/2.91 ((~(leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) <=> (addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one))) | (addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one)),
% 4.10/2.91 inference(unit_resolution,[status(thm)],[372, 371])).
% 4.10/2.91 tff(374,plain,
% 4.10/2.91 (addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = one),
% 4.10/2.91 inference(unit_resolution,[status(thm)],[373, 180])).
% 4.10/2.91 tff(375,plain,
% 4.10/2.91 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))), one) = addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)),
% 4.10/2.91 inference(monotonicity,[status(thm)],[355])).
% 4.10/2.91 tff(376,plain,
% 4.10/2.91 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one)) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))), one))),
% 4.10/2.91 inference(quant_inst,[status(thm)],[])).
% 4.10/2.91 tff(377,plain,
% 4.10/2.91 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one)) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))), one)),
% 4.10/2.92 inference(unit_resolution,[status(thm)],[376, 162])).
% 4.10/2.92 tff(378,plain,
% 4.10/2.92 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one)) = one),
% 4.10/2.92 inference(transitivity,[status(thm)],[377, 375, 374])).
% 4.10/2.92 tff(379,plain,
% 4.10/2.92 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = addition(one, addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.92 inference(monotonicity,[status(thm)],[378])).
% 4.10/2.92 tff(380,plain,
% 4.10/2.92 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))))),
% 4.10/2.92 inference(quant_inst,[status(thm)],[])).
% 4.10/2.92 tff(381,plain,
% 4.10/2.92 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.92 inference(unit_resolution,[status(thm)],[380, 162])).
% 4.10/2.92 tff(382,plain,
% 4.10/2.92 ((~![A: $i] : (addition(A, A) = A)) | (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1))) = multiplication(c(X0!2), c(X1!1)))),
% 4.10/2.92 inference(quant_inst,[status(thm)],[])).
% 4.10/2.92 tff(383,plain,
% 4.10/2.92 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1))) = multiplication(c(X0!2), c(X1!1))),
% 4.10/2.92 inference(unit_resolution,[status(thm)],[382, 152])).
% 4.10/2.92 tff(384,plain,
% 4.10/2.92 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))))),
% 4.10/2.92 inference(monotonicity,[status(thm)],[383])).
% 4.10/2.92 tff(385,plain,
% 4.10/2.92 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))))),
% 4.10/2.92 inference(quant_inst,[status(thm)],[])).
% 4.10/2.92 tff(386,plain,
% 4.10/2.92 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.92 inference(unit_resolution,[status(thm)],[385, 162])).
% 4.10/2.92 tff(387,plain,
% 4.10/2.92 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))))),
% 4.10/2.92 inference(symmetry,[status(thm)],[386])).
% 4.10/2.92 tff(388,plain,
% 4.10/2.92 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one)))),
% 4.10/2.92 inference(quant_inst,[status(thm)],[])).
% 4.10/2.92 tff(389,plain,
% 4.10/2.92 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one))),
% 4.10/2.92 inference(unit_resolution,[status(thm)],[388, 162])).
% 4.10/2.92 tff(390,plain,
% 4.10/2.92 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))), one) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one))),
% 4.10/2.92 inference(symmetry,[status(thm)],[377])).
% 4.10/2.92 tff(391,plain,
% 4.10/2.92 (addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))), one)),
% 4.10/2.92 inference(symmetry,[status(thm)],[375])).
% 4.10/2.92 tff(392,plain,
% 4.10/2.92 (one = addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)),
% 4.10/2.92 inference(symmetry,[status(thm)],[374])).
% 4.10/2.92 tff(393,plain,
% 4.10/2.92 (one = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one))),
% 4.10/2.92 inference(transitivity,[status(thm)],[392, 391, 390])).
% 4.10/2.92 tff(394,plain,
% 4.10/2.92 (addition(multiplication(c(X0!2), c(X1!1)), one) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one)))),
% 4.10/2.92 inference(monotonicity,[status(thm)],[393])).
% 4.10/2.92 tff(395,plain,
% 4.10/2.92 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), c(X1!1)), one) = addition(one, multiplication(c(X0!2), c(X1!1))))),
% 4.10/2.92 inference(quant_inst,[status(thm)],[])).
% 4.10/2.92 tff(396,plain,
% 4.10/2.92 (addition(multiplication(c(X0!2), c(X1!1)), one) = addition(one, multiplication(c(X0!2), c(X1!1)))),
% 4.10/2.92 inference(unit_resolution,[status(thm)],[395, 122])).
% 4.10/2.92 tff(397,plain,
% 4.10/2.92 (addition(one, multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), one)),
% 4.10/2.92 inference(symmetry,[status(thm)],[396])).
% 4.10/2.92 tff(398,plain,
% 4.10/2.92 (addition(one, multiplication(c(X0!2), c(X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one))),
% 4.10/2.92 inference(transitivity,[status(thm)],[397, 394, 389])).
% 4.10/2.92 tff(399,plain,
% 4.10/2.92 (addition(addition(one, multiplication(c(X0!2), c(X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), one)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.92 inference(monotonicity,[status(thm)],[398])).
% 4.10/2.92 tff(400,plain,
% 4.10/2.92 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 4.10/2.92 inference(symmetry,[status(thm)],[124])).
% 4.10/2.92 tff(401,plain,
% 4.10/2.92 (addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 4.10/2.92 inference(monotonicity,[status(thm)],[277])).
% 4.10/2.92 tff(402,plain,
% 4.10/2.92 (addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = one),
% 4.10/2.92 inference(transitivity,[status(thm)],[401, 400, 77])).
% 4.10/2.92 tff(403,plain,
% 4.10/2.92 (addition(addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), multiplication(c(X0!2), c(X1!1))) = addition(one, multiplication(c(X0!2), c(X1!1)))),
% 4.10/2.92 inference(monotonicity,[status(thm)],[402])).
% 4.10/2.92 tff(404,plain,
% 4.10/2.92 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X0!2), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), multiplication(c(X0!2), c(X1!1))))),
% 4.10/2.92 inference(quant_inst,[status(thm)],[])).
% 4.10/2.92 tff(405,plain,
% 4.10/2.92 (addition(tptp_fun_X1_0(X0!2), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), multiplication(c(X0!2), c(X1!1)))),
% 4.10/2.92 inference(unit_resolution,[status(thm)],[404, 162])).
% 4.10/2.92 tff(406,plain,
% 4.10/2.92 (addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = addition(tptp_fun_X1_0(X0!2), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(c(X0!2), c(X1!1))))),
% 4.10/2.92 inference(monotonicity,[status(thm)],[199])).
% 4.10/2.92 tff(407,plain,
% 4.10/2.92 (addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = addition(one, multiplication(c(X0!2), c(X1!1)))),
% 4.10/2.92 inference(transitivity,[status(thm)],[406, 405, 403])).
% 4.10/2.92 tff(408,plain,
% 4.10/2.92 (addition(addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = addition(addition(one, multiplication(c(X0!2), c(X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.92 inference(monotonicity,[status(thm)],[407])).
% 4.10/2.92 tff(409,plain,
% 4.10/2.92 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X0!2), addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))) = addition(addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))))),
% 4.10/2.92 inference(quant_inst,[status(thm)],[])).
% 4.10/2.92 tff(410,plain,
% 4.10/2.92 (addition(tptp_fun_X1_0(X0!2), addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))) = addition(addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.92 inference(unit_resolution,[status(thm)],[409, 162])).
% 4.10/2.92 tff(411,plain,
% 4.10/2.92 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 4.10/2.92 inference(monotonicity,[status(thm)],[143])).
% 4.10/2.92 tff(412,plain,
% 4.10/2.92 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.92 inference(symmetry,[status(thm)],[411])).
% 4.10/2.92 tff(413,plain,
% 4.10/2.92 (addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.10/2.92 inference(transitivity,[status(thm)],[354, 319, 313, 412])).
% 4.10/2.92 tff(414,plain,
% 4.10/2.92 (addition(tptp_fun_X1_0(X0!2), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(tptp_fun_X1_0(X0!2), addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))))),
% 4.10/2.92 inference(monotonicity,[status(thm)],[413])).
% 4.10/2.92 tff(415,plain,
% 4.10/2.92 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)) = tptp_fun_X1_0(X0!2)),
% 4.10/2.92 inference(transitivity,[status(thm)],[206, 262, 229, 219, 217])).
% 4.10/2.92 tff(416,plain,
% 4.10/2.92 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(tptp_fun_X1_0(X0!2), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 4.10/2.92 inference(monotonicity,[status(thm)],[415])).
% 4.10/2.92 tff(417,plain,
% 4.10/2.92 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 4.10/2.92 inference(quant_inst,[status(thm)],[])).
% 4.10/2.92 tff(418,plain,
% 4.10/2.92 (addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 4.10/2.92 inference(unit_resolution,[status(thm)],[417, 152])).
% 4.10/2.92 tff(419,plain,
% 4.10/2.92 (addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))) = addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))),
% 4.10/2.92 inference(symmetry,[status(thm)],[321])).
% 4.10/2.92 tff(420,plain,
% 4.10/2.92 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)))),
% 4.10/2.92 inference(monotonicity,[status(thm)],[419])).
% 4.10/2.92 tff(421,plain,
% 4.10/2.92 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(X0!2), X1!1), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))))),
% 4.10/2.92 inference(symmetry,[status(thm)],[420])).
% 4.10/2.92 tff(422,plain,
% 4.10/2.92 (addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))),
% 4.10/2.92 inference(transitivity,[status(thm)],[354, 421, 325])).
% 4.10/2.92 tff(423,plain,
% 4.10/2.92 (addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 4.10/2.92 inference(monotonicity,[status(thm)],[422])).
% 4.10/2.92 tff(424,plain,
% 4.10/2.92 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 4.10/2.92 inference(symmetry,[status(thm)],[423])).
% 4.10/2.92 tff(425,plain,
% 4.10/2.92 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 4.10/2.92 inference(quant_inst,[status(thm)],[])).
% 4.10/2.92 tff(426,plain,
% 4.10/2.92 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 4.10/2.92 inference(unit_resolution,[status(thm)],[425, 162])).
% 4.10/2.92 tff(427,plain,
% 4.10/2.92 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 4.10/2.92 inference(transitivity,[status(thm)],[426, 424, 418])).
% 4.10/2.92 tff(428,plain,
% 4.10/2.92 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 4.10/2.92 inference(monotonicity,[status(thm)],[427])).
% 4.10/2.92 tff(429,plain,
% 4.10/2.92 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))))),
% 4.10/2.92 inference(quant_inst,[status(thm)],[])).
% 4.10/2.92 tff(430,plain,
% 4.10/2.92 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 4.10/2.92 inference(unit_resolution,[status(thm)],[429, 162])).
% 4.10/2.92 tff(431,plain,
% 4.10/2.92 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))))),
% 4.10/2.92 inference(symmetry,[status(thm)],[430])).
% 4.10/2.92 tff(432,plain,
% 4.10/2.92 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))),
% 4.10/2.92 inference(symmetry,[status(thm)],[286])).
% 4.10/2.92 tff(433,plain,
% 4.10/2.92 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 4.22/2.93 inference(monotonicity,[status(thm)],[432])).
% 4.22/2.93 tff(434,plain,
% 4.22/2.93 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 4.22/2.93 inference(symmetry,[status(thm)],[426])).
% 4.22/2.93 tff(435,plain,
% 4.22/2.93 (addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 4.22/2.93 inference(symmetry,[status(thm)],[418])).
% 4.22/2.93 tff(436,plain,
% 4.22/2.93 (addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = one),
% 4.22/2.93 inference(transitivity,[status(thm)],[435, 423, 434, 433, 431, 428, 416, 414, 410, 408, 399, 387, 384, 381, 379, 171, 168, 164, 155, 145, 53])).
% 4.22/2.93 tff(437,plain,
% 4.22/2.93 ((one = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = one)),
% 4.22/2.93 inference(commutativity,[status(thm)],[])).
% 4.22/2.93 tff(438,plain,
% 4.22/2.93 (addition(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)),
% 4.22/2.93 inference(symmetry,[status(thm)],[364])).
% 4.22/2.93 tff(439,plain,
% 4.22/2.93 (addition(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = one),
% 4.22/2.93 inference(transitivity,[status(thm)],[438, 374])).
% 4.22/2.93 tff(440,plain,
% 4.22/2.93 ((addition(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (one = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 4.22/2.93 inference(monotonicity,[status(thm)],[439])).
% 4.22/2.93 tff(441,plain,
% 4.22/2.93 ((addition(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = one)),
% 4.22/2.93 inference(transitivity,[status(thm)],[440, 437])).
% 4.22/2.93 tff(442,plain,
% 4.22/2.93 ((~(addition(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) <=> (~(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = one))),
% 4.22/2.93 inference(monotonicity,[status(thm)],[441])).
% 4.22/2.93 tff(443,plain,
% 4.22/2.93 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 4.22/2.93 inference(quant_inst,[status(thm)],[])).
% 4.22/2.93 tff(444,plain,
% 4.22/2.93 (leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 4.22/2.93 inference(unit_resolution,[status(thm)],[443, 178])).
% 4.22/2.93 tff(445,plain,
% 4.22/2.93 ((~(~((~leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))))) <=> ((~leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)))),
% 4.22/2.93 inference(rewrite,[status(thm)],[])).
% 4.22/2.93 tff(446,plain,
% 4.22/2.93 ((leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) & leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)) <=> (~((~leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))))),
% 4.22/2.93 inference(rewrite,[status(thm)],[])).
% 4.22/2.93 tff(447,plain,
% 4.22/2.93 ((~(leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) & leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))) <=> (~(~((~leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)))))),
% 4.22/2.93 inference(monotonicity,[status(thm)],[446])).
% 4.22/2.93 tff(448,plain,
% 4.22/2.93 ((~(leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) & leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))) <=> ((~leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)))),
% 4.22/2.93 inference(transitivity,[status(thm)],[447, 445])).
% 4.22/2.93 tff(449,plain,
% 4.22/2.93 (~(leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) & leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))),
% 4.22/2.93 inference(or_elim,[status(thm)],[43])).
% 4.22/2.93 tff(450,plain,
% 4.22/2.93 ((~leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))),
% 4.22/2.93 inference(modus_ponens,[status(thm)],[449, 448])).
% 4.22/2.93 tff(451,plain,
% 4.22/2.93 (~leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 4.22/2.93 inference(unit_resolution,[status(thm)],[450, 371])).
% 4.22/2.93 tff(452,plain,
% 4.22/2.93 ((~(leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))) | leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) | (~(addition(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 4.22/2.94 inference(tautology,[status(thm)],[])).
% 4.22/2.94 tff(453,plain,
% 4.22/2.94 ((~(leq(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))) | (~(addition(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 4.22/2.94 inference(unit_resolution,[status(thm)],[452, 451])).
% 4.22/2.94 tff(454,plain,
% 4.22/2.94 (~(addition(one, addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 4.22/2.94 inference(unit_resolution,[status(thm)],[453, 444])).
% 4.22/2.94 tff(455,plain,
% 4.22/2.94 (~(addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = one)),
% 4.22/2.94 inference(modus_ponens,[status(thm)],[454, 442])).
% 4.22/2.94 tff(456,plain,
% 4.22/2.94 ($false),
% 4.22/2.94 inference(unit_resolution,[status(thm)],[455, 436])).
% 4.22/2.94 % SZS output end Proof
%------------------------------------------------------------------------------