TSTP Solution File: KLE016+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE016+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 17:23:50 EDT 2022
% Result : Theorem 226.70s 145.75s
% Output : Proof 226.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE016+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 07:43:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 226.70/145.75 % SZS status Theorem
% 226.70/145.75 % SZS output start Proof
% 226.70/145.75 tff(complement_type, type, (
% 226.70/145.75 complement: ( $i * $i ) > $o)).
% 226.70/145.75 tff(multiplication_type, type, (
% 226.70/145.75 multiplication: ( $i * $i ) > $i)).
% 226.70/145.75 tff(tptp_fun_X0_2_type, type, (
% 226.70/145.75 tptp_fun_X0_2: $i)).
% 226.70/145.75 tff(tptp_fun_X1_1_type, type, (
% 226.70/145.75 tptp_fun_X1_1: $i)).
% 226.70/145.75 tff(test_type, type, (
% 226.70/145.75 test: $i > $o)).
% 226.70/145.75 tff(tptp_fun_X1_0_type, type, (
% 226.70/145.75 tptp_fun_X1_0: $i > $i)).
% 226.70/145.75 tff(addition_type, type, (
% 226.70/145.75 addition: ( $i * $i ) > $i)).
% 226.70/145.75 tff(c_type, type, (
% 226.70/145.75 c: $i > $i)).
% 226.70/145.75 tff(one_type, type, (
% 226.70/145.75 one: $i)).
% 226.70/145.75 tff(zero_type, type, (
% 226.70/145.75 zero: $i)).
% 226.70/145.75 tff(1,plain,
% 226.70/145.75 (^[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)))))))),
% 226.70/145.75 inference(bind,[status(th)],[])).
% 226.70/145.75 tff(2,plain,
% 226.70/145.75 (![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))))))),
% 226.70/145.75 inference(quant_intro,[status(thm)],[1])).
% 226.70/145.75 tff(3,plain,
% 226.70/145.75 (^[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)))))))),
% 226.70/145.75 inference(bind,[status(th)],[])).
% 226.70/145.75 tff(4,plain,
% 226.70/145.75 (![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))))))),
% 226.70/145.75 inference(quant_intro,[status(thm)],[3])).
% 226.70/145.75 tff(5,plain,
% 226.70/145.75 (![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))))))),
% 226.70/145.75 inference(transitivity,[status(thm)],[4, 2])).
% 226.70/145.75 tff(6,plain,
% 226.70/145.75 (^[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))))))))),
% 226.70/145.75 inference(bind,[status(th)],[])).
% 226.70/145.75 tff(7,plain,
% 226.70/145.75 (![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))))))),
% 226.70/145.75 inference(quant_intro,[status(thm)],[6])).
% 226.70/145.75 tff(8,plain,
% 226.70/145.75 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 226.70/145.75 inference(rewrite,[status(thm)],[])).
% 226.70/145.75 tff(9,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_1')).
% 226.70/145.75 tff(10,plain,
% 226.70/145.75 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 226.70/145.75 inference(modus_ponens,[status(thm)],[9, 8])).
% 226.70/145.75 tff(11,plain,(
% 226.70/145.75 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 226.70/145.75 inference(skolemize,[status(sab)],[10])).
% 226.70/145.75 tff(12,plain,
% 226.70/145.75 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 226.70/145.75 inference(modus_ponens,[status(thm)],[11, 7])).
% 226.70/145.75 tff(13,plain,
% 226.70/145.75 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 226.70/145.75 inference(modus_ponens,[status(thm)],[12, 5])).
% 226.70/145.75 tff(14,plain,
% 226.70/145.75 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(multiplication(X1!1, X0!2))) | complement(tptp_fun_X1_0(multiplication(X1!1, X0!2)), multiplication(X1!1, X0!2)))) | (~(test(multiplication(X1!1, X0!2)) | ![X1: $i] : (~complement(X1, multiplication(X1!1, X0!2)))))))),
% 226.70/145.75 inference(quant_inst,[status(thm)],[])).
% 226.70/145.75 tff(15,plain,
% 226.70/145.75 (~((~((~test(multiplication(X1!1, X0!2))) | complement(tptp_fun_X1_0(multiplication(X1!1, X0!2)), multiplication(X1!1, X0!2)))) | (~(test(multiplication(X1!1, X0!2)) | ![X1: $i] : (~complement(X1, multiplication(X1!1, X0!2))))))),
% 226.70/145.75 inference(unit_resolution,[status(thm)],[14, 13])).
% 226.70/145.75 tff(16,plain,
% 226.70/145.75 (((~((~test(multiplication(X1!1, X0!2))) | complement(tptp_fun_X1_0(multiplication(X1!1, X0!2)), multiplication(X1!1, X0!2)))) | (~(test(multiplication(X1!1, X0!2)) | ![X1: $i] : (~complement(X1, multiplication(X1!1, X0!2)))))) | (test(multiplication(X1!1, X0!2)) | ![X1: $i] : (~complement(X1, multiplication(X1!1, X0!2))))),
% 226.70/145.75 inference(tautology,[status(thm)],[])).
% 226.70/145.75 tff(17,plain,
% 226.70/145.75 (test(multiplication(X1!1, X0!2)) | ![X1: $i] : (~complement(X1, multiplication(X1!1, X0!2)))),
% 226.70/145.75 inference(unit_resolution,[status(thm)],[16, 15])).
% 226.70/145.75 tff(18,plain,
% 226.70/145.75 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 226.70/145.75 inference(bind,[status(th)],[])).
% 226.70/145.75 tff(19,plain,
% 226.70/145.75 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 226.70/145.75 inference(quant_intro,[status(thm)],[18])).
% 226.70/145.75 tff(20,plain,
% 226.70/145.75 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 226.70/145.75 inference(rewrite,[status(thm)],[])).
% 226.70/145.75 tff(21,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 226.70/145.75 tff(22,plain,
% 226.70/145.75 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 226.70/145.75 inference(modus_ponens,[status(thm)],[21, 20])).
% 226.70/145.75 tff(23,plain,(
% 226.70/145.75 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 226.70/145.75 inference(skolemize,[status(sab)],[22])).
% 226.70/145.75 tff(24,plain,
% 226.70/145.75 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 226.70/145.75 inference(modus_ponens,[status(thm)],[23, 19])).
% 226.70/145.75 tff(25,plain,
% 226.70/145.75 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(c(X0!2), c(X1!1)) = addition(c(X1!1), c(X0!2)))),
% 226.70/145.75 inference(quant_inst,[status(thm)],[])).
% 226.70/145.75 tff(26,plain,
% 226.70/145.75 (addition(c(X0!2), c(X1!1)) = addition(c(X1!1), c(X0!2))),
% 226.70/145.75 inference(unit_resolution,[status(thm)],[25, 24])).
% 226.70/145.75 tff(27,plain,
% 226.70/145.75 (addition(c(X1!1), c(X0!2)) = addition(c(X0!2), c(X1!1))),
% 226.70/145.75 inference(symmetry,[status(thm)],[26])).
% 226.70/145.75 tff(28,plain,
% 226.70/145.75 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 226.70/145.75 inference(bind,[status(th)],[])).
% 226.70/145.75 tff(29,plain,
% 226.70/145.75 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 226.70/145.75 inference(quant_intro,[status(thm)],[28])).
% 226.70/145.75 tff(30,plain,
% 226.70/145.75 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 226.70/145.75 inference(rewrite,[status(thm)],[])).
% 226.70/145.75 tff(31,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 226.70/145.75 tff(32,plain,
% 226.70/145.75 (![A: $i] : (multiplication(one, A) = A)),
% 226.70/145.75 inference(modus_ponens,[status(thm)],[31, 30])).
% 226.70/145.75 tff(33,plain,(
% 226.70/145.75 ![A: $i] : (multiplication(one, A) = A)),
% 226.70/145.75 inference(skolemize,[status(sab)],[32])).
% 226.70/145.75 tff(34,plain,
% 226.70/145.75 (![A: $i] : (multiplication(one, A) = A)),
% 226.70/145.75 inference(modus_ponens,[status(thm)],[33, 29])).
% 226.70/145.75 tff(35,plain,
% 226.70/145.75 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, multiplication(X1!1, X0!2)) = multiplication(X1!1, X0!2))),
% 226.70/145.75 inference(quant_inst,[status(thm)],[])).
% 226.70/145.75 tff(36,plain,
% 226.70/145.75 (multiplication(one, multiplication(X1!1, X0!2)) = multiplication(X1!1, X0!2)),
% 226.81/145.75 inference(unit_resolution,[status(thm)],[35, 34])).
% 226.81/145.75 tff(37,plain,
% 226.81/145.75 (^[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))))))),
% 226.81/145.75 inference(bind,[status(th)],[])).
% 226.81/145.75 tff(38,plain,
% 226.81/145.75 (![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)))))),
% 226.81/145.75 inference(quant_intro,[status(thm)],[37])).
% 226.81/145.75 tff(39,plain,
% 226.81/145.75 (^[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))))))),
% 226.81/145.75 inference(bind,[status(th)],[])).
% 226.81/145.75 tff(40,plain,
% 226.81/145.75 (![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)))))),
% 226.81/145.75 inference(quant_intro,[status(thm)],[39])).
% 226.81/145.75 tff(41,plain,
% 226.81/145.75 (![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)))),
% 226.81/145.75 inference(rewrite,[status(thm)],[])).
% 226.81/145.75 tff(42,plain,
% 226.81/145.75 (^[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))))),
% 226.81/145.75 inference(bind,[status(th)],[])).
% 226.81/145.75 tff(43,plain,
% 226.81/145.75 (![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)))),
% 226.81/145.75 inference(quant_intro,[status(thm)],[42])).
% 226.81/145.75 tff(44,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')).
% 226.81/145.75 tff(45,plain,
% 226.81/145.75 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 226.81/145.75 inference(modus_ponens,[status(thm)],[44, 43])).
% 226.81/145.75 tff(46,plain,
% 226.81/145.75 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 226.81/145.75 inference(modus_ponens,[status(thm)],[45, 41])).
% 226.81/145.75 tff(47,plain,(
% 226.81/145.75 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 226.81/145.75 inference(skolemize,[status(sab)],[46])).
% 226.81/145.75 tff(48,plain,
% 226.81/145.75 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 226.81/145.75 inference(modus_ponens,[status(thm)],[47, 40])).
% 226.81/145.75 tff(49,plain,
% 226.81/145.75 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 226.81/145.75 inference(modus_ponens,[status(thm)],[48, 38])).
% 226.81/145.75 tff(50,plain,
% 226.81/145.75 ((~![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)))))),
% 226.81/145.75 inference(quant_inst,[status(thm)],[])).
% 226.81/145.75 tff(51,plain,
% 226.81/145.75 (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))))),
% 226.81/145.75 inference(unit_resolution,[status(thm)],[50, 49])).
% 226.81/145.75 tff(52,plain,
% 226.81/145.75 ((~![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))))))),
% 226.81/145.75 inference(quant_inst,[status(thm)],[])).
% 226.81/145.75 tff(53,plain,
% 226.81/145.75 (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2)))))),
% 226.81/145.75 inference(unit_resolution,[status(thm)],[52, 13])).
% 226.81/145.75 tff(54,plain,
% 226.81/145.75 (((~((~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))),
% 226.81/145.75 inference(tautology,[status(thm)],[])).
% 226.81/145.75 tff(55,plain,
% 226.81/145.75 ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 226.81/145.75 inference(unit_resolution,[status(thm)],[54, 53])).
% 226.81/145.75 tff(56,plain,
% 226.81/145.75 ((~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))))),
% 226.81/145.75 inference(rewrite,[status(thm)],[])).
% 226.81/145.75 tff(57,plain,
% 226.81/145.75 ((~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))))),
% 226.81/145.75 inference(rewrite,[status(thm)],[])).
% 226.81/145.75 tff(58,axiom,(~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 226.81/145.75 tff(59,plain,
% 226.81/145.75 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 226.81/145.75 inference(modus_ponens,[status(thm)],[58, 57])).
% 226.81/145.75 tff(60,plain,
% 226.81/145.75 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 226.81/145.75 inference(modus_ponens,[status(thm)],[59, 56])).
% 226.81/145.75 tff(61,plain,
% 226.81/145.75 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 226.81/145.75 inference(modus_ponens,[status(thm)],[60, 56])).
% 226.81/145.75 tff(62,plain,
% 226.81/145.75 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 226.81/145.75 inference(modus_ponens,[status(thm)],[61, 56])).
% 226.81/145.75 tff(63,plain,
% 226.81/145.75 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 226.81/145.75 inference(modus_ponens,[status(thm)],[62, 56])).
% 226.81/145.75 tff(64,plain,
% 226.81/145.75 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 226.81/145.75 inference(modus_ponens,[status(thm)],[63, 56])).
% 226.81/145.75 tff(65,plain,
% 226.81/145.75 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 226.81/145.75 inference(modus_ponens,[status(thm)],[64, 56])).
% 226.81/145.75 tff(66,plain,(
% 226.81/145.75 ~((~(test(X1!1) & test(X0!2))) | (c(multiplication(X0!2, X1!1)) = addition(c(X0!2), c(X1!1))))),
% 226.81/145.75 inference(skolemize,[status(sab)],[65])).
% 226.81/145.75 tff(67,plain,
% 226.81/145.75 (test(X1!1) & test(X0!2)),
% 226.81/145.75 inference(or_elim,[status(thm)],[66])).
% 226.81/145.75 tff(68,plain,
% 226.81/145.75 (test(X0!2)),
% 226.81/145.75 inference(and_elim,[status(thm)],[67])).
% 226.81/145.75 tff(69,plain,
% 226.81/145.75 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 226.81/145.75 inference(tautology,[status(thm)],[])).
% 226.81/145.75 tff(70,plain,
% 226.81/145.75 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 226.81/145.75 inference(unit_resolution,[status(thm)],[69, 68])).
% 226.81/145.75 tff(71,plain,
% 226.81/145.75 (complement(tptp_fun_X1_0(X0!2), X0!2)),
% 226.81/145.75 inference(unit_resolution,[status(thm)],[70, 55])).
% 226.81/145.75 tff(72,plain,
% 226.81/145.75 ((~(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))))),
% 226.81/145.75 inference(tautology,[status(thm)],[])).
% 226.81/145.75 tff(73,plain,
% 226.81/145.75 ((~(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))))),
% 226.81/145.75 inference(unit_resolution,[status(thm)],[72, 71])).
% 226.81/145.75 tff(74,plain,
% 226.81/145.75 (~((~(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)))),
% 226.81/145.75 inference(unit_resolution,[status(thm)],[73, 51])).
% 226.81/145.75 tff(75,plain,
% 226.81/145.75 (((~(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)),
% 226.81/145.75 inference(tautology,[status(thm)],[])).
% 226.81/145.75 tff(76,plain,
% 226.81/145.75 (addition(X0!2, tptp_fun_X1_0(X0!2)) = one),
% 226.81/145.75 inference(unit_resolution,[status(thm)],[75, 74])).
% 226.81/145.75 tff(77,assumption,((~((~test(tptp_fun_X1_0(X0!2))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))) | (~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))))), introduced(assumption)).
% 226.81/145.75 tff(78,plain,
% 226.81/145.75 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(tptp_fun_X1_0(X0!2))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))) | (~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))))))),
% 226.81/145.75 inference(quant_inst,[status(thm)],[])).
% 226.81/145.75 tff(79,plain,
% 226.81/145.75 ($false),
% 226.81/145.75 inference(unit_resolution,[status(thm)],[78, 13, 77])).
% 226.81/145.75 tff(80,plain,(~((~((~test(tptp_fun_X1_0(X0!2))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))) | (~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2))))))), inference(lemma,lemma(discharge,[]))).
% 226.81/145.75 tff(81,plain,
% 226.81/145.75 (((~((~test(tptp_fun_X1_0(X0!2))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))) | (~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))))) | (test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2))))),
% 226.81/145.75 inference(tautology,[status(thm)],[])).
% 226.81/145.75 tff(82,plain,
% 226.81/145.75 (test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))),
% 226.81/145.75 inference(unit_resolution,[status(thm)],[81, 80])).
% 226.81/145.75 tff(83,assumption,(![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))), introduced(assumption)).
% 226.81/145.75 tff(84,plain,
% 226.81/145.75 (((~![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))))))),
% 226.81/145.75 inference(rewrite,[status(thm)],[])).
% 226.81/145.75 tff(85,plain,
% 226.81/145.75 ((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)))))),
% 226.81/145.76 inference(rewrite,[status(thm)],[])).
% 226.81/145.76 tff(86,plain,
% 226.81/145.76 (((~![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))))))),
% 226.81/145.76 inference(monotonicity,[status(thm)],[85])).
% 226.81/145.76 tff(87,plain,
% 226.81/145.76 (((~![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))))))),
% 226.81/145.76 inference(transitivity,[status(thm)],[86, 84])).
% 226.81/145.76 tff(88,plain,
% 226.81/145.76 ((~![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)))))),
% 226.81/145.76 inference(quant_inst,[status(thm)],[])).
% 226.81/145.76 tff(89,plain,
% 226.81/145.76 ((~![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)))))),
% 226.81/145.76 inference(modus_ponens,[status(thm)],[88, 87])).
% 226.81/145.76 tff(90,plain,
% 226.81/145.76 (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))))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[89, 49])).
% 226.81/145.76 tff(91,plain,
% 226.81/145.76 ((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))),
% 226.81/145.76 inference(commutativity,[status(thm)],[])).
% 226.81/145.76 tff(92,plain,
% 226.81/145.76 (one = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 226.81/145.76 inference(symmetry,[status(thm)],[76])).
% 226.81/145.76 tff(93,plain,
% 226.81/145.76 ((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)))),
% 226.81/145.76 inference(monotonicity,[status(thm)],[92])).
% 226.81/145.76 tff(94,plain,
% 226.81/145.76 ((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))),
% 226.81/145.76 inference(transitivity,[status(thm)],[93, 91])).
% 226.81/145.76 tff(95,plain,
% 226.81/145.76 ((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)),
% 226.81/145.76 inference(symmetry,[status(thm)],[94])).
% 226.81/145.76 tff(96,plain,
% 226.81/145.76 ((~![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))),
% 226.81/145.76 inference(quant_inst,[status(thm)],[])).
% 226.81/145.76 tff(97,plain,
% 226.81/145.76 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[96, 24])).
% 226.81/145.76 tff(98,plain,
% 226.81/145.76 (addition(tptp_fun_X1_0(X0!2), X0!2) = one),
% 226.81/145.76 inference(modus_ponens,[status(thm)],[97, 95])).
% 226.81/145.76 tff(99,plain,
% 226.81/145.76 (((~(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)),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(100,plain,
% 226.81/145.76 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[99, 74])).
% 226.81/145.76 tff(101,plain,
% 226.81/145.76 (((~(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)),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(102,plain,
% 226.81/145.76 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[101, 74])).
% 226.81/145.76 tff(103,plain,
% 226.81/145.76 ((~((~(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))),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(104,plain,
% 226.81/145.76 ((~((~(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))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[103, 102, 100])).
% 226.81/145.76 tff(105,plain,
% 226.81/145.76 (~((~(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)))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[104, 98])).
% 226.81/145.76 tff(106,plain,
% 226.81/145.76 ((~(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)))),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(107,plain,
% 226.81/145.76 (complement(X0!2, tptp_fun_X1_0(X0!2))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[106, 105, 90])).
% 226.81/145.76 tff(108,plain,
% 226.81/145.76 ((~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))) | (~complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 226.81/145.76 inference(quant_inst,[status(thm)],[])).
% 226.81/145.76 tff(109,plain,
% 226.81/145.76 ($false),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[108, 107, 83])).
% 226.81/145.76 tff(110,plain,(~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))), inference(lemma,lemma(discharge,[]))).
% 226.81/145.76 tff(111,plain,
% 226.81/145.76 ((~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2))))) | test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(112,plain,
% 226.81/145.76 ((~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2))))) | test(tptp_fun_X1_0(X0!2))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[111, 110])).
% 226.81/145.76 tff(113,plain,
% 226.81/145.76 (test(tptp_fun_X1_0(X0!2))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[112, 82])).
% 226.81/145.76 tff(114,plain,
% 226.81/145.76 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 226.81/145.76 inference(bind,[status(th)],[])).
% 226.81/145.76 tff(115,plain,
% 226.81/145.76 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 226.81/145.76 inference(quant_intro,[status(thm)],[114])).
% 226.81/145.76 tff(116,plain,
% 226.81/145.76 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 226.81/145.76 inference(rewrite,[status(thm)],[])).
% 226.81/145.76 tff(117,plain,
% 226.81/145.76 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 226.81/145.76 inference(bind,[status(th)],[])).
% 226.81/145.76 tff(118,plain,
% 226.81/145.76 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 226.81/145.76 inference(quant_intro,[status(thm)],[117])).
% 226.81/145.76 tff(119,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_3')).
% 226.81/145.76 tff(120,plain,
% 226.81/145.76 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 226.81/145.76 inference(modus_ponens,[status(thm)],[119, 118])).
% 226.81/145.76 tff(121,plain,
% 226.81/145.76 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 226.81/145.76 inference(modus_ponens,[status(thm)],[120, 116])).
% 226.81/145.76 tff(122,plain,(
% 226.81/145.76 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 226.81/145.76 inference(skolemize,[status(sab)],[121])).
% 226.81/145.76 tff(123,plain,
% 226.81/145.76 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 226.81/145.76 inference(modus_ponens,[status(thm)],[122, 115])).
% 226.81/145.76 tff(124,plain,
% 226.81/145.76 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X0!2))) | ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X0!2))) | ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2)))),
% 226.81/145.76 inference(rewrite,[status(thm)],[])).
% 226.81/145.76 tff(125,plain,
% 226.81/145.76 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X0!2))) | ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2)))),
% 226.81/145.76 inference(quant_inst,[status(thm)],[])).
% 226.81/145.76 tff(126,plain,
% 226.81/145.76 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X0!2))) | ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2))),
% 226.81/145.76 inference(modus_ponens,[status(thm)],[125, 124])).
% 226.81/145.76 tff(127,plain,
% 226.81/145.76 ((~test(tptp_fun_X1_0(X0!2))) | ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[126, 123])).
% 226.81/145.76 tff(128,plain,
% 226.81/145.76 ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2)),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[127, 113])).
% 226.81/145.76 tff(129,plain,
% 226.81/145.76 ((~((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2))) | (c(tptp_fun_X1_0(X0!2)) = X0!2) | (~complement(tptp_fun_X1_0(X0!2), X0!2))),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(130,plain,
% 226.81/145.76 ((~((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2))) | (c(tptp_fun_X1_0(X0!2)) = X0!2)),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[129, 71])).
% 226.81/145.76 tff(131,plain,
% 226.81/145.76 (c(tptp_fun_X1_0(X0!2)) = X0!2),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[130, 128])).
% 226.81/145.76 tff(132,plain,
% 226.81/145.76 (addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 226.81/145.76 inference(monotonicity,[status(thm)],[131])).
% 226.81/145.76 tff(133,plain,
% 226.81/145.76 (addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)) = one),
% 226.81/145.76 inference(transitivity,[status(thm)],[132, 76])).
% 226.81/145.76 tff(134,plain,
% 226.81/145.76 (multiplication(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(X1!1, X0!2)) = multiplication(one, multiplication(X1!1, X0!2))),
% 226.81/145.76 inference(monotonicity,[status(thm)],[133])).
% 226.81/145.76 tff(135,plain,
% 226.81/145.76 (^[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))))),
% 226.81/145.76 inference(bind,[status(th)],[])).
% 226.81/145.76 tff(136,plain,
% 226.81/145.76 (![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)))),
% 226.81/145.76 inference(quant_intro,[status(thm)],[135])).
% 226.81/145.76 tff(137,plain,
% 226.81/145.76 (![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)))),
% 226.81/145.76 inference(rewrite,[status(thm)],[])).
% 226.81/145.76 tff(138,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')).
% 226.81/145.76 tff(139,plain,
% 226.81/145.76 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 226.81/145.76 inference(modus_ponens,[status(thm)],[138, 137])).
% 226.81/145.76 tff(140,plain,(
% 226.81/145.76 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 226.81/145.76 inference(skolemize,[status(sab)],[139])).
% 226.81/145.76 tff(141,plain,
% 226.81/145.76 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 226.81/145.76 inference(modus_ponens,[status(thm)],[140, 136])).
% 226.81/145.76 tff(142,plain,
% 226.81/145.76 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(X1!1, X0!2)) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(X1!1, X0!2)), multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, X0!2))))),
% 226.81/145.76 inference(quant_inst,[status(thm)],[])).
% 226.81/145.76 tff(143,plain,
% 226.81/145.76 (multiplication(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(X1!1, X0!2)) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(X1!1, X0!2)), multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, X0!2)))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[142, 141])).
% 226.81/145.76 tff(144,plain,
% 226.81/145.76 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(X1!1, X0!2)), multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, X0!2))) = multiplication(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(X1!1, X0!2))),
% 226.81/145.76 inference(symmetry,[status(thm)],[143])).
% 226.81/145.76 tff(145,assumption,((~((~test(tptp_fun_X1_0(X1!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))) | (~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))))), introduced(assumption)).
% 226.81/145.76 tff(146,plain,
% 226.81/145.76 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(tptp_fun_X1_0(X1!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))) | (~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))))))),
% 226.81/145.76 inference(quant_inst,[status(thm)],[])).
% 226.81/145.76 tff(147,plain,
% 226.81/145.76 ($false),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[146, 13, 145])).
% 226.81/145.76 tff(148,plain,(~((~((~test(tptp_fun_X1_0(X1!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))) | (~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))))), inference(lemma,lemma(discharge,[]))).
% 226.81/145.76 tff(149,plain,
% 226.81/145.76 (((~((~test(tptp_fun_X1_0(X1!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))) | (~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))))) | (test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(150,plain,
% 226.81/145.76 (test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[149, 148])).
% 226.81/145.76 tff(151,assumption,(![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))), introduced(assumption)).
% 226.81/145.76 tff(152,plain,
% 226.81/145.76 (((~![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))))))),
% 226.81/145.76 inference(rewrite,[status(thm)],[])).
% 226.81/145.76 tff(153,plain,
% 226.81/145.76 ((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)))))),
% 226.81/145.76 inference(rewrite,[status(thm)],[])).
% 226.81/145.76 tff(154,plain,
% 226.81/145.76 (((~![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))))))),
% 226.81/145.76 inference(monotonicity,[status(thm)],[153])).
% 226.81/145.76 tff(155,plain,
% 226.81/145.76 (((~![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))))))),
% 226.81/145.76 inference(transitivity,[status(thm)],[154, 152])).
% 226.81/145.76 tff(156,plain,
% 226.81/145.76 ((~![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)))))),
% 226.81/145.76 inference(quant_inst,[status(thm)],[])).
% 226.81/145.76 tff(157,plain,
% 226.81/145.76 ((~![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)))))),
% 226.81/145.76 inference(modus_ponens,[status(thm)],[156, 155])).
% 226.81/145.76 tff(158,plain,
% 226.81/145.76 (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))))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[157, 49])).
% 226.81/145.76 tff(159,plain,
% 226.81/145.76 ((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))),
% 226.81/145.76 inference(commutativity,[status(thm)],[])).
% 226.81/145.76 tff(160,plain,
% 226.81/145.76 ((~![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)))))),
% 226.81/145.76 inference(quant_inst,[status(thm)],[])).
% 226.81/145.76 tff(161,plain,
% 226.81/145.76 (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))))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[160, 49])).
% 226.81/145.76 tff(162,plain,
% 226.81/145.76 ((~![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))))))),
% 226.81/145.76 inference(quant_inst,[status(thm)],[])).
% 226.81/145.76 tff(163,plain,
% 226.81/145.76 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[162, 13])).
% 226.81/145.76 tff(164,plain,
% 226.81/145.76 (((~((~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))),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(165,plain,
% 226.81/145.76 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[164, 163])).
% 226.81/145.76 tff(166,plain,
% 226.81/145.76 (test(X1!1)),
% 226.81/145.76 inference(and_elim,[status(thm)],[67])).
% 226.81/145.76 tff(167,plain,
% 226.81/145.76 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(168,plain,
% 226.81/145.76 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[167, 166])).
% 226.81/145.76 tff(169,plain,
% 226.81/145.76 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[168, 165])).
% 226.81/145.76 tff(170,plain,
% 226.81/145.76 ((~(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))))),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(171,plain,
% 226.81/145.76 ((~(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))))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[170, 169])).
% 226.81/145.76 tff(172,plain,
% 226.81/145.76 (~((~(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)))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[171, 161])).
% 226.81/145.76 tff(173,plain,
% 226.81/145.76 (((~(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)),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(174,plain,
% 226.81/145.76 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[173, 172])).
% 226.81/145.76 tff(175,plain,
% 226.81/145.76 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 226.81/145.76 inference(symmetry,[status(thm)],[174])).
% 226.81/145.76 tff(176,plain,
% 226.81/145.76 ((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)))),
% 226.81/145.76 inference(monotonicity,[status(thm)],[175])).
% 226.81/145.76 tff(177,plain,
% 226.81/145.76 ((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))),
% 226.81/145.76 inference(transitivity,[status(thm)],[176, 159])).
% 226.81/145.76 tff(178,plain,
% 226.81/145.76 ((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)),
% 226.81/145.76 inference(symmetry,[status(thm)],[177])).
% 226.81/145.76 tff(179,plain,
% 226.81/145.76 ((~![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))),
% 226.81/145.76 inference(quant_inst,[status(thm)],[])).
% 226.81/145.76 tff(180,plain,
% 226.81/145.76 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[179, 24])).
% 226.81/145.76 tff(181,plain,
% 226.81/145.76 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 226.81/145.76 inference(modus_ponens,[status(thm)],[180, 178])).
% 226.81/145.76 tff(182,plain,
% 226.81/145.76 (((~(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)),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(183,plain,
% 226.81/145.76 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[182, 172])).
% 226.81/145.76 tff(184,plain,
% 226.81/145.76 (((~(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)),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(185,plain,
% 226.81/145.76 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[184, 172])).
% 226.81/145.76 tff(186,plain,
% 226.81/145.76 ((~((~(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))),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(187,plain,
% 226.81/145.76 ((~((~(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))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[186, 185, 183])).
% 226.81/145.76 tff(188,plain,
% 226.81/145.76 (~((~(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)))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[187, 181])).
% 226.81/145.76 tff(189,plain,
% 226.81/145.76 ((~(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)))),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(190,plain,
% 226.81/145.76 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[189, 188, 158])).
% 226.81/145.76 tff(191,plain,
% 226.81/145.76 ((~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))) | (~complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 226.81/145.76 inference(quant_inst,[status(thm)],[])).
% 226.81/145.76 tff(192,plain,
% 226.81/145.76 ($false),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[191, 190, 151])).
% 226.81/145.76 tff(193,plain,(~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))), inference(lemma,lemma(discharge,[]))).
% 226.81/145.76 tff(194,plain,
% 226.81/145.76 ((~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))) | test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(195,plain,
% 226.81/145.76 ((~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))) | test(tptp_fun_X1_0(X1!1))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[194, 193])).
% 226.81/145.76 tff(196,plain,
% 226.81/145.76 (test(tptp_fun_X1_0(X1!1))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[195, 150])).
% 226.81/145.76 tff(197,plain,
% 226.81/145.76 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)))),
% 226.81/145.76 inference(rewrite,[status(thm)],[])).
% 226.81/145.76 tff(198,plain,
% 226.81/145.76 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)))),
% 226.81/145.76 inference(quant_inst,[status(thm)],[])).
% 226.81/145.76 tff(199,plain,
% 226.81/145.76 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1))),
% 226.81/145.76 inference(modus_ponens,[status(thm)],[198, 197])).
% 226.81/145.76 tff(200,plain,
% 226.81/145.76 ((~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1))),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[199, 123])).
% 226.81/145.76 tff(201,plain,
% 226.81/145.76 ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[200, 196])).
% 226.81/145.76 tff(202,plain,
% 226.81/145.76 ((~((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1))) | (c(tptp_fun_X1_0(X1!1)) = X1!1) | (~complement(tptp_fun_X1_0(X1!1), X1!1))),
% 226.81/145.76 inference(tautology,[status(thm)],[])).
% 226.81/145.76 tff(203,plain,
% 226.81/145.76 ((~((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1))) | (c(tptp_fun_X1_0(X1!1)) = X1!1)),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[202, 169])).
% 226.81/145.76 tff(204,plain,
% 226.81/145.76 (c(tptp_fun_X1_0(X1!1)) = X1!1),
% 226.81/145.76 inference(unit_resolution,[status(thm)],[203, 201])).
% 226.81/145.76 tff(205,plain,
% 226.81/145.76 (multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(X1!1, X0!2)),
% 226.81/145.76 inference(monotonicity,[status(thm)],[204, 131])).
% 226.81/145.77 tff(206,plain,
% 226.81/145.77 (multiplication(X1!1, X0!2) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(symmetry,[status(thm)],[205])).
% 226.81/145.77 tff(207,plain,
% 226.81/145.77 (multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, X0!2)) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 226.81/145.77 inference(monotonicity,[status(thm)],[206])).
% 226.81/145.77 tff(208,plain,
% 226.81/145.77 (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, X0!2))),
% 226.81/145.77 inference(symmetry,[status(thm)],[207])).
% 226.81/145.77 tff(209,plain,
% 226.81/145.77 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)))),
% 226.81/145.77 inference(bind,[status(th)],[])).
% 226.81/145.77 tff(210,plain,
% 226.81/145.77 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 226.81/145.77 inference(quant_intro,[status(thm)],[209])).
% 226.81/145.77 tff(211,plain,
% 226.81/145.77 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 226.81/145.77 inference(rewrite,[status(thm)],[])).
% 226.81/145.77 tff(212,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_associativity')).
% 226.81/145.77 tff(213,plain,
% 226.81/145.77 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 226.81/145.77 inference(modus_ponens,[status(thm)],[212, 211])).
% 226.81/145.77 tff(214,plain,(
% 226.81/145.77 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 226.81/145.77 inference(skolemize,[status(sab)],[213])).
% 226.81/145.77 tff(215,plain,
% 226.81/145.77 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 226.81/145.77 inference(modus_ponens,[status(thm)],[214, 210])).
% 226.81/145.77 tff(216,plain,
% 226.81/145.77 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))))),
% 226.81/145.77 inference(quant_inst,[status(thm)],[])).
% 226.81/145.77 tff(217,plain,
% 226.81/145.77 (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(unit_resolution,[status(thm)],[216, 215])).
% 226.81/145.77 tff(218,plain,
% 226.81/145.77 (multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 226.81/145.77 inference(symmetry,[status(thm)],[217])).
% 226.81/145.77 tff(219,plain,
% 226.81/145.77 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 226.81/145.77 inference(bind,[status(th)],[])).
% 226.81/145.77 tff(220,plain,
% 226.81/145.77 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 226.81/145.77 inference(quant_intro,[status(thm)],[219])).
% 226.81/145.77 tff(221,plain,
% 226.81/145.77 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 226.81/145.77 inference(rewrite,[status(thm)],[])).
% 226.81/145.77 tff(222,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 226.81/145.77 tff(223,plain,
% 226.81/145.77 (![A: $i] : (multiplication(A, one) = A)),
% 226.81/145.77 inference(modus_ponens,[status(thm)],[222, 221])).
% 226.81/145.77 tff(224,plain,(
% 226.81/145.77 ![A: $i] : (multiplication(A, one) = A)),
% 226.81/145.77 inference(skolemize,[status(sab)],[223])).
% 226.81/145.77 tff(225,plain,
% 226.81/145.77 (![A: $i] : (multiplication(A, one) = A)),
% 226.81/145.77 inference(modus_ponens,[status(thm)],[224, 220])).
% 226.81/145.77 tff(226,plain,
% 226.81/145.77 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(tptp_fun_X1_0(X0!2), one) = tptp_fun_X1_0(X0!2))),
% 226.81/145.77 inference(quant_inst,[status(thm)],[])).
% 226.81/145.77 tff(227,plain,
% 226.81/145.77 (multiplication(tptp_fun_X1_0(X0!2), one) = tptp_fun_X1_0(X0!2)),
% 226.81/145.77 inference(unit_resolution,[status(thm)],[226, 225])).
% 226.81/145.77 tff(228,plain,
% 226.81/145.77 (multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), one)),
% 226.81/145.77 inference(monotonicity,[status(thm)],[133])).
% 226.81/145.77 tff(229,plain,
% 226.81/145.77 (^[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))))),
% 226.81/145.77 inference(bind,[status(th)],[])).
% 226.81/145.77 tff(230,plain,
% 226.81/145.77 (![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)))),
% 226.81/145.77 inference(quant_intro,[status(thm)],[229])).
% 226.81/145.77 tff(231,plain,
% 226.81/145.77 (![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)))),
% 226.81/145.77 inference(rewrite,[status(thm)],[])).
% 226.81/145.77 tff(232,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')).
% 226.81/145.77 tff(233,plain,
% 226.81/145.77 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 226.81/145.77 inference(modus_ponens,[status(thm)],[232, 231])).
% 226.81/145.77 tff(234,plain,(
% 226.81/145.77 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 226.81/145.77 inference(skolemize,[status(sab)],[233])).
% 226.81/145.77 tff(235,plain,
% 226.81/145.77 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 226.81/145.77 inference(modus_ponens,[status(thm)],[234, 230])).
% 226.81/145.77 tff(236,plain,
% 226.81/145.77 ((~![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(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))))),
% 226.81/145.77 inference(quant_inst,[status(thm)],[])).
% 226.81/145.77 tff(237,plain,
% 226.81/145.77 (multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(unit_resolution,[status(thm)],[236, 235])).
% 226.81/145.77 tff(238,plain,
% 226.81/145.77 (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(symmetry,[status(thm)],[237])).
% 226.81/145.77 tff(239,plain,
% 226.81/145.77 (multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), X0!2)),
% 226.81/145.77 inference(monotonicity,[status(thm)],[131])).
% 226.81/145.77 tff(240,plain,
% 226.81/145.77 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(symmetry,[status(thm)],[239])).
% 226.81/145.77 tff(241,plain,
% 226.81/145.77 (zero = multiplication(tptp_fun_X1_0(X0!2), X0!2)),
% 226.81/145.77 inference(symmetry,[status(thm)],[100])).
% 226.81/145.77 tff(242,plain,
% 226.81/145.77 (zero = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(transitivity,[status(thm)],[241, 240])).
% 226.81/145.77 tff(243,plain,
% 226.81/145.77 (addition(zero, multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(monotonicity,[status(thm)],[242])).
% 226.81/145.77 tff(244,plain,
% 226.81/145.77 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), zero))),
% 226.81/145.77 inference(quant_inst,[status(thm)],[])).
% 226.81/145.77 tff(245,plain,
% 226.81/145.77 (addition(zero, multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), zero)),
% 226.81/145.77 inference(unit_resolution,[status(thm)],[244, 24])).
% 226.81/145.77 tff(246,plain,
% 226.81/145.77 (addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), zero) = addition(zero, multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(symmetry,[status(thm)],[245])).
% 226.81/145.77 tff(247,plain,
% 226.81/145.77 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 226.81/145.77 inference(bind,[status(th)],[])).
% 226.81/145.77 tff(248,plain,
% 226.81/145.77 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 226.81/145.77 inference(quant_intro,[status(thm)],[247])).
% 226.81/145.77 tff(249,plain,
% 226.81/145.77 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 226.81/145.77 inference(rewrite,[status(thm)],[])).
% 226.81/145.77 tff(250,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 226.81/145.77 tff(251,plain,
% 226.81/145.77 (![A: $i] : (addition(A, zero) = A)),
% 226.81/145.77 inference(modus_ponens,[status(thm)],[250, 249])).
% 226.81/145.77 tff(252,plain,(
% 226.81/145.77 ![A: $i] : (addition(A, zero) = A)),
% 226.81/145.77 inference(skolemize,[status(sab)],[251])).
% 226.81/145.77 tff(253,plain,
% 226.81/145.77 (![A: $i] : (addition(A, zero) = A)),
% 226.81/145.77 inference(modus_ponens,[status(thm)],[252, 248])).
% 226.81/145.77 tff(254,plain,
% 226.81/145.77 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), zero) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(quant_inst,[status(thm)],[])).
% 226.81/145.77 tff(255,plain,
% 226.81/145.77 (addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), zero) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))),
% 226.81/145.77 inference(unit_resolution,[status(thm)],[254, 253])).
% 226.81/145.77 tff(256,plain,
% 226.81/145.77 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), zero)),
% 226.81/145.77 inference(symmetry,[status(thm)],[255])).
% 226.81/145.77 tff(257,plain,
% 226.81/145.77 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)) = tptp_fun_X1_0(X0!2)),
% 226.81/145.77 inference(transitivity,[status(thm)],[256, 246, 243, 238, 228, 227])).
% 226.81/145.77 tff(258,plain,
% 226.81/145.77 (multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))),
% 226.81/145.77 inference(monotonicity,[status(thm)],[257])).
% 226.81/145.77 tff(259,plain,
% 226.81/145.77 (multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))),
% 226.81/145.77 inference(symmetry,[status(thm)],[258])).
% 226.81/145.77 tff(260,plain,
% 226.81/145.77 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 226.81/145.77 inference(symmetry,[status(thm)],[132])).
% 226.81/145.77 tff(261,plain,
% 226.81/145.77 (one = addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 226.81/145.77 inference(transitivity,[status(thm)],[92, 260])).
% 226.81/145.77 tff(262,plain,
% 226.81/145.77 (multiplication(one, tptp_fun_X1_0(X0!2)) = multiplication(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 226.81/145.77 inference(monotonicity,[status(thm)],[261])).
% 226.81/145.77 tff(263,plain,
% 226.81/145.77 (multiplication(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)) = multiplication(one, tptp_fun_X1_0(X0!2))),
% 226.81/145.77 inference(symmetry,[status(thm)],[262])).
% 226.81/145.77 tff(264,plain,
% 226.81/145.77 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))))),
% 226.81/145.77 inference(quant_inst,[status(thm)],[])).
% 226.81/145.77 tff(265,plain,
% 226.81/145.77 (multiplication(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(unit_resolution,[status(thm)],[264, 141])).
% 226.81/145.77 tff(266,plain,
% 226.81/145.77 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = multiplication(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 226.81/145.77 inference(symmetry,[status(thm)],[265])).
% 226.81/145.77 tff(267,plain,
% 226.81/145.77 (multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)) = multiplication(X0!2, tptp_fun_X1_0(X0!2))),
% 226.81/145.77 inference(monotonicity,[status(thm)],[131])).
% 226.81/145.77 tff(268,plain,
% 226.81/145.77 (multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(transitivity,[status(thm)],[267, 102, 241, 240])).
% 226.81/145.77 tff(269,plain,
% 226.81/145.77 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(monotonicity,[status(thm)],[268])).
% 226.81/145.77 tff(270,plain,
% 226.81/145.77 (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(symmetry,[status(thm)],[269])).
% 226.81/145.77 tff(271,plain,
% 226.81/145.77 (multiplication(tptp_fun_X1_0(X0!2), one) = multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(symmetry,[status(thm)],[228])).
% 226.81/145.77 tff(272,plain,
% 226.81/145.77 (tptp_fun_X1_0(X0!2) = multiplication(tptp_fun_X1_0(X0!2), one)),
% 226.81/145.77 inference(symmetry,[status(thm)],[227])).
% 226.81/145.77 tff(273,plain,
% 226.81/145.77 (tptp_fun_X1_0(X0!2) = multiplication(one, tptp_fun_X1_0(X0!2))),
% 226.81/145.77 inference(transitivity,[status(thm)],[272, 271, 237, 270, 266, 263])).
% 226.81/145.77 tff(274,plain,
% 226.81/145.77 (multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))) = multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))),
% 226.81/145.77 inference(monotonicity,[status(thm)],[273])).
% 226.81/145.77 tff(275,plain,
% 226.81/145.77 (multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))),
% 226.81/145.77 inference(symmetry,[status(thm)],[274])).
% 226.81/145.77 tff(276,plain,
% 226.81/145.77 (multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))),
% 226.81/145.77 inference(transitivity,[status(thm)],[275, 259])).
% 226.81/145.77 tff(277,plain,
% 226.81/145.77 (addition(multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), multiplication(zero, c(tptp_fun_X1_0(X1!1)))) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), multiplication(zero, c(tptp_fun_X1_0(X1!1))))),
% 226.81/145.77 inference(monotonicity,[status(thm)],[276])).
% 226.81/145.77 tff(278,plain,
% 226.81/145.77 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), multiplication(zero, c(tptp_fun_X1_0(X1!1)))) = addition(multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), multiplication(zero, c(tptp_fun_X1_0(X1!1))))),
% 226.81/145.77 inference(symmetry,[status(thm)],[277])).
% 226.81/145.77 tff(279,plain,
% 226.81/145.77 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), zero), c(tptp_fun_X1_0(X1!1))) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), multiplication(zero, c(tptp_fun_X1_0(X1!1)))))),
% 226.81/145.77 inference(quant_inst,[status(thm)],[])).
% 226.81/145.77 tff(280,plain,
% 226.81/145.77 (multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), zero), c(tptp_fun_X1_0(X1!1))) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), multiplication(zero, c(tptp_fun_X1_0(X1!1))))),
% 226.81/145.77 inference(unit_resolution,[status(thm)],[279, 141])).
% 226.81/145.77 tff(281,plain,
% 226.81/145.77 (addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), zero) = tptp_fun_X1_0(X0!2)),
% 226.81/145.77 inference(transitivity,[status(thm)],[246, 243, 238, 228, 227])).
% 226.81/145.77 tff(282,plain,
% 226.81/145.77 (multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), zero), c(tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))),
% 226.81/145.77 inference(monotonicity,[status(thm)],[281])).
% 226.81/145.77 tff(283,plain,
% 226.81/145.77 (multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))) = multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), zero), c(tptp_fun_X1_0(X1!1)))),
% 226.81/145.77 inference(symmetry,[status(thm)],[282])).
% 226.81/145.77 tff(284,plain,
% 226.81/145.77 (multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))) = addition(multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), multiplication(zero, c(tptp_fun_X1_0(X1!1))))),
% 226.81/145.77 inference(transitivity,[status(thm)],[283, 280, 278])).
% 226.81/145.77 tff(285,plain,
% 226.81/145.77 (multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(addition(multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), multiplication(zero, c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(monotonicity,[status(thm)],[284])).
% 226.81/145.77 tff(286,plain,
% 226.81/145.77 (multiplication(addition(multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), multiplication(zero, c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(symmetry,[status(thm)],[285])).
% 226.81/145.77 tff(287,plain,
% 226.81/145.77 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), multiplication(zero, c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(zero, c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))))),
% 226.81/145.77 inference(quant_inst,[status(thm)],[])).
% 226.81/145.77 tff(288,plain,
% 226.81/145.77 (multiplication(addition(multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), multiplication(zero, c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(zero, c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))))),
% 226.81/145.77 inference(unit_resolution,[status(thm)],[287, 141])).
% 226.81/145.77 tff(289,plain,
% 226.81/145.77 (addition(multiplication(multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(zero, c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))) = multiplication(addition(multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), multiplication(zero, c(tptp_fun_X1_0(X1!1)))), c(tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(symmetry,[status(thm)],[288])).
% 226.81/145.77 tff(290,plain,
% 226.81/145.77 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 226.81/145.77 inference(bind,[status(th)],[])).
% 226.81/145.77 tff(291,plain,
% 226.81/145.77 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 226.81/145.77 inference(quant_intro,[status(thm)],[290])).
% 226.81/145.77 tff(292,plain,
% 226.81/145.77 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 226.81/145.77 inference(rewrite,[status(thm)],[])).
% 226.81/145.77 tff(293,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 226.81/145.77 tff(294,plain,
% 226.81/145.77 (![A: $i] : (multiplication(zero, A) = zero)),
% 226.81/145.77 inference(modus_ponens,[status(thm)],[293, 292])).
% 226.81/145.77 tff(295,plain,(
% 226.81/145.77 ![A: $i] : (multiplication(zero, A) = zero)),
% 226.81/145.77 inference(skolemize,[status(sab)],[294])).
% 226.81/145.77 tff(296,plain,
% 226.81/145.77 (![A: $i] : (multiplication(zero, A) = zero)),
% 226.81/145.77 inference(modus_ponens,[status(thm)],[295, 291])).
% 226.81/145.77 tff(297,plain,
% 226.81/145.77 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, multiplication(X1!1, X0!2)) = zero)),
% 226.81/145.77 inference(quant_inst,[status(thm)],[])).
% 226.81/145.77 tff(298,plain,
% 226.81/145.77 (multiplication(zero, multiplication(X1!1, X0!2)) = zero),
% 226.81/145.77 inference(unit_resolution,[status(thm)],[297, 296])).
% 226.81/145.77 tff(299,plain,
% 226.81/145.77 (multiplication(zero, multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(zero, multiplication(X1!1, X0!2))),
% 226.81/145.77 inference(monotonicity,[status(thm)],[205])).
% 226.81/145.77 tff(300,plain,
% 226.81/145.77 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(zero, multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(zero, c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))))),
% 226.81/145.77 inference(quant_inst,[status(thm)],[])).
% 226.81/145.77 tff(301,plain,
% 226.81/145.77 (multiplication(zero, multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(zero, c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(unit_resolution,[status(thm)],[300, 215])).
% 226.81/145.77 tff(302,plain,
% 226.81/145.77 (multiplication(multiplication(zero, c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(zero, multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 226.81/145.77 inference(symmetry,[status(thm)],[301])).
% 226.81/145.77 tff(303,plain,
% 226.81/145.77 (multiplication(multiplication(zero, c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = zero),
% 226.81/145.77 inference(transitivity,[status(thm)],[302, 299, 298])).
% 226.81/145.77 tff(304,plain,
% 226.81/145.77 (multiplication(multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 226.81/145.77 inference(monotonicity,[status(thm)],[275])).
% 226.81/145.77 tff(305,plain,
% 226.81/145.77 (addition(multiplication(multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(zero, c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), zero)),
% 226.81/145.77 inference(monotonicity,[status(thm)],[304, 303])).
% 226.81/145.77 tff(306,plain,
% 226.81/145.77 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), zero) = addition(multiplication(multiplication(multiplication(one, tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(zero, c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))))),
% 226.81/145.77 inference(symmetry,[status(thm)],[305])).
% 226.81/145.77 tff(307,plain,
% 226.81/145.77 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), zero) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 226.81/145.77 inference(monotonicity,[status(thm)],[242])).
% 226.81/145.77 tff(308,plain,
% 226.81/145.77 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), zero)),
% 226.81/145.77 inference(symmetry,[status(thm)],[307])).
% 226.81/145.77 tff(309,plain,
% 226.81/145.77 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))))),
% 226.81/145.77 inference(quant_inst,[status(thm)],[])).
% 226.81/145.77 tff(310,plain,
% 226.81/145.77 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.77 inference(unit_resolution,[status(thm)],[309, 141])).
% 226.83/145.77 tff(311,plain,
% 226.83/145.77 (addition(tptp_fun_X1_0(X1!1), X1!1) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 226.83/145.77 inference(symmetry,[status(thm)],[180])).
% 226.83/145.77 tff(312,plain,
% 226.83/145.77 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 226.83/145.77 inference(bind,[status(th)],[])).
% 226.83/145.77 tff(313,plain,
% 226.83/145.77 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 226.83/145.77 inference(quant_intro,[status(thm)],[312])).
% 226.83/145.77 tff(314,plain,
% 226.83/145.77 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 226.83/145.77 inference(rewrite,[status(thm)],[])).
% 226.83/145.77 tff(315,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 226.83/145.77 tff(316,plain,
% 226.83/145.77 (![A: $i] : (addition(A, A) = A)),
% 226.83/145.77 inference(modus_ponens,[status(thm)],[315, 314])).
% 226.83/145.77 tff(317,plain,(
% 226.83/145.77 ![A: $i] : (addition(A, A) = A)),
% 226.83/145.77 inference(skolemize,[status(sab)],[316])).
% 226.83/145.77 tff(318,plain,
% 226.83/145.77 (![A: $i] : (addition(A, A) = A)),
% 226.83/145.77 inference(modus_ponens,[status(thm)],[317, 313])).
% 226.83/145.77 tff(319,plain,
% 226.83/145.77 ((~![A: $i] : (addition(A, A) = A)) | (addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)) = tptp_fun_X1_0(X1!1))),
% 226.83/145.77 inference(quant_inst,[status(thm)],[])).
% 226.83/145.77 tff(320,plain,
% 226.83/145.77 (addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)) = tptp_fun_X1_0(X1!1)),
% 226.83/145.77 inference(unit_resolution,[status(thm)],[319, 318])).
% 226.83/145.77 tff(321,plain,
% 226.83/145.77 (addition(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 226.83/145.77 inference(monotonicity,[status(thm)],[320, 204])).
% 226.83/145.77 tff(322,plain,
% 226.83/145.77 (^[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)))),
% 226.83/145.77 inference(bind,[status(th)],[])).
% 226.83/145.77 tff(323,plain,
% 226.83/145.77 (![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))),
% 226.83/145.77 inference(quant_intro,[status(thm)],[322])).
% 226.83/145.77 tff(324,plain,
% 226.83/145.77 (![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))),
% 226.83/145.77 inference(rewrite,[status(thm)],[])).
% 226.83/145.77 tff(325,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')).
% 226.83/145.77 tff(326,plain,
% 226.83/145.77 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 226.83/145.77 inference(modus_ponens,[status(thm)],[325, 324])).
% 226.83/145.77 tff(327,plain,(
% 226.83/145.77 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 226.83/145.77 inference(skolemize,[status(sab)],[326])).
% 226.83/145.77 tff(328,plain,
% 226.83/145.77 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 226.83/145.77 inference(modus_ponens,[status(thm)],[327, 323])).
% 226.83/145.77 tff(329,plain,
% 226.83/145.77 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))) = addition(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1))))),
% 226.83/145.77 inference(quant_inst,[status(thm)],[])).
% 226.83/145.77 tff(330,plain,
% 226.83/145.77 (addition(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))) = addition(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X1!1)))),
% 226.83/145.77 inference(unit_resolution,[status(thm)],[329, 328])).
% 226.83/145.77 tff(331,plain,
% 226.83/145.77 (addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 226.83/145.77 inference(monotonicity,[status(thm)],[204])).
% 226.83/145.77 tff(332,plain,
% 226.83/145.77 (addition(tptp_fun_X1_0(X1!1), X1!1) = addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))),
% 226.83/145.77 inference(symmetry,[status(thm)],[331])).
% 226.83/145.77 tff(333,plain,
% 226.83/145.77 (one = addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))),
% 226.83/145.77 inference(transitivity,[status(thm)],[175, 180, 332])).
% 226.83/145.77 tff(334,plain,
% 226.83/145.77 (addition(tptp_fun_X1_0(X1!1), one) = addition(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))))),
% 226.83/145.77 inference(monotonicity,[status(thm)],[333])).
% 226.83/145.77 tff(335,plain,
% 226.83/145.77 (addition(tptp_fun_X1_0(X1!1), one) = addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 226.83/145.77 inference(transitivity,[status(thm)],[334, 330, 321, 311, 174, 92, 260])).
% 226.83/145.77 tff(336,plain,
% 226.83/145.77 (multiplication(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), one)) = multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.77 inference(monotonicity,[status(thm)],[335])).
% 226.83/145.77 tff(337,plain,
% 226.83/145.77 ((~![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(tptp_fun_X1_0(X1!1), one)) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), one)))),
% 226.83/145.77 inference(quant_inst,[status(thm)],[])).
% 226.83/145.77 tff(338,plain,
% 226.83/145.77 (multiplication(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), one)) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), one))),
% 226.83/145.77 inference(unit_resolution,[status(thm)],[337, 235])).
% 226.83/145.77 tff(339,plain,
% 226.83/145.77 (addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), one)) = multiplication(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), one))),
% 226.83/145.77 inference(symmetry,[status(thm)],[338])).
% 226.83/145.77 tff(340,plain,
% 226.83/145.77 (((~![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))))),
% 226.83/145.77 inference(rewrite,[status(thm)],[])).
% 226.83/145.77 tff(341,plain,
% 226.83/145.77 ((~![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))))),
% 226.83/145.77 inference(quant_inst,[status(thm)],[])).
% 226.83/145.77 tff(342,plain,
% 226.83/145.77 ((~![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)))),
% 226.83/145.77 inference(modus_ponens,[status(thm)],[341, 340])).
% 226.83/145.77 tff(343,plain,
% 226.83/145.77 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 226.83/145.77 inference(unit_resolution,[status(thm)],[342, 123, 166])).
% 226.83/145.77 tff(344,plain,
% 226.83/145.77 ((~((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)))),
% 226.83/145.77 inference(tautology,[status(thm)],[])).
% 226.83/145.77 tff(345,plain,
% 226.83/145.77 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 226.83/145.77 inference(unit_resolution,[status(thm)],[344, 190, 343])).
% 226.83/145.77 tff(346,plain,
% 226.83/145.77 (tptp_fun_X1_0(X1!1) = c(X1!1)),
% 226.83/145.77 inference(symmetry,[status(thm)],[345])).
% 226.83/145.77 tff(347,plain,
% 226.83/145.77 (((~![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))))),
% 226.83/145.77 inference(rewrite,[status(thm)],[])).
% 226.83/145.77 tff(348,plain,
% 226.83/145.77 ((~![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))))),
% 226.83/145.77 inference(quant_inst,[status(thm)],[])).
% 226.83/145.77 tff(349,plain,
% 226.83/145.77 ((~![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)))),
% 226.83/145.77 inference(modus_ponens,[status(thm)],[348, 347])).
% 226.83/145.77 tff(350,plain,
% 226.83/145.77 ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))),
% 226.83/145.77 inference(unit_resolution,[status(thm)],[349, 123, 68])).
% 226.83/145.77 tff(351,plain,
% 226.83/145.77 ((~((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)))),
% 226.83/145.77 inference(tautology,[status(thm)],[])).
% 226.83/145.77 tff(352,plain,
% 226.83/145.77 (c(X0!2) = tptp_fun_X1_0(X0!2)),
% 226.83/145.77 inference(unit_resolution,[status(thm)],[351, 107, 350])).
% 226.83/145.77 tff(353,plain,
% 226.83/145.77 (tptp_fun_X1_0(X0!2) = c(X0!2)),
% 226.83/145.77 inference(symmetry,[status(thm)],[352])).
% 226.83/145.77 tff(354,plain,
% 226.83/145.77 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)) = multiplication(c(X0!2), c(X1!1))),
% 226.83/145.77 inference(monotonicity,[status(thm)],[353, 346])).
% 226.83/145.77 tff(355,plain,
% 226.83/145.77 (multiplication(c(X0!2), c(X1!1)) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 226.83/145.77 inference(symmetry,[status(thm)],[354])).
% 226.83/145.77 tff(356,plain,
% 226.83/145.77 (addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), one))),
% 226.83/145.77 inference(monotonicity,[status(thm)],[355, 272])).
% 226.83/145.77 tff(357,plain,
% 226.83/145.77 (addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)) = tptp_fun_X1_0(X0!2)),
% 226.83/145.77 inference(transitivity,[status(thm)],[356, 339, 336, 228, 227])).
% 226.83/145.77 tff(358,plain,
% 226.83/145.77 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), X0!2)),
% 226.83/145.77 inference(monotonicity,[status(thm)],[357, 131])).
% 226.83/145.77 tff(359,plain,
% 226.83/145.77 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.77 inference(symmetry,[status(thm)],[358])).
% 226.83/145.77 tff(360,plain,
% 226.83/145.77 (zero = addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), zero)),
% 226.83/145.77 inference(transitivity,[status(thm)],[241, 359, 310, 308])).
% 226.83/145.77 tff(361,plain,
% 226.83/145.77 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), zero) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), zero))),
% 226.83/145.77 inference(monotonicity,[status(thm)],[360])).
% 226.83/145.77 tff(362,plain,
% 226.83/145.77 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), zero)) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), zero)),
% 226.83/145.77 inference(symmetry,[status(thm)],[361])).
% 226.83/145.77 tff(363,plain,
% 226.83/145.77 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), zero)) = addition(addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2)))), zero))),
% 226.83/145.77 inference(quant_inst,[status(thm)],[])).
% 226.83/145.77 tff(364,plain,
% 226.83/145.77 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), zero)) = addition(addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2)))), zero)),
% 226.83/145.77 inference(unit_resolution,[status(thm)],[363, 328])).
% 226.83/145.77 tff(365,plain,
% 226.83/145.77 (addition(addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2)))), zero) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), zero))),
% 226.83/145.77 inference(symmetry,[status(thm)],[364])).
% 226.83/145.77 tff(366,plain,
% 226.83/145.77 (multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = multiplication(X1!1, tptp_fun_X1_0(X1!1))),
% 226.83/145.77 inference(monotonicity,[status(thm)],[204])).
% 226.83/145.77 tff(367,plain,
% 226.83/145.77 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 226.83/145.77 inference(symmetry,[status(thm)],[366])).
% 226.83/145.77 tff(368,plain,
% 226.83/145.77 (zero = multiplication(X1!1, tptp_fun_X1_0(X1!1))),
% 226.83/145.77 inference(symmetry,[status(thm)],[185])).
% 226.83/145.77 tff(369,plain,
% 226.83/145.77 (zero = multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 226.83/145.77 inference(transitivity,[status(thm)],[368, 367])).
% 226.83/145.77 tff(370,plain,
% 226.83/145.77 (addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 226.83/145.77 inference(monotonicity,[status(thm)],[204])).
% 226.83/145.77 tff(371,plain,
% 226.83/145.77 (addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 226.83/145.77 inference(transitivity,[status(thm)],[370, 174, 92, 260])).
% 226.83/145.77 tff(372,plain,
% 226.83/145.77 (multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.77 inference(monotonicity,[status(thm)],[371])).
% 226.83/145.77 tff(373,plain,
% 226.83/145.77 ((~![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(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))))),
% 226.83/145.77 inference(quant_inst,[status(thm)],[])).
% 226.83/145.77 tff(374,plain,
% 226.83/145.77 (multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 226.83/145.77 inference(unit_resolution,[status(thm)],[373, 235])).
% 226.83/145.77 tff(375,plain,
% 226.83/145.77 (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(symmetry,[status(thm)],[374])).
% 226.83/145.78 tff(376,plain,
% 226.83/145.78 (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[355])).
% 226.83/145.78 tff(377,plain,
% 226.83/145.78 (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1))) = tptp_fun_X1_0(X0!2)),
% 226.83/145.78 inference(transitivity,[status(thm)],[376, 375, 372, 228, 227])).
% 226.83/145.78 tff(378,plain,
% 226.83/145.78 (multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), X0!2)),
% 226.83/145.78 inference(monotonicity,[status(thm)],[377, 131])).
% 226.83/145.78 tff(379,plain,
% 226.83/145.78 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1))), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2)))))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(380,plain,
% 226.83/145.78 (multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1))), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[379, 141])).
% 226.83/145.78 tff(381,plain,
% 226.83/145.78 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.78 inference(symmetry,[status(thm)],[380])).
% 226.83/145.78 tff(382,plain,
% 226.83/145.78 (addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 226.83/145.78 inference(transitivity,[status(thm)],[381, 378, 100, 368, 367])).
% 226.83/145.78 tff(383,plain,
% 226.83/145.78 (addition(addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2)))), zero) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[382, 369])).
% 226.83/145.78 tff(384,plain,
% 226.83/145.78 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = addition(addition(multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2)))), zero)),
% 226.83/145.78 inference(symmetry,[status(thm)],[383])).
% 226.83/145.78 tff(385,plain,
% 226.83/145.78 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(386,plain,
% 226.83/145.78 (multiplication(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[385, 235])).
% 226.83/145.78 tff(387,plain,
% 226.83/145.78 (multiplication(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(X1!1, tptp_fun_X1_0(X1!1))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[204, 320])).
% 226.83/145.78 tff(388,plain,
% 226.83/145.78 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(symmetry,[status(thm)],[387])).
% 226.83/145.78 tff(389,plain,
% 226.83/145.78 (multiplication(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[371])).
% 226.83/145.78 tff(390,plain,
% 226.83/145.78 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(391,plain,
% 226.83/145.78 (multiplication(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[390, 141])).
% 226.83/145.78 tff(392,plain,
% 226.83/145.78 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 226.83/145.78 inference(symmetry,[status(thm)],[391])).
% 226.83/145.78 tff(393,plain,
% 226.83/145.78 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(c(X1!1), c(X0!2))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[346, 353])).
% 226.83/145.78 tff(394,plain,
% 226.83/145.78 (multiplication(c(X1!1), c(X0!2)) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))),
% 226.83/145.78 inference(symmetry,[status(thm)],[393])).
% 226.83/145.78 tff(395,plain,
% 226.83/145.78 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[394])).
% 226.83/145.78 tff(396,plain,
% 226.83/145.78 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))) = tptp_fun_X1_0(X0!2)),
% 226.83/145.78 inference(transitivity,[status(thm)],[395, 392, 389, 265, 269, 238, 228, 227])).
% 226.83/145.78 tff(397,plain,
% 226.83/145.78 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2)))) = multiplication(X0!2, tptp_fun_X1_0(X0!2))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[131, 396])).
% 226.83/145.78 tff(398,plain,
% 226.83/145.78 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2)))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2)))))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(399,plain,
% 226.83/145.78 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2)))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[398, 235])).
% 226.83/145.78 tff(400,plain,
% 226.83/145.78 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2)))) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))))),
% 226.83/145.78 inference(symmetry,[status(thm)],[399])).
% 226.83/145.78 tff(401,plain,
% 226.83/145.78 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(multiplication(c(X0!2), c(X1!1)), one) = multiplication(c(X0!2), c(X1!1)))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(402,plain,
% 226.83/145.78 (multiplication(multiplication(c(X0!2), c(X1!1)), one) = multiplication(c(X0!2), c(X1!1))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[401, 225])).
% 226.83/145.78 tff(403,plain,
% 226.83/145.78 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 226.83/145.78 inference(symmetry,[status(thm)],[97])).
% 226.83/145.78 tff(404,plain,
% 226.83/145.78 (addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 226.83/145.78 inference(monotonicity,[status(thm)],[131])).
% 226.83/145.78 tff(405,plain,
% 226.83/145.78 (addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))) = one),
% 226.83/145.78 inference(transitivity,[status(thm)],[404, 403, 76])).
% 226.83/145.78 tff(406,plain,
% 226.83/145.78 (multiplication(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(c(X0!2), c(X1!1)), one)),
% 226.83/145.78 inference(monotonicity,[status(thm)],[405])).
% 226.83/145.78 tff(407,plain,
% 226.83/145.78 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2)))))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(408,plain,
% 226.83/145.78 (multiplication(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[407, 235])).
% 226.83/145.78 tff(409,plain,
% 226.83/145.78 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(c(X0!2), c(X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.78 inference(symmetry,[status(thm)],[408])).
% 226.83/145.78 tff(410,plain,
% 226.83/145.78 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, tptp_fun_X1_0(X1!1)) = tptp_fun_X1_0(X1!1))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(411,plain,
% 226.83/145.78 (multiplication(one, tptp_fun_X1_0(X1!1)) = tptp_fun_X1_0(X1!1)),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[410, 34])).
% 226.83/145.78 tff(412,plain,
% 226.83/145.78 (multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = multiplication(one, tptp_fun_X1_0(X1!1))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[405])).
% 226.83/145.78 tff(413,plain,
% 226.83/145.78 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.78 inference(symmetry,[status(thm)],[404])).
% 226.83/145.78 tff(414,plain,
% 226.83/145.78 (addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))) = addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.78 inference(transitivity,[status(thm)],[331, 311, 174, 92, 97, 413])).
% 226.83/145.78 tff(415,plain,
% 226.83/145.78 (multiplication(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[414])).
% 226.83/145.78 tff(416,plain,
% 226.83/145.78 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(417,plain,
% 226.83/145.78 (multiplication(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[416, 141])).
% 226.83/145.78 tff(418,plain,
% 226.83/145.78 (addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = multiplication(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1))),
% 226.83/145.78 inference(symmetry,[status(thm)],[417])).
% 226.83/145.78 tff(419,plain,
% 226.83/145.78 (addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), zero) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[369])).
% 226.83/145.78 tff(420,plain,
% 226.83/145.78 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), zero) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(421,plain,
% 226.83/145.78 (addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), zero) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[420, 253])).
% 226.83/145.78 tff(422,plain,
% 226.83/145.78 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), zero)),
% 226.83/145.78 inference(symmetry,[status(thm)],[421])).
% 226.83/145.78 tff(423,plain,
% 226.83/145.78 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)) = c(X1!1)),
% 226.83/145.78 inference(transitivity,[status(thm)],[422, 419, 418, 415, 412, 411, 346])).
% 226.83/145.78 tff(424,plain,
% 226.83/145.78 (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), c(X1!1))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[353, 423])).
% 226.83/145.78 tff(425,plain,
% 226.83/145.78 (multiplication(c(X0!2), c(X1!1)) = multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(symmetry,[status(thm)],[424])).
% 226.83/145.78 tff(426,plain,
% 226.83/145.78 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(tptp_fun_X1_0(X0!2), zero)) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), zero))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[425])).
% 226.83/145.78 tff(427,plain,
% 226.83/145.78 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), zero)) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(tptp_fun_X1_0(X0!2), zero))),
% 226.83/145.78 inference(symmetry,[status(thm)],[426])).
% 226.83/145.78 tff(428,plain,
% 226.83/145.78 ((~![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(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), zero)) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), zero)))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(429,plain,
% 226.83/145.78 (multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), zero)) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), zero))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[428, 235])).
% 226.83/145.78 tff(430,plain,
% 226.83/145.78 (multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), zero)) = multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[421])).
% 226.83/145.78 tff(431,plain,
% 226.83/145.78 (multiplication(tptp_fun_X1_0(X0!2), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), zero))),
% 226.83/145.78 inference(symmetry,[status(thm)],[430])).
% 226.83/145.78 tff(432,plain,
% 226.83/145.78 (multiplication(c(X0!2), c(X1!1)) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(tptp_fun_X1_0(X0!2), zero))),
% 226.83/145.78 inference(transitivity,[status(thm)],[425, 431, 429, 427])).
% 226.83/145.78 tff(433,plain,
% 226.83/145.78 (multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(tptp_fun_X1_0(X0!2), zero)), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[432])).
% 226.83/145.78 tff(434,plain,
% 226.83/145.78 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(tptp_fun_X1_0(X0!2), zero)), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.78 inference(symmetry,[status(thm)],[433])).
% 226.83/145.78 tff(435,plain,
% 226.83/145.78 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(tptp_fun_X1_0(X0!2), zero)), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(tptp_fun_X1_0(X0!2), zero), c(tptp_fun_X1_0(X0!2)))))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(436,plain,
% 226.83/145.78 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(tptp_fun_X1_0(X0!2), zero)), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(tptp_fun_X1_0(X0!2), zero), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[435, 141])).
% 226.83/145.78 tff(437,plain,
% 226.83/145.78 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(tptp_fun_X1_0(X0!2), zero), c(tptp_fun_X1_0(X0!2)))) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), multiplication(tptp_fun_X1_0(X0!2), zero)), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.78 inference(symmetry,[status(thm)],[436])).
% 226.83/145.78 tff(438,plain,
% 226.83/145.78 (^[A: $i] : refl((multiplication(A, zero) = zero) <=> (multiplication(A, zero) = zero))),
% 226.83/145.78 inference(bind,[status(th)],[])).
% 226.83/145.78 tff(439,plain,
% 226.83/145.78 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 226.83/145.78 inference(quant_intro,[status(thm)],[438])).
% 226.83/145.78 tff(440,plain,
% 226.83/145.78 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 226.83/145.78 inference(rewrite,[status(thm)],[])).
% 226.83/145.78 tff(441,axiom,(![A: $i] : (multiplication(A, zero) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','right_annihilation')).
% 226.83/145.78 tff(442,plain,
% 226.83/145.78 (![A: $i] : (multiplication(A, zero) = zero)),
% 226.83/145.78 inference(modus_ponens,[status(thm)],[441, 440])).
% 226.83/145.78 tff(443,plain,(
% 226.83/145.78 ![A: $i] : (multiplication(A, zero) = zero)),
% 226.83/145.78 inference(skolemize,[status(sab)],[442])).
% 226.83/145.78 tff(444,plain,
% 226.83/145.78 (![A: $i] : (multiplication(A, zero) = zero)),
% 226.83/145.78 inference(modus_ponens,[status(thm)],[443, 439])).
% 226.83/145.78 tff(445,plain,
% 226.83/145.78 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(tptp_fun_X1_0(X0!2), zero) = zero)),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(446,plain,
% 226.83/145.78 (multiplication(tptp_fun_X1_0(X0!2), zero) = zero),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[445, 444])).
% 226.83/145.78 tff(447,plain,
% 226.83/145.78 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, c(tptp_fun_X1_0(X0!2))) = zero)),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(448,plain,
% 226.83/145.78 (multiplication(zero, c(tptp_fun_X1_0(X0!2))) = zero),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[447, 296])).
% 226.83/145.78 tff(449,plain,
% 226.83/145.78 (multiplication(tptp_fun_X1_0(X0!2), multiplication(zero, c(tptp_fun_X1_0(X0!2)))) = multiplication(tptp_fun_X1_0(X0!2), zero)),
% 226.83/145.78 inference(monotonicity,[status(thm)],[448])).
% 226.83/145.78 tff(450,plain,
% 226.83/145.78 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X0!2), multiplication(zero, c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), zero), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(451,plain,
% 226.83/145.78 (multiplication(tptp_fun_X1_0(X0!2), multiplication(zero, c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), zero), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[450, 215])).
% 226.83/145.78 tff(452,plain,
% 226.83/145.78 (multiplication(multiplication(tptp_fun_X1_0(X0!2), zero), c(tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(zero, c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.78 inference(symmetry,[status(thm)],[451])).
% 226.83/145.78 tff(453,plain,
% 226.83/145.78 (multiplication(multiplication(tptp_fun_X1_0(X0!2), zero), c(tptp_fun_X1_0(X0!2))) = zero),
% 226.83/145.78 inference(transitivity,[status(thm)],[452, 449, 446])).
% 226.83/145.78 tff(454,plain,
% 226.83/145.78 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(tptp_fun_X1_0(X0!2), zero), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), zero)),
% 226.83/145.78 inference(monotonicity,[status(thm)],[453])).
% 226.83/145.78 tff(455,plain,
% 226.83/145.78 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), zero) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(multiplication(tptp_fun_X1_0(X0!2), zero), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.78 inference(symmetry,[status(thm)],[454])).
% 226.83/145.78 tff(456,plain,
% 226.83/145.78 (zero = multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.78 inference(transitivity,[status(thm)],[241, 359, 310, 308, 455, 437, 434])).
% 226.83/145.78 tff(457,plain,
% 226.83/145.78 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), zero) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(multiplication(c(X0!2), c(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[456])).
% 226.83/145.78 tff(458,plain,
% 226.83/145.78 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(c(tptp_fun_X1_0(X0!2)), one) = c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(459,plain,
% 226.83/145.78 (multiplication(c(tptp_fun_X1_0(X0!2)), one) = c(tptp_fun_X1_0(X0!2))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[458, 225])).
% 226.83/145.78 tff(460,plain,
% 226.83/145.78 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(tptp_fun_X1_0(X1!1), one) = addition(one, tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(461,plain,
% 226.83/145.78 (addition(tptp_fun_X1_0(X1!1), one) = addition(one, tptp_fun_X1_0(X1!1))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[460, 24])).
% 226.83/145.78 tff(462,plain,
% 226.83/145.78 (addition(one, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), one)),
% 226.83/145.78 inference(symmetry,[status(thm)],[461])).
% 226.83/145.78 tff(463,plain,
% 226.83/145.78 (addition(one, tptp_fun_X1_0(X1!1)) = one),
% 226.83/145.78 inference(transitivity,[status(thm)],[462, 334, 330, 321, 311, 174])).
% 226.83/145.78 tff(464,plain,
% 226.83/145.78 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(one, tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), one)),
% 226.83/145.78 inference(monotonicity,[status(thm)],[463])).
% 226.83/145.78 tff(465,plain,
% 226.83/145.78 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(tptp_fun_X1_0(X0!2)), addition(one, tptp_fun_X1_0(X1!1))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), one), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(466,plain,
% 226.83/145.78 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(one, tptp_fun_X1_0(X1!1))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), one), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[465, 235])).
% 226.83/145.78 tff(467,plain,
% 226.83/145.78 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), one), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(one, tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(symmetry,[status(thm)],[466])).
% 226.83/145.78 tff(468,plain,
% 226.83/145.78 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(469,plain,
% 226.83/145.78 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[468, 24])).
% 226.83/145.78 tff(470,plain,
% 226.83/145.78 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[355])).
% 226.83/145.78 tff(471,plain,
% 226.83/145.78 (addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(symmetry,[status(thm)],[470])).
% 226.83/145.78 tff(472,plain,
% 226.83/145.78 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(473,plain,
% 226.83/145.78 (multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[472, 141])).
% 226.83/145.78 tff(474,plain,
% 226.83/145.78 (multiplication(one, tptp_fun_X1_0(X1!1)) = multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 226.83/145.78 inference(symmetry,[status(thm)],[412])).
% 226.83/145.78 tff(475,plain,
% 226.83/145.78 (tptp_fun_X1_0(X1!1) = multiplication(one, tptp_fun_X1_0(X1!1))),
% 226.83/145.78 inference(symmetry,[status(thm)],[411])).
% 226.83/145.78 tff(476,plain,
% 226.83/145.78 (tptp_fun_X1_0(X1!1) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 226.83/145.78 inference(transitivity,[status(thm)],[475, 474, 473, 471, 469])).
% 226.83/145.78 tff(477,plain,
% 226.83/145.78 (multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[476])).
% 226.83/145.78 tff(478,plain,
% 226.83/145.78 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 226.83/145.78 inference(symmetry,[status(thm)],[477])).
% 226.83/145.78 tff(479,plain,
% 226.83/145.78 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(480,plain,
% 226.83/145.78 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[479, 235])).
% 226.83/145.78 tff(481,plain,
% 226.83/145.78 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 226.83/145.78 inference(symmetry,[status(thm)],[480])).
% 226.83/145.78 tff(482,plain,
% 226.83/145.78 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 226.83/145.78 inference(transitivity,[status(thm)],[481, 478])).
% 226.83/145.78 tff(483,plain,
% 226.83/145.78 (c(tptp_fun_X1_0(X0!2)) = multiplication(c(tptp_fun_X1_0(X0!2)), one)),
% 226.83/145.78 inference(symmetry,[status(thm)],[459])).
% 226.83/145.78 tff(484,plain,
% 226.83/145.78 (addition(c(tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), one), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[483, 482])).
% 226.83/145.78 tff(485,plain,
% 226.83/145.78 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), c(tptp_fun_X1_0(X0!2))) = addition(c(tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(486,plain,
% 226.83/145.78 (addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), c(tptp_fun_X1_0(X0!2))) = addition(c(tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))))),
% 226.83/145.78 inference(unit_resolution,[status(thm)],[485, 24])).
% 226.83/145.78 tff(487,plain,
% 226.83/145.78 (multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))),
% 226.83/145.78 inference(transitivity,[status(thm)],[477, 480])).
% 226.83/145.78 tff(488,plain,
% 226.83/145.78 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[487])).
% 226.83/145.78 tff(489,plain,
% 226.83/145.78 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = X0!2),
% 226.83/145.78 inference(transitivity,[status(thm)],[488, 486, 484, 467, 464, 459, 131])).
% 226.83/145.78 tff(490,plain,
% 226.83/145.78 (multiplication(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)) = multiplication(X0!2, tptp_fun_X1_0(X0!2))),
% 226.83/145.78 inference(monotonicity,[status(thm)],[489])).
% 226.83/145.78 tff(491,plain,
% 226.83/145.78 (multiplication(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)) = zero),
% 226.83/145.78 inference(transitivity,[status(thm)],[490, 102])).
% 226.83/145.78 tff(492,plain,
% 226.83/145.78 (addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), zero)),
% 226.83/145.78 inference(monotonicity,[status(thm)],[491])).
% 226.83/145.78 tff(493,plain,
% 226.83/145.78 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))), tptp_fun_X1_0(X0!2)) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))))),
% 226.83/145.78 inference(quant_inst,[status(thm)],[])).
% 226.83/145.78 tff(494,plain,
% 226.83/145.78 (multiplication(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))), tptp_fun_X1_0(X0!2)) = addition(multiplication(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(unit_resolution,[status(thm)],[493, 141])).
% 226.83/145.79 tff(495,plain,
% 226.83/145.79 ((~![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(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.79 inference(quant_inst,[status(thm)],[])).
% 226.83/145.79 tff(496,plain,
% 226.83/145.79 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(unit_resolution,[status(thm)],[495, 328])).
% 226.83/145.79 tff(497,plain,
% 226.83/145.79 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.79 inference(symmetry,[status(thm)],[496])).
% 226.83/145.79 tff(498,plain,
% 226.83/145.79 (addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 226.83/145.79 inference(symmetry,[status(thm)],[473])).
% 226.83/145.79 tff(499,plain,
% 226.83/145.79 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = tptp_fun_X1_0(X1!1)),
% 226.83/145.79 inference(transitivity,[status(thm)],[470, 498, 412, 411])).
% 226.83/145.79 tff(500,plain,
% 226.83/145.79 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[499])).
% 226.83/145.79 tff(501,plain,
% 226.83/145.79 (addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(symmetry,[status(thm)],[500])).
% 226.83/145.79 tff(502,plain,
% 226.83/145.79 (addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.79 inference(transitivity,[status(thm)],[501, 497])).
% 226.83/145.79 tff(503,plain,
% 226.83/145.79 (multiplication(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)) = multiplication(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))), tptp_fun_X1_0(X0!2))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[502])).
% 226.83/145.79 tff(504,plain,
% 226.83/145.79 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))))),
% 226.83/145.79 inference(quant_inst,[status(thm)],[])).
% 226.83/145.79 tff(505,plain,
% 226.83/145.79 (multiplication(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(unit_resolution,[status(thm)],[504, 141])).
% 226.83/145.79 tff(506,plain,
% 226.83/145.79 (addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = multiplication(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))),
% 226.83/145.79 inference(symmetry,[status(thm)],[505])).
% 226.83/145.79 tff(507,plain,
% 226.83/145.79 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 226.83/145.79 inference(symmetry,[status(thm)],[267])).
% 226.83/145.79 tff(508,plain,
% 226.83/145.79 (zero = multiplication(X0!2, tptp_fun_X1_0(X0!2))),
% 226.83/145.79 inference(symmetry,[status(thm)],[102])).
% 226.83/145.79 tff(509,plain,
% 226.83/145.79 (zero = multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 226.83/145.79 inference(transitivity,[status(thm)],[508, 507])).
% 226.83/145.79 tff(510,plain,
% 226.83/145.79 (addition(multiplication(c(X1!1), c(X0!2)), zero) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[394, 509])).
% 226.83/145.79 tff(511,plain,
% 226.83/145.79 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(tptp_fun_X1_0(X1!1), zero) = zero)),
% 226.83/145.79 inference(quant_inst,[status(thm)],[])).
% 226.83/145.79 tff(512,plain,
% 226.83/145.79 (multiplication(tptp_fun_X1_0(X1!1), zero) = zero),
% 226.83/145.79 inference(unit_resolution,[status(thm)],[511, 444])).
% 226.83/145.79 tff(513,plain,
% 226.83/145.79 (addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), zero)) = addition(multiplication(c(X1!1), c(X0!2)), zero)),
% 226.83/145.79 inference(monotonicity,[status(thm)],[393, 512])).
% 226.83/145.79 tff(514,plain,
% 226.83/145.79 ((~![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(tptp_fun_X1_0(X0!2), zero)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), zero)))),
% 226.83/145.79 inference(quant_inst,[status(thm)],[])).
% 226.83/145.79 tff(515,plain,
% 226.83/145.79 (multiplication(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), zero)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), zero))),
% 226.83/145.79 inference(unit_resolution,[status(thm)],[514, 235])).
% 226.83/145.79 tff(516,plain,
% 226.83/145.79 (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = addition(zero, multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(symmetry,[status(thm)],[243])).
% 226.83/145.79 tff(517,plain,
% 226.83/145.79 (tptp_fun_X1_0(X0!2) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))),
% 226.83/145.79 inference(transitivity,[status(thm)],[272, 271, 237, 516, 245, 255])).
% 226.83/145.79 tff(518,plain,
% 226.83/145.79 (addition(tptp_fun_X1_0(X0!2), zero) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), zero)),
% 226.83/145.79 inference(monotonicity,[status(thm)],[517])).
% 226.83/145.79 tff(519,plain,
% 226.83/145.79 (addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), zero) = addition(tptp_fun_X1_0(X0!2), zero)),
% 226.83/145.79 inference(symmetry,[status(thm)],[518])).
% 226.83/145.79 tff(520,plain,
% 226.83/145.79 (c(X0!2) = addition(tptp_fun_X1_0(X0!2), zero)),
% 226.83/145.79 inference(transitivity,[status(thm)],[352, 272, 271, 237, 516, 245, 519])).
% 226.83/145.79 tff(521,plain,
% 226.83/145.79 (multiplication(c(X1!1), c(X0!2)) = multiplication(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), zero))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[345, 520])).
% 226.83/145.79 tff(522,plain,
% 226.83/145.79 (multiplication(c(X1!1), c(X0!2)) = multiplication(c(X0!2), c(X1!1))),
% 226.83/145.79 inference(transitivity,[status(thm)],[521, 515, 513, 510, 506, 503, 494, 492, 457, 409, 406, 402])).
% 226.83/145.79 tff(523,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[522])).
% 226.83/145.79 tff(524,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2)))),
% 226.83/145.79 inference(symmetry,[status(thm)],[523])).
% 226.83/145.79 tff(525,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[355])).
% 226.83/145.79 tff(526,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))),
% 226.83/145.79 inference(symmetry,[status(thm)],[525])).
% 226.83/145.79 tff(527,plain,
% 226.83/145.79 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.79 inference(quant_inst,[status(thm)],[])).
% 226.83/145.79 tff(528,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 226.83/145.79 inference(unit_resolution,[status(thm)],[527, 215])).
% 226.83/145.79 tff(529,plain,
% 226.83/145.79 (multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 226.83/145.79 inference(symmetry,[status(thm)],[528])).
% 226.83/145.79 tff(530,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)) = zero),
% 226.83/145.79 inference(transitivity,[status(thm)],[267, 102])).
% 226.83/145.79 tff(531,plain,
% 226.83/145.79 (multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(zero, tptp_fun_X1_0(X1!1))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[530])).
% 226.83/145.79 tff(532,plain,
% 226.83/145.79 (multiplication(zero, tptp_fun_X1_0(X1!1)) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 226.83/145.79 inference(symmetry,[status(thm)],[531])).
% 226.83/145.79 tff(533,plain,
% 226.83/145.79 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, tptp_fun_X1_0(X1!1)) = zero)),
% 226.83/145.79 inference(quant_inst,[status(thm)],[])).
% 226.83/145.79 tff(534,plain,
% 226.83/145.79 (multiplication(zero, tptp_fun_X1_0(X1!1)) = zero),
% 226.83/145.79 inference(unit_resolution,[status(thm)],[533, 296])).
% 226.83/145.79 tff(535,plain,
% 226.83/145.79 (zero = multiplication(zero, tptp_fun_X1_0(X1!1))),
% 226.83/145.79 inference(symmetry,[status(thm)],[534])).
% 226.83/145.79 tff(536,plain,
% 226.83/145.79 (zero = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2)))),
% 226.83/145.79 inference(transitivity,[status(thm)],[535, 532, 529, 526, 524])).
% 226.83/145.79 tff(537,plain,
% 226.83/145.79 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))), zero) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[536])).
% 226.83/145.79 tff(538,plain,
% 226.83/145.79 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))), zero) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))))),
% 226.83/145.79 inference(quant_inst,[status(thm)],[])).
% 226.83/145.79 tff(539,plain,
% 226.83/145.79 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))), zero) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(unit_resolution,[status(thm)],[538, 253])).
% 226.83/145.79 tff(540,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))), zero)),
% 226.83/145.79 inference(symmetry,[status(thm)],[539])).
% 226.83/145.79 tff(541,plain,
% 226.83/145.79 (multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 226.83/145.79 inference(monotonicity,[status(thm)],[204])).
% 226.83/145.79 tff(542,plain,
% 226.83/145.79 (multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))) = zero),
% 226.83/145.79 inference(transitivity,[status(thm)],[541, 183])).
% 226.83/145.79 tff(543,plain,
% 226.83/145.79 (multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(zero, c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[542])).
% 226.83/145.79 tff(544,plain,
% 226.83/145.79 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))),
% 226.83/145.79 inference(symmetry,[status(thm)],[541])).
% 226.83/145.79 tff(545,plain,
% 226.83/145.79 (zero = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 226.83/145.79 inference(symmetry,[status(thm)],[183])).
% 226.83/145.79 tff(546,plain,
% 226.83/145.79 (multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))),
% 226.83/145.79 inference(transitivity,[status(thm)],[239, 100, 545, 544])).
% 226.83/145.79 tff(547,plain,
% 226.83/145.79 (multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[546])).
% 226.83/145.79 tff(548,plain,
% 226.83/145.79 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.79 inference(quant_inst,[status(thm)],[])).
% 226.83/145.79 tff(549,plain,
% 226.83/145.79 (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(unit_resolution,[status(thm)],[548, 215])).
% 226.83/145.79 tff(550,plain,
% 226.83/145.79 (multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))) = multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(transitivity,[status(thm)],[549, 547, 543, 448, 241, 240])).
% 226.83/145.79 tff(551,plain,
% 226.83/145.79 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[550])).
% 226.83/145.79 tff(552,plain,
% 226.83/145.79 ((~![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(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))))),
% 226.83/145.79 inference(quant_inst,[status(thm)],[])).
% 226.83/145.79 tff(553,plain,
% 226.83/145.79 (multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(unit_resolution,[status(thm)],[552, 235])).
% 226.83/145.79 tff(554,plain,
% 226.83/145.79 (multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))) = tptp_fun_X1_0(X0!2)),
% 226.83/145.79 inference(transitivity,[status(thm)],[553, 551, 238, 228, 227])).
% 226.83/145.79 tff(555,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[554])).
% 226.83/145.79 tff(556,plain,
% 226.83/145.79 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))))),
% 226.83/145.79 inference(quant_inst,[status(thm)],[])).
% 226.83/145.79 tff(557,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(unit_resolution,[status(thm)],[556, 215])).
% 226.83/145.79 tff(558,plain,
% 226.83/145.79 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))))),
% 226.83/145.79 inference(symmetry,[status(thm)],[557])).
% 226.83/145.79 tff(559,plain,
% 226.83/145.79 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 226.83/145.79 inference(transitivity,[status(thm)],[558, 555])).
% 226.83/145.79 tff(560,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[559])).
% 226.83/145.79 tff(561,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))) = multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, X0!2))),
% 226.83/145.79 inference(transitivity,[status(thm)],[560, 540, 537, 400, 397, 102, 368, 388, 386, 384, 365, 362, 306, 289, 286, 218, 208])).
% 226.83/145.79 tff(562,plain,
% 226.83/145.79 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(X1!1, X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(X1!1, X0!2)), multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, X0!2)))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[561])).
% 226.83/145.79 tff(563,plain,
% 226.83/145.79 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(tptp_fun_X1_0(X0!2)), addition(multiplication(X1!1, X0!2), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(X1!1, X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))))))),
% 226.83/145.79 inference(quant_inst,[status(thm)],[])).
% 226.83/145.79 tff(564,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(multiplication(X1!1, X0!2), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(X1!1, X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))))),
% 226.83/145.79 inference(unit_resolution,[status(thm)],[563, 235])).
% 226.83/145.79 tff(565,plain,
% 226.83/145.79 (addition(multiplication(X1!1, X0!2), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[206, 559])).
% 226.83/145.79 tff(566,plain,
% 226.83/145.79 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = addition(multiplication(X1!1, X0!2), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))))),
% 226.83/145.79 inference(symmetry,[status(thm)],[565])).
% 226.83/145.79 tff(567,plain,
% 226.83/145.79 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(tptp_fun_X1_0(X1!1)), addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))))),
% 226.83/145.79 inference(quant_inst,[status(thm)],[])).
% 226.83/145.79 tff(568,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X1!1)), addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(unit_resolution,[status(thm)],[567, 235])).
% 226.83/145.79 tff(569,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X1!1)), addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), one)),
% 226.83/145.79 inference(monotonicity,[status(thm)],[133])).
% 226.83/145.79 tff(570,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X1!1)), one) = multiplication(c(tptp_fun_X1_0(X1!1)), addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.79 inference(symmetry,[status(thm)],[569])).
% 226.83/145.79 tff(571,plain,
% 226.83/145.79 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(c(tptp_fun_X1_0(X1!1)), one) = c(tptp_fun_X1_0(X1!1)))),
% 226.83/145.79 inference(quant_inst,[status(thm)],[])).
% 226.83/145.79 tff(572,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X1!1)), one) = c(tptp_fun_X1_0(X1!1))),
% 226.83/145.79 inference(unit_resolution,[status(thm)],[571, 225])).
% 226.83/145.79 tff(573,plain,
% 226.83/145.79 (c(tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), one)),
% 226.83/145.79 inference(symmetry,[status(thm)],[572])).
% 226.83/145.79 tff(574,plain,
% 226.83/145.79 (X1!1 = c(tptp_fun_X1_0(X1!1))),
% 226.83/145.79 inference(symmetry,[status(thm)],[204])).
% 226.83/145.79 tff(575,plain,
% 226.83/145.79 (X1!1 = addition(multiplication(X1!1, X0!2), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))))),
% 226.83/145.79 inference(transitivity,[status(thm)],[574, 573, 570, 568, 566])).
% 226.83/145.79 tff(576,plain,
% 226.83/145.79 (X0!2 = c(tptp_fun_X1_0(X0!2))),
% 226.83/145.79 inference(symmetry,[status(thm)],[131])).
% 226.83/145.79 tff(577,plain,
% 226.83/145.79 (multiplication(X0!2, X1!1) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(multiplication(X1!1, X0!2), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[576, 575])).
% 226.83/145.79 tff(578,plain,
% 226.83/145.79 (multiplication(X0!2, X1!1) = multiplication(X1!1, X0!2)),
% 226.83/145.79 inference(transitivity,[status(thm)],[577, 564, 562, 144, 134, 36])).
% 226.83/145.79 tff(579,plain,
% 226.83/145.79 (c(multiplication(X0!2, X1!1)) = c(multiplication(X1!1, X0!2))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[578])).
% 226.83/145.79 tff(580,plain,
% 226.83/145.79 (c(multiplication(X1!1, X0!2)) = c(multiplication(X0!2, X1!1))),
% 226.83/145.79 inference(symmetry,[status(thm)],[579])).
% 226.83/145.79 tff(581,plain,
% 226.83/145.79 ((c(multiplication(X1!1, X0!2)) = addition(c(X1!1), c(X0!2))) <=> (c(multiplication(X0!2, X1!1)) = addition(c(X0!2), c(X1!1)))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[580, 27])).
% 226.83/145.79 tff(582,plain,
% 226.83/145.79 ((c(multiplication(X0!2, X1!1)) = addition(c(X0!2), c(X1!1))) <=> (c(multiplication(X1!1, X0!2)) = addition(c(X1!1), c(X0!2)))),
% 226.83/145.79 inference(symmetry,[status(thm)],[581])).
% 226.83/145.79 tff(583,plain,
% 226.83/145.79 ((~(c(multiplication(X0!2, X1!1)) = addition(c(X0!2), c(X1!1)))) <=> (~(c(multiplication(X1!1, X0!2)) = addition(c(X1!1), c(X0!2))))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[582])).
% 226.83/145.79 tff(584,plain,
% 226.83/145.79 (~(c(multiplication(X0!2, X1!1)) = addition(c(X0!2), c(X1!1)))),
% 226.83/145.79 inference(or_elim,[status(thm)],[66])).
% 226.83/145.79 tff(585,plain,
% 226.83/145.79 (~(c(multiplication(X1!1, X0!2)) = addition(c(X1!1), c(X0!2)))),
% 226.83/145.79 inference(modus_ponens,[status(thm)],[584, 583])).
% 226.83/145.79 tff(586,plain,
% 226.83/145.79 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) <=> (~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) <=> (~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one))))))),
% 226.83/145.79 inference(rewrite,[status(thm)],[])).
% 226.83/145.79 tff(587,plain,
% 226.83/145.79 ((complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) <=> (~((~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one))))) <=> (complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) <=> (~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one)))))),
% 226.83/145.79 inference(rewrite,[status(thm)],[])).
% 226.83/145.79 tff(588,plain,
% 226.83/145.79 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) <=> (~((~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) <=> (~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one))))))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[587])).
% 226.83/145.79 tff(589,plain,
% 226.83/145.79 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) <=> (~((~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) <=> (~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one))))))),
% 226.83/145.79 inference(transitivity,[status(thm)],[588, 586])).
% 226.83/145.79 tff(590,plain,
% 226.83/145.79 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) <=> (~((~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one)))))),
% 226.83/145.79 inference(quant_inst,[status(thm)],[])).
% 226.83/145.79 tff(591,plain,
% 226.83/145.79 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) <=> (~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one)))))),
% 226.83/145.79 inference(modus_ponens,[status(thm)],[590, 589])).
% 226.83/145.79 tff(592,plain,
% 226.83/145.79 (complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) <=> (~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one))))),
% 226.83/145.79 inference(unit_resolution,[status(thm)],[591, 49])).
% 226.83/145.79 tff(593,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), one)),
% 226.83/145.79 inference(monotonicity,[status(thm)],[405])).
% 226.83/145.79 tff(594,plain,
% 226.83/145.79 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))))),
% 226.83/145.79 inference(quant_inst,[status(thm)],[])).
% 226.83/145.79 tff(595,plain,
% 226.83/145.79 (multiplication(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.79 inference(unit_resolution,[status(thm)],[594, 235])).
% 226.83/145.79 tff(596,plain,
% 226.83/145.79 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.79 inference(symmetry,[status(thm)],[595])).
% 226.83/145.79 tff(597,plain,
% 226.83/145.79 (addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))), multiplication(X1!1, X0!2)) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.79 inference(monotonicity,[status(thm)],[559, 206])).
% 226.83/145.79 tff(598,plain,
% 226.83/145.79 (addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))), multiplication(X1!1, X0!2)) = X1!1),
% 226.83/145.79 inference(transitivity,[status(thm)],[597, 596, 593, 572, 204])).
% 226.83/145.79 tff(599,plain,
% 226.83/145.79 (addition(tptp_fun_X1_0(X1!1), addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))), multiplication(X1!1, X0!2))) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 226.83/145.79 inference(monotonicity,[status(thm)],[598])).
% 226.83/145.79 tff(600,plain,
% 226.83/145.79 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X1!1), addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))), multiplication(X1!1, X0!2))) = addition(addition(tptp_fun_X1_0(X1!1), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))), multiplication(X1!1, X0!2)))),
% 226.83/145.80 inference(quant_inst,[status(thm)],[])).
% 226.83/145.80 tff(601,plain,
% 226.83/145.80 (addition(tptp_fun_X1_0(X1!1), addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))), multiplication(X1!1, X0!2))) = addition(addition(tptp_fun_X1_0(X1!1), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))), multiplication(X1!1, X0!2))),
% 226.83/145.80 inference(unit_resolution,[status(thm)],[600, 328])).
% 226.83/145.80 tff(602,plain,
% 226.83/145.80 (addition(addition(tptp_fun_X1_0(X1!1), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))), multiplication(X1!1, X0!2)) = addition(tptp_fun_X1_0(X1!1), addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))), multiplication(X1!1, X0!2)))),
% 226.83/145.80 inference(symmetry,[status(thm)],[601])).
% 226.83/145.80 tff(603,plain,
% 226.83/145.80 (addition(tptp_fun_X1_0(X1!1), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))) = addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[559])).
% 226.83/145.80 tff(604,plain,
% 226.83/145.80 (addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = addition(tptp_fun_X1_0(X1!1), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))))),
% 226.83/145.80 inference(symmetry,[status(thm)],[603])).
% 226.83/145.80 tff(605,plain,
% 226.83/145.80 (addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), multiplication(c(X1!1), c(X0!2))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[482, 522])).
% 226.83/145.80 tff(606,plain,
% 226.83/145.80 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), multiplication(c(X1!1), c(X0!2)))),
% 226.83/145.80 inference(symmetry,[status(thm)],[605])).
% 226.83/145.80 tff(607,plain,
% 226.83/145.80 (tptp_fun_X1_0(X1!1) = addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), multiplication(c(X1!1), c(X0!2)))),
% 226.83/145.80 inference(transitivity,[status(thm)],[475, 474, 473, 471, 469, 606])).
% 226.83/145.80 tff(608,plain,
% 226.83/145.80 (addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = addition(addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), multiplication(c(X1!1), c(X0!2))), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[607])).
% 226.83/145.80 tff(609,plain,
% 226.83/145.80 (addition(addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), multiplication(c(X1!1), c(X0!2))), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(symmetry,[status(thm)],[608])).
% 226.83/145.80 tff(610,plain,
% 226.83/145.80 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X1!1), c(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))) = addition(addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), multiplication(c(X1!1), c(X0!2))), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))))),
% 226.83/145.80 inference(quant_inst,[status(thm)],[])).
% 226.83/145.80 tff(611,plain,
% 226.83/145.80 (addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X1!1), c(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))) = addition(addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), multiplication(c(X1!1), c(X0!2))), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(unit_resolution,[status(thm)],[610, 328])).
% 226.83/145.80 tff(612,plain,
% 226.83/145.80 (addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))) = addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 226.83/145.80 inference(transitivity,[status(thm)],[331, 311, 174, 92, 260])).
% 226.83/145.80 tff(613,plain,
% 226.83/145.80 (multiplication(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)) = multiplication(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[612])).
% 226.83/145.80 tff(614,plain,
% 226.83/145.80 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))))),
% 226.83/145.80 inference(quant_inst,[status(thm)],[])).
% 226.83/145.80 tff(615,plain,
% 226.83/145.80 (multiplication(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(unit_resolution,[status(thm)],[614, 141])).
% 226.83/145.80 tff(616,plain,
% 226.83/145.80 (addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2))),
% 226.83/145.80 inference(symmetry,[status(thm)],[615])).
% 226.83/145.80 tff(617,plain,
% 226.83/145.80 (addition(multiplication(c(X1!1), c(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[394])).
% 226.83/145.80 tff(618,plain,
% 226.83/145.80 (addition(multiplication(c(X1!1), c(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = tptp_fun_X1_0(X0!2)),
% 226.83/145.80 inference(transitivity,[status(thm)],[617, 616, 613, 265, 269, 238, 228, 227])).
% 226.83/145.80 tff(619,plain,
% 226.83/145.80 (addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X1!1), c(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[482, 618])).
% 226.83/145.80 tff(620,plain,
% 226.83/145.80 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X1!1), c(X0!2)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))))),
% 226.83/145.80 inference(symmetry,[status(thm)],[619])).
% 226.83/145.80 tff(621,plain,
% 226.83/145.80 (addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), one)) = addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2))),
% 226.83/145.80 inference(symmetry,[status(thm)],[356])).
% 226.83/145.80 tff(622,plain,
% 226.83/145.80 (multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), one))),
% 226.83/145.80 inference(symmetry,[status(thm)],[336])).
% 226.83/145.80 tff(623,plain,
% 226.83/145.80 (tptp_fun_X1_0(X0!2) = addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2))),
% 226.83/145.80 inference(transitivity,[status(thm)],[272, 271, 622, 338, 621])).
% 226.83/145.80 tff(624,plain,
% 226.83/145.80 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[623])).
% 226.83/145.80 tff(625,plain,
% 226.83/145.80 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 226.83/145.80 inference(symmetry,[status(thm)],[624])).
% 226.83/145.80 tff(626,plain,
% 226.83/145.80 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2))) = addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))), tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(quant_inst,[status(thm)],[])).
% 226.83/145.80 tff(627,plain,
% 226.83/145.80 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2))) = addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))), tptp_fun_X1_0(X0!2))),
% 226.83/145.80 inference(unit_resolution,[status(thm)],[626, 328])).
% 226.83/145.80 tff(628,plain,
% 226.83/145.80 (addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))), tptp_fun_X1_0(X0!2)) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(symmetry,[status(thm)],[627])).
% 226.83/145.80 tff(629,plain,
% 226.83/145.80 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.80 inference(symmetry,[status(thm)],[469])).
% 226.83/145.80 tff(630,plain,
% 226.83/145.80 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))) = c(X1!1)),
% 226.83/145.80 inference(transitivity,[status(thm)],[629, 470, 498, 412, 411, 346])).
% 226.83/145.80 tff(631,plain,
% 226.83/145.80 (addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))), tptp_fun_X1_0(X0!2)) = addition(c(X1!1), c(X0!2))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[630, 353])).
% 226.83/145.80 tff(632,plain,
% 226.83/145.80 (addition(c(X1!1), c(X0!2)) = addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))), tptp_fun_X1_0(X0!2))),
% 226.83/145.80 inference(symmetry,[status(thm)],[631])).
% 226.83/145.80 tff(633,plain,
% 226.83/145.80 (addition(c(X1!1), c(X0!2)) = addition(tptp_fun_X1_0(X1!1), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))))),
% 226.83/145.80 inference(transitivity,[status(thm)],[632, 628, 625, 620, 611, 609, 604])).
% 226.83/145.80 tff(634,plain,
% 226.83/145.80 (addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = addition(addition(tptp_fun_X1_0(X1!1), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))), multiplication(X1!1, X0!2))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[633])).
% 226.83/145.80 tff(635,plain,
% 226.83/145.80 (addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one),
% 226.83/145.80 inference(transitivity,[status(thm)],[634, 602, 599, 311, 174])).
% 226.83/145.80 tff(636,plain,
% 226.83/145.80 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)))),
% 226.83/145.80 inference(symmetry,[status(thm)],[386])).
% 226.83/145.80 tff(637,plain,
% 226.83/145.80 (multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 226.83/145.80 inference(transitivity,[status(thm)],[207, 217, 285, 288, 305, 361, 364, 383, 636, 387, 367])).
% 226.83/145.80 tff(638,plain,
% 226.83/145.80 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.80 inference(quant_inst,[status(thm)],[])).
% 226.83/145.80 tff(639,plain,
% 226.83/145.80 (multiplication(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(unit_resolution,[status(thm)],[638, 215])).
% 226.83/145.80 tff(640,plain,
% 226.83/145.80 (multiplication(tptp_fun_X1_0(X1!1), multiplication(X1!1, X0!2)) = multiplication(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[206])).
% 226.83/145.80 tff(641,plain,
% 226.83/145.80 (multiplication(tptp_fun_X1_0(X1!1), multiplication(X1!1, X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 226.83/145.80 inference(transitivity,[status(thm)],[640, 639, 543, 448, 368, 367])).
% 226.83/145.80 tff(642,plain,
% 226.83/145.80 (addition(multiplication(tptp_fun_X1_0(X1!1), multiplication(X1!1, X0!2)), multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, X0!2))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[641, 637])).
% 226.83/145.80 tff(643,plain,
% 226.83/145.80 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(X1!1, X0!2)) = addition(multiplication(tptp_fun_X1_0(X1!1), multiplication(X1!1, X0!2)), multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, X0!2))))),
% 226.83/145.80 inference(quant_inst,[status(thm)],[])).
% 226.83/145.80 tff(644,plain,
% 226.83/145.80 (multiplication(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(X1!1, X0!2)) = addition(multiplication(tptp_fun_X1_0(X1!1), multiplication(X1!1, X0!2)), multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, X0!2)))),
% 226.83/145.80 inference(unit_resolution,[status(thm)],[643, 141])).
% 226.83/145.80 tff(645,plain,
% 226.83/145.80 (addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = addition(c(X1!1), c(X0!2))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[346, 353])).
% 226.83/145.80 tff(646,plain,
% 226.83/145.80 (addition(c(X1!1), c(X0!2)) = addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))),
% 226.83/145.80 inference(symmetry,[status(thm)],[645])).
% 226.83/145.80 tff(647,plain,
% 226.83/145.80 (multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = multiplication(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(X1!1, X0!2))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[646])).
% 226.83/145.80 tff(648,plain,
% 226.83/145.80 (multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero),
% 226.83/145.80 inference(transitivity,[status(thm)],[647, 644, 642, 636, 387, 185])).
% 226.83/145.80 tff(649,plain,
% 226.83/145.80 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(c(tptp_fun_X1_0(X1!1)), zero) = zero)),
% 226.83/145.80 inference(quant_inst,[status(thm)],[])).
% 226.83/145.80 tff(650,plain,
% 226.83/145.80 (multiplication(c(tptp_fun_X1_0(X1!1)), zero) = zero),
% 226.83/145.80 inference(unit_resolution,[status(thm)],[649, 444])).
% 226.83/145.80 tff(651,plain,
% 226.83/145.80 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), zero)),
% 226.83/145.80 inference(monotonicity,[status(thm)],[530])).
% 226.83/145.80 tff(652,plain,
% 226.83/145.80 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(quant_inst,[status(thm)],[])).
% 226.83/145.80 tff(653,plain,
% 226.83/145.80 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))),
% 226.83/145.80 inference(unit_resolution,[status(thm)],[652, 215])).
% 226.83/145.80 tff(654,plain,
% 226.83/145.80 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(symmetry,[status(thm)],[653])).
% 226.83/145.80 tff(655,plain,
% 226.83/145.80 (multiplication(multiplication(X1!1, X0!2), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[206])).
% 226.83/145.80 tff(656,plain,
% 226.83/145.80 (multiplication(multiplication(X1!1, X0!2), tptp_fun_X1_0(X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 226.83/145.80 inference(transitivity,[status(thm)],[655, 654, 651, 650, 368, 367])).
% 226.83/145.80 tff(657,plain,
% 226.83/145.80 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))) = tptp_fun_X1_0(X1!1)),
% 226.83/145.80 inference(transitivity,[status(thm)],[629, 470, 498, 412, 411])).
% 226.83/145.80 tff(658,plain,
% 226.83/145.80 (addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[657])).
% 226.83/145.80 tff(659,plain,
% 226.83/145.80 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))) = addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))), tptp_fun_X1_0(X1!1)))),
% 226.83/145.80 inference(quant_inst,[status(thm)],[])).
% 226.83/145.80 tff(660,plain,
% 226.83/145.80 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))) = addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))), tptp_fun_X1_0(X1!1))),
% 226.83/145.80 inference(unit_resolution,[status(thm)],[659, 328])).
% 226.83/145.80 tff(661,plain,
% 226.83/145.80 (addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[482])).
% 226.83/145.80 tff(662,plain,
% 226.83/145.80 (addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))) = tptp_fun_X1_0(X1!1)),
% 226.83/145.80 inference(transitivity,[status(thm)],[661, 660, 658, 320])).
% 226.83/145.80 tff(663,plain,
% 226.83/145.80 (multiplication(c(tptp_fun_X1_0(X1!1)), addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)))) = multiplication(X1!1, tptp_fun_X1_0(X1!1))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[204, 662])).
% 226.83/145.80 tff(664,plain,
% 226.83/145.80 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(tptp_fun_X1_0(X1!1)), addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))), multiplication(c(tptp_fun_X1_0(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)))))),
% 226.83/145.80 inference(quant_inst,[status(thm)],[])).
% 226.83/145.80 tff(665,plain,
% 226.83/145.80 (multiplication(c(tptp_fun_X1_0(X1!1)), addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))), multiplication(c(tptp_fun_X1_0(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))))),
% 226.83/145.80 inference(unit_resolution,[status(thm)],[664, 235])).
% 226.83/145.80 tff(666,plain,
% 226.83/145.80 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))), multiplication(c(tptp_fun_X1_0(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X1!1)), addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))))),
% 226.83/145.80 inference(symmetry,[status(thm)],[665])).
% 226.83/145.80 tff(667,plain,
% 226.83/145.80 (addition(tptp_fun_X1_0(X1!1), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[657])).
% 226.83/145.80 tff(668,plain,
% 226.83/145.80 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X1!1), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1))))),
% 226.83/145.80 inference(quant_inst,[status(thm)],[])).
% 226.83/145.80 tff(669,plain,
% 226.83/145.80 (addition(tptp_fun_X1_0(X1!1), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1)))),
% 226.83/145.80 inference(unit_resolution,[status(thm)],[668, 328])).
% 226.83/145.80 tff(670,plain,
% 226.83/145.80 (addition(addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1))) = addition(tptp_fun_X1_0(X1!1), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 226.83/145.80 inference(symmetry,[status(thm)],[669])).
% 226.83/145.80 tff(671,plain,
% 226.83/145.80 (addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)) = c(X1!1)),
% 226.83/145.80 inference(transitivity,[status(thm)],[320, 346])).
% 226.83/145.80 tff(672,plain,
% 226.83/145.80 (multiplication(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), c(X1!1))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[353, 671])).
% 226.83/145.80 tff(673,plain,
% 226.83/145.80 ((~![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(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))))),
% 226.83/145.80 inference(quant_inst,[status(thm)],[])).
% 226.83/145.80 tff(674,plain,
% 226.83/145.80 (multiplication(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 226.83/145.80 inference(unit_resolution,[status(thm)],[673, 235])).
% 226.83/145.80 tff(675,plain,
% 226.83/145.80 (addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)))),
% 226.83/145.80 inference(symmetry,[status(thm)],[674])).
% 226.83/145.80 tff(676,plain,
% 226.83/145.80 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[355, 355])).
% 226.83/145.80 tff(677,plain,
% 226.83/145.80 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1))) = multiplication(c(X0!2), c(X1!1))),
% 226.83/145.80 inference(transitivity,[status(thm)],[676, 675, 672])).
% 226.83/145.80 tff(678,plain,
% 226.83/145.80 (addition(addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1)))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[677])).
% 226.83/145.80 tff(679,plain,
% 226.83/145.80 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1))), multiplication(c(X0!2), c(X1!1))))),
% 226.83/145.80 inference(quant_inst,[status(thm)],[])).
% 226.83/145.80 tff(680,plain,
% 226.83/145.80 (addition(addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1))), multiplication(c(X0!2), c(X1!1)))),
% 226.83/145.80 inference(unit_resolution,[status(thm)],[679, 328])).
% 226.83/145.80 tff(681,plain,
% 226.83/145.80 (addition(addition(addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1))), multiplication(c(X0!2), c(X1!1))) = addition(addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 226.83/145.80 inference(symmetry,[status(thm)],[680])).
% 226.83/145.80 tff(682,plain,
% 226.83/145.80 (addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 226.83/145.80 inference(symmetry,[status(thm)],[667])).
% 226.83/145.80 tff(683,plain,
% 226.83/145.80 (tptp_fun_X1_0(X1!1) = addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))),
% 226.83/145.80 inference(symmetry,[status(thm)],[320])).
% 226.83/145.80 tff(684,plain,
% 226.83/145.80 (tptp_fun_X1_0(X1!1) = addition(addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1)))),
% 226.83/145.80 inference(transitivity,[status(thm)],[683, 682, 669])).
% 226.83/145.80 tff(685,plain,
% 226.83/145.80 (addition(tptp_fun_X1_0(X1!1), multiplication(c(X0!2), c(X1!1))) = addition(addition(addition(tptp_fun_X1_0(X1!1), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(X0!2), c(X1!1))), multiplication(c(X0!2), c(X1!1)))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[684])).
% 226.83/145.80 tff(686,plain,
% 226.83/145.80 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(tptp_fun_X1_0(X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.80 inference(quant_inst,[status(thm)],[])).
% 226.83/145.80 tff(687,plain,
% 226.83/145.80 (addition(tptp_fun_X1_0(X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))),
% 226.83/145.80 inference(unit_resolution,[status(thm)],[686, 24])).
% 226.83/145.80 tff(688,plain,
% 226.83/145.80 (addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), multiplication(c(X0!2), c(X1!1)))),
% 226.83/145.80 inference(symmetry,[status(thm)],[687])).
% 226.83/145.80 tff(689,plain,
% 226.83/145.80 (addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)) = tptp_fun_X1_0(X1!1)),
% 226.83/145.80 inference(transitivity,[status(thm)],[688, 685, 681, 678, 670, 667, 320])).
% 226.83/145.80 tff(690,plain,
% 226.83/145.80 (multiplication(c(tptp_fun_X1_0(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))) = multiplication(X1!1, tptp_fun_X1_0(X1!1))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[204, 689])).
% 226.83/145.80 tff(691,plain,
% 226.83/145.80 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.80 inference(symmetry,[status(thm)],[690])).
% 226.83/145.80 tff(692,plain,
% 226.83/145.80 (zero = multiplication(c(tptp_fun_X1_0(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.80 inference(transitivity,[status(thm)],[368, 691])).
% 226.83/145.80 tff(693,plain,
% 226.83/145.80 (multiplication(c(tptp_fun_X1_0(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[482])).
% 226.83/145.80 tff(694,plain,
% 226.83/145.80 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))))),
% 226.83/145.80 inference(symmetry,[status(thm)],[693])).
% 226.83/145.80 tff(695,plain,
% 226.83/145.80 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), zero) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))), multiplication(c(tptp_fun_X1_0(X1!1)), addition(multiplication(c(X0!2), c(X1!1)), tptp_fun_X1_0(X1!1))))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[694, 692])).
% 226.83/145.80 tff(696,plain,
% 226.83/145.80 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))), multiplication(c(tptp_fun_X1_0(X1!1)), zero)) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), zero)),
% 226.83/145.80 inference(monotonicity,[status(thm)],[693, 650])).
% 226.83/145.80 tff(697,plain,
% 226.83/145.80 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(tptp_fun_X1_0(X1!1)), addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), zero)) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))), multiplication(c(tptp_fun_X1_0(X1!1)), zero)))),
% 226.83/145.80 inference(quant_inst,[status(thm)],[])).
% 226.83/145.80 tff(698,plain,
% 226.83/145.80 (multiplication(c(tptp_fun_X1_0(X1!1)), addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), zero)) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))), multiplication(c(tptp_fun_X1_0(X1!1)), zero))),
% 226.83/145.80 inference(unit_resolution,[status(thm)],[697, 235])).
% 226.83/145.80 tff(699,plain,
% 226.83/145.80 (multiplication(c(tptp_fun_X1_0(X0!2)), zero) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[242])).
% 226.83/145.80 tff(700,plain,
% 226.83/145.80 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = multiplication(c(tptp_fun_X1_0(X0!2)), zero)),
% 226.83/145.80 inference(symmetry,[status(thm)],[699])).
% 226.83/145.80 tff(701,plain,
% 226.83/145.80 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.80 inference(quant_inst,[status(thm)],[])).
% 226.83/145.80 tff(702,plain,
% 226.83/145.80 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(unit_resolution,[status(thm)],[701, 215])).
% 226.83/145.80 tff(703,plain,
% 226.83/145.80 (multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 226.83/145.80 inference(symmetry,[status(thm)],[702])).
% 226.83/145.80 tff(704,plain,
% 226.83/145.80 (multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1)))),
% 226.83/145.80 inference(transitivity,[status(thm)],[267, 102, 545, 544])).
% 226.83/145.80 tff(705,plain,
% 226.83/145.80 (multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[704])).
% 226.83/145.80 tff(706,plain,
% 226.83/145.80 (multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(symmetry,[status(thm)],[705])).
% 226.83/145.80 tff(707,plain,
% 226.83/145.80 (multiplication(zero, c(tptp_fun_X1_0(X0!2))) = multiplication(multiplication(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(symmetry,[status(thm)],[543])).
% 226.83/145.80 tff(708,plain,
% 226.83/145.80 (zero = multiplication(zero, c(tptp_fun_X1_0(X0!2)))),
% 226.83/145.80 inference(symmetry,[status(thm)],[448])).
% 226.83/145.80 tff(709,plain,
% 226.83/145.80 (zero = multiplication(c(tptp_fun_X1_0(X0!2)), zero)),
% 226.83/145.80 inference(transitivity,[status(thm)],[708, 707, 706, 703, 700])).
% 226.83/145.80 tff(710,plain,
% 226.83/145.80 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)) = tptp_fun_X1_0(X1!1)),
% 226.83/145.80 inference(transitivity,[status(thm)],[422, 419, 418, 415, 412, 411])).
% 226.83/145.80 tff(711,plain,
% 226.83/145.80 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 226.83/145.80 inference(monotonicity,[status(thm)],[710])).
% 226.83/145.80 tff(712,plain,
% 226.83/145.80 (multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)))),
% 226.83/145.80 inference(symmetry,[status(thm)],[711])).
% 226.83/145.80 tff(713,plain,
% 226.83/145.80 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)))),
% 226.83/145.80 inference(transitivity,[status(thm)],[481, 478, 712])).
% 226.83/145.81 tff(714,plain,
% 226.83/145.81 (addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), zero) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), zero))),
% 226.83/145.81 inference(monotonicity,[status(thm)],[713, 709])).
% 226.83/145.81 tff(715,plain,
% 226.83/145.81 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), zero)) = addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), zero)),
% 226.83/145.81 inference(symmetry,[status(thm)],[714])).
% 226.83/145.81 tff(716,plain,
% 226.83/145.81 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(tptp_fun_X1_0(X0!2)), addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), zero)) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), zero)))),
% 226.83/145.81 inference(quant_inst,[status(thm)],[])).
% 226.83/145.81 tff(717,plain,
% 226.83/145.81 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), zero)) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), zero))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[716, 235])).
% 226.83/145.81 tff(718,plain,
% 226.83/145.81 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), zero)) = multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)))),
% 226.83/145.81 inference(monotonicity,[status(thm)],[421])).
% 226.83/145.81 tff(719,plain,
% 226.83/145.81 (multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X1!1)), zero))),
% 226.83/145.81 inference(symmetry,[status(thm)],[718])).
% 226.83/145.81 tff(720,plain,
% 226.83/145.81 (multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), zero)),
% 226.83/145.81 inference(transitivity,[status(thm)],[712, 719, 717, 715])).
% 226.83/145.81 tff(721,plain,
% 226.83/145.81 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X1!1)), addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))), zero))),
% 226.83/145.81 inference(monotonicity,[status(thm)],[720])).
% 226.83/145.81 tff(722,plain,
% 226.83/145.81 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)))),
% 226.83/145.81 inference(quant_inst,[status(thm)],[])).
% 226.83/145.81 tff(723,plain,
% 226.83/145.81 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[722, 215])).
% 226.83/145.81 tff(724,plain,
% 226.83/145.81 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.81 inference(symmetry,[status(thm)],[723])).
% 226.83/145.81 tff(725,plain,
% 226.83/145.81 (multiplication(multiplication(X1!1, X0!2), tptp_fun_X1_0(X1!1)) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 226.83/145.81 inference(monotonicity,[status(thm)],[206])).
% 226.83/145.81 tff(726,plain,
% 226.83/145.81 (multiplication(multiplication(X1!1, X0!2), tptp_fun_X1_0(X1!1)) = multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))),
% 226.83/145.81 inference(transitivity,[status(thm)],[725, 724, 721, 698, 696, 695, 666, 663, 367])).
% 226.83/145.81 tff(727,plain,
% 226.83/145.81 (addition(multiplication(multiplication(X1!1, X0!2), tptp_fun_X1_0(X1!1)), multiplication(multiplication(X1!1, X0!2), tptp_fun_X1_0(X0!2))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.81 inference(monotonicity,[status(thm)],[726, 656])).
% 226.83/145.81 tff(728,plain,
% 226.83/145.81 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(multiplication(X1!1, X0!2), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(X1!1, X0!2), tptp_fun_X1_0(X1!1)), multiplication(multiplication(X1!1, X0!2), tptp_fun_X1_0(X0!2))))),
% 226.83/145.81 inference(quant_inst,[status(thm)],[])).
% 226.83/145.81 tff(729,plain,
% 226.83/145.81 (multiplication(multiplication(X1!1, X0!2), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(X1!1, X0!2), tptp_fun_X1_0(X1!1)), multiplication(multiplication(X1!1, X0!2), tptp_fun_X1_0(X0!2)))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[728, 235])).
% 226.83/145.81 tff(730,plain,
% 226.83/145.81 (multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = multiplication(multiplication(X1!1, X0!2), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 226.83/145.81 inference(monotonicity,[status(thm)],[646])).
% 226.83/145.81 tff(731,plain,
% 226.83/145.81 (multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero),
% 226.83/145.81 inference(transitivity,[status(thm)],[730, 729, 727, 636, 387, 185])).
% 226.83/145.81 tff(732,plain,
% 226.83/145.81 ((~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one)))) | (~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one))),
% 226.83/145.81 inference(tautology,[status(thm)],[])).
% 226.83/145.81 tff(733,plain,
% 226.83/145.81 (~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one)))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[732, 731, 648, 635])).
% 226.83/145.81 tff(734,plain,
% 226.83/145.81 ((~(complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) <=> (~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one)))))) | complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) | ((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one)))),
% 226.83/145.81 inference(tautology,[status(thm)],[])).
% 226.83/145.81 tff(735,plain,
% 226.83/145.81 ((~(complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) <=> (~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = one)))))) | complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2)))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[734, 733])).
% 226.83/145.81 tff(736,plain,
% 226.83/145.81 (complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2)))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[735, 592])).
% 226.83/145.81 tff(737,plain,
% 226.83/145.81 ((~((c(multiplication(X1!1, X0!2)) = addition(c(X1!1), c(X0!2))) <=> complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))))) | (c(multiplication(X1!1, X0!2)) = addition(c(X1!1), c(X0!2))) | (~complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))))),
% 226.83/145.81 inference(tautology,[status(thm)],[])).
% 226.83/145.81 tff(738,plain,
% 226.83/145.81 ((~((c(multiplication(X1!1, X0!2)) = addition(c(X1!1), c(X0!2))) <=> complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))))) | (c(multiplication(X1!1, X0!2)) = addition(c(X1!1), c(X0!2)))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[737, 736])).
% 226.83/145.81 tff(739,plain,
% 226.83/145.81 (~((c(multiplication(X1!1, X0!2)) = addition(c(X1!1), c(X0!2))) <=> complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[738, 585])).
% 226.83/145.81 tff(740,plain,
% 226.83/145.81 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(multiplication(X1!1, X0!2))) | ((c(multiplication(X1!1, X0!2)) = addition(c(X1!1), c(X0!2))) <=> complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(multiplication(X1!1, X0!2))) | ((c(multiplication(X1!1, X0!2)) = addition(c(X1!1), c(X0!2))) <=> complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2)))))),
% 226.83/145.81 inference(rewrite,[status(thm)],[])).
% 226.83/145.81 tff(741,plain,
% 226.83/145.81 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(multiplication(X1!1, X0!2))) | ((c(multiplication(X1!1, X0!2)) = addition(c(X1!1), c(X0!2))) <=> complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2)))))),
% 226.83/145.81 inference(quant_inst,[status(thm)],[])).
% 226.83/145.81 tff(742,plain,
% 226.83/145.81 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(multiplication(X1!1, X0!2))) | ((c(multiplication(X1!1, X0!2)) = addition(c(X1!1), c(X0!2))) <=> complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))))),
% 226.83/145.81 inference(modus_ponens,[status(thm)],[741, 740])).
% 226.83/145.81 tff(743,plain,
% 226.83/145.81 ((~test(multiplication(X1!1, X0!2))) | ((c(multiplication(X1!1, X0!2)) = addition(c(X1!1), c(X0!2))) <=> complement(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[742, 123])).
% 226.83/145.81 tff(744,plain,
% 226.83/145.81 (~test(multiplication(X1!1, X0!2))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[743, 739])).
% 226.83/145.81 tff(745,plain,
% 226.83/145.81 ((~(test(multiplication(X1!1, X0!2)) | ![X1: $i] : (~complement(X1, multiplication(X1!1, X0!2))))) | test(multiplication(X1!1, X0!2)) | ![X1: $i] : (~complement(X1, multiplication(X1!1, X0!2)))),
% 226.83/145.81 inference(tautology,[status(thm)],[])).
% 226.83/145.81 tff(746,plain,
% 226.83/145.81 ((~(test(multiplication(X1!1, X0!2)) | ![X1: $i] : (~complement(X1, multiplication(X1!1, X0!2))))) | ![X1: $i] : (~complement(X1, multiplication(X1!1, X0!2)))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[745, 744])).
% 226.83/145.81 tff(747,plain,
% 226.83/145.81 (![X1: $i] : (~complement(X1, multiplication(X1!1, X0!2)))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[746, 17])).
% 226.83/145.81 tff(748,plain,
% 226.83/145.81 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) <=> (~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = one)))))),
% 226.83/145.81 inference(quant_inst,[status(thm)],[])).
% 226.83/145.81 tff(749,plain,
% 226.83/145.81 (complement(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) <=> (~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = one))))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[748, 49])).
% 226.83/145.81 tff(750,plain,
% 226.83/145.81 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))), multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.81 inference(symmetry,[status(thm)],[568])).
% 226.83/145.81 tff(751,plain,
% 226.83/145.81 (addition(multiplication(X1!1, X0!2), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))) = X1!1),
% 226.83/145.81 inference(transitivity,[status(thm)],[565, 750, 569, 572, 204])).
% 226.83/145.81 tff(752,plain,
% 226.83/145.81 (addition(addition(multiplication(X1!1, X0!2), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))), tptp_fun_X1_0(X1!1)) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 226.83/145.81 inference(monotonicity,[status(thm)],[751])).
% 226.83/145.81 tff(753,plain,
% 226.83/145.81 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X1!1, X0!2), addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))) = addition(addition(multiplication(X1!1, X0!2), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))), tptp_fun_X1_0(X1!1)))),
% 226.83/145.81 inference(quant_inst,[status(thm)],[])).
% 226.83/145.81 tff(754,plain,
% 226.83/145.81 (addition(multiplication(X1!1, X0!2), addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))) = addition(addition(multiplication(X1!1, X0!2), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2)))), tptp_fun_X1_0(X1!1))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[753, 328])).
% 226.83/145.81 tff(755,plain,
% 226.83/145.81 (addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 226.83/145.81 inference(monotonicity,[status(thm)],[559])).
% 226.83/145.81 tff(756,plain,
% 226.83/145.81 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 226.83/145.81 inference(symmetry,[status(thm)],[755])).
% 226.83/145.81 tff(757,plain,
% 226.83/145.81 (multiplication(c(X1!1), c(X0!2)) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 226.83/145.81 inference(transitivity,[status(thm)],[521, 515, 513, 510, 506, 503, 494, 492, 457, 409, 406, 402, 355])).
% 226.83/145.81 tff(758,plain,
% 226.83/145.81 (addition(multiplication(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.81 inference(monotonicity,[status(thm)],[757, 482])).
% 226.83/145.81 tff(759,plain,
% 226.83/145.81 (addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))))),
% 226.83/145.81 inference(symmetry,[status(thm)],[758])).
% 226.83/145.81 tff(760,plain,
% 226.83/145.81 (tptp_fun_X1_0(X1!1) = addition(multiplication(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))))),
% 226.83/145.81 inference(transitivity,[status(thm)],[475, 474, 473, 759])).
% 226.83/145.81 tff(761,plain,
% 226.83/145.81 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))))),
% 226.83/145.81 inference(monotonicity,[status(thm)],[760])).
% 226.83/145.81 tff(762,plain,
% 226.83/145.81 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 226.83/145.81 inference(symmetry,[status(thm)],[761])).
% 226.83/145.81 tff(763,plain,
% 226.83/145.81 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))))) = addition(addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))))),
% 226.83/145.81 inference(quant_inst,[status(thm)],[])).
% 226.83/145.81 tff(764,plain,
% 226.83/145.81 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))))) = addition(addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[763, 328])).
% 226.83/145.81 tff(765,plain,
% 226.83/145.81 (addition(addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))))),
% 226.83/145.81 inference(symmetry,[status(thm)],[764])).
% 226.83/145.81 tff(766,plain,
% 226.83/145.81 (addition(addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1))))) = addition(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.81 inference(monotonicity,[status(thm)],[396, 482])).
% 226.83/145.81 tff(767,plain,
% 226.83/145.81 (addition(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = addition(addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), multiplication(c(X0!2), c(X1!1)))))),
% 226.83/145.81 inference(symmetry,[status(thm)],[766])).
% 226.83/145.81 tff(768,plain,
% 226.83/145.81 (addition(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), one), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 226.83/145.81 inference(monotonicity,[status(thm)],[272, 355])).
% 226.83/145.81 tff(769,plain,
% 226.83/145.81 (addition(multiplication(tptp_fun_X1_0(X0!2), one), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = addition(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1)))),
% 226.83/145.81 inference(symmetry,[status(thm)],[768])).
% 226.83/145.81 tff(770,plain,
% 226.83/145.81 ((~![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(one, tptp_fun_X1_0(X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), one), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))))),
% 226.83/145.81 inference(quant_inst,[status(thm)],[])).
% 226.83/145.81 tff(771,plain,
% 226.83/145.81 (multiplication(tptp_fun_X1_0(X0!2), addition(one, tptp_fun_X1_0(X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), one), multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[770, 235])).
% 226.83/145.81 tff(772,plain,
% 226.83/145.81 (addition(one, tptp_fun_X1_0(X1!1)) = addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 226.83/145.81 inference(transitivity,[status(thm)],[462, 334, 330, 321, 311, 174, 92, 260])).
% 226.83/145.81 tff(773,plain,
% 226.83/145.81 (multiplication(tptp_fun_X1_0(X0!2), addition(one, tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))),
% 226.83/145.81 inference(monotonicity,[status(thm)],[772])).
% 226.83/145.81 tff(774,plain,
% 226.83/145.81 (multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), addition(one, tptp_fun_X1_0(X1!1)))),
% 226.83/145.81 inference(symmetry,[status(thm)],[773])).
% 226.83/145.81 tff(775,plain,
% 226.83/145.81 (tptp_fun_X1_0(X0!2) = addition(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1)))),
% 226.83/145.81 inference(transitivity,[status(thm)],[272, 271, 774, 771, 769])).
% 226.83/145.81 tff(776,plain,
% 226.83/145.81 (addition(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = addition(addition(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.81 inference(monotonicity,[status(thm)],[775])).
% 226.83/145.81 tff(777,plain,
% 226.83/145.81 (addition(addition(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = addition(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.81 inference(symmetry,[status(thm)],[776])).
% 226.83/145.81 tff(778,plain,
% 226.83/145.81 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))) = addition(addition(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))))),
% 226.83/145.81 inference(quant_inst,[status(thm)],[])).
% 226.83/145.81 tff(779,plain,
% 226.83/145.81 (addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))) = addition(addition(tptp_fun_X1_0(X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 226.83/145.81 inference(unit_resolution,[status(thm)],[778, 328])).
% 226.83/145.81 tff(780,plain,
% 226.83/145.81 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = c(X1!1)),
% 226.83/145.81 inference(transitivity,[status(thm)],[470, 498, 412, 411, 346])).
% 226.83/145.81 tff(781,plain,
% 226.83/145.81 (addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))) = addition(c(X0!2), c(X1!1))),
% 226.83/145.81 inference(monotonicity,[status(thm)],[353, 780])).
% 226.83/145.81 tff(782,plain,
% 226.83/145.81 (addition(c(X0!2), c(X1!1)) = addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))))),
% 226.83/145.81 inference(symmetry,[status(thm)],[781])).
% 226.83/145.81 tff(783,plain,
% 226.83/145.81 (addition(c(X1!1), c(X0!2)) = addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 226.87/145.82 inference(transitivity,[status(thm)],[27, 782, 779, 777, 767, 765, 762, 756])).
% 226.87/145.82 tff(784,plain,
% 226.87/145.82 (addition(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = addition(multiplication(X1!1, X0!2), addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)))),
% 226.87/145.82 inference(monotonicity,[status(thm)],[783])).
% 226.87/145.82 tff(785,plain,
% 226.87/145.82 (addition(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = one),
% 226.87/145.82 inference(transitivity,[status(thm)],[784, 754, 752, 174])).
% 226.87/145.82 tff(786,plain,
% 226.87/145.82 ((~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = one)))) | (~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = one))),
% 226.87/145.82 inference(tautology,[status(thm)],[])).
% 226.87/145.82 tff(787,plain,
% 226.87/145.82 (~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = one)))),
% 226.87/145.82 inference(unit_resolution,[status(thm)],[786, 731, 648, 785])).
% 226.87/145.82 tff(788,plain,
% 226.87/145.82 ((~(complement(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) <=> (~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = one)))))) | complement(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) | ((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = one)))),
% 226.87/145.82 inference(tautology,[status(thm)],[])).
% 226.87/145.82 tff(789,plain,
% 226.87/145.82 ((~(complement(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) <=> (~((~(multiplication(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = zero)) | (~(multiplication(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)) = zero)) | (~(addition(multiplication(X1!1, X0!2), addition(c(X1!1), c(X0!2))) = one)))))) | complement(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2))),
% 226.87/145.82 inference(unit_resolution,[status(thm)],[788, 787])).
% 226.87/145.82 tff(790,plain,
% 226.87/145.82 (complement(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2))),
% 226.87/145.82 inference(unit_resolution,[status(thm)],[789, 749])).
% 226.87/145.82 tff(791,plain,
% 226.87/145.82 ((~![X1: $i] : (~complement(X1, multiplication(X1!1, X0!2)))) | (~complement(addition(c(X1!1), c(X0!2)), multiplication(X1!1, X0!2)))),
% 226.87/145.82 inference(quant_inst,[status(thm)],[])).
% 226.87/145.82 tff(792,plain,
% 226.87/145.82 ($false),
% 226.87/145.82 inference(unit_resolution,[status(thm)],[791, 790, 747])).
% 226.87/145.82 % SZS output end Proof
%------------------------------------------------------------------------------