TSTP Solution File: KLE010+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE010+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:23:48 EDT 2022
% Result : Theorem 4.71s 3.28s
% Output : Proof 4.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE010+4 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.36 % Computer : n016.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Sep 1 08:07:19 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.13/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.37 Usage: tptp [options] [-file:]file
% 0.13/0.37 -h, -? prints this message.
% 0.13/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.37 -m, -model generate model.
% 0.13/0.37 -p, -proof generate proof.
% 0.13/0.37 -c, -core generate unsat core of named formulas.
% 0.13/0.37 -st, -statistics display statistics.
% 0.13/0.37 -t:timeout set timeout (in second).
% 0.13/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.37 -<param>:<value> configuration parameter and value.
% 0.13/0.37 -o:<output-file> file to place output in.
% 4.71/3.28 % SZS status Theorem
% 4.71/3.28 % SZS output start Proof
% 4.71/3.28 tff(one_type, type, (
% 4.71/3.28 one: $i)).
% 4.71/3.28 tff(addition_type, type, (
% 4.71/3.28 addition: ( $i * $i ) > $i)).
% 4.71/3.28 tff(multiplication_type, type, (
% 4.71/3.28 multiplication: ( $i * $i ) > $i)).
% 4.71/3.28 tff(c_type, type, (
% 4.71/3.28 c: $i > $i)).
% 4.71/3.28 tff(tptp_fun_X1_1_type, type, (
% 4.71/3.28 tptp_fun_X1_1: $i)).
% 4.71/3.28 tff(tptp_fun_X0_2_type, type, (
% 4.71/3.28 tptp_fun_X0_2: $i)).
% 4.71/3.28 tff(tptp_fun_X1_0_type, type, (
% 4.71/3.28 tptp_fun_X1_0: $i > $i)).
% 4.71/3.28 tff(zero_type, type, (
% 4.71/3.28 zero: $i)).
% 4.71/3.28 tff(complement_type, type, (
% 4.71/3.28 complement: ( $i * $i ) > $o)).
% 4.71/3.28 tff(test_type, type, (
% 4.71/3.28 test: $i > $o)).
% 4.71/3.28 tff(leq_type, type, (
% 4.71/3.28 leq: ( $i * $i ) > $o)).
% 4.71/3.28 tff(1,plain,
% 4.71/3.28 (^[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))))))),
% 4.71/3.28 inference(bind,[status(th)],[])).
% 4.71/3.28 tff(2,plain,
% 4.71/3.28 (![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)))))),
% 4.71/3.28 inference(quant_intro,[status(thm)],[1])).
% 4.71/3.28 tff(3,plain,
% 4.71/3.28 (^[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))))))),
% 4.71/3.28 inference(bind,[status(th)],[])).
% 4.71/3.28 tff(4,plain,
% 4.71/3.28 (![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)))))),
% 4.71/3.28 inference(quant_intro,[status(thm)],[3])).
% 4.71/3.28 tff(5,plain,
% 4.71/3.28 (![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)))),
% 4.71/3.28 inference(rewrite,[status(thm)],[])).
% 4.71/3.28 tff(6,plain,
% 4.71/3.28 (^[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))))),
% 4.71/3.28 inference(bind,[status(th)],[])).
% 4.71/3.28 tff(7,plain,
% 4.71/3.28 (![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)))),
% 4.71/3.28 inference(quant_intro,[status(thm)],[6])).
% 4.71/3.28 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/sandbox2/benchmark/Axioms/KLE001+1.ax','test_2')).
% 4.71/3.28 tff(9,plain,
% 4.71/3.28 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 4.71/3.28 inference(modus_ponens,[status(thm)],[8, 7])).
% 4.71/3.28 tff(10,plain,
% 4.71/3.28 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 4.71/3.28 inference(modus_ponens,[status(thm)],[9, 5])).
% 4.71/3.28 tff(11,plain,(
% 4.71/3.28 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 4.71/3.28 inference(skolemize,[status(sab)],[10])).
% 4.71/3.28 tff(12,plain,
% 4.71/3.28 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 4.71/3.28 inference(modus_ponens,[status(thm)],[11, 4])).
% 4.71/3.28 tff(13,plain,
% 4.71/3.28 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 4.71/3.28 inference(modus_ponens,[status(thm)],[12, 2])).
% 4.71/3.28 tff(14,plain,
% 4.71/3.28 ((~![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)))))),
% 4.71/3.28 inference(quant_inst,[status(thm)],[])).
% 4.71/3.28 tff(15,plain,
% 4.71/3.28 (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))))),
% 4.71/3.28 inference(unit_resolution,[status(thm)],[14, 13])).
% 4.71/3.28 tff(16,plain,
% 4.71/3.28 (^[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)))))))),
% 4.71/3.28 inference(bind,[status(th)],[])).
% 4.71/3.28 tff(17,plain,
% 4.71/3.28 (![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))))))),
% 4.71/3.28 inference(quant_intro,[status(thm)],[16])).
% 4.71/3.28 tff(18,plain,
% 4.71/3.28 (^[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)))))))),
% 4.71/3.28 inference(bind,[status(th)],[])).
% 4.71/3.28 tff(19,plain,
% 4.71/3.28 (![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))))))),
% 4.71/3.28 inference(quant_intro,[status(thm)],[18])).
% 4.71/3.28 tff(20,plain,
% 4.71/3.28 (![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))))))),
% 4.71/3.28 inference(transitivity,[status(thm)],[19, 17])).
% 4.71/3.28 tff(21,plain,
% 4.71/3.28 (^[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))))))))),
% 4.71/3.28 inference(bind,[status(th)],[])).
% 4.71/3.28 tff(22,plain,
% 4.71/3.28 (![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))))))),
% 4.71/3.28 inference(quant_intro,[status(thm)],[21])).
% 4.71/3.28 tff(23,plain,
% 4.71/3.28 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 4.71/3.28 inference(rewrite,[status(thm)],[])).
% 4.71/3.28 tff(24,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_1')).
% 4.71/3.28 tff(25,plain,
% 4.71/3.28 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 4.71/3.28 inference(modus_ponens,[status(thm)],[24, 23])).
% 4.71/3.28 tff(26,plain,(
% 4.71/3.28 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 4.71/3.28 inference(skolemize,[status(sab)],[25])).
% 4.71/3.28 tff(27,plain,
% 4.71/3.28 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 4.71/3.28 inference(modus_ponens,[status(thm)],[26, 22])).
% 4.71/3.28 tff(28,plain,
% 4.71/3.28 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 4.71/3.28 inference(modus_ponens,[status(thm)],[27, 20])).
% 4.71/3.28 tff(29,plain,
% 4.71/3.28 ((~![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))))))),
% 4.71/3.28 inference(quant_inst,[status(thm)],[])).
% 4.71/3.28 tff(30,plain,
% 4.71/3.28 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 4.71/3.28 inference(unit_resolution,[status(thm)],[29, 28])).
% 4.71/3.28 tff(31,plain,
% 4.71/3.28 (((~((~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))),
% 4.71/3.28 inference(tautology,[status(thm)],[])).
% 4.71/3.28 tff(32,plain,
% 4.71/3.28 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 4.71/3.28 inference(unit_resolution,[status(thm)],[31, 30])).
% 4.71/3.28 tff(33,plain,
% 4.71/3.28 ((~![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))))),
% 4.71/3.28 inference(rewrite,[status(thm)],[])).
% 4.71/3.28 tff(34,plain,
% 4.71/3.28 ((~![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))))),
% 4.71/3.28 inference(rewrite,[status(thm)],[])).
% 4.71/3.28 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/sandbox2/benchmark/theBenchmark.p','goals')).
% 4.71/3.28 tff(36,plain,
% 4.71/3.28 (~![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)))),
% 4.71/3.28 inference(modus_ponens,[status(thm)],[35, 34])).
% 4.71/3.28 tff(37,plain,
% 4.71/3.28 (~![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)))),
% 4.71/3.28 inference(modus_ponens,[status(thm)],[36, 33])).
% 4.71/3.28 tff(38,plain,
% 4.71/3.28 (~![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)))),
% 4.71/3.28 inference(modus_ponens,[status(thm)],[37, 33])).
% 4.71/3.28 tff(39,plain,
% 4.71/3.28 (~![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)))),
% 4.71/3.28 inference(modus_ponens,[status(thm)],[38, 33])).
% 4.71/3.28 tff(40,plain,
% 4.71/3.28 (~![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)))),
% 4.71/3.28 inference(modus_ponens,[status(thm)],[39, 33])).
% 4.71/3.28 tff(41,plain,
% 4.71/3.28 (~![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)))),
% 4.71/3.28 inference(modus_ponens,[status(thm)],[40, 33])).
% 4.71/3.28 tff(42,plain,
% 4.71/3.28 (~![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)))),
% 4.71/3.28 inference(modus_ponens,[status(thm)],[41, 33])).
% 4.71/3.28 tff(43,plain,(
% 4.71/3.28 ~((~(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)))),
% 4.71/3.28 inference(skolemize,[status(sab)],[42])).
% 4.71/3.28 tff(44,plain,
% 4.71/3.28 (test(X1!1) & test(X0!2)),
% 4.71/3.28 inference(or_elim,[status(thm)],[43])).
% 4.71/3.28 tff(45,plain,
% 4.71/3.28 (test(X1!1)),
% 4.71/3.28 inference(and_elim,[status(thm)],[44])).
% 4.71/3.28 tff(46,plain,
% 4.71/3.28 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 4.71/3.28 inference(tautology,[status(thm)],[])).
% 4.71/3.28 tff(47,plain,
% 4.71/3.28 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[46, 45])).
% 4.71/3.29 tff(48,plain,
% 4.71/3.29 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[47, 32])).
% 4.71/3.29 tff(49,plain,
% 4.71/3.29 ((~(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))))),
% 4.71/3.29 inference(tautology,[status(thm)],[])).
% 4.71/3.29 tff(50,plain,
% 4.71/3.29 ((~(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))))),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[49, 48])).
% 4.71/3.29 tff(51,plain,
% 4.71/3.29 (~((~(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)))),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[50, 15])).
% 4.71/3.29 tff(52,plain,
% 4.71/3.29 (((~(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)),
% 4.71/3.29 inference(tautology,[status(thm)],[])).
% 4.71/3.29 tff(53,plain,
% 4.71/3.29 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[52, 51])).
% 4.71/3.29 tff(54,plain,
% 4.71/3.29 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 4.71/3.29 inference(bind,[status(th)],[])).
% 4.71/3.29 tff(55,plain,
% 4.71/3.29 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 4.71/3.29 inference(quant_intro,[status(thm)],[54])).
% 4.71/3.29 tff(56,plain,
% 4.71/3.29 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 4.71/3.29 inference(rewrite,[status(thm)],[])).
% 4.71/3.29 tff(57,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 4.71/3.29 tff(58,plain,
% 4.71/3.29 (![A: $i] : (multiplication(one, A) = A)),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[57, 56])).
% 4.71/3.29 tff(59,plain,(
% 4.71/3.29 ![A: $i] : (multiplication(one, A) = A)),
% 4.71/3.29 inference(skolemize,[status(sab)],[58])).
% 4.71/3.29 tff(60,plain,
% 4.71/3.29 (![A: $i] : (multiplication(one, A) = A)),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[59, 55])).
% 4.71/3.29 tff(61,plain,
% 4.71/3.29 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X1!1) = X1!1)),
% 4.71/3.29 inference(quant_inst,[status(thm)],[])).
% 4.71/3.29 tff(62,plain,
% 4.71/3.29 (multiplication(one, X1!1) = X1!1),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[61, 60])).
% 4.71/3.29 tff(63,plain,
% 4.71/3.29 ((~![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)))))),
% 4.71/3.29 inference(quant_inst,[status(thm)],[])).
% 4.71/3.29 tff(64,plain,
% 4.71/3.29 (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))))),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[63, 13])).
% 4.71/3.29 tff(65,plain,
% 4.71/3.29 ((~![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))))))),
% 4.71/3.29 inference(quant_inst,[status(thm)],[])).
% 4.71/3.29 tff(66,plain,
% 4.71/3.29 (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2)))))),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[65, 28])).
% 4.71/3.29 tff(67,plain,
% 4.71/3.29 (((~((~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))),
% 4.71/3.29 inference(tautology,[status(thm)],[])).
% 4.71/3.29 tff(68,plain,
% 4.71/3.29 ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[67, 66])).
% 4.71/3.29 tff(69,plain,
% 4.71/3.29 (test(X0!2)),
% 4.71/3.29 inference(and_elim,[status(thm)],[44])).
% 4.71/3.29 tff(70,plain,
% 4.71/3.29 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 4.71/3.29 inference(tautology,[status(thm)],[])).
% 4.71/3.29 tff(71,plain,
% 4.71/3.29 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[70, 69])).
% 4.71/3.29 tff(72,plain,
% 4.71/3.29 (complement(tptp_fun_X1_0(X0!2), X0!2)),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[71, 68])).
% 4.71/3.29 tff(73,plain,
% 4.71/3.29 ((~(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))))),
% 4.71/3.29 inference(tautology,[status(thm)],[])).
% 4.71/3.29 tff(74,plain,
% 4.71/3.29 ((~(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))))),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[73, 72])).
% 4.71/3.29 tff(75,plain,
% 4.71/3.29 (~((~(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)))),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[74, 64])).
% 4.71/3.29 tff(76,plain,
% 4.71/3.29 (((~(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)),
% 4.71/3.29 inference(tautology,[status(thm)],[])).
% 4.71/3.29 tff(77,plain,
% 4.71/3.29 (addition(X0!2, tptp_fun_X1_0(X0!2)) = one),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[76, 75])).
% 4.71/3.29 tff(78,plain,
% 4.71/3.29 (one = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 4.71/3.29 inference(symmetry,[status(thm)],[77])).
% 4.71/3.29 tff(79,plain,
% 4.71/3.29 (multiplication(one, X1!1) = multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1)),
% 4.71/3.29 inference(monotonicity,[status(thm)],[78])).
% 4.71/3.29 tff(80,plain,
% 4.71/3.29 (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1) = multiplication(one, X1!1)),
% 4.71/3.29 inference(symmetry,[status(thm)],[79])).
% 4.71/3.29 tff(81,plain,
% 4.71/3.29 (^[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))))),
% 4.71/3.29 inference(bind,[status(th)],[])).
% 4.71/3.29 tff(82,plain,
% 4.71/3.29 (![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)))),
% 4.71/3.29 inference(quant_intro,[status(thm)],[81])).
% 4.71/3.29 tff(83,plain,
% 4.71/3.29 (![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)))),
% 4.71/3.29 inference(rewrite,[status(thm)],[])).
% 4.71/3.29 tff(84,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','left_distributivity')).
% 4.71/3.29 tff(85,plain,
% 4.71/3.29 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[84, 83])).
% 4.71/3.29 tff(86,plain,(
% 4.71/3.29 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 4.71/3.29 inference(skolemize,[status(sab)],[85])).
% 4.71/3.29 tff(87,plain,
% 4.71/3.29 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[86, 82])).
% 4.71/3.29 tff(88,plain,
% 4.71/3.29 ((~![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)))),
% 4.71/3.29 inference(quant_inst,[status(thm)],[])).
% 4.71/3.29 tff(89,plain,
% 4.71/3.29 (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))),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[88, 87])).
% 4.71/3.29 tff(90,plain,
% 4.71/3.29 (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)),
% 4.71/3.29 inference(symmetry,[status(thm)],[89])).
% 4.71/3.29 tff(91,plain,
% 4.71/3.29 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 4.71/3.29 inference(bind,[status(th)],[])).
% 4.71/3.29 tff(92,plain,
% 4.71/3.29 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.71/3.29 inference(quant_intro,[status(thm)],[91])).
% 4.71/3.29 tff(93,plain,
% 4.71/3.29 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.71/3.29 inference(rewrite,[status(thm)],[])).
% 4.71/3.29 tff(94,plain,
% 4.71/3.29 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 4.71/3.29 inference(bind,[status(th)],[])).
% 4.71/3.29 tff(95,plain,
% 4.71/3.29 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.71/3.29 inference(quant_intro,[status(thm)],[94])).
% 4.71/3.29 tff(96,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_3')).
% 4.71/3.29 tff(97,plain,
% 4.71/3.29 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[96, 95])).
% 4.71/3.29 tff(98,plain,
% 4.71/3.29 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[97, 93])).
% 4.71/3.29 tff(99,plain,(
% 4.71/3.29 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.71/3.29 inference(skolemize,[status(sab)],[98])).
% 4.71/3.29 tff(100,plain,
% 4.71/3.29 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[99, 92])).
% 4.71/3.29 tff(101,plain,
% 4.71/3.29 (((~![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))))),
% 4.71/3.29 inference(rewrite,[status(thm)],[])).
% 4.71/3.29 tff(102,plain,
% 4.71/3.29 ((~![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))))),
% 4.71/3.29 inference(quant_inst,[status(thm)],[])).
% 4.71/3.29 tff(103,plain,
% 4.71/3.29 ((~![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)))),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[102, 101])).
% 4.71/3.29 tff(104,plain,
% 4.71/3.29 ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[103, 100, 69])).
% 4.71/3.29 tff(105,plain,
% 4.71/3.29 (((~![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))))))),
% 4.71/3.29 inference(rewrite,[status(thm)],[])).
% 4.71/3.29 tff(106,plain,
% 4.71/3.29 ((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)))))),
% 4.71/3.29 inference(rewrite,[status(thm)],[])).
% 4.71/3.29 tff(107,plain,
% 4.71/3.29 (((~![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))))))),
% 4.71/3.29 inference(monotonicity,[status(thm)],[106])).
% 4.71/3.29 tff(108,plain,
% 4.71/3.29 (((~![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))))))),
% 4.71/3.29 inference(transitivity,[status(thm)],[107, 105])).
% 4.71/3.29 tff(109,plain,
% 4.71/3.29 ((~![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)))))),
% 4.71/3.29 inference(quant_inst,[status(thm)],[])).
% 4.71/3.29 tff(110,plain,
% 4.71/3.29 ((~![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)))))),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[109, 108])).
% 4.71/3.29 tff(111,plain,
% 4.71/3.29 (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))))),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[110, 13])).
% 4.71/3.29 tff(112,plain,
% 4.71/3.29 ((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))),
% 4.71/3.29 inference(commutativity,[status(thm)],[])).
% 4.71/3.29 tff(113,plain,
% 4.71/3.29 ((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)))),
% 4.71/3.29 inference(monotonicity,[status(thm)],[78])).
% 4.71/3.29 tff(114,plain,
% 4.71/3.29 ((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))),
% 4.71/3.29 inference(transitivity,[status(thm)],[113, 112])).
% 4.71/3.29 tff(115,plain,
% 4.71/3.29 ((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)),
% 4.71/3.29 inference(symmetry,[status(thm)],[114])).
% 4.71/3.29 tff(116,plain,
% 4.71/3.29 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 4.71/3.29 inference(bind,[status(th)],[])).
% 4.71/3.29 tff(117,plain,
% 4.71/3.29 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 4.71/3.29 inference(quant_intro,[status(thm)],[116])).
% 4.71/3.29 tff(118,plain,
% 4.71/3.29 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 4.71/3.29 inference(rewrite,[status(thm)],[])).
% 4.71/3.29 tff(119,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 4.71/3.29 tff(120,plain,
% 4.71/3.29 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[119, 118])).
% 4.71/3.29 tff(121,plain,(
% 4.71/3.29 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 4.71/3.29 inference(skolemize,[status(sab)],[120])).
% 4.71/3.29 tff(122,plain,
% 4.71/3.29 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[121, 117])).
% 4.71/3.29 tff(123,plain,
% 4.71/3.29 ((~![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))),
% 4.71/3.29 inference(quant_inst,[status(thm)],[])).
% 4.71/3.29 tff(124,plain,
% 4.71/3.29 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[123, 122])).
% 4.71/3.29 tff(125,plain,
% 4.71/3.29 (addition(tptp_fun_X1_0(X0!2), X0!2) = one),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[124, 115])).
% 4.71/3.29 tff(126,plain,
% 4.71/3.29 (((~(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)),
% 4.71/3.29 inference(tautology,[status(thm)],[])).
% 4.71/3.29 tff(127,plain,
% 4.71/3.29 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[126, 75])).
% 4.71/3.29 tff(128,plain,
% 4.71/3.29 (((~(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)),
% 4.71/3.29 inference(tautology,[status(thm)],[])).
% 4.71/3.29 tff(129,plain,
% 4.71/3.29 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[128, 75])).
% 4.71/3.29 tff(130,plain,
% 4.71/3.29 ((~((~(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))),
% 4.71/3.29 inference(tautology,[status(thm)],[])).
% 4.71/3.29 tff(131,plain,
% 4.71/3.29 ((~((~(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))),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[130, 129, 127])).
% 4.71/3.29 tff(132,plain,
% 4.71/3.29 (~((~(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)))),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[131, 125])).
% 4.71/3.29 tff(133,plain,
% 4.71/3.29 ((~(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)))),
% 4.71/3.29 inference(tautology,[status(thm)],[])).
% 4.71/3.29 tff(134,plain,
% 4.71/3.29 (complement(X0!2, tptp_fun_X1_0(X0!2))),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[133, 132, 111])).
% 4.71/3.29 tff(135,plain,
% 4.71/3.29 ((~((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)))),
% 4.71/3.29 inference(tautology,[status(thm)],[])).
% 4.71/3.29 tff(136,plain,
% 4.71/3.29 (c(X0!2) = tptp_fun_X1_0(X0!2)),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[135, 134, 104])).
% 4.71/3.29 tff(137,plain,
% 4.71/3.29 (tptp_fun_X1_0(X0!2) = c(X0!2)),
% 4.71/3.29 inference(symmetry,[status(thm)],[136])).
% 4.71/3.29 tff(138,plain,
% 4.71/3.29 (multiplication(tptp_fun_X1_0(X0!2), X1!1) = multiplication(c(X0!2), X1!1)),
% 4.71/3.29 inference(monotonicity,[status(thm)],[137])).
% 4.71/3.29 tff(139,plain,
% 4.71/3.29 (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))),
% 4.71/3.29 inference(monotonicity,[status(thm)],[138])).
% 4.71/3.29 tff(140,plain,
% 4.71/3.29 (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))),
% 4.71/3.29 inference(symmetry,[status(thm)],[139])).
% 4.71/3.29 tff(141,plain,
% 4.71/3.29 ((~![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)))),
% 4.71/3.29 inference(quant_inst,[status(thm)],[])).
% 4.71/3.29 tff(142,plain,
% 4.71/3.29 (addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[141, 122])).
% 4.71/3.29 tff(143,plain,
% 4.71/3.29 (addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))),
% 4.71/3.29 inference(symmetry,[status(thm)],[142])).
% 4.71/3.29 tff(144,plain,
% 4.71/3.29 (addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)) = X1!1),
% 4.71/3.29 inference(transitivity,[status(thm)],[143, 140, 90, 80, 62])).
% 4.71/3.29 tff(145,plain,
% 4.71/3.29 (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))),
% 4.71/3.29 inference(monotonicity,[status(thm)],[144])).
% 4.71/3.29 tff(146,plain,
% 4.71/3.29 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 4.71/3.29 inference(bind,[status(th)],[])).
% 4.71/3.29 tff(147,plain,
% 4.71/3.29 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 4.71/3.29 inference(quant_intro,[status(thm)],[146])).
% 4.71/3.29 tff(148,plain,
% 4.71/3.29 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 4.71/3.29 inference(rewrite,[status(thm)],[])).
% 4.71/3.29 tff(149,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 4.71/3.29 tff(150,plain,
% 4.71/3.29 (![A: $i] : (addition(A, A) = A)),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[149, 148])).
% 4.71/3.29 tff(151,plain,(
% 4.71/3.29 ![A: $i] : (addition(A, A) = A)),
% 4.71/3.29 inference(skolemize,[status(sab)],[150])).
% 4.71/3.29 tff(152,plain,
% 4.71/3.29 (![A: $i] : (addition(A, A) = A)),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[151, 147])).
% 4.71/3.29 tff(153,plain,
% 4.71/3.29 ((~![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)))),
% 4.71/3.29 inference(quant_inst,[status(thm)],[])).
% 4.71/3.29 tff(154,plain,
% 4.71/3.29 (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))),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[153, 152])).
% 4.71/3.29 tff(155,plain,
% 4.71/3.29 (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))),
% 4.71/3.29 inference(monotonicity,[status(thm)],[154])).
% 4.71/3.29 tff(156,plain,
% 4.71/3.29 (^[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)))),
% 4.71/3.29 inference(bind,[status(th)],[])).
% 4.71/3.29 tff(157,plain,
% 4.71/3.29 (![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))),
% 4.71/3.29 inference(quant_intro,[status(thm)],[156])).
% 4.71/3.29 tff(158,plain,
% 4.71/3.29 (![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))),
% 4.71/3.29 inference(rewrite,[status(thm)],[])).
% 4.71/3.29 tff(159,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_associativity')).
% 4.71/3.29 tff(160,plain,
% 4.71/3.29 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[159, 158])).
% 4.71/3.29 tff(161,plain,(
% 4.71/3.29 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 4.71/3.29 inference(skolemize,[status(sab)],[160])).
% 4.71/3.29 tff(162,plain,
% 4.71/3.29 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[161, 157])).
% 4.71/3.29 tff(163,plain,
% 4.71/3.29 ((~![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)))),
% 4.71/3.29 inference(quant_inst,[status(thm)],[])).
% 4.71/3.29 tff(164,plain,
% 4.71/3.29 (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))),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[163, 162])).
% 4.71/3.29 tff(165,plain,
% 4.71/3.29 (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))),
% 4.71/3.29 inference(symmetry,[status(thm)],[145])).
% 4.71/3.29 tff(166,plain,
% 4.71/3.29 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 4.71/3.29 inference(symmetry,[status(thm)],[53])).
% 4.71/3.29 tff(167,plain,
% 4.71/3.29 (one = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1))),
% 4.71/3.29 inference(transitivity,[status(thm)],[166, 165])).
% 4.71/3.29 tff(168,plain,
% 4.71/3.29 (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)))),
% 4.71/3.29 inference(monotonicity,[status(thm)],[167])).
% 4.71/3.29 tff(169,plain,
% 4.71/3.29 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 4.71/3.29 inference(bind,[status(th)],[])).
% 4.71/3.29 tff(170,plain,
% 4.71/3.29 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 4.71/3.29 inference(quant_intro,[status(thm)],[169])).
% 4.71/3.29 tff(171,plain,
% 4.71/3.29 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 4.71/3.29 inference(rewrite,[status(thm)],[])).
% 4.71/3.29 tff(172,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','order')).
% 4.71/3.29 tff(173,plain,
% 4.71/3.29 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[172, 171])).
% 4.71/3.29 tff(174,plain,(
% 4.71/3.29 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 4.71/3.29 inference(skolemize,[status(sab)],[173])).
% 4.71/3.29 tff(175,plain,
% 4.71/3.29 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 4.71/3.29 inference(modus_ponens,[status(thm)],[174, 170])).
% 4.71/3.29 tff(176,plain,
% 4.71/3.29 ((~![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))),
% 4.71/3.29 inference(quant_inst,[status(thm)],[])).
% 4.71/3.29 tff(177,plain,
% 4.71/3.29 (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)),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[176, 175])).
% 4.71/3.29 tff(178,plain,
% 4.71/3.29 ((~![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))))),
% 4.71/3.29 inference(quant_inst,[status(thm)],[])).
% 4.71/3.29 tff(179,plain,
% 4.71/3.29 (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)))),
% 4.71/3.29 inference(unit_resolution,[status(thm)],[178, 122])).
% 4.71/3.29 tff(180,plain,
% 4.71/3.29 (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)))),
% 4.71/3.29 inference(symmetry,[status(thm)],[179])).
% 4.71/3.29 tff(181,plain,
% 4.71/3.29 ((~![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))))),
% 4.71/3.30 inference(quant_inst,[status(thm)],[])).
% 4.71/3.30 tff(182,plain,
% 4.71/3.30 (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)))),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[181, 122])).
% 4.71/3.30 tff(183,plain,
% 4.71/3.30 (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))),
% 4.71/3.30 inference(symmetry,[status(thm)],[182])).
% 4.71/3.30 tff(184,plain,
% 4.71/3.30 (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)))),
% 4.71/3.30 inference(monotonicity,[status(thm)],[183])).
% 4.71/3.30 tff(185,plain,
% 4.71/3.30 ((~![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))))),
% 4.71/3.30 inference(quant_inst,[status(thm)],[])).
% 4.71/3.30 tff(186,plain,
% 4.71/3.30 (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)))),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[185, 162])).
% 4.71/3.30 tff(187,plain,
% 4.71/3.30 (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))))),
% 4.71/3.30 inference(symmetry,[status(thm)],[186])).
% 4.71/3.30 tff(188,plain,
% 4.71/3.30 ((~![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)))),
% 4.71/3.30 inference(quant_inst,[status(thm)],[])).
% 4.71/3.30 tff(189,plain,
% 4.71/3.30 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[188, 122])).
% 4.71/3.30 tff(190,plain,
% 4.71/3.30 (addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 4.71/3.30 inference(symmetry,[status(thm)],[189])).
% 4.71/3.30 tff(191,plain,
% 4.71/3.30 (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))),
% 4.71/3.30 inference(monotonicity,[status(thm)],[190])).
% 4.71/3.30 tff(192,plain,
% 4.71/3.30 (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)))),
% 4.71/3.30 inference(monotonicity,[status(thm)],[191])).
% 4.71/3.30 tff(193,plain,
% 4.71/3.30 ((~![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)))),
% 4.71/3.30 inference(quant_inst,[status(thm)],[])).
% 4.71/3.30 tff(194,plain,
% 4.71/3.30 (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))),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[193, 162])).
% 4.71/3.30 tff(195,plain,
% 4.71/3.30 (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)))),
% 4.71/3.30 inference(symmetry,[status(thm)],[194])).
% 4.71/3.30 tff(196,plain,
% 4.71/3.30 ((~![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))))),
% 4.71/3.30 inference(quant_inst,[status(thm)],[])).
% 4.71/3.30 tff(197,plain,
% 4.71/3.30 (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)))),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[196, 122])).
% 4.71/3.30 tff(198,plain,
% 4.71/3.30 ((~![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)))),
% 4.71/3.30 inference(quant_inst,[status(thm)],[])).
% 4.71/3.30 tff(199,plain,
% 4.71/3.30 (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))),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[198, 122])).
% 4.71/3.30 tff(200,plain,
% 4.71/3.30 (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)))),
% 4.71/3.30 inference(symmetry,[status(thm)],[199])).
% 4.71/3.30 tff(201,plain,
% 4.71/3.30 (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))))),
% 4.71/3.30 inference(monotonicity,[status(thm)],[200])).
% 4.71/3.30 tff(202,plain,
% 4.71/3.30 (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)))),
% 4.71/3.30 inference(symmetry,[status(thm)],[201])).
% 4.71/3.30 tff(203,plain,
% 4.71/3.30 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 4.71/3.30 inference(bind,[status(th)],[])).
% 4.71/3.30 tff(204,plain,
% 4.71/3.30 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 4.71/3.30 inference(quant_intro,[status(thm)],[203])).
% 4.71/3.30 tff(205,plain,
% 4.71/3.30 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 4.71/3.30 inference(rewrite,[status(thm)],[])).
% 4.71/3.30 tff(206,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 4.71/3.30 tff(207,plain,
% 4.71/3.30 (![A: $i] : (multiplication(A, one) = A)),
% 4.71/3.30 inference(modus_ponens,[status(thm)],[206, 205])).
% 4.71/3.30 tff(208,plain,(
% 4.71/3.30 ![A: $i] : (multiplication(A, one) = A)),
% 4.71/3.30 inference(skolemize,[status(sab)],[207])).
% 4.71/3.30 tff(209,plain,
% 4.71/3.30 (![A: $i] : (multiplication(A, one) = A)),
% 4.71/3.30 inference(modus_ponens,[status(thm)],[208, 204])).
% 4.71/3.30 tff(210,plain,
% 4.71/3.30 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(tptp_fun_X1_0(X0!2), one) = tptp_fun_X1_0(X0!2))),
% 4.71/3.30 inference(quant_inst,[status(thm)],[])).
% 4.71/3.30 tff(211,plain,
% 4.71/3.30 (multiplication(tptp_fun_X1_0(X0!2), one) = tptp_fun_X1_0(X0!2)),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[210, 209])).
% 4.71/3.30 tff(212,plain,
% 4.71/3.30 (multiplication(tptp_fun_X1_0(X0!2), addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), one)),
% 4.71/3.30 inference(monotonicity,[status(thm)],[53])).
% 4.71/3.30 tff(213,plain,
% 4.71/3.30 (^[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))))),
% 4.71/3.30 inference(bind,[status(th)],[])).
% 4.71/3.30 tff(214,plain,
% 4.71/3.30 (![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)))),
% 4.71/3.30 inference(quant_intro,[status(thm)],[213])).
% 4.71/3.30 tff(215,plain,
% 4.71/3.30 (![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)))),
% 4.71/3.30 inference(rewrite,[status(thm)],[])).
% 4.71/3.30 tff(216,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','right_distributivity')).
% 4.71/3.30 tff(217,plain,
% 4.71/3.30 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 4.71/3.30 inference(modus_ponens,[status(thm)],[216, 215])).
% 4.71/3.30 tff(218,plain,(
% 4.71/3.30 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 4.71/3.30 inference(skolemize,[status(sab)],[217])).
% 4.71/3.30 tff(219,plain,
% 4.71/3.30 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 4.71/3.30 inference(modus_ponens,[status(thm)],[218, 214])).
% 4.71/3.30 tff(220,plain,
% 4.71/3.30 ((~![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))))),
% 4.71/3.30 inference(quant_inst,[status(thm)],[])).
% 4.71/3.30 tff(221,plain,
% 4.71/3.30 (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)))),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[220, 219])).
% 4.71/3.30 tff(222,plain,
% 4.71/3.30 (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)))),
% 4.71/3.30 inference(symmetry,[status(thm)],[221])).
% 4.71/3.30 tff(223,plain,
% 4.71/3.30 (((~![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))))),
% 4.71/3.30 inference(rewrite,[status(thm)],[])).
% 4.71/3.30 tff(224,plain,
% 4.71/3.30 ((~![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))))),
% 4.71/3.30 inference(quant_inst,[status(thm)],[])).
% 4.71/3.30 tff(225,plain,
% 4.71/3.30 ((~![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)))),
% 4.71/3.30 inference(modus_ponens,[status(thm)],[224, 223])).
% 4.71/3.30 tff(226,plain,
% 4.71/3.30 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[225, 100, 45])).
% 4.71/3.30 tff(227,plain,
% 4.71/3.30 (((~![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))))))),
% 4.71/3.30 inference(rewrite,[status(thm)],[])).
% 4.71/3.30 tff(228,plain,
% 4.71/3.30 ((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)))))),
% 4.71/3.30 inference(rewrite,[status(thm)],[])).
% 4.71/3.30 tff(229,plain,
% 4.71/3.30 (((~![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))))))),
% 4.71/3.30 inference(monotonicity,[status(thm)],[228])).
% 4.71/3.30 tff(230,plain,
% 4.71/3.30 (((~![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))))))),
% 4.71/3.30 inference(transitivity,[status(thm)],[229, 227])).
% 4.71/3.30 tff(231,plain,
% 4.71/3.30 ((~![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)))))),
% 4.71/3.30 inference(quant_inst,[status(thm)],[])).
% 4.71/3.30 tff(232,plain,
% 4.71/3.30 ((~![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)))))),
% 4.71/3.30 inference(modus_ponens,[status(thm)],[231, 230])).
% 4.71/3.30 tff(233,plain,
% 4.71/3.30 (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))))),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[232, 13])).
% 4.71/3.30 tff(234,plain,
% 4.71/3.30 ((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))),
% 4.71/3.30 inference(commutativity,[status(thm)],[])).
% 4.71/3.30 tff(235,plain,
% 4.71/3.30 ((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)))),
% 4.71/3.30 inference(monotonicity,[status(thm)],[166])).
% 4.71/3.30 tff(236,plain,
% 4.71/3.30 ((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))),
% 4.71/3.30 inference(transitivity,[status(thm)],[235, 234])).
% 4.71/3.30 tff(237,plain,
% 4.71/3.30 ((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)),
% 4.71/3.30 inference(symmetry,[status(thm)],[236])).
% 4.71/3.30 tff(238,plain,
% 4.71/3.30 ((~![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))),
% 4.71/3.30 inference(quant_inst,[status(thm)],[])).
% 4.71/3.30 tff(239,plain,
% 4.71/3.30 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[238, 122])).
% 4.71/3.30 tff(240,plain,
% 4.71/3.30 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 4.71/3.30 inference(modus_ponens,[status(thm)],[239, 237])).
% 4.71/3.30 tff(241,plain,
% 4.71/3.30 (((~(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)),
% 4.71/3.30 inference(tautology,[status(thm)],[])).
% 4.71/3.30 tff(242,plain,
% 4.71/3.30 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[241, 51])).
% 4.71/3.30 tff(243,plain,
% 4.71/3.30 (((~(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)),
% 4.71/3.30 inference(tautology,[status(thm)],[])).
% 4.71/3.30 tff(244,plain,
% 4.71/3.30 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[243, 51])).
% 4.71/3.30 tff(245,plain,
% 4.71/3.30 ((~((~(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))),
% 4.71/3.30 inference(tautology,[status(thm)],[])).
% 4.71/3.30 tff(246,plain,
% 4.71/3.30 ((~((~(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))),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[245, 244, 242])).
% 4.71/3.30 tff(247,plain,
% 4.71/3.30 (~((~(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)))),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[246, 240])).
% 4.71/3.30 tff(248,plain,
% 4.71/3.30 ((~(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)))),
% 4.71/3.30 inference(tautology,[status(thm)],[])).
% 4.71/3.30 tff(249,plain,
% 4.71/3.30 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[248, 247, 233])).
% 4.71/3.30 tff(250,plain,
% 4.71/3.30 ((~((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)))),
% 4.71/3.30 inference(tautology,[status(thm)],[])).
% 4.71/3.30 tff(251,plain,
% 4.71/3.30 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[250, 249, 226])).
% 4.71/3.30 tff(252,plain,
% 4.71/3.30 (tptp_fun_X1_0(X1!1) = c(X1!1)),
% 4.71/3.30 inference(symmetry,[status(thm)],[251])).
% 4.71/3.30 tff(253,plain,
% 4.71/3.30 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)) = multiplication(c(X0!2), c(X1!1))),
% 4.71/3.30 inference(monotonicity,[status(thm)],[137, 252])).
% 4.71/3.30 tff(254,plain,
% 4.71/3.30 (multiplication(c(X0!2), c(X1!1)) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 4.71/3.30 inference(symmetry,[status(thm)],[253])).
% 4.71/3.30 tff(255,plain,
% 4.71/3.30 (multiplication(c(X0!2), X1!1) = multiplication(tptp_fun_X1_0(X0!2), X1!1)),
% 4.71/3.30 inference(symmetry,[status(thm)],[138])).
% 4.71/3.30 tff(256,plain,
% 4.71/3.30 (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)))),
% 4.71/3.30 inference(monotonicity,[status(thm)],[255, 254])).
% 4.71/3.30 tff(257,plain,
% 4.71/3.30 (addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = tptp_fun_X1_0(X0!2)),
% 4.71/3.30 inference(transitivity,[status(thm)],[256, 222, 212, 211])).
% 4.71/3.30 tff(258,plain,
% 4.71/3.30 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!2) = X0!2)),
% 4.71/3.30 inference(quant_inst,[status(thm)],[])).
% 4.71/3.30 tff(259,plain,
% 4.71/3.30 (multiplication(one, X0!2) = X0!2),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[258, 60])).
% 4.71/3.30 tff(260,plain,
% 4.71/3.30 (multiplication(one, X0!2) = multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2)),
% 4.71/3.30 inference(monotonicity,[status(thm)],[166])).
% 4.71/3.30 tff(261,plain,
% 4.71/3.30 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = multiplication(one, X0!2)),
% 4.71/3.30 inference(symmetry,[status(thm)],[260])).
% 4.71/3.30 tff(262,plain,
% 4.71/3.30 ((~![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)))),
% 4.71/3.30 inference(quant_inst,[status(thm)],[])).
% 4.71/3.30 tff(263,plain,
% 4.71/3.30 (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))),
% 4.71/3.30 inference(unit_resolution,[status(thm)],[262, 87])).
% 4.71/3.30 tff(264,plain,
% 4.71/3.30 (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)),
% 4.71/3.30 inference(symmetry,[status(thm)],[263])).
% 4.71/3.30 tff(265,plain,
% 4.71/3.30 (multiplication(tptp_fun_X1_0(X1!1), X0!2) = multiplication(c(X1!1), X0!2)),
% 4.71/3.30 inference(monotonicity,[status(thm)],[252])).
% 4.71/3.30 tff(266,plain,
% 4.71/3.30 (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))),
% 4.71/3.30 inference(monotonicity,[status(thm)],[265])).
% 4.71/3.30 tff(267,plain,
% 4.71/3.30 (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))),
% 4.71/3.30 inference(symmetry,[status(thm)],[266])).
% 4.71/3.30 tff(268,plain,
% 4.71/3.30 (addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)) = X0!2),
% 4.71/3.30 inference(transitivity,[status(thm)],[190, 267, 264, 261, 259])).
% 4.71/3.30 tff(269,plain,
% 4.71/3.30 (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))),
% 4.71/3.30 inference(monotonicity,[status(thm)],[268, 257])).
% 4.71/3.30 tff(270,plain,
% 4.71/3.30 (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))))),
% 4.71/3.30 inference(symmetry,[status(thm)],[269])).
% 4.71/3.30 tff(271,plain,
% 4.71/3.30 (one = 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)))),
% 4.71/3.30 inference(transitivity,[status(thm)],[78, 270, 202, 197])).
% 4.71/3.30 tff(272,plain,
% 4.71/3.30 (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))),
% 4.71/3.30 inference(monotonicity,[status(thm)],[271])).
% 4.71/3.30 tff(273,plain,
% 4.71/3.30 (X0!2 = multiplication(one, X0!2)),
% 4.71/3.31 inference(symmetry,[status(thm)],[259])).
% 4.71/3.31 tff(274,plain,
% 4.71/3.31 (X0!2 = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 4.71/3.31 inference(transitivity,[status(thm)],[273, 260, 263, 266, 189])).
% 4.71/3.31 tff(275,plain,
% 4.71/3.31 (multiplication(X0!2, X1!1) = multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), X1!1)),
% 4.71/3.31 inference(monotonicity,[status(thm)],[274])).
% 4.71/3.31 tff(276,plain,
% 4.71/3.31 (multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), X1!1) = multiplication(X0!2, X1!1)),
% 4.71/3.31 inference(symmetry,[status(thm)],[275])).
% 4.71/3.31 tff(277,plain,
% 4.71/3.31 ((~![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)))),
% 4.71/3.31 inference(quant_inst,[status(thm)],[])).
% 4.71/3.31 tff(278,plain,
% 4.71/3.31 (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))),
% 4.71/3.31 inference(unit_resolution,[status(thm)],[277, 87])).
% 4.71/3.31 tff(279,plain,
% 4.71/3.31 (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)),
% 4.71/3.31 inference(symmetry,[status(thm)],[278])).
% 4.71/3.31 tff(280,plain,
% 4.71/3.31 (addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1)) = multiplication(X0!2, X1!1)),
% 4.71/3.31 inference(transitivity,[status(thm)],[279, 276])).
% 4.71/3.31 tff(281,plain,
% 4.71/3.31 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 4.71/3.31 inference(quant_inst,[status(thm)],[])).
% 4.71/3.31 tff(282,plain,
% 4.71/3.31 (addition(one, one) = one),
% 4.71/3.31 inference(unit_resolution,[status(thm)],[281, 152])).
% 4.71/3.31 tff(283,plain,
% 4.71/3.31 (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))),
% 4.71/3.31 inference(monotonicity,[status(thm)],[282, 280])).
% 4.71/3.31 tff(284,plain,
% 4.71/3.31 ((~![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))))),
% 4.71/3.31 inference(quant_inst,[status(thm)],[])).
% 4.71/3.31 tff(285,plain,
% 4.71/3.31 (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)))),
% 4.71/3.31 inference(unit_resolution,[status(thm)],[284, 162])).
% 4.71/3.31 tff(286,plain,
% 4.71/3.31 (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))),
% 4.71/3.31 inference(monotonicity,[status(thm)],[280])).
% 4.71/3.31 tff(287,plain,
% 4.71/3.31 (addition(one, multiplication(X0!2, X1!1)) = addition(one, addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1)))),
% 4.71/3.31 inference(symmetry,[status(thm)],[286])).
% 4.71/3.31 tff(288,plain,
% 4.71/3.31 (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))),
% 4.71/3.31 inference(symmetry,[status(thm)],[272])).
% 4.71/3.31 tff(289,plain,
% 4.71/3.31 (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)))),
% 4.71/3.31 inference(symmetry,[status(thm)],[192])).
% 4.71/3.31 tff(290,plain,
% 4.71/3.31 (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))))),
% 4.71/3.31 inference(symmetry,[status(thm)],[184])).
% 4.71/3.31 tff(291,plain,
% 4.71/3.31 (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(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1)))),
% 4.71/3.31 inference(transitivity,[status(thm)],[179, 290, 186, 289, 194, 288, 287])).
% 4.71/3.31 tff(292,plain,
% 4.71/3.31 (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))))),
% 4.71/3.31 inference(monotonicity,[status(thm)],[291])).
% 4.71/3.31 tff(293,plain,
% 4.71/3.31 ((~![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)))))),
% 4.71/3.31 inference(quant_inst,[status(thm)],[])).
% 4.71/3.31 tff(294,plain,
% 4.71/3.31 (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))))),
% 4.71/3.31 inference(unit_resolution,[status(thm)],[293, 122])).
% 4.71/3.31 tff(295,plain,
% 4.71/3.31 (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(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)))),
% 4.71/3.31 inference(transitivity,[status(thm)],[294, 292, 285, 283, 272, 195, 192, 187, 184, 180])).
% 4.71/3.31 tff(296,plain,
% 4.71/3.31 ((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(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)),
% 4.71/3.31 inference(monotonicity,[status(thm)],[295])).
% 4.71/3.31 tff(297,plain,
% 4.71/3.31 ((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)),
% 4.71/3.31 inference(symmetry,[status(thm)],[296])).
% 4.71/3.31 tff(298,plain,
% 4.71/3.31 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 4.71/3.31 inference(symmetry,[status(thm)],[124])).
% 4.71/3.31 tff(299,plain,
% 4.71/3.31 (c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 4.71/3.31 inference(monotonicity,[status(thm)],[190])).
% 4.71/3.31 tff(300,plain,
% 4.71/3.31 (c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.71/3.31 inference(symmetry,[status(thm)],[299])).
% 4.71/3.31 tff(301,plain,
% 4.71/3.31 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = X0!2),
% 4.71/3.31 inference(transitivity,[status(thm)],[267, 264, 261, 259])).
% 4.71/3.31 tff(302,plain,
% 4.71/3.31 (c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = c(X0!2)),
% 4.71/3.31 inference(monotonicity,[status(thm)],[301])).
% 4.71/3.31 tff(303,plain,
% 4.71/3.31 (c(X0!2) = c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 4.71/3.31 inference(symmetry,[status(thm)],[302])).
% 4.71/3.31 tff(304,plain,
% 4.71/3.31 (tptp_fun_X1_0(X0!2) = c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.71/3.31 inference(transitivity,[status(thm)],[137, 303, 300])).
% 4.71/3.31 tff(305,plain,
% 4.71/3.31 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)) = c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.71/3.31 inference(transitivity,[status(thm)],[200, 256, 222, 212, 211, 137, 303, 300])).
% 4.71/3.31 tff(306,plain,
% 4.71/3.31 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), tptp_fun_X1_0(X0!2)) = addition(c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))),
% 4.71/3.31 inference(monotonicity,[status(thm)],[305, 304])).
% 4.71/3.31 tff(307,plain,
% 4.71/3.31 (addition(c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), c(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)), tptp_fun_X1_0(X0!2))),
% 4.71/3.31 inference(symmetry,[status(thm)],[306])).
% 4.71/3.31 tff(308,plain,
% 4.71/3.31 (test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) <=> test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 4.71/3.31 inference(monotonicity,[status(thm)],[190])).
% 4.71/3.31 tff(309,plain,
% 4.71/3.31 (test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) <=> test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.71/3.31 inference(symmetry,[status(thm)],[308])).
% 4.71/3.31 tff(310,plain,
% 4.71/3.31 (X0!2 = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 4.71/3.31 inference(transitivity,[status(thm)],[273, 260, 263, 266])).
% 4.71/3.31 tff(311,plain,
% 4.71/3.31 (test(X0!2) <=> test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 4.71/3.31 inference(monotonicity,[status(thm)],[310])).
% 4.71/3.31 tff(312,plain,
% 4.71/3.31 (test(X0!2) <=> test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.71/3.31 inference(transitivity,[status(thm)],[311, 309])).
% 4.71/3.31 tff(313,plain,
% 4.71/3.31 (test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.71/3.31 inference(modus_ponens,[status(thm)],[69, 312])).
% 4.71/3.31 tff(314,plain,
% 4.71/3.31 (^[X0: $i, X1: $i] : refl(((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0))) <=> ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0))))),
% 4.71/3.31 inference(bind,[status(th)],[])).
% 4.71/3.31 tff(315,plain,
% 4.71/3.31 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 4.71/3.31 inference(quant_intro,[status(thm)],[314])).
% 4.71/3.31 tff(316,plain,
% 4.71/3.31 (^[X0: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((test(X0) & test(X1)) <=> (~((~test(X1)) | (~test(X0))))), ((~(test(X0) & test(X1))) <=> (~(~((~test(X1)) | (~test(X0))))))), rewrite((~(~((~test(X1)) | (~test(X0))))) <=> ((~test(X1)) | (~test(X0)))), ((~(test(X0) & test(X1))) <=> ((~test(X1)) | (~test(X0))))), (((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> (((~test(X1)) | (~test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))))), rewrite((((~test(X1)) | (~test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))), (((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))))),
% 4.71/3.31 inference(bind,[status(th)],[])).
% 4.71/3.31 tff(317,plain,
% 4.71/3.31 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 4.71/3.31 inference(quant_intro,[status(thm)],[316])).
% 4.71/3.31 tff(318,plain,
% 4.71/3.31 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 4.71/3.31 inference(rewrite,[status(thm)],[])).
% 4.71/3.31 tff(319,plain,
% 4.71/3.31 (^[X0: $i, X1: $i] : rewrite(((test(X0) & test(X1)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))))),
% 4.71/3.31 inference(bind,[status(th)],[])).
% 4.71/3.31 tff(320,plain,
% 4.71/3.31 (![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 4.71/3.31 inference(quant_intro,[status(thm)],[319])).
% 4.71/3.31 tff(321,axiom,(![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax','test_deMorgan2')).
% 4.71/3.31 tff(322,plain,
% 4.71/3.31 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 4.71/3.31 inference(modus_ponens,[status(thm)],[321, 320])).
% 4.71/3.31 tff(323,plain,
% 4.71/3.31 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 4.71/3.31 inference(modus_ponens,[status(thm)],[322, 318])).
% 4.71/3.31 tff(324,plain,(
% 4.71/3.31 ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 4.71/3.31 inference(skolemize,[status(sab)],[323])).
% 4.71/3.31 tff(325,plain,
% 4.71/3.31 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 4.71/3.31 inference(modus_ponens,[status(thm)],[324, 317])).
% 4.71/3.31 tff(326,plain,
% 4.71/3.31 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 4.71/3.31 inference(modus_ponens,[status(thm)],[325, 315])).
% 4.71/3.31 tff(327,plain,
% 4.71/3.31 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = addition(c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = addition(c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))))),
% 4.71/3.31 inference(rewrite,[status(thm)],[])).
% 4.71/3.31 tff(328,plain,
% 4.71/3.31 (((~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = addition(c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))) | (~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))) <=> ((~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = addition(c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))))),
% 4.71/3.31 inference(rewrite,[status(thm)],[])).
% 4.71/3.31 tff(329,plain,
% 4.71/3.31 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = addition(c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))) | (~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = addition(c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))))))),
% 4.71/3.31 inference(monotonicity,[status(thm)],[328])).
% 4.71/3.31 tff(330,plain,
% 4.71/3.31 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = addition(c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))) | (~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = addition(c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))))),
% 4.71/3.31 inference(transitivity,[status(thm)],[329, 327])).
% 4.71/3.31 tff(331,plain,
% 4.71/3.31 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = addition(c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))) | (~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))))),
% 4.71/3.31 inference(quant_inst,[status(thm)],[])).
% 4.71/3.31 tff(332,plain,
% 4.71/3.31 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = addition(c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))))),
% 4.71/3.31 inference(modus_ponens,[status(thm)],[331, 330])).
% 4.71/3.31 tff(333,plain,
% 4.71/3.31 (c(multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = addition(c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))),
% 4.71/3.31 inference(unit_resolution,[status(thm)],[332, 326, 313])).
% 4.71/3.31 tff(334,plain,
% 4.71/3.31 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 4.71/3.31 inference(transitivity,[status(thm)],[77, 166])).
% 4.71/3.31 tff(335,plain,
% 4.71/3.31 (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X0!2) = multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2)),
% 4.71/3.31 inference(monotonicity,[status(thm)],[334])).
% 4.71/3.31 tff(336,plain,
% 4.71/3.31 ((~![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)), X0!2) = addition(multiplication(X0!2, X0!2), multiplication(tptp_fun_X1_0(X0!2), X0!2)))),
% 4.71/3.31 inference(quant_inst,[status(thm)],[])).
% 4.71/3.31 tff(337,plain,
% 4.71/3.31 (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X0!2) = addition(multiplication(X0!2, X0!2), multiplication(tptp_fun_X1_0(X0!2), X0!2))),
% 4.71/3.31 inference(unit_resolution,[status(thm)],[336, 87])).
% 4.71/3.31 tff(338,plain,
% 4.71/3.31 (addition(multiplication(X0!2, X0!2), multiplication(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X0!2)),
% 4.71/3.31 inference(symmetry,[status(thm)],[337])).
% 4.71/3.31 tff(339,plain,
% 4.71/3.31 (zero = multiplication(tptp_fun_X1_0(X0!2), X0!2)),
% 4.71/3.31 inference(symmetry,[status(thm)],[127])).
% 4.71/3.31 tff(340,plain,
% 4.71/3.31 (addition(multiplication(X0!2, X0!2), zero) = addition(multiplication(X0!2, X0!2), multiplication(tptp_fun_X1_0(X0!2), X0!2))),
% 4.71/3.31 inference(monotonicity,[status(thm)],[339])).
% 4.71/3.31 tff(341,plain,
% 4.71/3.31 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 4.71/3.31 inference(bind,[status(th)],[])).
% 4.71/3.31 tff(342,plain,
% 4.71/3.31 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 4.71/3.31 inference(quant_intro,[status(thm)],[341])).
% 4.71/3.31 tff(343,plain,
% 4.71/3.31 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 4.71/3.31 inference(rewrite,[status(thm)],[])).
% 4.71/3.31 tff(344,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 4.71/3.31 tff(345,plain,
% 4.71/3.31 (![A: $i] : (addition(A, zero) = A)),
% 4.71/3.31 inference(modus_ponens,[status(thm)],[344, 343])).
% 4.71/3.31 tff(346,plain,(
% 4.71/3.31 ![A: $i] : (addition(A, zero) = A)),
% 4.71/3.31 inference(skolemize,[status(sab)],[345])).
% 4.71/3.31 tff(347,plain,
% 4.71/3.31 (![A: $i] : (addition(A, zero) = A)),
% 4.71/3.31 inference(modus_ponens,[status(thm)],[346, 342])).
% 4.71/3.31 tff(348,plain,
% 4.71/3.31 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(X0!2, X0!2), zero) = multiplication(X0!2, X0!2))),
% 4.71/3.31 inference(quant_inst,[status(thm)],[])).
% 4.71/3.31 tff(349,plain,
% 4.71/3.31 (addition(multiplication(X0!2, X0!2), zero) = multiplication(X0!2, X0!2)),
% 4.71/3.31 inference(unit_resolution,[status(thm)],[348, 347])).
% 4.71/3.31 tff(350,plain,
% 4.71/3.31 (multiplication(X0!2, X0!2) = addition(multiplication(X0!2, X0!2), zero)),
% 4.71/3.31 inference(symmetry,[status(thm)],[349])).
% 4.71/3.31 tff(351,plain,
% 4.71/3.31 (multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = multiplication(X0!2, X0!2)),
% 4.71/3.31 inference(monotonicity,[status(thm)],[268, 268])).
% 4.71/3.31 tff(352,plain,
% 4.71/3.31 (multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 4.71/3.31 inference(transitivity,[status(thm)],[351, 350, 340, 338, 335, 263, 266])).
% 4.71/3.31 tff(353,plain,
% 4.71/3.31 (c(multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 4.71/3.31 inference(monotonicity,[status(thm)],[352])).
% 4.71/3.31 tff(354,plain,
% 4.71/3.32 (c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = c(multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))),
% 4.71/3.32 inference(symmetry,[status(thm)],[353])).
% 4.71/3.32 tff(355,plain,
% 4.71/3.32 (tptp_fun_X1_0(X0!2) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), tptp_fun_X1_0(X0!2))),
% 4.71/3.32 inference(transitivity,[status(thm)],[137, 303, 354, 333, 307])).
% 4.71/3.32 tff(356,plain,
% 4.71/3.32 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.71/3.32 inference(monotonicity,[status(thm)],[355, 274])).
% 4.71/3.32 tff(357,plain,
% 4.71/3.32 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), 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)),
% 4.71/3.32 inference(symmetry,[status(thm)],[356])).
% 4.71/3.32 tff(358,plain,
% 4.71/3.32 ((~![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(tptp_fun_X1_0(X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))),
% 4.71/3.32 inference(quant_inst,[status(thm)],[])).
% 4.71/3.32 tff(359,plain,
% 4.71/3.32 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.71/3.32 inference(unit_resolution,[status(thm)],[358, 162])).
% 4.71/3.32 tff(360,plain,
% 4.71/3.32 (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)),
% 4.71/3.32 inference(monotonicity,[status(thm)],[268])).
% 4.71/3.32 tff(361,plain,
% 4.71/3.32 (addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = one),
% 4.71/3.32 inference(transitivity,[status(thm)],[360, 298, 77])).
% 4.71/3.32 tff(362,plain,
% 4.71/3.32 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one)),
% 4.71/3.32 inference(monotonicity,[status(thm)],[200, 361])).
% 4.71/3.32 tff(363,plain,
% 4.71/3.32 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))),
% 4.71/3.32 inference(symmetry,[status(thm)],[362])).
% 4.71/3.32 tff(364,plain,
% 4.71/3.32 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 4.71/3.32 inference(monotonicity,[status(thm)],[199, 166])).
% 4.71/3.32 tff(365,plain,
% 4.71/3.32 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(X1!1, tptp_fun_X1_0(X1!1))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one)),
% 4.71/3.32 inference(symmetry,[status(thm)],[364])).
% 4.71/3.32 tff(366,plain,
% 4.71/3.32 ((~![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(X1!1, tptp_fun_X1_0(X1!1))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), X1!1), tptp_fun_X1_0(X1!1)))),
% 4.71/3.32 inference(quant_inst,[status(thm)],[])).
% 4.71/3.32 tff(367,plain,
% 4.71/3.32 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(X1!1, tptp_fun_X1_0(X1!1))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), X1!1), tptp_fun_X1_0(X1!1))),
% 4.71/3.32 inference(unit_resolution,[status(thm)],[366, 162])).
% 4.71/3.32 tff(368,plain,
% 4.71/3.32 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), X1!1), tptp_fun_X1_0(X1!1)) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 4.71/3.32 inference(symmetry,[status(thm)],[367])).
% 4.71/3.32 tff(369,plain,
% 4.71/3.32 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))))),
% 4.71/3.32 inference(quant_inst,[status(thm)],[])).
% 4.71/3.32 tff(370,plain,
% 4.71/3.32 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.71/3.32 inference(unit_resolution,[status(thm)],[369, 122])).
% 4.71/3.32 tff(371,plain,
% 4.71/3.32 (addition(tptp_fun_X1_0(X0!2), 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(X0!2))),
% 4.71/3.32 inference(symmetry,[status(thm)],[370])).
% 4.71/3.32 tff(372,plain,
% 4.71/3.32 (X1!1 = multiplication(one, X1!1)),
% 4.71/3.32 inference(symmetry,[status(thm)],[62])).
% 4.71/3.32 tff(373,plain,
% 4.71/3.32 (X1!1 = addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))),
% 4.71/3.32 inference(transitivity,[status(thm)],[372, 79, 89, 139, 142])).
% 4.71/3.32 tff(374,plain,
% 4.71/3.32 (addition(tptp_fun_X1_0(X0!2), X1!1) = addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.71/3.32 inference(monotonicity,[status(thm)],[373])).
% 4.71/3.32 tff(375,plain,
% 4.71/3.32 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)) = tptp_fun_X1_0(X0!2)),
% 4.71/3.32 inference(transitivity,[status(thm)],[200, 256, 222, 212, 211])).
% 4.71/3.32 tff(376,plain,
% 4.71/3.32 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), X1!1) = addition(tptp_fun_X1_0(X0!2), X1!1)),
% 4.71/3.32 inference(monotonicity,[status(thm)],[375])).
% 4.71/3.32 tff(377,plain,
% 4.71/3.32 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), X1!1) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X0!2))),
% 4.71/3.32 inference(transitivity,[status(thm)],[376, 374, 371])).
% 4.71/3.32 tff(378,plain,
% 4.71/3.32 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), X1!1), tptp_fun_X1_0(X1!1)) = addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 4.71/3.32 inference(monotonicity,[status(thm)],[377])).
% 4.71/3.32 tff(379,plain,
% 4.71/3.32 (addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), X1!1), tptp_fun_X1_0(X1!1))),
% 4.71/3.32 inference(symmetry,[status(thm)],[378])).
% 4.71/3.32 tff(380,plain,
% 4.71/3.32 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(c(X1!1), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))),
% 4.71/3.32 inference(monotonicity,[status(thm)],[252, 304])).
% 4.71/3.32 tff(381,plain,
% 4.71/3.32 (multiplication(c(X1!1), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))),
% 4.71/3.32 inference(symmetry,[status(thm)],[380])).
% 4.71/3.32 tff(382,plain,
% 4.71/3.32 (^[X0: $i, X1: $i] : refl(((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))))),
% 4.71/3.32 inference(bind,[status(th)],[])).
% 4.71/3.32 tff(383,plain,
% 4.71/3.32 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 4.71/3.32 inference(quant_intro,[status(thm)],[382])).
% 4.71/3.32 tff(384,plain,
% 4.71/3.32 (^[X0: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((test(X0) & test(X1)) <=> (~((~test(X1)) | (~test(X0))))), ((~(test(X0) & test(X1))) <=> (~(~((~test(X1)) | (~test(X0))))))), rewrite((~(~((~test(X1)) | (~test(X0))))) <=> ((~test(X1)) | (~test(X0)))), ((~(test(X0) & test(X1))) <=> ((~test(X1)) | (~test(X0))))), (((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> (((~test(X1)) | (~test(X0))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))))), rewrite((((~test(X1)) | (~test(X0))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))), (((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))))),
% 4.71/3.32 inference(bind,[status(th)],[])).
% 4.71/3.32 tff(385,plain,
% 4.71/3.32 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 4.71/3.32 inference(quant_intro,[status(thm)],[384])).
% 4.71/3.32 tff(386,plain,
% 4.71/3.32 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 4.71/3.32 inference(rewrite,[status(thm)],[])).
% 4.71/3.32 tff(387,plain,
% 4.71/3.32 (^[X0: $i, X1: $i] : rewrite(((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))))),
% 4.71/3.32 inference(bind,[status(th)],[])).
% 4.71/3.32 tff(388,plain,
% 4.71/3.32 (![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 4.71/3.32 inference(quant_intro,[status(thm)],[387])).
% 4.71/3.32 tff(389,axiom,(![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax','test_deMorgan1')).
% 4.71/3.32 tff(390,plain,
% 4.71/3.32 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 4.71/3.32 inference(modus_ponens,[status(thm)],[389, 388])).
% 4.71/3.32 tff(391,plain,
% 4.71/3.32 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 4.71/3.32 inference(modus_ponens,[status(thm)],[390, 386])).
% 4.71/3.32 tff(392,plain,(
% 4.71/3.32 ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 4.71/3.32 inference(skolemize,[status(sab)],[391])).
% 4.71/3.32 tff(393,plain,
% 4.71/3.32 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 4.71/3.32 inference(modus_ponens,[status(thm)],[392, 385])).
% 4.71/3.32 tff(394,plain,
% 4.71/3.32 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 4.71/3.32 inference(modus_ponens,[status(thm)],[393, 383])).
% 4.71/3.32 tff(395,plain,
% 4.71/3.32 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(addition(X1!1, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = multiplication(c(X1!1), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(addition(X1!1, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = multiplication(c(X1!1), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))))),
% 4.71/3.32 inference(rewrite,[status(thm)],[])).
% 4.71/3.32 tff(396,plain,
% 4.71/3.32 (((~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(addition(X1!1, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = multiplication(c(X1!1), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))) | (~test(X1!1))) <=> ((~test(X1!1)) | (~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(addition(X1!1, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = multiplication(c(X1!1), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))))),
% 4.71/3.32 inference(rewrite,[status(thm)],[])).
% 4.71/3.32 tff(397,plain,
% 4.71/3.32 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(addition(X1!1, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = multiplication(c(X1!1), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))) | (~test(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(addition(X1!1, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = multiplication(c(X1!1), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))))))),
% 4.71/3.32 inference(monotonicity,[status(thm)],[396])).
% 4.71/3.32 tff(398,plain,
% 4.71/3.32 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(addition(X1!1, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = multiplication(c(X1!1), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))) | (~test(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(addition(X1!1, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = multiplication(c(X1!1), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))))),
% 4.71/3.32 inference(transitivity,[status(thm)],[397, 395])).
% 4.71/3.32 tff(399,plain,
% 4.71/3.32 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(addition(X1!1, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = multiplication(c(X1!1), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))) | (~test(X1!1)))),
% 4.71/3.32 inference(quant_inst,[status(thm)],[])).
% 4.71/3.32 tff(400,plain,
% 4.71/3.32 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) | (c(addition(X1!1, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = multiplication(c(X1!1), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))))),
% 4.71/3.32 inference(modus_ponens,[status(thm)],[399, 398])).
% 4.71/3.32 tff(401,plain,
% 4.71/3.32 (c(addition(X1!1, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = multiplication(c(X1!1), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))),
% 4.71/3.32 inference(unit_resolution,[status(thm)],[400, 394, 45, 313])).
% 4.71/3.32 tff(402,plain,
% 4.71/3.32 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, X1!1) = addition(X1!1, X0!2))),
% 4.71/3.32 inference(quant_inst,[status(thm)],[])).
% 4.71/3.32 tff(403,plain,
% 4.71/3.32 (addition(X0!2, X1!1) = addition(X1!1, X0!2)),
% 4.71/3.32 inference(unit_resolution,[status(thm)],[402, 122])).
% 4.71/3.32 tff(404,plain,
% 4.71/3.32 (addition(X1!1, X0!2) = addition(X0!2, X1!1)),
% 4.71/3.32 inference(symmetry,[status(thm)],[403])).
% 4.71/3.32 tff(405,plain,
% 4.71/3.32 (addition(X1!1, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(X1!1, X0!2)),
% 4.71/3.32 inference(monotonicity,[status(thm)],[268])).
% 4.71/3.32 tff(406,plain,
% 4.71/3.32 (addition(X1!1, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(X0!2, X1!1)),
% 4.71/3.32 inference(transitivity,[status(thm)],[405, 404])).
% 4.71/3.32 tff(407,plain,
% 4.71/3.32 (c(addition(X1!1, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = c(addition(X0!2, X1!1))),
% 4.71/3.32 inference(monotonicity,[status(thm)],[406])).
% 4.71/3.32 tff(408,plain,
% 4.71/3.32 (c(addition(X0!2, X1!1)) = c(addition(X1!1, addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))),
% 4.71/3.32 inference(symmetry,[status(thm)],[407])).
% 4.71/3.32 tff(409,plain,
% 4.71/3.32 ((~![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)))),
% 4.71/3.32 inference(quant_inst,[status(thm)],[])).
% 4.71/3.32 tff(410,plain,
% 4.71/3.32 (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))),
% 4.71/3.32 inference(unit_resolution,[status(thm)],[409, 162])).
% 4.71/3.32 tff(411,plain,
% 4.71/3.32 (X1!1 = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))),
% 4.71/3.32 inference(transitivity,[status(thm)],[372, 79, 89, 139])).
% 4.71/3.32 tff(412,plain,
% 4.71/3.32 (addition(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)))),
% 4.71/3.32 inference(monotonicity,[status(thm)],[310, 411])).
% 4.71/3.32 tff(413,plain,
% 4.71/3.32 (addition(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))),
% 4.71/3.32 inference(transitivity,[status(thm)],[412, 410])).
% 4.71/3.32 tff(414,plain,
% 4.71/3.32 (c(addition(X0!2, X1!1)) = c(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)))),
% 4.71/3.32 inference(monotonicity,[status(thm)],[413])).
% 4.71/3.32 tff(415,plain,
% 4.71/3.32 (c(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))) = c(addition(X0!2, X1!1))),
% 4.71/3.32 inference(symmetry,[status(thm)],[414])).
% 4.71/3.32 tff(416,plain,
% 4.71/3.32 (c(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(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))),
% 4.71/3.32 inference(transitivity,[status(thm)],[415, 408, 401, 381])).
% 4.71/3.32 tff(417,plain,
% 4.71/3.32 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(tptp_fun_X1_0(X1!1), one) = tptp_fun_X1_0(X1!1))),
% 4.71/3.32 inference(quant_inst,[status(thm)],[])).
% 4.71/3.32 tff(418,plain,
% 4.71/3.32 (multiplication(tptp_fun_X1_0(X1!1), one) = tptp_fun_X1_0(X1!1)),
% 4.71/3.32 inference(unit_resolution,[status(thm)],[417, 209])).
% 4.71/3.32 tff(419,plain,
% 4.71/3.32 (tptp_fun_X1_0(X1!1) = multiplication(tptp_fun_X1_0(X1!1), one)),
% 4.71/3.32 inference(symmetry,[status(thm)],[418])).
% 4.71/3.32 tff(420,plain,
% 4.71/3.32 (addition(tptp_fun_X1_0(X1!1), c(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(tptp_fun_X1_0(X1!1), one), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 4.71/3.32 inference(monotonicity,[status(thm)],[419, 416])).
% 4.71/3.32 tff(421,plain,
% 4.71/3.32 (addition(multiplication(tptp_fun_X1_0(X1!1), one), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = addition(tptp_fun_X1_0(X1!1), c(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))))),
% 4.71/3.32 inference(symmetry,[status(thm)],[420])).
% 4.81/3.32 tff(422,plain,
% 4.81/3.32 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(tptp_fun_X1_0(X1!1), addition(one, tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X1!1), one), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))))),
% 4.81/3.32 inference(quant_inst,[status(thm)],[])).
% 4.81/3.32 tff(423,plain,
% 4.81/3.32 (multiplication(tptp_fun_X1_0(X1!1), addition(one, tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X1!1), one), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 4.81/3.32 inference(unit_resolution,[status(thm)],[422, 219])).
% 4.81/3.32 tff(424,plain,
% 4.81/3.32 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), one) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one)),
% 4.81/3.32 inference(monotonicity,[status(thm)],[200])).
% 4.81/3.32 tff(425,plain,
% 4.81/3.32 ((~![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))))),
% 4.81/3.32 inference(quant_inst,[status(thm)],[])).
% 4.81/3.32 tff(426,plain,
% 4.81/3.32 (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)))),
% 4.81/3.32 inference(unit_resolution,[status(thm)],[425, 122])).
% 4.81/3.32 tff(427,plain,
% 4.81/3.32 (addition(one, 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)), one)),
% 4.81/3.32 inference(symmetry,[status(thm)],[426])).
% 4.81/3.32 tff(428,plain,
% 4.81/3.32 (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)))),
% 4.81/3.32 inference(symmetry,[status(thm)],[256])).
% 4.81/3.32 tff(429,plain,
% 4.81/3.32 (multiplication(tptp_fun_X1_0(X0!2), one) = multiplication(tptp_fun_X1_0(X0!2), addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 4.81/3.32 inference(symmetry,[status(thm)],[212])).
% 4.81/3.32 tff(430,plain,
% 4.81/3.32 (tptp_fun_X1_0(X0!2) = multiplication(tptp_fun_X1_0(X0!2), one)),
% 4.81/3.32 inference(symmetry,[status(thm)],[211])).
% 4.81/3.32 tff(431,plain,
% 4.81/3.32 (tptp_fun_X1_0(X0!2) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))),
% 4.81/3.32 inference(transitivity,[status(thm)],[430, 429, 221, 428, 199])).
% 4.81/3.32 tff(432,plain,
% 4.81/3.32 (addition(one, tptp_fun_X1_0(X0!2)) = addition(one, addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))),
% 4.81/3.32 inference(monotonicity,[status(thm)],[431])).
% 4.81/3.32 tff(433,plain,
% 4.81/3.32 (addition(one, tptp_fun_X1_0(X0!2)) = one),
% 4.81/3.32 inference(transitivity,[status(thm)],[432, 427, 424, 363, 359, 357, 298, 77])).
% 4.81/3.32 tff(434,plain,
% 4.81/3.32 (multiplication(tptp_fun_X1_0(X1!1), addition(one, tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X1!1), one)),
% 4.81/3.32 inference(monotonicity,[status(thm)],[433])).
% 4.81/3.32 tff(435,plain,
% 4.81/3.32 (multiplication(tptp_fun_X1_0(X1!1), one) = multiplication(tptp_fun_X1_0(X1!1), addition(one, tptp_fun_X1_0(X0!2)))),
% 4.81/3.32 inference(symmetry,[status(thm)],[434])).
% 4.81/3.32 tff(436,plain,
% 4.81/3.32 (tptp_fun_X1_0(X1!1) = addition(tptp_fun_X1_0(X1!1), c(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))))),
% 4.81/3.32 inference(transitivity,[status(thm)],[419, 435, 423, 421])).
% 4.81/3.32 tff(437,plain,
% 4.81/3.32 (addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))) = addition(tptp_fun_X1_0(X0!2), X1!1)),
% 4.81/3.32 inference(symmetry,[status(thm)],[374])).
% 4.81/3.32 tff(438,plain,
% 4.81/3.32 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X1!1)),
% 4.81/3.32 inference(transitivity,[status(thm)],[370, 437])).
% 4.81/3.32 tff(439,plain,
% 4.81/3.32 (addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(addition(tptp_fun_X1_0(X0!2), X1!1), addition(tptp_fun_X1_0(X1!1), c(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)))))),
% 4.81/3.32 inference(monotonicity,[status(thm)],[438, 436])).
% 4.81/3.32 tff(440,plain,
% 4.81/3.32 (addition(addition(tptp_fun_X1_0(X0!2), X1!1), addition(tptp_fun_X1_0(X1!1), c(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(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 4.81/3.32 inference(symmetry,[status(thm)],[439])).
% 4.81/3.32 tff(441,plain,
% 4.81/3.32 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(tptp_fun_X1_0(X0!2), X1!1), addition(tptp_fun_X1_0(X1!1), c(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(tptp_fun_X1_0(X0!2), X1!1), tptp_fun_X1_0(X1!1)), c(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)))))),
% 4.81/3.32 inference(quant_inst,[status(thm)],[])).
% 4.81/3.32 tff(442,plain,
% 4.81/3.32 (addition(addition(tptp_fun_X1_0(X0!2), X1!1), addition(tptp_fun_X1_0(X1!1), c(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(tptp_fun_X1_0(X0!2), X1!1), tptp_fun_X1_0(X1!1)), c(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))))),
% 4.81/3.32 inference(unit_resolution,[status(thm)],[441, 162])).
% 4.81/3.32 tff(443,plain,
% 4.81/3.32 (addition(addition(addition(tptp_fun_X1_0(X0!2), X1!1), tptp_fun_X1_0(X1!1)), c(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(tptp_fun_X1_0(X0!2), X1!1), addition(tptp_fun_X1_0(X1!1), c(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)))))),
% 4.81/3.32 inference(symmetry,[status(thm)],[442])).
% 4.81/3.32 tff(444,plain,
% 4.81/3.32 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))))),
% 4.81/3.32 inference(rewrite,[status(thm)],[])).
% 4.81/3.32 tff(445,plain,
% 4.81/3.32 (((~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))) | (~test(X0!2))) <=> ((~test(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))))),
% 4.81/3.32 inference(rewrite,[status(thm)],[])).
% 4.81/3.32 tff(446,plain,
% 4.81/3.32 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))) | (~test(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1)))))),
% 4.81/3.32 inference(monotonicity,[status(thm)],[445])).
% 4.81/3.32 tff(447,plain,
% 4.81/3.32 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))) | (~test(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))))),
% 4.81/3.32 inference(transitivity,[status(thm)],[446, 444])).
% 4.81/3.32 tff(448,plain,
% 4.81/3.33 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))) | (~test(X0!2)))),
% 4.81/3.33 inference(quant_inst,[status(thm)],[])).
% 4.81/3.33 tff(449,plain,
% 4.81/3.33 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1)))),
% 4.81/3.33 inference(modus_ponens,[status(thm)],[448, 447])).
% 4.81/3.33 tff(450,plain,
% 4.81/3.33 (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))),
% 4.81/3.33 inference(unit_resolution,[status(thm)],[449, 394, 45, 69])).
% 4.81/3.33 tff(451,plain,
% 4.81/3.33 (c(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))),
% 4.81/3.33 inference(transitivity,[status(thm)],[415, 450])).
% 4.81/3.33 tff(452,plain,
% 4.81/3.33 (addition(tptp_fun_X1_0(X0!2), X1!1) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), X1!1)),
% 4.81/3.33 inference(symmetry,[status(thm)],[376])).
% 4.81/3.33 tff(453,plain,
% 4.81/3.33 (addition(addition(tptp_fun_X1_0(X0!2), X1!1), tptp_fun_X1_0(X1!1)) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), X1!1), tptp_fun_X1_0(X1!1))),
% 4.81/3.33 inference(monotonicity,[status(thm)],[452])).
% 4.81/3.33 tff(454,plain,
% 4.81/3.33 (addition(addition(tptp_fun_X1_0(X0!2), X1!1), tptp_fun_X1_0(X1!1)) = one),
% 4.81/3.33 inference(transitivity,[status(thm)],[453, 368, 365, 363, 359, 357, 298, 77])).
% 4.81/3.33 tff(455,plain,
% 4.81/3.33 (addition(addition(addition(tptp_fun_X1_0(X0!2), X1!1), tptp_fun_X1_0(X1!1)), c(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(one, multiplication(c(X0!2), c(X1!1)))),
% 4.81/3.33 inference(monotonicity,[status(thm)],[454, 451])).
% 4.81/3.33 tff(456,plain,
% 4.81/3.33 (addition(one, multiplication(c(X0!2), c(X1!1))) = addition(addition(addition(tptp_fun_X1_0(X0!2), X1!1), tptp_fun_X1_0(X1!1)), c(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))))),
% 4.81/3.33 inference(symmetry,[status(thm)],[455])).
% 4.81/3.33 tff(457,plain,
% 4.81/3.33 ((~![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))))),
% 4.81/3.33 inference(quant_inst,[status(thm)],[])).
% 4.81/3.33 tff(458,plain,
% 4.81/3.33 (addition(multiplication(c(X0!2), c(X1!1)), one) = addition(one, multiplication(c(X0!2), c(X1!1)))),
% 4.81/3.33 inference(unit_resolution,[status(thm)],[457, 122])).
% 4.81/3.33 tff(459,plain,
% 4.81/3.33 ((~![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), X1!1), multiplication(X0!2, X1!1))) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(c(X0!2), X1!1)), multiplication(X0!2, X1!1)))),
% 4.81/3.33 inference(quant_inst,[status(thm)],[])).
% 4.81/3.33 tff(460,plain,
% 4.81/3.33 (addition(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(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(c(X0!2), X1!1)), multiplication(X0!2, X1!1))),
% 4.81/3.33 inference(unit_resolution,[status(thm)],[459, 162])).
% 4.81/3.33 tff(461,plain,
% 4.81/3.33 (addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(c(X0!2), X1!1)), multiplication(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(X0!2, X1!1)))),
% 4.81/3.33 inference(symmetry,[status(thm)],[460])).
% 4.81/3.33 tff(462,plain,
% 4.81/3.33 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!2, X1!1), addition(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), X1!1)), multiplication(X0!2, X1!1)))),
% 4.81/3.33 inference(quant_inst,[status(thm)],[])).
% 4.81/3.33 tff(463,plain,
% 4.81/3.33 (addition(multiplication(X0!2, X1!1), addition(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), X1!1)), multiplication(X0!2, X1!1))),
% 4.81/3.33 inference(unit_resolution,[status(thm)],[462, 122])).
% 4.81/3.33 tff(464,plain,
% 4.81/3.33 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X0!2, X1!1), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(X0!2, X1!1), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), multiplication(c(X0!2), X1!1)))),
% 4.81/3.33 inference(quant_inst,[status(thm)],[])).
% 4.81/3.33 tff(465,plain,
% 4.81/3.33 (addition(multiplication(X0!2, X1!1), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(X0!2, X1!1), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), multiplication(c(X0!2), X1!1))),
% 4.81/3.33 inference(unit_resolution,[status(thm)],[464, 162])).
% 4.81/3.33 tff(466,plain,
% 4.81/3.33 (addition(addition(multiplication(X0!2, X1!1), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), multiplication(c(X0!2), X1!1)) = addition(multiplication(X0!2, X1!1), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), multiplication(c(X0!2), X1!1)))),
% 4.81/3.33 inference(symmetry,[status(thm)],[465])).
% 4.81/3.33 tff(467,plain,
% 4.81/3.33 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 4.81/3.33 inference(quant_inst,[status(thm)],[])).
% 4.81/3.33 tff(468,plain,
% 4.81/3.33 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 4.81/3.33 inference(unit_resolution,[status(thm)],[467, 122])).
% 4.81/3.33 tff(469,plain,
% 4.81/3.33 (addition(multiplication(X0!2, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))),
% 4.81/3.33 inference(symmetry,[status(thm)],[468])).
% 4.81/3.33 tff(470,plain,
% 4.81/3.33 (addition(multiplication(X0!2, X1!1), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(multiplication(X0!2, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 4.81/3.33 inference(monotonicity,[status(thm)],[190])).
% 4.81/3.33 tff(471,plain,
% 4.81/3.33 (addition(multiplication(X0!2, X1!1), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))),
% 4.81/3.33 inference(transitivity,[status(thm)],[470, 469])).
% 4.81/3.33 tff(472,plain,
% 4.81/3.33 (addition(addition(multiplication(X0!2, X1!1), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), 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))),
% 4.81/3.33 inference(monotonicity,[status(thm)],[471])).
% 4.81/3.33 tff(473,plain,
% 4.81/3.33 (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(multiplication(X0!2, X1!1), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), multiplication(c(X0!2), X1!1))),
% 4.81/3.33 inference(symmetry,[status(thm)],[472])).
% 4.81/3.33 tff(474,plain,
% 4.81/3.33 (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(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.81/3.33 inference(transitivity,[status(thm)],[473, 466, 463, 461])).
% 4.81/3.33 tff(475,plain,
% 4.81/3.33 (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)), tptp_fun_X1_0(X1!1)) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))), tptp_fun_X1_0(X1!1))),
% 4.81/3.33 inference(monotonicity,[status(thm)],[474])).
% 4.81/3.33 tff(476,plain,
% 4.81/3.33 (addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))), tptp_fun_X1_0(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)), tptp_fun_X1_0(X1!1))),
% 4.81/3.33 inference(symmetry,[status(thm)],[475])).
% 4.81/3.33 tff(477,plain,
% 4.81/3.33 ((~![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), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1))) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))), tptp_fun_X1_0(X1!1)))),
% 4.81/3.33 inference(quant_inst,[status(thm)],[])).
% 4.81/3.33 tff(478,plain,
% 4.81/3.33 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1))) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))), tptp_fun_X1_0(X1!1))),
% 4.81/3.33 inference(unit_resolution,[status(thm)],[477, 162])).
% 4.81/3.33 tff(479,plain,
% 4.81/3.33 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1)) = one),
% 4.81/3.33 inference(transitivity,[status(thm)],[145, 53])).
% 4.81/3.33 tff(480,plain,
% 4.81/3.33 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1))) = addition(X0!2, one)),
% 4.81/3.33 inference(monotonicity,[status(thm)],[268, 479])).
% 4.81/3.33 tff(481,plain,
% 4.81/3.33 (addition(X0!2, one) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X1!1)))),
% 4.81/3.33 inference(symmetry,[status(thm)],[480])).
% 4.81/3.33 tff(482,plain,
% 4.81/3.33 (tptp_fun_X1_0(X0!2) = addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 4.81/3.33 inference(transitivity,[status(thm)],[430, 429, 221, 428])).
% 4.81/3.33 tff(483,plain,
% 4.81/3.33 (addition(tptp_fun_X1_0(X0!2), one) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one)),
% 4.81/3.33 inference(monotonicity,[status(thm)],[482])).
% 4.81/3.33 tff(484,plain,
% 4.81/3.33 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one) = addition(tptp_fun_X1_0(X0!2), one)),
% 4.81/3.33 inference(symmetry,[status(thm)],[483])).
% 4.81/3.33 tff(485,plain,
% 4.81/3.33 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), tptp_fun_X1_0(X0!2)), 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(tptp_fun_X1_0(X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))),
% 4.81/3.33 inference(symmetry,[status(thm)],[359])).
% 4.81/3.33 tff(486,plain,
% 4.81/3.33 (one = addition(tptp_fun_X1_0(X0!2), one)),
% 4.81/3.33 inference(transitivity,[status(thm)],[78, 124, 356, 485, 362, 484])).
% 4.81/3.33 tff(487,plain,
% 4.81/3.33 (addition(X0!2, one) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(tptp_fun_X1_0(X0!2), one))),
% 4.81/3.33 inference(monotonicity,[status(thm)],[274, 486])).
% 4.81/3.33 tff(488,plain,
% 4.81/3.33 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(tptp_fun_X1_0(X0!2), one)) = addition(X0!2, one)),
% 4.81/3.33 inference(symmetry,[status(thm)],[487])).
% 4.81/3.33 tff(489,plain,
% 4.81/3.33 ((~![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(tptp_fun_X1_0(X0!2), one)) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), tptp_fun_X1_0(X0!2)), one))),
% 4.81/3.33 inference(quant_inst,[status(thm)],[])).
% 4.81/3.33 tff(490,plain,
% 4.81/3.33 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(tptp_fun_X1_0(X0!2), one)) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), tptp_fun_X1_0(X0!2)), one)),
% 4.81/3.33 inference(unit_resolution,[status(thm)],[489, 162])).
% 4.81/3.33 tff(491,plain,
% 4.81/3.33 (addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), tptp_fun_X1_0(X0!2)), one) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(tptp_fun_X1_0(X0!2), one))),
% 4.81/3.33 inference(symmetry,[status(thm)],[490])).
% 4.81/3.33 tff(492,plain,
% 4.81/3.33 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), tptp_fun_X1_0(X0!2)) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 4.81/3.33 inference(monotonicity,[status(thm)],[268])).
% 4.81/3.33 tff(493,plain,
% 4.81/3.33 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, 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))))),
% 4.81/3.33 inference(transitivity,[status(thm)],[492, 270])).
% 4.81/3.33 tff(494,plain,
% 4.81/3.33 (addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), tptp_fun_X1_0(X0!2)), one) = addition(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)))), one)),
% 4.81/3.33 inference(monotonicity,[status(thm)],[493])).
% 4.81/3.33 tff(495,plain,
% 4.81/3.33 (addition(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)))), one) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), tptp_fun_X1_0(X0!2)), one)),
% 4.81/3.33 inference(symmetry,[status(thm)],[494])).
% 4.81/3.33 tff(496,plain,
% 4.81/3.33 (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)))) = one),
% 4.81/3.33 inference(transitivity,[status(thm)],[269, 77])).
% 4.81/3.33 tff(497,plain,
% 4.81/3.33 (addition(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)))), one) = addition(one, one)),
% 4.81/3.33 inference(monotonicity,[status(thm)],[496])).
% 4.81/3.33 tff(498,plain,
% 4.81/3.33 (addition(one, one) = addition(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)))), one)),
% 4.81/3.33 inference(symmetry,[status(thm)],[497])).
% 4.81/3.33 tff(499,plain,
% 4.81/3.33 (one = addition(one, one)),
% 4.81/3.33 inference(symmetry,[status(thm)],[282])).
% 4.81/3.33 tff(500,plain,
% 4.81/3.33 (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)), tptp_fun_X1_0(X1!1))),
% 4.81/3.33 inference(transitivity,[status(thm)],[499, 498, 495, 491, 488, 481, 478, 476])).
% 4.81/3.33 tff(501,plain,
% 4.81/3.33 (addition(multiplication(c(X0!2), c(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)), tptp_fun_X1_0(X1!1)))),
% 4.81/3.33 inference(monotonicity,[status(thm)],[500])).
% 4.81/3.33 tff(502,plain,
% 4.81/3.33 (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)), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), one)),
% 4.81/3.33 inference(symmetry,[status(thm)],[501])).
% 4.81/3.33 tff(503,plain,
% 4.81/3.33 ((~![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)), tptp_fun_X1_0(X1!1))) = 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))), tptp_fun_X1_0(X1!1)))),
% 4.81/3.33 inference(quant_inst,[status(thm)],[])).
% 4.81/3.33 tff(504,plain,
% 4.81/3.33 (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)), tptp_fun_X1_0(X1!1))) = 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))), tptp_fun_X1_0(X1!1))),
% 4.81/3.33 inference(unit_resolution,[status(thm)],[503, 162])).
% 4.81/3.33 tff(505,plain,
% 4.81/3.33 (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))), tptp_fun_X1_0(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)), tptp_fun_X1_0(X1!1)))),
% 4.81/3.33 inference(symmetry,[status(thm)],[504])).
% 4.81/3.33 tff(506,plain,
% 4.81/3.33 (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))), tptp_fun_X1_0(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))), tptp_fun_X1_0(X1!1))),
% 4.81/3.33 inference(monotonicity,[status(thm)],[180])).
% 4.81/3.33 tff(507,plain,
% 4.81/3.33 (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))), tptp_fun_X1_0(X1!1)) = 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))), tptp_fun_X1_0(X1!1))),
% 4.81/3.33 inference(symmetry,[status(thm)],[506])).
% 4.81/3.33 tff(508,plain,
% 4.81/3.33 ((~![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))), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(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)))))),
% 4.81/3.33 inference(quant_inst,[status(thm)],[])).
% 4.81/3.33 tff(509,plain,
% 4.81/3.33 (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))), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(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))))),
% 4.81/3.33 inference(unit_resolution,[status(thm)],[508, 122])).
% 4.81/3.33 tff(510,plain,
% 4.81/3.33 (addition(tptp_fun_X1_0(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))), tptp_fun_X1_0(X1!1))),
% 4.81/3.33 inference(symmetry,[status(thm)],[509])).
% 4.81/3.33 tff(511,plain,
% 4.81/3.33 ((~![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)))),
% 4.81/3.33 inference(quant_inst,[status(thm)],[])).
% 4.81/3.33 tff(512,plain,
% 4.81/3.33 (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))),
% 4.81/3.33 inference(unit_resolution,[status(thm)],[511, 162])).
% 4.81/3.33 tff(513,plain,
% 4.81/3.33 (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)))),
% 4.81/3.33 inference(symmetry,[status(thm)],[512])).
% 4.81/3.33 tff(514,plain,
% 4.81/3.33 (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), 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)))),
% 4.81/3.33 inference(monotonicity,[status(thm)],[513, 143])).
% 4.81/3.33 tff(515,plain,
% 4.81/3.33 (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), multiplication(X0!2, X1!1)))),
% 4.81/3.33 inference(symmetry,[status(thm)],[514])).
% 4.81/3.33 tff(516,plain,
% 4.81/3.33 ((~![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))))),
% 4.81/3.33 inference(quant_inst,[status(thm)],[])).
% 4.81/3.33 tff(517,plain,
% 4.81/3.33 (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)))),
% 4.81/3.33 inference(unit_resolution,[status(thm)],[516, 162])).
% 4.81/3.33 tff(518,plain,
% 4.81/3.33 (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)))),
% 4.81/3.33 inference(monotonicity,[status(thm)],[190])).
% 4.81/3.33 tff(519,plain,
% 4.81/3.33 (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))),
% 4.81/3.33 inference(transitivity,[status(thm)],[518, 410])).
% 4.81/3.34 tff(520,plain,
% 4.81/3.34 (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)))),
% 4.81/3.34 inference(monotonicity,[status(thm)],[519])).
% 4.81/3.34 tff(521,plain,
% 4.81/3.34 (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))))),
% 4.81/3.34 inference(symmetry,[status(thm)],[520])).
% 4.81/3.34 tff(522,plain,
% 4.81/3.34 (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(X1!1), X0!2)), multiplication(X1!1, X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 4.81/3.34 inference(transitivity,[status(thm)],[179, 521, 517, 515])).
% 4.81/3.34 tff(523,plain,
% 4.81/3.34 (addition(tptp_fun_X1_0(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(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), multiplication(X0!2, X1!1))))),
% 4.81/3.34 inference(monotonicity,[status(thm)],[522])).
% 4.81/3.34 tff(524,plain,
% 4.81/3.34 (addition(tptp_fun_X1_0(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), multiplication(X0!2, X1!1)))) = addition(tptp_fun_X1_0(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))))),
% 4.81/3.34 inference(symmetry,[status(thm)],[523])).
% 4.81/3.34 tff(525,plain,
% 4.81/3.34 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(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), multiplication(X0!2, X1!1)))) = addition(addition(tptp_fun_X1_0(X1!1), 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), multiplication(X0!2, X1!1))))),
% 4.81/3.34 inference(quant_inst,[status(thm)],[])).
% 4.81/3.34 tff(526,plain,
% 4.81/3.34 (addition(tptp_fun_X1_0(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), multiplication(X0!2, X1!1)))) = addition(addition(tptp_fun_X1_0(X1!1), 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), multiplication(X0!2, X1!1)))),
% 4.81/3.34 inference(unit_resolution,[status(thm)],[525, 162])).
% 4.81/3.34 tff(527,plain,
% 4.81/3.34 (addition(addition(tptp_fun_X1_0(X1!1), 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), multiplication(X0!2, X1!1))) = addition(tptp_fun_X1_0(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), multiplication(X0!2, X1!1))))),
% 4.81/3.34 inference(symmetry,[status(thm)],[526])).
% 4.81/3.34 tff(528,plain,
% 4.81/3.34 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), 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)))),
% 4.81/3.34 inference(monotonicity,[status(thm)],[373])).
% 4.81/3.34 tff(529,plain,
% 4.81/3.34 (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(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), X1!1)),
% 4.81/3.34 inference(symmetry,[status(thm)],[528])).
% 4.81/3.34 tff(530,plain,
% 4.81/3.34 (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)))),
% 4.81/3.34 inference(symmetry,[status(thm)],[154])).
% 4.81/3.34 tff(531,plain,
% 4.81/3.34 (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)), X1!1)),
% 4.81/3.34 inference(transitivity,[status(thm)],[530, 529])).
% 4.81/3.34 tff(532,plain,
% 4.81/3.34 (addition(addition(tptp_fun_X1_0(X1!1), 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), multiplication(X0!2, X1!1))) = addition(addition(tptp_fun_X1_0(X1!1), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2))), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), X1!1))),
% 4.81/3.34 inference(monotonicity,[status(thm)],[531])).
% 4.81/3.34 tff(533,plain,
% 4.81/3.34 (addition(addition(tptp_fun_X1_0(X1!1), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2))), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), X1!1)) = addition(addition(tptp_fun_X1_0(X1!1), 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), multiplication(X0!2, X1!1)))),
% 4.81/3.34 inference(symmetry,[status(thm)],[532])).
% 4.81/3.34 tff(534,plain,
% 4.81/3.34 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X1!1), addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), X1!1))) = addition(addition(tptp_fun_X1_0(X1!1), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2))), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), X1!1)))),
% 4.81/3.34 inference(quant_inst,[status(thm)],[])).
% 4.81/3.34 tff(535,plain,
% 4.81/3.34 (addition(tptp_fun_X1_0(X1!1), addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), X1!1))) = addition(addition(tptp_fun_X1_0(X1!1), addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2))), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), X1!1))),
% 4.81/3.34 inference(unit_resolution,[status(thm)],[534, 162])).
% 4.81/3.34 tff(536,plain,
% 4.81/3.34 (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(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))))),
% 4.81/3.34 inference(symmetry,[status(thm)],[517])).
% 4.81/3.34 tff(537,plain,
% 4.81/3.34 (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)))),
% 4.81/3.34 inference(monotonicity,[status(thm)],[143])).
% 4.81/3.34 tff(538,plain,
% 4.81/3.34 (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(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)))),
% 4.81/3.34 inference(transitivity,[status(thm)],[537, 536, 520, 180])).
% 4.81/3.34 tff(539,plain,
% 4.81/3.34 (addition(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))), 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))), X1!1)),
% 4.81/3.34 inference(monotonicity,[status(thm)],[538])).
% 4.81/3.34 tff(540,plain,
% 4.81/3.34 ((~![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)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), X1!1)) = addition(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))), X1!1))),
% 4.81/3.34 inference(quant_inst,[status(thm)],[])).
% 4.81/3.34 tff(541,plain,
% 4.81/3.34 (addition(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), X1!1), multiplication(X0!2, X1!1)), X1!1)) = addition(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))), X1!1)),
% 4.81/3.34 inference(unit_resolution,[status(thm)],[540, 162])).
% 4.81/3.34 tff(542,plain,
% 4.81/3.34 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), X1!1)) = addition(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), X1!1), multiplication(X0!2, X1!1)), X1!1))),
% 4.81/3.34 inference(monotonicity,[status(thm)],[513])).
% 4.81/3.34 tff(543,plain,
% 4.81/3.34 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), 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))), X1!1)),
% 4.81/3.34 inference(transitivity,[status(thm)],[542, 541, 539])).
% 4.81/3.34 tff(544,plain,
% 4.81/3.34 (addition(tptp_fun_X1_0(X1!1), addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), X1!1))) = addition(tptp_fun_X1_0(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))), X1!1))),
% 4.81/3.34 inference(monotonicity,[status(thm)],[543])).
% 4.81/3.34 tff(545,plain,
% 4.81/3.34 (addition(tptp_fun_X1_0(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))), X1!1)) = addition(tptp_fun_X1_0(X1!1), addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)), addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), X1!1)))),
% 4.81/3.34 inference(symmetry,[status(thm)],[544])).
% 4.81/3.34 tff(546,plain,
% 4.81/3.34 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(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))), X1!1), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(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))), X1!1)))),
% 4.81/3.34 inference(quant_inst,[status(thm)],[])).
% 4.81/3.34 tff(547,plain,
% 4.81/3.34 (addition(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))), X1!1), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(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))), X1!1))),
% 4.81/3.34 inference(unit_resolution,[status(thm)],[546, 122])).
% 4.81/3.34 tff(548,plain,
% 4.81/3.34 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (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(X1!1, tptp_fun_X1_0(X1!1))) = addition(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))), X1!1), tptp_fun_X1_0(X1!1)))),
% 4.81/3.34 inference(quant_inst,[status(thm)],[])).
% 4.81/3.34 tff(549,plain,
% 4.81/3.34 (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(X1!1, tptp_fun_X1_0(X1!1))) = addition(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))), X1!1), tptp_fun_X1_0(X1!1))),
% 4.81/3.34 inference(unit_resolution,[status(thm)],[548, 162])).
% 4.81/3.34 tff(550,plain,
% 4.81/3.34 (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(X1!1, tptp_fun_X1_0(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)),
% 4.81/3.34 inference(monotonicity,[status(thm)],[53])).
% 4.81/3.34 tff(551,plain,
% 4.81/3.34 (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(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(X1!1, tptp_fun_X1_0(X1!1)))),
% 4.81/3.34 inference(symmetry,[status(thm)],[550])).
% 4.81/3.34 tff(552,plain,
% 4.81/3.34 (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)),
% 4.81/3.34 inference(symmetry,[status(thm)],[294])).
% 4.81/3.34 tff(553,plain,
% 4.81/3.34 (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))))),
% 4.81/3.34 inference(symmetry,[status(thm)],[292])).
% 4.81/3.34 tff(554,plain,
% 4.81/3.34 (addition(addition(one, one), addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1))) = addition(one, addition(one, addition(multiplication(multiplication(c(X1!1), X0!2), X1!1), multiplication(multiplication(X1!1, X0!2), X1!1))))),
% 4.81/3.34 inference(symmetry,[status(thm)],[285])).
% 4.81/3.34 tff(555,plain,
% 4.81/3.34 (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)))),
% 4.81/3.34 inference(symmetry,[status(thm)],[283])).
% 4.81/3.34 tff(556,plain,
% 4.81/3.34 (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),
% 4.81/3.34 inference(transitivity,[status(thm)],[179, 290, 186, 289, 194, 288, 555, 554, 553, 552, 551, 549, 547, 545, 535, 533, 527, 524, 510, 507, 505, 502, 458, 456, 443, 440, 379, 368, 365, 363, 359, 357, 298, 77])).
% 4.81/3.34 tff(557,plain,
% 4.81/3.34 (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),
% 4.81/3.34 inference(modus_ponens,[status(thm)],[556, 297])).
% 4.81/3.34 tff(558,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)).
% 4.81/3.34 tff(559,plain,
% 4.81/3.34 ((~(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))),
% 4.81/3.34 inference(tautology,[status(thm)],[])).
% 4.81/3.34 tff(560,plain,
% 4.81/3.34 ((~(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))),
% 4.81/3.34 inference(unit_resolution,[status(thm)],[559, 558])).
% 4.81/3.34 tff(561,plain,
% 4.81/3.34 (~(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)),
% 4.81/3.34 inference(unit_resolution,[status(thm)],[560, 177])).
% 4.81/3.34 tff(562,plain,
% 4.81/3.34 ($false),
% 4.81/3.34 inference(unit_resolution,[status(thm)],[561, 557])).
% 4.81/3.34 tff(563,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,[]))).
% 4.81/3.35 tff(564,plain,
% 4.81/3.35 ((~(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)),
% 4.81/3.35 inference(tautology,[status(thm)],[])).
% 4.81/3.35 tff(565,plain,
% 4.81/3.35 ((~(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)),
% 4.81/3.35 inference(unit_resolution,[status(thm)],[564, 563])).
% 4.81/3.35 tff(566,plain,
% 4.81/3.35 (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),
% 4.81/3.35 inference(unit_resolution,[status(thm)],[565, 177])).
% 4.81/3.35 tff(567,plain,
% 4.81/3.35 (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)))),
% 4.81/3.35 inference(transitivity,[status(thm)],[187, 184, 180])).
% 4.81/3.35 tff(568,plain,
% 4.81/3.35 (addition(one, 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(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))))),
% 4.81/3.35 inference(monotonicity,[status(thm)],[567])).
% 4.81/3.35 tff(569,plain,
% 4.81/3.35 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, 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(one, 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))))),
% 4.81/3.35 inference(quant_inst,[status(thm)],[])).
% 4.81/3.35 tff(570,plain,
% 4.81/3.35 (addition(one, 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(one, 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)))),
% 4.81/3.35 inference(unit_resolution,[status(thm)],[569, 162])).
% 4.81/3.35 tff(571,plain,
% 4.81/3.35 (addition(addition(one, 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(one, 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))))),
% 4.81/3.35 inference(symmetry,[status(thm)],[570])).
% 4.81/3.35 tff(572,plain,
% 4.81/3.35 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), one)),
% 4.81/3.35 inference(symmetry,[status(thm)],[424])).
% 4.81/3.35 tff(573,plain,
% 4.81/3.35 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X0!2), addition(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(addition(tptp_fun_X1_0(X0!2), 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)))))),
% 4.81/3.35 inference(quant_inst,[status(thm)],[])).
% 4.81/3.35 tff(574,plain,
% 4.81/3.35 (addition(tptp_fun_X1_0(X0!2), addition(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(addition(tptp_fun_X1_0(X0!2), 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))))),
% 4.81/3.35 inference(unit_resolution,[status(thm)],[573, 162])).
% 4.81/3.35 tff(575,plain,
% 4.81/3.35 (addition(addition(tptp_fun_X1_0(X0!2), 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(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)))))),
% 4.81/3.35 inference(symmetry,[status(thm)],[574])).
% 4.81/3.35 tff(576,plain,
% 4.81/3.35 (addition(tptp_fun_X1_0(X0!2), X0!2) = one),
% 4.81/3.35 inference(transitivity,[status(thm)],[298, 77])).
% 4.81/3.35 tff(577,plain,
% 4.81/3.35 (addition(addition(tptp_fun_X1_0(X0!2), 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(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))))),
% 4.81/3.35 inference(monotonicity,[status(thm)],[576])).
% 4.81/3.35 tff(578,plain,
% 4.81/3.35 (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(tptp_fun_X1_0(X0!2), 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))))),
% 4.81/3.35 inference(symmetry,[status(thm)],[577])).
% 4.81/3.35 tff(579,plain,
% 4.81/3.35 (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)),
% 4.81/3.35 inference(symmetry,[status(thm)],[566])).
% 4.81/3.35 tff(580,plain,
% 4.81/3.35 (one = addition(tptp_fun_X1_0(X0!2), addition(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)))))),
% 4.81/3.35 inference(transitivity,[status(thm)],[579, 294, 578, 575])).
% 4.81/3.35 tff(581,plain,
% 4.81/3.35 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(tptp_fun_X1_0(X0!2), addition(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))))))),
% 4.81/3.35 inference(monotonicity,[status(thm)],[199, 580])).
% 4.81/3.35 tff(582,plain,
% 4.81/3.35 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(tptp_fun_X1_0(X0!2), addition(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(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), one)),
% 4.81/3.35 inference(symmetry,[status(thm)],[581])).
% 4.81/3.35 tff(583,plain,
% 4.81/3.35 ((~![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(tptp_fun_X1_0(X0!2), addition(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(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), tptp_fun_X1_0(X0!2)), addition(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))))))),
% 4.81/3.35 inference(quant_inst,[status(thm)],[])).
% 4.81/3.35 tff(584,plain,
% 4.81/3.35 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(tptp_fun_X1_0(X0!2), addition(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(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), tptp_fun_X1_0(X0!2)), addition(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)))))),
% 4.81/3.35 inference(unit_resolution,[status(thm)],[583, 162])).
% 4.81/3.35 tff(585,plain,
% 4.81/3.35 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), tptp_fun_X1_0(X0!2)), addition(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(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(tptp_fun_X1_0(X0!2), addition(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))))))),
% 4.81/3.35 inference(symmetry,[status(thm)],[584])).
% 4.81/3.35 tff(586,plain,
% 4.81/3.35 (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))), X0!2) = 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(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.81/3.35 inference(monotonicity,[status(thm)],[274])).
% 4.81/3.35 tff(587,plain,
% 4.81/3.35 (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(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = 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))), X0!2)),
% 4.81/3.35 inference(symmetry,[status(thm)],[586])).
% 4.81/3.35 tff(588,plain,
% 4.81/3.35 ((~![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))), 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(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)))))),
% 4.81/3.35 inference(quant_inst,[status(thm)],[])).
% 4.81/3.35 tff(589,plain,
% 4.81/3.35 (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(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(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))))),
% 4.81/3.35 inference(unit_resolution,[status(thm)],[588, 122])).
% 4.81/3.35 tff(590,plain,
% 4.81/3.35 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, 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(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(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.81/3.35 inference(symmetry,[status(thm)],[589])).
% 4.81/3.35 tff(591,plain,
% 4.81/3.35 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, 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(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))))),
% 4.81/3.35 inference(monotonicity,[status(thm)],[268])).
% 4.81/3.35 tff(592,plain,
% 4.81/3.35 (addition(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(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, 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))))),
% 4.81/3.35 inference(symmetry,[status(thm)],[591])).
% 4.81/3.35 tff(593,plain,
% 4.81/3.35 (addition(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(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))), X0!2)),
% 4.81/3.35 inference(transitivity,[status(thm)],[592, 590, 587])).
% 4.81/3.35 tff(594,plain,
% 4.81/3.35 (addition(c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))), c(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))) = c(multiplication(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))),
% 4.81/3.35 inference(symmetry,[status(thm)],[333])).
% 4.81/3.35 tff(595,plain,
% 4.81/3.35 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), tptp_fun_X1_0(X0!2)) = tptp_fun_X1_0(X0!2)),
% 4.81/3.35 inference(transitivity,[status(thm)],[306, 594, 353, 302, 136])).
% 4.81/3.35 tff(596,plain,
% 4.81/3.35 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), tptp_fun_X1_0(X0!2)), addition(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(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))), X0!2))),
% 4.81/3.35 inference(monotonicity,[status(thm)],[595, 593])).
% 4.81/3.35 tff(597,plain,
% 4.81/3.35 (addition(tptp_fun_X1_0(X0!2), 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))), X0!2)) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), tptp_fun_X1_0(X0!2)), addition(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)))))),
% 4.81/3.35 inference(symmetry,[status(thm)],[596])).
% 4.81/3.35 tff(598,plain,
% 4.81/3.35 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(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))), X0!2), tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), 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))), X0!2)))),
% 4.81/3.35 inference(quant_inst,[status(thm)],[])).
% 4.81/3.35 tff(599,plain,
% 4.81/3.35 (addition(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))), X0!2), tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), 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))), X0!2))),
% 4.81/3.35 inference(unit_resolution,[status(thm)],[598, 122])).
% 4.81/3.35 tff(600,plain,
% 4.81/3.35 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (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(X0!2, tptp_fun_X1_0(X0!2))) = addition(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))), X0!2), tptp_fun_X1_0(X0!2)))),
% 4.81/3.35 inference(quant_inst,[status(thm)],[])).
% 4.81/3.35 tff(601,plain,
% 4.81/3.35 (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(X0!2, tptp_fun_X1_0(X0!2))) = addition(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))), X0!2), tptp_fun_X1_0(X0!2))),
% 4.81/3.35 inference(unit_resolution,[status(thm)],[600, 162])).
% 4.81/3.35 tff(602,plain,
% 4.81/3.35 (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(X0!2, tptp_fun_X1_0(X0!2))) = 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)),
% 4.81/3.35 inference(monotonicity,[status(thm)],[77])).
% 4.81/3.35 tff(603,plain,
% 4.81/3.35 (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(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(X0!2, tptp_fun_X1_0(X0!2)))),
% 4.81/3.35 inference(symmetry,[status(thm)],[602])).
% 4.81/3.35 tff(604,plain,
% 4.81/3.35 (one = addition(one, addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))),
% 4.81/3.35 inference(transitivity,[status(thm)],[579, 603, 601, 599, 597, 585, 582, 572, 426])).
% 4.81/3.35 tff(605,plain,
% 4.81/3.35 (addition(one, addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))) = addition(addition(one, 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)))),
% 4.81/3.35 inference(monotonicity,[status(thm)],[604])).
% 4.81/3.35 tff(606,plain,
% 4.81/3.35 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), tptp_fun_X1_0(X0!2)) = one),
% 4.81/3.35 inference(transitivity,[status(thm)],[492, 77])).
% 4.81/3.35 tff(607,plain,
% 4.81/3.35 (addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), tptp_fun_X1_0(X0!2)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))) = addition(one, addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))),
% 4.81/3.35 inference(monotonicity,[status(thm)],[606])).
% 4.81/3.35 tff(608,plain,
% 4.81/3.35 ((~![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(tptp_fun_X1_0(X0!2), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), tptp_fun_X1_0(X0!2)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))))),
% 4.81/3.35 inference(quant_inst,[status(thm)],[])).
% 4.81/3.35 tff(609,plain,
% 4.81/3.35 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(tptp_fun_X1_0(X0!2), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), tptp_fun_X1_0(X0!2)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))),
% 4.81/3.35 inference(unit_resolution,[status(thm)],[608, 162])).
% 4.81/3.35 tff(610,plain,
% 4.81/3.35 (addition(tptp_fun_X1_0(X0!2), 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)))),
% 4.81/3.35 inference(monotonicity,[status(thm)],[431])).
% 4.81/3.35 tff(611,plain,
% 4.81/3.35 (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(tptp_fun_X1_0(X0!2), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))),
% 4.81/3.35 inference(symmetry,[status(thm)],[610])).
% 4.81/3.35 tff(612,plain,
% 4.81/3.35 (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(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))),
% 4.81/3.36 inference(transitivity,[status(thm)],[179, 290, 186, 611])).
% 4.81/3.36 tff(613,plain,
% 4.81/3.36 (addition(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(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(tptp_fun_X1_0(X0!2), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))))),
% 4.81/3.36 inference(monotonicity,[status(thm)],[274, 612])).
% 4.81/3.36 tff(614,plain,
% 4.81/3.36 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, 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)))) = one),
% 4.81/3.36 inference(transitivity,[status(thm)],[591, 613, 609, 607, 605, 571, 568, 552, 566])).
% 4.81/3.36 tff(615,plain,
% 4.81/3.36 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, 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(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), one)),
% 4.81/3.36 inference(monotonicity,[status(thm)],[614])).
% 4.81/3.36 tff(616,plain,
% 4.81/3.36 ((~![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(X1!1), X0!2), multiplication(X1!1, 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(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, 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)))))),
% 4.81/3.36 inference(quant_inst,[status(thm)],[])).
% 4.81/3.36 tff(617,plain,
% 4.81/3.36 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, 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(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, 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))))),
% 4.81/3.36 inference(unit_resolution,[status(thm)],[616, 162])).
% 4.81/3.36 tff(618,plain,
% 4.81/3.36 (addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, 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(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, 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)))))),
% 4.81/3.36 inference(symmetry,[status(thm)],[617])).
% 4.81/3.36 tff(619,plain,
% 4.81/3.36 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.81/3.36 inference(monotonicity,[status(thm)],[143])).
% 4.81/3.36 tff(620,plain,
% 4.81/3.36 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.81/3.36 inference(symmetry,[status(thm)],[619])).
% 4.81/3.36 tff(621,plain,
% 4.81/3.36 ((~![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(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))))),
% 4.81/3.36 inference(quant_inst,[status(thm)],[])).
% 4.81/3.36 tff(622,plain,
% 4.81/3.36 (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(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.81/3.36 inference(unit_resolution,[status(thm)],[621, 122])).
% 4.81/3.36 tff(623,plain,
% 4.81/3.36 (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(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 4.81/3.36 inference(symmetry,[status(thm)],[518])).
% 4.81/3.36 tff(624,plain,
% 4.81/3.36 (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(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 4.81/3.36 inference(symmetry,[status(thm)],[410])).
% 4.81/3.36 tff(625,plain,
% 4.81/3.36 (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(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 4.81/3.36 inference(transitivity,[status(thm)],[624, 623, 622, 620])).
% 4.81/3.36 tff(626,plain,
% 4.81/3.36 (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)), 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), X1!1), multiplication(X0!2, X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, 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))))),
% 4.81/3.36 inference(monotonicity,[status(thm)],[625])).
% 4.81/3.36 tff(627,plain,
% 4.81/3.36 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(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))))),
% 4.81/3.36 inference(quant_inst,[status(thm)],[])).
% 4.81/3.36 tff(628,plain,
% 4.81/3.36 (addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(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)))),
% 4.81/3.36 inference(unit_resolution,[status(thm)],[627, 162])).
% 4.81/3.36 tff(629,plain,
% 4.81/3.36 (addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), 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)), tptp_fun_X1_0(X0!2))),
% 4.81/3.36 inference(monotonicity,[status(thm)],[257])).
% 4.81/3.36 tff(630,plain,
% 4.81/3.36 (addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X0!2)) = addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 4.81/3.36 inference(symmetry,[status(thm)],[629])).
% 4.81/3.36 tff(631,plain,
% 4.81/3.36 (addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X0!2)) = addition(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)), tptp_fun_X1_0(X0!2)))),
% 4.81/3.36 inference(monotonicity,[status(thm)],[355])).
% 4.81/3.36 tff(632,plain,
% 4.81/3.36 (addition(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)), tptp_fun_X1_0(X0!2))) = addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), tptp_fun_X1_0(X0!2))),
% 4.81/3.36 inference(symmetry,[status(thm)],[631])).
% 4.81/3.36 tff(633,plain,
% 4.81/3.36 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(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)), 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)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))), tptp_fun_X1_0(X0!2)))),
% 4.81/3.36 inference(quant_inst,[status(thm)],[])).
% 4.81/3.36 tff(634,plain,
% 4.81/3.36 (addition(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)), 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)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))), tptp_fun_X1_0(X0!2))),
% 4.81/3.36 inference(unit_resolution,[status(thm)],[633, 162])).
% 4.81/3.36 tff(635,plain,
% 4.81/3.36 (addition(addition(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)), multiplication(c(X0!2), X1!1))), tptp_fun_X1_0(X0!2)) = addition(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)), tptp_fun_X1_0(X0!2)))),
% 4.81/3.36 inference(symmetry,[status(thm)],[634])).
% 4.81/3.36 tff(636,plain,
% 4.81/3.36 (addition(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))), 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)))),
% 4.81/3.36 inference(monotonicity,[status(thm)],[183])).
% 4.81/3.36 tff(637,plain,
% 4.81/3.36 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(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), c(X1!1)))) = addition(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))), multiplication(c(X0!2), c(X1!1))))),
% 4.81/3.36 inference(quant_inst,[status(thm)],[])).
% 4.81/3.36 tff(638,plain,
% 4.81/3.36 (addition(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), c(X1!1)))) = addition(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))), multiplication(c(X0!2), c(X1!1)))),
% 4.81/3.36 inference(unit_resolution,[status(thm)],[637, 162])).
% 4.81/3.36 tff(639,plain,
% 4.81/3.36 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(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), 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), c(X1!1))), multiplication(c(X0!2), X1!1)))),
% 4.81/3.36 inference(quant_inst,[status(thm)],[])).
% 4.81/3.36 tff(640,plain,
% 4.81/3.36 (addition(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), 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), c(X1!1))), multiplication(c(X0!2), X1!1))),
% 4.81/3.36 inference(unit_resolution,[status(thm)],[639, 122])).
% 4.81/3.36 tff(641,plain,
% 4.81/3.36 (addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(c(X0!2), X1!1)) = addition(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), c(X1!1))))),
% 4.81/3.36 inference(symmetry,[status(thm)],[640])).
% 4.81/3.36 tff(642,plain,
% 4.81/3.36 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(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)), 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), c(X1!1))), multiplication(c(X0!2), X1!1)))),
% 4.81/3.36 inference(quant_inst,[status(thm)],[])).
% 4.81/3.36 tff(643,plain,
% 4.81/3.36 (addition(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)), 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), c(X1!1))), multiplication(c(X0!2), X1!1))),
% 4.81/3.36 inference(unit_resolution,[status(thm)],[642, 162])).
% 4.81/3.36 tff(644,plain,
% 4.81/3.36 (addition(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)), 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)))),
% 4.81/3.36 inference(transitivity,[status(thm)],[643, 641, 638, 636])).
% 4.81/3.36 tff(645,plain,
% 4.81/3.36 (addition(addition(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)), multiplication(c(X0!2), X1!1))), tptp_fun_X1_0(X0!2)) = 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))), tptp_fun_X1_0(X0!2))),
% 4.81/3.36 inference(monotonicity,[status(thm)],[644])).
% 4.81/3.36 tff(646,plain,
% 4.81/3.36 (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))), 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)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))), tptp_fun_X1_0(X0!2))),
% 4.81/3.36 inference(symmetry,[status(thm)],[645])).
% 4.81/3.36 tff(647,plain,
% 4.81/3.36 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (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)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2))) = 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))), tptp_fun_X1_0(X0!2)))),
% 4.81/3.36 inference(quant_inst,[status(thm)],[])).
% 4.81/3.36 tff(648,plain,
% 4.81/3.36 (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)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2))) = 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))), tptp_fun_X1_0(X0!2))),
% 4.81/3.36 inference(unit_resolution,[status(thm)],[647, 162])).
% 4.81/3.36 tff(649,plain,
% 4.81/3.36 (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)), addition(multiplication(c(X0!2), c(X1!1)), 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)))),
% 4.81/3.36 inference(transitivity,[status(thm)],[648, 646, 635, 632, 630, 628])).
% 4.81/3.36 tff(650,plain,
% 4.81/3.36 (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)), 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)), addition(multiplication(c(X0!2), c(X1!1)), 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)), 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))))),
% 4.81/3.36 inference(monotonicity,[status(thm)],[649])).
% 4.81/3.36 tff(651,plain,
% 4.81/3.36 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (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)), 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)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)))) = 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)), 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)), tptp_fun_X1_0(X0!2))))),
% 4.81/3.37 inference(quant_inst,[status(thm)],[])).
% 4.81/3.37 tff(652,plain,
% 4.81/3.37 (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)), 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)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)))) = 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)), 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)), tptp_fun_X1_0(X0!2)))),
% 4.81/3.37 inference(unit_resolution,[status(thm)],[651, 162])).
% 4.81/3.37 tff(653,plain,
% 4.81/3.37 (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)), 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)), 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)), 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)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2))))),
% 4.81/3.37 inference(symmetry,[status(thm)],[652])).
% 4.81/3.37 tff(654,plain,
% 4.81/3.37 ((~![A: $i] : (addition(A, A) = 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)), 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(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)))),
% 4.81/3.37 inference(quant_inst,[status(thm)],[])).
% 4.81/3.37 tff(655,plain,
% 4.81/3.37 (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)), 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(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))),
% 4.81/3.37 inference(unit_resolution,[status(thm)],[654, 152])).
% 4.81/3.37 tff(656,plain,
% 4.81/3.37 (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)), 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)))),
% 4.81/3.37 inference(symmetry,[status(thm)],[655])).
% 4.81/3.37 tff(657,plain,
% 4.81/3.37 (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)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2))) = 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)), 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)), tptp_fun_X1_0(X0!2)))),
% 4.81/3.37 inference(monotonicity,[status(thm)],[656])).
% 4.81/3.37 tff(658,plain,
% 4.81/3.37 (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))), 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)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)))),
% 4.81/3.37 inference(symmetry,[status(thm)],[648])).
% 4.81/3.37 tff(659,plain,
% 4.81/3.37 (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(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 4.81/3.37 inference(symmetry,[status(thm)],[628])).
% 4.81/3.37 tff(660,plain,
% 4.81/3.37 (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),
% 4.81/3.37 inference(transitivity,[status(thm)],[659, 629, 631, 634, 645, 658, 657, 653, 650, 626, 618, 615, 168, 164, 155, 145, 53])).
% 4.81/3.37 tff(661,plain,
% 4.81/3.37 ((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)),
% 4.81/3.37 inference(commutativity,[status(thm)],[])).
% 4.81/3.37 tff(662,plain,
% 4.81/3.37 (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),
% 4.81/3.37 inference(transitivity,[status(thm)],[552, 566])).
% 4.81/3.37 tff(663,plain,
% 4.81/3.37 ((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))))),
% 4.81/3.37 inference(monotonicity,[status(thm)],[662])).
% 4.81/3.37 tff(664,plain,
% 4.81/3.37 ((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)),
% 4.81/3.37 inference(transitivity,[status(thm)],[663, 661])).
% 4.81/3.37 tff(665,plain,
% 4.81/3.37 ((~(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))),
% 4.81/3.37 inference(monotonicity,[status(thm)],[664])).
% 4.81/3.37 tff(666,plain,
% 4.81/3.37 ((~![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)))))),
% 4.81/3.37 inference(quant_inst,[status(thm)],[])).
% 4.81/3.37 tff(667,plain,
% 4.81/3.37 (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))))),
% 4.81/3.37 inference(unit_resolution,[status(thm)],[666, 175])).
% 4.81/3.37 tff(668,plain,
% 4.81/3.37 ((~(~((~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)))),
% 4.81/3.37 inference(rewrite,[status(thm)],[])).
% 4.81/3.37 tff(669,plain,
% 4.81/3.37 ((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))))),
% 4.81/3.37 inference(rewrite,[status(thm)],[])).
% 4.81/3.37 tff(670,plain,
% 4.81/3.37 ((~(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)))))),
% 4.81/3.37 inference(monotonicity,[status(thm)],[669])).
% 4.81/3.37 tff(671,plain,
% 4.81/3.37 ((~(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)))),
% 4.81/3.37 inference(transitivity,[status(thm)],[670, 668])).
% 4.81/3.37 tff(672,plain,
% 4.81/3.37 (~(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))),
% 4.81/3.37 inference(or_elim,[status(thm)],[43])).
% 4.81/3.37 tff(673,plain,
% 4.81/3.37 ((~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))),
% 4.81/3.37 inference(modus_ponens,[status(thm)],[672, 671])).
% 4.81/3.37 tff(674,plain,
% 4.81/3.37 (~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))))),
% 4.81/3.37 inference(unit_resolution,[status(thm)],[673, 563])).
% 4.81/3.37 tff(675,plain,
% 4.81/3.37 ((~(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)))))),
% 4.81/3.37 inference(tautology,[status(thm)],[])).
% 4.81/3.37 tff(676,plain,
% 4.81/3.37 ((~(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)))))),
% 4.81/3.38 inference(unit_resolution,[status(thm)],[675, 674])).
% 4.81/3.38 tff(677,plain,
% 4.81/3.38 (~(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))))),
% 4.81/3.38 inference(unit_resolution,[status(thm)],[676, 667])).
% 4.81/3.38 tff(678,plain,
% 4.81/3.38 (~(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)),
% 4.81/3.38 inference(modus_ponens,[status(thm)],[677, 665])).
% 4.81/3.38 tff(679,plain,
% 4.81/3.38 ($false),
% 4.81/3.38 inference(unit_resolution,[status(thm)],[678, 660])).
% 4.81/3.38 % SZS output end Proof
%------------------------------------------------------------------------------