TSTP Solution File: KLE012+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE012+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 17:23:49 EDT 2022
% Result : Theorem 1.71s 1.34s
% Output : Proof 1.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE012+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 07:47:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.71/1.34 % SZS status Theorem
% 1.71/1.34 % SZS output start Proof
% 1.71/1.34 tff(multiplication_type, type, (
% 1.71/1.34 multiplication: ( $i * $i ) > $i)).
% 1.71/1.34 tff(tptp_fun_X0_2_type, type, (
% 1.71/1.34 tptp_fun_X0_2: $i)).
% 1.71/1.34 tff(tptp_fun_X1_1_type, type, (
% 1.71/1.34 tptp_fun_X1_1: $i)).
% 1.71/1.34 tff(one_type, type, (
% 1.71/1.34 one: $i)).
% 1.71/1.34 tff(addition_type, type, (
% 1.71/1.34 addition: ( $i * $i ) > $i)).
% 1.71/1.34 tff(tptp_fun_X1_0_type, type, (
% 1.71/1.34 tptp_fun_X1_0: $i > $i)).
% 1.71/1.34 tff(zero_type, type, (
% 1.71/1.34 zero: $i)).
% 1.71/1.34 tff(complement_type, type, (
% 1.71/1.34 complement: ( $i * $i ) > $o)).
% 1.71/1.34 tff(test_type, type, (
% 1.71/1.34 test: $i > $o)).
% 1.71/1.34 tff(1,plain,
% 1.71/1.34 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 1.71/1.34 inference(bind,[status(th)],[])).
% 1.71/1.34 tff(2,plain,
% 1.71/1.34 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 1.71/1.34 inference(quant_intro,[status(thm)],[1])).
% 1.71/1.34 tff(3,plain,
% 1.71/1.34 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 1.71/1.34 inference(rewrite,[status(thm)],[])).
% 1.71/1.34 tff(4,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 1.71/1.34 tff(5,plain,
% 1.71/1.34 (![A: $i] : (multiplication(one, A) = A)),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.71/1.34 tff(6,plain,(
% 1.71/1.34 ![A: $i] : (multiplication(one, A) = A)),
% 1.71/1.34 inference(skolemize,[status(sab)],[5])).
% 1.71/1.34 tff(7,plain,
% 1.71/1.34 (![A: $i] : (multiplication(one, A) = A)),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.71/1.34 tff(8,plain,
% 1.71/1.34 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!2) = X0!2)),
% 1.71/1.34 inference(quant_inst,[status(thm)],[])).
% 1.71/1.34 tff(9,plain,
% 1.71/1.34 (multiplication(one, X0!2) = X0!2),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.71/1.34 tff(10,plain,
% 1.71/1.34 (X0!2 = multiplication(one, X0!2)),
% 1.71/1.34 inference(symmetry,[status(thm)],[9])).
% 1.71/1.34 tff(11,plain,
% 1.71/1.34 (multiplication(X1!1, X0!2) = multiplication(X1!1, multiplication(one, X0!2))),
% 1.71/1.34 inference(monotonicity,[status(thm)],[10])).
% 1.71/1.34 tff(12,plain,
% 1.71/1.34 (multiplication(X1!1, multiplication(one, X0!2)) = multiplication(X1!1, X0!2)),
% 1.71/1.34 inference(symmetry,[status(thm)],[11])).
% 1.71/1.34 tff(13,plain,
% 1.71/1.34 (^[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)))),
% 1.71/1.34 inference(bind,[status(th)],[])).
% 1.71/1.34 tff(14,plain,
% 1.71/1.34 (![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))),
% 1.71/1.34 inference(quant_intro,[status(thm)],[13])).
% 1.71/1.34 tff(15,plain,
% 1.71/1.34 (![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))),
% 1.71/1.34 inference(rewrite,[status(thm)],[])).
% 1.71/1.34 tff(16,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_associativity')).
% 1.71/1.34 tff(17,plain,
% 1.71/1.34 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.71/1.34 tff(18,plain,(
% 1.71/1.34 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 1.71/1.34 inference(skolemize,[status(sab)],[17])).
% 1.71/1.34 tff(19,plain,
% 1.71/1.34 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.71/1.34 tff(20,plain,
% 1.71/1.34 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X1!1, multiplication(one, X0!2)) = multiplication(multiplication(X1!1, one), X0!2))),
% 1.71/1.34 inference(quant_inst,[status(thm)],[])).
% 1.71/1.34 tff(21,plain,
% 1.71/1.34 (multiplication(X1!1, multiplication(one, X0!2)) = multiplication(multiplication(X1!1, one), X0!2)),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[20, 19])).
% 1.71/1.34 tff(22,plain,
% 1.71/1.34 (multiplication(multiplication(X1!1, one), X0!2) = multiplication(X1!1, multiplication(one, X0!2))),
% 1.71/1.34 inference(symmetry,[status(thm)],[21])).
% 1.71/1.34 tff(23,plain,
% 1.71/1.34 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, multiplication(multiplication(X1!1, one), X0!2)) = multiplication(multiplication(X1!1, one), X0!2))),
% 1.71/1.34 inference(quant_inst,[status(thm)],[])).
% 1.71/1.34 tff(24,plain,
% 1.71/1.34 (multiplication(one, multiplication(multiplication(X1!1, one), X0!2)) = multiplication(multiplication(X1!1, one), X0!2)),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[23, 7])).
% 1.71/1.34 tff(25,plain,
% 1.71/1.34 (multiplication(multiplication(X1!1, one), X0!2) = multiplication(X1!1, X0!2)),
% 1.71/1.34 inference(transitivity,[status(thm)],[22, 12])).
% 1.71/1.34 tff(26,plain,
% 1.71/1.34 (multiplication(one, multiplication(multiplication(X1!1, one), X0!2)) = multiplication(one, multiplication(X1!1, X0!2))),
% 1.71/1.34 inference(monotonicity,[status(thm)],[25])).
% 1.71/1.34 tff(27,plain,
% 1.71/1.34 (multiplication(one, multiplication(X1!1, X0!2)) = multiplication(one, multiplication(multiplication(X1!1, one), X0!2))),
% 1.71/1.34 inference(symmetry,[status(thm)],[26])).
% 1.71/1.34 tff(28,plain,
% 1.71/1.34 (multiplication(X1!1, X0!2) = multiplication(multiplication(X1!1, one), X0!2)),
% 1.71/1.34 inference(transitivity,[status(thm)],[11, 21])).
% 1.71/1.34 tff(29,plain,
% 1.71/1.34 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 1.71/1.34 inference(bind,[status(th)],[])).
% 1.71/1.34 tff(30,plain,
% 1.71/1.34 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.71/1.34 inference(quant_intro,[status(thm)],[29])).
% 1.71/1.34 tff(31,plain,
% 1.71/1.34 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.71/1.34 inference(rewrite,[status(thm)],[])).
% 1.71/1.34 tff(32,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 1.71/1.34 tff(33,plain,
% 1.71/1.34 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.71/1.34 tff(34,plain,(
% 1.71/1.34 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.71/1.34 inference(skolemize,[status(sab)],[33])).
% 1.71/1.34 tff(35,plain,
% 1.71/1.34 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[34, 30])).
% 1.71/1.34 tff(36,plain,
% 1.71/1.34 ((~![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))),
% 1.71/1.34 inference(quant_inst,[status(thm)],[])).
% 1.71/1.34 tff(37,plain,
% 1.71/1.34 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[36, 35])).
% 1.71/1.34 tff(38,plain,
% 1.71/1.34 (^[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))))))),
% 1.71/1.34 inference(bind,[status(th)],[])).
% 1.71/1.34 tff(39,plain,
% 1.71/1.34 (![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)))))),
% 1.71/1.34 inference(quant_intro,[status(thm)],[38])).
% 1.71/1.34 tff(40,plain,
% 1.71/1.34 (^[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))))))),
% 1.71/1.34 inference(bind,[status(th)],[])).
% 1.71/1.34 tff(41,plain,
% 1.71/1.34 (![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)))))),
% 1.71/1.34 inference(quant_intro,[status(thm)],[40])).
% 1.71/1.34 tff(42,plain,
% 1.71/1.34 (![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)))),
% 1.71/1.34 inference(rewrite,[status(thm)],[])).
% 1.71/1.34 tff(43,plain,
% 1.71/1.34 (^[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))))),
% 1.71/1.34 inference(bind,[status(th)],[])).
% 1.71/1.34 tff(44,plain,
% 1.71/1.34 (![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)))),
% 1.71/1.34 inference(quant_intro,[status(thm)],[43])).
% 1.71/1.34 tff(45,axiom,(![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_2')).
% 1.71/1.34 tff(46,plain,
% 1.71/1.34 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.71/1.34 tff(47,plain,
% 1.71/1.34 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[46, 42])).
% 1.71/1.34 tff(48,plain,(
% 1.71/1.34 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 1.71/1.34 inference(skolemize,[status(sab)],[47])).
% 1.71/1.34 tff(49,plain,
% 1.71/1.34 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[48, 41])).
% 1.71/1.34 tff(50,plain,
% 1.71/1.34 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[49, 39])).
% 1.71/1.34 tff(51,plain,
% 1.71/1.34 ((~![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)))))),
% 1.71/1.34 inference(quant_inst,[status(thm)],[])).
% 1.71/1.34 tff(52,plain,
% 1.71/1.34 (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))))),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[51, 50])).
% 1.71/1.34 tff(53,plain,
% 1.71/1.34 (^[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)))))))),
% 1.71/1.34 inference(bind,[status(th)],[])).
% 1.71/1.34 tff(54,plain,
% 1.71/1.34 (![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))))))),
% 1.71/1.34 inference(quant_intro,[status(thm)],[53])).
% 1.71/1.34 tff(55,plain,
% 1.71/1.34 (^[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)))))))),
% 1.71/1.34 inference(bind,[status(th)],[])).
% 1.71/1.34 tff(56,plain,
% 1.71/1.34 (![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))))))),
% 1.71/1.34 inference(quant_intro,[status(thm)],[55])).
% 1.71/1.34 tff(57,plain,
% 1.71/1.34 (![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))))))),
% 1.71/1.34 inference(transitivity,[status(thm)],[56, 54])).
% 1.71/1.34 tff(58,plain,
% 1.71/1.34 (^[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))))))))),
% 1.71/1.34 inference(bind,[status(th)],[])).
% 1.71/1.34 tff(59,plain,
% 1.71/1.34 (![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))))))),
% 1.71/1.34 inference(quant_intro,[status(thm)],[58])).
% 1.71/1.34 tff(60,plain,
% 1.71/1.34 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 1.71/1.34 inference(rewrite,[status(thm)],[])).
% 1.71/1.34 tff(61,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_1')).
% 1.71/1.34 tff(62,plain,
% 1.71/1.34 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[61, 60])).
% 1.71/1.34 tff(63,plain,(
% 1.71/1.34 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 1.71/1.34 inference(skolemize,[status(sab)],[62])).
% 1.71/1.34 tff(64,plain,
% 1.71/1.34 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[63, 59])).
% 1.71/1.34 tff(65,plain,
% 1.71/1.34 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[64, 57])).
% 1.71/1.34 tff(66,plain,
% 1.71/1.34 ((~![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))))))),
% 1.71/1.34 inference(quant_inst,[status(thm)],[])).
% 1.71/1.34 tff(67,plain,
% 1.71/1.34 (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2)))))),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[66, 65])).
% 1.71/1.34 tff(68,plain,
% 1.71/1.34 (((~((~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))),
% 1.71/1.34 inference(tautology,[status(thm)],[])).
% 1.71/1.34 tff(69,plain,
% 1.71/1.34 ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[68, 67])).
% 1.71/1.34 tff(70,plain,
% 1.71/1.34 ((~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (multiplication(X0, X1) = multiplication(X1, X0)))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (multiplication(X0, X1) = multiplication(X1, X0))))),
% 1.71/1.34 inference(rewrite,[status(thm)],[])).
% 1.71/1.34 tff(71,plain,
% 1.71/1.34 ((~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (multiplication(X0, X1) = multiplication(X1, X0)))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (multiplication(X0, X1) = multiplication(X1, X0))))),
% 1.71/1.34 inference(rewrite,[status(thm)],[])).
% 1.71/1.34 tff(72,axiom,(~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (multiplication(X0, X1) = multiplication(X1, X0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 1.71/1.34 tff(73,plain,
% 1.71/1.34 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (multiplication(X0, X1) = multiplication(X1, X0)))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[72, 71])).
% 1.71/1.34 tff(74,plain,
% 1.71/1.34 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (multiplication(X0, X1) = multiplication(X1, X0)))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[73, 70])).
% 1.71/1.34 tff(75,plain,
% 1.71/1.34 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (multiplication(X0, X1) = multiplication(X1, X0)))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[74, 70])).
% 1.71/1.34 tff(76,plain,
% 1.71/1.34 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (multiplication(X0, X1) = multiplication(X1, X0)))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[75, 70])).
% 1.71/1.34 tff(77,plain,
% 1.71/1.34 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (multiplication(X0, X1) = multiplication(X1, X0)))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[76, 70])).
% 1.71/1.34 tff(78,plain,
% 1.71/1.34 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (multiplication(X0, X1) = multiplication(X1, X0)))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[77, 70])).
% 1.71/1.34 tff(79,plain,
% 1.71/1.34 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (multiplication(X0, X1) = multiplication(X1, X0)))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[78, 70])).
% 1.71/1.34 tff(80,plain,(
% 1.71/1.34 ~((~(test(X1!1) & test(X0!2))) | (multiplication(X0!2, X1!1) = multiplication(X1!1, X0!2)))),
% 1.71/1.34 inference(skolemize,[status(sab)],[79])).
% 1.71/1.34 tff(81,plain,
% 1.71/1.34 (test(X1!1) & test(X0!2)),
% 1.71/1.34 inference(or_elim,[status(thm)],[80])).
% 1.71/1.34 tff(82,plain,
% 1.71/1.34 (test(X0!2)),
% 1.71/1.34 inference(and_elim,[status(thm)],[81])).
% 1.71/1.34 tff(83,plain,
% 1.71/1.34 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 1.71/1.34 inference(tautology,[status(thm)],[])).
% 1.71/1.34 tff(84,plain,
% 1.71/1.34 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[83, 82])).
% 1.71/1.34 tff(85,plain,
% 1.71/1.34 (complement(tptp_fun_X1_0(X0!2), X0!2)),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[84, 69])).
% 1.71/1.34 tff(86,plain,
% 1.71/1.34 ((~(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))))),
% 1.71/1.34 inference(tautology,[status(thm)],[])).
% 1.71/1.34 tff(87,plain,
% 1.71/1.34 ((~(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))))),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[86, 85])).
% 1.71/1.34 tff(88,plain,
% 1.71/1.34 (~((~(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)))),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[87, 52])).
% 1.71/1.34 tff(89,plain,
% 1.71/1.34 (((~(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)),
% 1.71/1.34 inference(tautology,[status(thm)],[])).
% 1.71/1.34 tff(90,plain,
% 1.71/1.34 (addition(X0!2, tptp_fun_X1_0(X0!2)) = one),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[89, 88])).
% 1.71/1.34 tff(91,plain,
% 1.71/1.34 (one = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 1.71/1.34 inference(symmetry,[status(thm)],[90])).
% 1.71/1.34 tff(92,plain,
% 1.71/1.34 (one = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 1.71/1.34 inference(transitivity,[status(thm)],[91, 37])).
% 1.71/1.34 tff(93,plain,
% 1.71/1.34 (multiplication(one, multiplication(X1!1, X0!2)) = multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), multiplication(multiplication(X1!1, one), X0!2))),
% 1.71/1.34 inference(monotonicity,[status(thm)],[92, 28])).
% 1.71/1.34 tff(94,plain,
% 1.71/1.34 (multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), multiplication(multiplication(X1!1, one), X0!2)) = multiplication(one, multiplication(X1!1, X0!2))),
% 1.71/1.34 inference(symmetry,[status(thm)],[93])).
% 1.71/1.34 tff(95,plain,
% 1.71/1.34 (^[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))))),
% 1.71/1.34 inference(bind,[status(th)],[])).
% 1.71/1.34 tff(96,plain,
% 1.71/1.34 (![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)))),
% 1.71/1.34 inference(quant_intro,[status(thm)],[95])).
% 1.71/1.34 tff(97,plain,
% 1.71/1.34 (![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)))),
% 1.71/1.34 inference(rewrite,[status(thm)],[])).
% 1.71/1.34 tff(98,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_distributivity')).
% 1.71/1.34 tff(99,plain,
% 1.71/1.34 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[98, 97])).
% 1.71/1.34 tff(100,plain,(
% 1.71/1.34 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 1.71/1.34 inference(skolemize,[status(sab)],[99])).
% 1.71/1.34 tff(101,plain,
% 1.71/1.34 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[100, 96])).
% 1.71/1.34 tff(102,plain,
% 1.71/1.34 ((~![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), X0!2), multiplication(multiplication(X1!1, one), X0!2)) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(X1!1, one), X0!2)), multiplication(X0!2, multiplication(multiplication(X1!1, one), X0!2))))),
% 1.71/1.34 inference(quant_inst,[status(thm)],[])).
% 1.71/1.34 tff(103,plain,
% 1.71/1.34 (multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), multiplication(multiplication(X1!1, one), X0!2)) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(X1!1, one), X0!2)), multiplication(X0!2, multiplication(multiplication(X1!1, one), X0!2)))),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[102, 101])).
% 1.71/1.34 tff(104,plain,
% 1.71/1.34 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(X1!1, one), X0!2)), multiplication(X0!2, multiplication(multiplication(X1!1, one), X0!2))) = multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), multiplication(multiplication(X1!1, one), X0!2))),
% 1.71/1.34 inference(symmetry,[status(thm)],[103])).
% 1.71/1.34 tff(105,plain,
% 1.71/1.34 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!2, multiplication(X1!1, X0!2)) = multiplication(multiplication(X0!2, X1!1), X0!2))),
% 1.71/1.34 inference(quant_inst,[status(thm)],[])).
% 1.71/1.34 tff(106,plain,
% 1.71/1.34 (multiplication(X0!2, multiplication(X1!1, X0!2)) = multiplication(multiplication(X0!2, X1!1), X0!2)),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[105, 19])).
% 1.71/1.34 tff(107,plain,
% 1.71/1.34 (multiplication(X0!2, multiplication(multiplication(X1!1, one), X0!2)) = multiplication(X0!2, multiplication(X1!1, X0!2))),
% 1.71/1.34 inference(monotonicity,[status(thm)],[25])).
% 1.71/1.34 tff(108,plain,
% 1.71/1.34 (multiplication(X0!2, multiplication(multiplication(X1!1, one), X0!2)) = multiplication(multiplication(X0!2, X1!1), X0!2)),
% 1.71/1.34 inference(transitivity,[status(thm)],[107, 106])).
% 1.71/1.34 tff(109,plain,
% 1.71/1.34 (((~(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)),
% 1.71/1.34 inference(tautology,[status(thm)],[])).
% 1.71/1.34 tff(110,plain,
% 1.71/1.34 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[109, 88])).
% 1.71/1.34 tff(111,plain,
% 1.71/1.34 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 1.71/1.34 inference(bind,[status(th)],[])).
% 1.71/1.34 tff(112,plain,
% 1.71/1.34 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 1.71/1.34 inference(quant_intro,[status(thm)],[111])).
% 1.71/1.34 tff(113,plain,
% 1.71/1.34 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 1.71/1.34 inference(rewrite,[status(thm)],[])).
% 1.71/1.34 tff(114,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 1.71/1.34 tff(115,plain,
% 1.71/1.34 (![A: $i] : (addition(A, A) = A)),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.71/1.34 tff(116,plain,(
% 1.71/1.34 ![A: $i] : (addition(A, A) = A)),
% 1.71/1.34 inference(skolemize,[status(sab)],[115])).
% 1.71/1.34 tff(117,plain,
% 1.71/1.34 (![A: $i] : (addition(A, A) = A)),
% 1.71/1.34 inference(modus_ponens,[status(thm)],[116, 112])).
% 1.71/1.34 tff(118,plain,
% 1.71/1.34 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!2, X0!2) = X0!2)),
% 1.71/1.34 inference(quant_inst,[status(thm)],[])).
% 1.71/1.34 tff(119,plain,
% 1.71/1.34 (addition(X0!2, X0!2) = X0!2),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[118, 117])).
% 1.71/1.34 tff(120,plain,
% 1.71/1.34 ((~![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)))))),
% 1.71/1.34 inference(quant_inst,[status(thm)],[])).
% 1.71/1.34 tff(121,plain,
% 1.71/1.34 (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))))),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[120, 50])).
% 1.71/1.34 tff(122,plain,
% 1.71/1.34 ((~![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))))))),
% 1.71/1.34 inference(quant_inst,[status(thm)],[])).
% 1.71/1.34 tff(123,plain,
% 1.71/1.34 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[122, 65])).
% 1.71/1.34 tff(124,plain,
% 1.71/1.34 (((~((~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))),
% 1.71/1.34 inference(tautology,[status(thm)],[])).
% 1.71/1.34 tff(125,plain,
% 1.71/1.34 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[124, 123])).
% 1.71/1.34 tff(126,plain,
% 1.71/1.34 (test(X1!1)),
% 1.71/1.34 inference(and_elim,[status(thm)],[81])).
% 1.71/1.34 tff(127,plain,
% 1.71/1.34 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 1.71/1.34 inference(tautology,[status(thm)],[])).
% 1.71/1.34 tff(128,plain,
% 1.71/1.34 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[127, 126])).
% 1.71/1.34 tff(129,plain,
% 1.71/1.34 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[128, 125])).
% 1.71/1.34 tff(130,plain,
% 1.71/1.34 ((~(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))))),
% 1.71/1.34 inference(tautology,[status(thm)],[])).
% 1.71/1.34 tff(131,plain,
% 1.71/1.34 ((~(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))))),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[130, 129])).
% 1.71/1.34 tff(132,plain,
% 1.71/1.34 (~((~(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)))),
% 1.71/1.34 inference(unit_resolution,[status(thm)],[131, 121])).
% 1.71/1.34 tff(133,plain,
% 1.71/1.34 (((~(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)),
% 1.71/1.34 inference(tautology,[status(thm)],[])).
% 1.71/1.34 tff(134,plain,
% 1.71/1.34 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[133, 132])).
% 1.71/1.35 tff(135,plain,
% 1.71/1.35 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = multiplication(one, X0!2)),
% 1.71/1.35 inference(monotonicity,[status(thm)],[134])).
% 1.71/1.35 tff(136,plain,
% 1.71/1.35 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(137,plain,
% 1.71/1.35 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[136, 101])).
% 1.71/1.35 tff(138,plain,
% 1.71/1.35 (addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2)),
% 1.71/1.35 inference(symmetry,[status(thm)],[137])).
% 1.71/1.35 tff(139,plain,
% 1.71/1.35 (addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = X0!2),
% 1.71/1.35 inference(transitivity,[status(thm)],[138, 135, 9])).
% 1.71/1.35 tff(140,plain,
% 1.71/1.35 (addition(addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)), X0!2) = addition(X0!2, X0!2)),
% 1.71/1.35 inference(monotonicity,[status(thm)],[139])).
% 1.71/1.35 tff(141,plain,
% 1.71/1.35 (^[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)))),
% 1.71/1.35 inference(bind,[status(th)],[])).
% 1.71/1.35 tff(142,plain,
% 1.71/1.35 (![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))),
% 1.71/1.35 inference(quant_intro,[status(thm)],[141])).
% 1.71/1.35 tff(143,plain,
% 1.71/1.35 (![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))),
% 1.71/1.35 inference(rewrite,[status(thm)],[])).
% 1.71/1.35 tff(144,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_associativity')).
% 1.71/1.35 tff(145,plain,
% 1.71/1.35 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.71/1.35 tff(146,plain,(
% 1.71/1.35 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 1.71/1.35 inference(skolemize,[status(sab)],[145])).
% 1.71/1.35 tff(147,plain,
% 1.71/1.35 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[146, 142])).
% 1.71/1.35 tff(148,plain,
% 1.71/1.35 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X1!1, X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2)) = addition(addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)), X0!2))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(149,plain,
% 1.71/1.35 (addition(multiplication(X1!1, X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2)) = addition(addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)), X0!2)),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[148, 147])).
% 1.71/1.35 tff(150,plain,
% 1.71/1.35 (addition(multiplication(multiplication(X1!1, one), X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2)) = addition(multiplication(X1!1, X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[25])).
% 1.71/1.35 tff(151,plain,
% 1.71/1.35 (addition(multiplication(multiplication(X1!1, one), X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2)) = X0!2),
% 1.71/1.35 inference(transitivity,[status(thm)],[150, 149, 140, 119])).
% 1.71/1.35 tff(152,plain,
% 1.71/1.35 (multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(multiplication(X1!1, one), X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2))) = multiplication(tptp_fun_X1_0(X0!2), X0!2)),
% 1.71/1.35 inference(monotonicity,[status(thm)],[151])).
% 1.71/1.35 tff(153,plain,
% 1.71/1.35 (^[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))))),
% 1.71/1.35 inference(bind,[status(th)],[])).
% 1.71/1.35 tff(154,plain,
% 1.71/1.35 (![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)))),
% 1.71/1.35 inference(quant_intro,[status(thm)],[153])).
% 1.71/1.35 tff(155,plain,
% 1.71/1.35 (![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)))),
% 1.71/1.35 inference(rewrite,[status(thm)],[])).
% 1.71/1.35 tff(156,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','right_distributivity')).
% 1.71/1.35 tff(157,plain,
% 1.71/1.35 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[156, 155])).
% 1.71/1.35 tff(158,plain,(
% 1.71/1.35 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 1.71/1.35 inference(skolemize,[status(sab)],[157])).
% 1.71/1.35 tff(159,plain,
% 1.71/1.35 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[158, 154])).
% 1.71/1.35 tff(160,plain,
% 1.71/1.35 ((~![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(multiplication(X1!1, one), X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(X1!1, one), X0!2)), multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2))))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(161,plain,
% 1.71/1.35 (multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(multiplication(X1!1, one), X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(X1!1, one), X0!2)), multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2)))),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[160, 159])).
% 1.71/1.35 tff(162,plain,
% 1.71/1.35 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(X1!1, one), X0!2)), multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2))) = multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(multiplication(X1!1, one), X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2)))),
% 1.71/1.35 inference(symmetry,[status(thm)],[161])).
% 1.71/1.35 tff(163,plain,
% 1.71/1.35 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(164,plain,
% 1.71/1.35 (addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[163, 35])).
% 1.71/1.35 tff(165,plain,
% 1.71/1.35 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 1.71/1.35 inference(symmetry,[status(thm)],[164])).
% 1.71/1.35 tff(166,plain,
% 1.71/1.35 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2)) = X0!2),
% 1.71/1.35 inference(transitivity,[status(thm)],[165, 138, 135, 9])).
% 1.71/1.35 tff(167,plain,
% 1.71/1.35 (addition(addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2)), X0!2) = addition(X0!2, X0!2)),
% 1.71/1.35 inference(monotonicity,[status(thm)],[166])).
% 1.71/1.35 tff(168,plain,
% 1.71/1.35 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(X1!1, X0!2), X0!2)) = addition(addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2)), X0!2))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(169,plain,
% 1.71/1.35 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(X1!1, X0!2), X0!2)) = addition(addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2)), X0!2)),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[168, 147])).
% 1.71/1.35 tff(170,plain,
% 1.71/1.35 (multiplication(tptp_fun_X1_0(X1!1), X0!2) = multiplication(tptp_fun_X1_0(X1!1), multiplication(one, X0!2))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[10])).
% 1.71/1.35 tff(171,plain,
% 1.71/1.35 (multiplication(tptp_fun_X1_0(X1!1), multiplication(one, X0!2)) = multiplication(tptp_fun_X1_0(X1!1), X0!2)),
% 1.71/1.35 inference(symmetry,[status(thm)],[170])).
% 1.71/1.35 tff(172,plain,
% 1.71/1.35 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(tptp_fun_X1_0(X1!1), multiplication(one, X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(173,plain,
% 1.71/1.35 (multiplication(tptp_fun_X1_0(X1!1), multiplication(one, X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[172, 19])).
% 1.71/1.35 tff(174,plain,
% 1.71/1.35 (multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2) = multiplication(tptp_fun_X1_0(X1!1), multiplication(one, X0!2))),
% 1.71/1.35 inference(symmetry,[status(thm)],[173])).
% 1.71/1.35 tff(175,plain,
% 1.71/1.35 (multiplication(multiplication(tptp_fun_X1_0(X1!1), one), addition(X0!2, X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)),
% 1.71/1.35 inference(monotonicity,[status(thm)],[119])).
% 1.71/1.35 tff(176,plain,
% 1.71/1.35 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(multiplication(tptp_fun_X1_0(X1!1), one), addition(X0!2, X0!2)) = addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(177,plain,
% 1.71/1.35 (multiplication(multiplication(tptp_fun_X1_0(X1!1), one), addition(X0!2, X0!2)) = addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2))),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[176, 159])).
% 1.71/1.35 tff(178,plain,
% 1.71/1.35 (addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), one), addition(X0!2, X0!2))),
% 1.71/1.35 inference(symmetry,[status(thm)],[177])).
% 1.71/1.35 tff(179,plain,
% 1.71/1.35 (addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)) = multiplication(tptp_fun_X1_0(X1!1), X0!2)),
% 1.71/1.35 inference(transitivity,[status(thm)],[178, 175, 174, 171])).
% 1.71/1.35 tff(180,plain,
% 1.71/1.35 (addition(addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)), addition(multiplication(X1!1, X0!2), X0!2)) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(X1!1, X0!2), X0!2))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[179])).
% 1.71/1.35 tff(181,plain,
% 1.71/1.35 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), addition(multiplication(X1!1, X0!2), X0!2))) = addition(addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)), addition(multiplication(X1!1, X0!2), X0!2)))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(182,plain,
% 1.71/1.35 (addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), addition(multiplication(X1!1, X0!2), X0!2))) = addition(addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)), addition(multiplication(X1!1, X0!2), X0!2))),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[181, 147])).
% 1.71/1.35 tff(183,plain,
% 1.71/1.35 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), addition(multiplication(X1!1, X0!2), X0!2)) = addition(addition(multiplication(X1!1, X0!2), X0!2), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(184,plain,
% 1.71/1.35 (addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), addition(multiplication(X1!1, X0!2), X0!2)) = addition(addition(multiplication(X1!1, X0!2), X0!2), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2))),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[183, 35])).
% 1.71/1.35 tff(185,plain,
% 1.71/1.35 (addition(addition(multiplication(X1!1, X0!2), X0!2), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)) = addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), addition(multiplication(X1!1, X0!2), X0!2))),
% 1.71/1.35 inference(symmetry,[status(thm)],[184])).
% 1.71/1.35 tff(186,plain,
% 1.71/1.35 (addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), addition(addition(multiplication(X1!1, X0!2), X0!2), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2))) = addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), addition(multiplication(X1!1, X0!2), X0!2)))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[185])).
% 1.71/1.35 tff(187,plain,
% 1.71/1.35 (multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2) = multiplication(tptp_fun_X1_0(X1!1), X0!2)),
% 1.71/1.35 inference(transitivity,[status(thm)],[174, 171])).
% 1.71/1.35 tff(188,plain,
% 1.71/1.35 (addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), addition(multiplication(X1!1, X0!2), X0!2)) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(X1!1, X0!2), X0!2))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[187])).
% 1.71/1.35 tff(189,plain,
% 1.71/1.35 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(X1!1, X0!2), X0!2)) = addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), addition(multiplication(X1!1, X0!2), X0!2))),
% 1.71/1.35 inference(symmetry,[status(thm)],[188])).
% 1.71/1.35 tff(190,plain,
% 1.71/1.35 (addition(addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2)), X0!2) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(X1!1, X0!2), X0!2))),
% 1.71/1.35 inference(symmetry,[status(thm)],[169])).
% 1.71/1.35 tff(191,plain,
% 1.71/1.35 (addition(X0!2, X0!2) = addition(addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2)), X0!2)),
% 1.71/1.35 inference(symmetry,[status(thm)],[167])).
% 1.71/1.35 tff(192,plain,
% 1.71/1.35 (X0!2 = addition(X0!2, X0!2)),
% 1.71/1.35 inference(symmetry,[status(thm)],[119])).
% 1.71/1.35 tff(193,plain,
% 1.71/1.35 (X0!2 = addition(addition(multiplication(X1!1, X0!2), X0!2), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2))),
% 1.71/1.35 inference(transitivity,[status(thm)],[192, 191, 190, 189, 184])).
% 1.71/1.35 tff(194,plain,
% 1.71/1.35 (multiplication(tptp_fun_X1_0(X1!1), X0!2) = multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)),
% 1.71/1.35 inference(transitivity,[status(thm)],[170, 173])).
% 1.71/1.35 tff(195,plain,
% 1.71/1.35 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2) = addition(multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2), addition(addition(multiplication(X1!1, X0!2), X0!2), multiplication(multiplication(tptp_fun_X1_0(X1!1), one), X0!2)))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[194, 193])).
% 1.71/1.35 tff(196,plain,
% 1.71/1.35 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2) = X0!2),
% 1.71/1.35 inference(transitivity,[status(thm)],[195, 186, 182, 180, 169, 167, 119])).
% 1.71/1.35 tff(197,plain,
% 1.71/1.35 (multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2)) = multiplication(tptp_fun_X1_0(X0!2), X0!2)),
% 1.71/1.35 inference(monotonicity,[status(thm)],[196])).
% 1.71/1.35 tff(198,plain,
% 1.71/1.35 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2))),
% 1.71/1.35 inference(symmetry,[status(thm)],[197])).
% 1.71/1.35 tff(199,plain,
% 1.71/1.35 (zero = multiplication(tptp_fun_X1_0(X0!2), X0!2)),
% 1.71/1.35 inference(symmetry,[status(thm)],[110])).
% 1.71/1.35 tff(200,plain,
% 1.71/1.35 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 1.71/1.35 inference(bind,[status(th)],[])).
% 1.71/1.35 tff(201,plain,
% 1.71/1.35 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 1.71/1.35 inference(quant_intro,[status(thm)],[200])).
% 1.71/1.35 tff(202,plain,
% 1.71/1.35 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 1.71/1.35 inference(rewrite,[status(thm)],[])).
% 1.71/1.35 tff(203,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 1.71/1.35 tff(204,plain,
% 1.71/1.35 (![A: $i] : (multiplication(zero, A) = zero)),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[203, 202])).
% 1.71/1.35 tff(205,plain,(
% 1.71/1.35 ![A: $i] : (multiplication(zero, A) = zero)),
% 1.71/1.35 inference(skolemize,[status(sab)],[204])).
% 1.71/1.35 tff(206,plain,
% 1.71/1.35 (![A: $i] : (multiplication(zero, A) = zero)),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[205, 201])).
% 1.71/1.35 tff(207,plain,
% 1.71/1.35 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, zero) = zero)),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(208,plain,
% 1.71/1.35 (multiplication(zero, zero) = zero),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[207, 206])).
% 1.71/1.35 tff(209,plain,
% 1.71/1.35 (multiplication(zero, zero) = multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2))),
% 1.71/1.35 inference(transitivity,[status(thm)],[208, 199, 198])).
% 1.71/1.35 tff(210,plain,
% 1.71/1.35 (multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(X1!1, one), X0!2)) = multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, X0!2))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[25])).
% 1.71/1.35 tff(211,plain,
% 1.71/1.35 (multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, X0!2)) = multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(X1!1, one), X0!2))),
% 1.71/1.35 inference(symmetry,[status(thm)],[210])).
% 1.71/1.35 tff(212,plain,
% 1.71/1.35 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, X0!2)), multiplication(zero, zero)) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(X1!1, one), X0!2)), multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), X0!2)))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[211, 209])).
% 1.71/1.35 tff(213,plain,
% 1.71/1.35 (zero = multiplication(zero, zero)),
% 1.71/1.35 inference(symmetry,[status(thm)],[208])).
% 1.71/1.35 tff(214,plain,
% 1.71/1.35 (^[A: $i] : refl((multiplication(A, zero) = zero) <=> (multiplication(A, zero) = zero))),
% 1.71/1.35 inference(bind,[status(th)],[])).
% 1.71/1.35 tff(215,plain,
% 1.71/1.35 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 1.71/1.35 inference(quant_intro,[status(thm)],[214])).
% 1.71/1.35 tff(216,plain,
% 1.71/1.35 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 1.71/1.35 inference(rewrite,[status(thm)],[])).
% 1.71/1.35 tff(217,axiom,(![A: $i] : (multiplication(A, zero) = zero)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','right_annihilation')).
% 1.71/1.35 tff(218,plain,
% 1.71/1.35 (![A: $i] : (multiplication(A, zero) = zero)),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[217, 216])).
% 1.71/1.35 tff(219,plain,(
% 1.71/1.35 ![A: $i] : (multiplication(A, zero) = zero)),
% 1.71/1.35 inference(skolemize,[status(sab)],[218])).
% 1.71/1.35 tff(220,plain,
% 1.71/1.35 (![A: $i] : (multiplication(A, zero) = zero)),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[219, 215])).
% 1.71/1.35 tff(221,plain,
% 1.71/1.35 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(tptp_fun_X1_0(X0!2), zero) = zero)),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(222,plain,
% 1.71/1.35 (multiplication(tptp_fun_X1_0(X0!2), zero) = zero),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[221, 220])).
% 1.71/1.35 tff(223,plain,
% 1.71/1.35 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(X1!1, zero) = zero)),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(224,plain,
% 1.71/1.35 (multiplication(X1!1, zero) = zero),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[223, 220])).
% 1.71/1.35 tff(225,plain,
% 1.71/1.35 (multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, zero)) = multiplication(tptp_fun_X1_0(X0!2), zero)),
% 1.71/1.35 inference(monotonicity,[status(thm)],[224])).
% 1.71/1.35 tff(226,plain,
% 1.71/1.35 (multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, zero)) = multiplication(zero, zero)),
% 1.71/1.35 inference(transitivity,[status(thm)],[225, 222, 213])).
% 1.71/1.35 tff(227,plain,
% 1.71/1.35 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(X1!1, one), X0!2)), multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, zero))) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, X0!2)), multiplication(zero, zero))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[210, 226])).
% 1.71/1.35 tff(228,plain,
% 1.71/1.35 ((~![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(multiplication(X1!1, one), X0!2), multiplication(X1!1, zero))) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(X1!1, one), X0!2)), multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, zero))))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(229,plain,
% 1.71/1.35 (multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(multiplication(X1!1, one), X0!2), multiplication(X1!1, zero))) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(X1!1, one), X0!2)), multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, zero)))),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[228, 159])).
% 1.71/1.35 tff(230,plain,
% 1.71/1.35 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 1.71/1.35 inference(bind,[status(th)],[])).
% 1.71/1.35 tff(231,plain,
% 1.71/1.35 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 1.71/1.35 inference(quant_intro,[status(thm)],[230])).
% 1.71/1.35 tff(232,plain,
% 1.71/1.35 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 1.71/1.35 inference(rewrite,[status(thm)],[])).
% 1.71/1.35 tff(233,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 1.71/1.35 tff(234,plain,
% 1.71/1.35 (![A: $i] : (multiplication(A, one) = A)),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[233, 232])).
% 1.71/1.35 tff(235,plain,(
% 1.71/1.35 ![A: $i] : (multiplication(A, one) = A)),
% 1.71/1.35 inference(skolemize,[status(sab)],[234])).
% 1.71/1.35 tff(236,plain,
% 1.71/1.35 (![A: $i] : (multiplication(A, one) = A)),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[235, 231])).
% 1.71/1.35 tff(237,plain,
% 1.71/1.35 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X0!2, one) = X0!2)),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(238,plain,
% 1.71/1.35 (multiplication(X0!2, one) = X0!2),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[237, 236])).
% 1.71/1.35 tff(239,plain,
% 1.71/1.35 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 1.71/1.35 inference(symmetry,[status(thm)],[37])).
% 1.71/1.35 tff(240,plain,
% 1.71/1.35 (addition(tptp_fun_X1_0(X0!2), X0!2) = one),
% 1.71/1.35 inference(transitivity,[status(thm)],[239, 90])).
% 1.71/1.35 tff(241,plain,
% 1.71/1.35 (multiplication(X0!2, addition(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(X0!2, one)),
% 1.71/1.35 inference(monotonicity,[status(thm)],[240])).
% 1.71/1.35 tff(242,plain,
% 1.71/1.35 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!2, addition(tptp_fun_X1_0(X0!2), X0!2)) = addition(multiplication(X0!2, tptp_fun_X1_0(X0!2)), multiplication(X0!2, X0!2)))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(243,plain,
% 1.71/1.35 (multiplication(X0!2, addition(tptp_fun_X1_0(X0!2), X0!2)) = addition(multiplication(X0!2, tptp_fun_X1_0(X0!2)), multiplication(X0!2, X0!2))),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[242, 159])).
% 1.71/1.35 tff(244,plain,
% 1.71/1.35 (addition(multiplication(X0!2, tptp_fun_X1_0(X0!2)), multiplication(X0!2, X0!2)) = multiplication(X0!2, addition(tptp_fun_X1_0(X0!2), X0!2))),
% 1.71/1.35 inference(symmetry,[status(thm)],[243])).
% 1.71/1.35 tff(245,plain,
% 1.71/1.35 (((~(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)),
% 1.71/1.35 inference(tautology,[status(thm)],[])).
% 1.71/1.35 tff(246,plain,
% 1.71/1.35 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[245, 88])).
% 1.71/1.35 tff(247,plain,
% 1.71/1.35 (zero = multiplication(X0!2, tptp_fun_X1_0(X0!2))),
% 1.71/1.35 inference(symmetry,[status(thm)],[246])).
% 1.71/1.35 tff(248,plain,
% 1.71/1.35 (addition(zero, multiplication(X0!2, X0!2)) = addition(multiplication(X0!2, tptp_fun_X1_0(X0!2)), multiplication(X0!2, X0!2))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[247])).
% 1.71/1.35 tff(249,plain,
% 1.71/1.35 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(zero, multiplication(X0!2, X0!2)) = addition(multiplication(X0!2, X0!2), zero))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(250,plain,
% 1.71/1.35 (addition(zero, multiplication(X0!2, X0!2)) = addition(multiplication(X0!2, X0!2), zero)),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[249, 35])).
% 1.71/1.35 tff(251,plain,
% 1.71/1.35 (addition(multiplication(X0!2, X0!2), zero) = addition(zero, multiplication(X0!2, X0!2))),
% 1.71/1.35 inference(symmetry,[status(thm)],[250])).
% 1.71/1.35 tff(252,plain,
% 1.71/1.35 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 1.71/1.35 inference(bind,[status(th)],[])).
% 1.71/1.35 tff(253,plain,
% 1.71/1.35 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 1.71/1.35 inference(quant_intro,[status(thm)],[252])).
% 1.71/1.35 tff(254,plain,
% 1.71/1.35 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 1.71/1.35 inference(rewrite,[status(thm)],[])).
% 1.71/1.35 tff(255,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 1.71/1.35 tff(256,plain,
% 1.71/1.35 (![A: $i] : (addition(A, zero) = A)),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[255, 254])).
% 1.71/1.35 tff(257,plain,(
% 1.71/1.35 ![A: $i] : (addition(A, zero) = A)),
% 1.71/1.35 inference(skolemize,[status(sab)],[256])).
% 1.71/1.35 tff(258,plain,
% 1.71/1.35 (![A: $i] : (addition(A, zero) = A)),
% 1.71/1.35 inference(modus_ponens,[status(thm)],[257, 253])).
% 1.71/1.35 tff(259,plain,
% 1.71/1.35 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(X0!2, X0!2), zero) = multiplication(X0!2, X0!2))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(260,plain,
% 1.71/1.35 (addition(multiplication(X0!2, X0!2), zero) = multiplication(X0!2, X0!2)),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[259, 258])).
% 1.71/1.35 tff(261,plain,
% 1.71/1.35 (multiplication(X0!2, X0!2) = addition(multiplication(X0!2, X0!2), zero)),
% 1.71/1.35 inference(symmetry,[status(thm)],[260])).
% 1.71/1.35 tff(262,plain,
% 1.71/1.35 (multiplication(X0!2, X0!2) = X0!2),
% 1.71/1.35 inference(transitivity,[status(thm)],[261, 251, 248, 244, 241, 238])).
% 1.71/1.35 tff(263,plain,
% 1.71/1.35 (multiplication(X1!1, multiplication(X0!2, X0!2)) = multiplication(X1!1, X0!2)),
% 1.71/1.35 inference(monotonicity,[status(thm)],[262])).
% 1.71/1.35 tff(264,plain,
% 1.71/1.35 (multiplication(X1!1, X0!2) = multiplication(X1!1, multiplication(X0!2, X0!2))),
% 1.71/1.35 inference(symmetry,[status(thm)],[263])).
% 1.71/1.35 tff(265,plain,
% 1.71/1.35 (multiplication(multiplication(X1!1, one), X0!2) = multiplication(X1!1, multiplication(X0!2, X0!2))),
% 1.71/1.35 inference(transitivity,[status(thm)],[22, 12, 264])).
% 1.71/1.35 tff(266,plain,
% 1.71/1.35 (addition(multiplication(multiplication(X1!1, one), X0!2), multiplication(X1!1, zero)) = addition(multiplication(X1!1, multiplication(X0!2, X0!2)), multiplication(X1!1, zero))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[265])).
% 1.71/1.35 tff(267,plain,
% 1.71/1.35 (addition(multiplication(X1!1, multiplication(X0!2, X0!2)), multiplication(X1!1, zero)) = addition(multiplication(multiplication(X1!1, one), X0!2), multiplication(X1!1, zero))),
% 1.71/1.35 inference(symmetry,[status(thm)],[266])).
% 1.71/1.35 tff(268,plain,
% 1.71/1.35 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X1!1, addition(multiplication(X0!2, X0!2), zero)) = addition(multiplication(X1!1, multiplication(X0!2, X0!2)), multiplication(X1!1, zero)))),
% 1.71/1.35 inference(quant_inst,[status(thm)],[])).
% 1.71/1.35 tff(269,plain,
% 1.71/1.35 (multiplication(X1!1, addition(multiplication(X0!2, X0!2), zero)) = addition(multiplication(X1!1, multiplication(X0!2, X0!2)), multiplication(X1!1, zero))),
% 1.71/1.35 inference(unit_resolution,[status(thm)],[268, 159])).
% 1.71/1.35 tff(270,plain,
% 1.71/1.35 (addition(multiplication(X0!2, X0!2), zero) = X0!2),
% 1.71/1.35 inference(transitivity,[status(thm)],[251, 248, 244, 241, 238])).
% 1.71/1.35 tff(271,plain,
% 1.71/1.35 (multiplication(X1!1, addition(multiplication(X0!2, X0!2), zero)) = multiplication(X1!1, X0!2)),
% 1.71/1.35 inference(monotonicity,[status(thm)],[270])).
% 1.71/1.35 tff(272,plain,
% 1.71/1.35 (multiplication(X1!1, X0!2) = multiplication(X1!1, addition(multiplication(X0!2, X0!2), zero))),
% 1.71/1.35 inference(symmetry,[status(thm)],[271])).
% 1.71/1.35 tff(273,plain,
% 1.71/1.35 (multiplication(X1!1, X0!2) = addition(multiplication(multiplication(X1!1, one), X0!2), multiplication(X1!1, zero))),
% 1.71/1.35 inference(transitivity,[status(thm)],[272, 269, 267])).
% 1.71/1.35 tff(274,plain,
% 1.71/1.35 (multiplication(tptp_fun_X1_0(X0!2), multiplication(X1!1, X0!2)) = multiplication(tptp_fun_X1_0(X0!2), addition(multiplication(multiplication(X1!1, one), X0!2), multiplication(X1!1, zero)))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[273])).
% 1.71/1.35 tff(275,plain,
% 1.71/1.35 (multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(X1!1, one), X0!2)) = zero),
% 1.71/1.35 inference(transitivity,[status(thm)],[210, 274, 229, 227, 212, 162, 152, 110])).
% 1.71/1.35 tff(276,plain,
% 1.71/1.35 (addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(X1!1, one), X0!2)), multiplication(X0!2, multiplication(multiplication(X1!1, one), X0!2))) = addition(zero, multiplication(multiplication(X0!2, X1!1), X0!2))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[275, 108])).
% 1.71/1.35 tff(277,plain,
% 1.71/1.35 (addition(zero, multiplication(multiplication(X0!2, X1!1), X0!2)) = addition(multiplication(tptp_fun_X1_0(X0!2), multiplication(multiplication(X1!1, one), X0!2)), multiplication(X0!2, multiplication(multiplication(X1!1, one), X0!2)))),
% 1.71/1.35 inference(symmetry,[status(thm)],[276])).
% 1.71/1.35 tff(278,plain,
% 1.71/1.35 (multiplication(X0!2, X1!1) = multiplication(multiplication(one, X0!2), X1!1)),
% 1.71/1.35 inference(monotonicity,[status(thm)],[10])).
% 1.71/1.35 tff(279,plain,
% 1.71/1.35 (multiplication(multiplication(one, X0!2), X1!1) = multiplication(X0!2, X1!1)),
% 1.71/1.35 inference(symmetry,[status(thm)],[278])).
% 1.71/1.35 tff(280,plain,
% 1.71/1.35 (multiplication(multiplication(multiplication(one, X0!2), X1!1), X0!2) = multiplication(multiplication(X0!2, X1!1), X0!2)),
% 1.71/1.35 inference(monotonicity,[status(thm)],[279])).
% 1.71/1.35 tff(281,plain,
% 1.71/1.35 (multiplication(multiplication(X0!2, X1!1), X0!2) = multiplication(multiplication(multiplication(one, X0!2), X1!1), X0!2)),
% 1.71/1.35 inference(symmetry,[status(thm)],[280])).
% 1.71/1.35 tff(282,plain,
% 1.71/1.35 (multiplication(multiplication(multiplication(one, X0!2), X1!1), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(X0!2, X1!1), tptp_fun_X1_0(X0!2))),
% 1.71/1.35 inference(monotonicity,[status(thm)],[279])).
% 1.71/1.35 tff(283,plain,
% 1.71/1.35 (multiplication(multiplication(X0!2, X1!1), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(multiplication(one, X0!2), X1!1), tptp_fun_X1_0(X0!2))),
% 1.71/1.36 inference(symmetry,[status(thm)],[282])).
% 1.71/1.36 tff(284,plain,
% 1.71/1.36 (multiplication(multiplication(X0!2, X0!2), X1!1) = multiplication(X0!2, X1!1)),
% 1.71/1.36 inference(monotonicity,[status(thm)],[262])).
% 1.71/1.36 tff(285,plain,
% 1.71/1.36 (multiplication(X0!2, X1!1) = multiplication(multiplication(X0!2, X0!2), X1!1)),
% 1.71/1.36 inference(symmetry,[status(thm)],[284])).
% 1.71/1.36 tff(286,plain,
% 1.71/1.36 (multiplication(multiplication(one, X0!2), X1!1) = multiplication(multiplication(X0!2, X0!2), X1!1)),
% 1.71/1.36 inference(transitivity,[status(thm)],[279, 285])).
% 1.71/1.36 tff(287,plain,
% 1.71/1.36 (addition(multiplication(multiplication(one, X0!2), X1!1), multiplication(zero, X1!1)) = addition(multiplication(multiplication(X0!2, X0!2), X1!1), multiplication(zero, X1!1))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[286])).
% 1.71/1.36 tff(288,plain,
% 1.71/1.36 (addition(multiplication(multiplication(X0!2, X0!2), X1!1), multiplication(zero, X1!1)) = addition(multiplication(multiplication(one, X0!2), X1!1), multiplication(zero, X1!1))),
% 1.71/1.36 inference(symmetry,[status(thm)],[287])).
% 1.71/1.36 tff(289,plain,
% 1.71/1.36 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(X0!2, X0!2), zero), X1!1) = addition(multiplication(multiplication(X0!2, X0!2), X1!1), multiplication(zero, X1!1)))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(290,plain,
% 1.71/1.36 (multiplication(addition(multiplication(X0!2, X0!2), zero), X1!1) = addition(multiplication(multiplication(X0!2, X0!2), X1!1), multiplication(zero, X1!1))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[289, 101])).
% 1.71/1.36 tff(291,plain,
% 1.71/1.36 (multiplication(addition(multiplication(X0!2, X0!2), zero), X1!1) = multiplication(X0!2, X1!1)),
% 1.71/1.36 inference(monotonicity,[status(thm)],[270])).
% 1.71/1.36 tff(292,plain,
% 1.71/1.36 (multiplication(X0!2, X1!1) = multiplication(addition(multiplication(X0!2, X0!2), zero), X1!1)),
% 1.71/1.36 inference(symmetry,[status(thm)],[291])).
% 1.71/1.36 tff(293,plain,
% 1.71/1.36 (multiplication(X0!2, X1!1) = addition(multiplication(multiplication(one, X0!2), X1!1), multiplication(zero, X1!1))),
% 1.71/1.36 inference(transitivity,[status(thm)],[292, 290, 288])).
% 1.71/1.36 tff(294,plain,
% 1.71/1.36 (multiplication(multiplication(X0!2, X1!1), tptp_fun_X1_0(X0!2)) = multiplication(addition(multiplication(multiplication(one, X0!2), X1!1), multiplication(zero, X1!1)), tptp_fun_X1_0(X0!2))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[293])).
% 1.71/1.36 tff(295,plain,
% 1.71/1.36 (multiplication(addition(multiplication(multiplication(one, X0!2), X1!1), multiplication(zero, X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(multiplication(X0!2, X1!1), tptp_fun_X1_0(X0!2))),
% 1.71/1.36 inference(symmetry,[status(thm)],[294])).
% 1.71/1.36 tff(296,plain,
% 1.71/1.36 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(multiplication(one, X0!2), X1!1), multiplication(zero, X1!1)), tptp_fun_X1_0(X0!2)) = addition(multiplication(multiplication(multiplication(one, X0!2), X1!1), tptp_fun_X1_0(X0!2)), multiplication(multiplication(zero, X1!1), tptp_fun_X1_0(X0!2))))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(297,plain,
% 1.71/1.36 (multiplication(addition(multiplication(multiplication(one, X0!2), X1!1), multiplication(zero, X1!1)), tptp_fun_X1_0(X0!2)) = addition(multiplication(multiplication(multiplication(one, X0!2), X1!1), tptp_fun_X1_0(X0!2)), multiplication(multiplication(zero, X1!1), tptp_fun_X1_0(X0!2)))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[296, 101])).
% 1.71/1.36 tff(298,plain,
% 1.71/1.36 (addition(multiplication(multiplication(multiplication(one, X0!2), X1!1), tptp_fun_X1_0(X0!2)), multiplication(multiplication(zero, X1!1), tptp_fun_X1_0(X0!2))) = multiplication(addition(multiplication(multiplication(one, X0!2), X1!1), multiplication(zero, X1!1)), tptp_fun_X1_0(X0!2))),
% 1.71/1.36 inference(symmetry,[status(thm)],[297])).
% 1.71/1.36 tff(299,plain,
% 1.71/1.36 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, tptp_fun_X1_0(X0!2)) = zero)),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(300,plain,
% 1.71/1.36 (multiplication(zero, tptp_fun_X1_0(X0!2)) = zero),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[299, 206])).
% 1.71/1.36 tff(301,plain,
% 1.71/1.36 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, X1!1) = zero)),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(302,plain,
% 1.71/1.36 (multiplication(zero, X1!1) = zero),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[301, 206])).
% 1.71/1.36 tff(303,plain,
% 1.71/1.36 (multiplication(multiplication(zero, X1!1), tptp_fun_X1_0(X0!2)) = multiplication(zero, tptp_fun_X1_0(X0!2))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[302])).
% 1.71/1.36 tff(304,plain,
% 1.71/1.36 (multiplication(multiplication(zero, X1!1), tptp_fun_X1_0(X0!2)) = multiplication(zero, zero)),
% 1.71/1.36 inference(transitivity,[status(thm)],[303, 300, 213])).
% 1.71/1.36 tff(305,plain,
% 1.71/1.36 (addition(multiplication(multiplication(multiplication(one, X0!2), X1!1), tptp_fun_X1_0(X0!2)), multiplication(multiplication(zero, X1!1), tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(X0!2, X1!1), tptp_fun_X1_0(X0!2)), multiplication(zero, zero))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[282, 304])).
% 1.71/1.36 tff(306,plain,
% 1.71/1.36 (addition(multiplication(multiplication(X0!2, X1!1), tptp_fun_X1_0(X0!2)), multiplication(zero, zero)) = addition(multiplication(multiplication(multiplication(one, X0!2), X1!1), tptp_fun_X1_0(X0!2)), multiplication(multiplication(zero, X1!1), tptp_fun_X1_0(X0!2)))),
% 1.71/1.36 inference(symmetry,[status(thm)],[305])).
% 1.71/1.36 tff(307,plain,
% 1.71/1.36 ((~![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))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(308,plain,
% 1.71/1.36 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[307, 35])).
% 1.71/1.36 tff(309,plain,
% 1.71/1.36 (addition(tptp_fun_X1_0(X1!1), X1!1) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 1.71/1.36 inference(symmetry,[status(thm)],[308])).
% 1.71/1.36 tff(310,plain,
% 1.71/1.36 (addition(tptp_fun_X1_0(X1!1), X1!1) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 1.71/1.36 inference(transitivity,[status(thm)],[309, 134, 91, 37])).
% 1.71/1.36 tff(311,plain,
% 1.71/1.36 (multiplication(X0!2, addition(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(X0!2, addition(tptp_fun_X1_0(X0!2), X0!2))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[310])).
% 1.71/1.36 tff(312,plain,
% 1.71/1.36 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!2, addition(tptp_fun_X1_0(X1!1), X1!1)) = addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1)))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(313,plain,
% 1.71/1.36 (multiplication(X0!2, addition(tptp_fun_X1_0(X1!1), X1!1)) = addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[312, 159])).
% 1.71/1.36 tff(314,plain,
% 1.71/1.36 (addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1)) = multiplication(X0!2, addition(tptp_fun_X1_0(X1!1), X1!1))),
% 1.71/1.36 inference(symmetry,[status(thm)],[313])).
% 1.71/1.36 tff(315,plain,
% 1.71/1.36 (addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1)) = X0!2),
% 1.71/1.36 inference(transitivity,[status(thm)],[314, 311, 241, 238])).
% 1.71/1.36 tff(316,plain,
% 1.71/1.36 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 1.71/1.36 inference(symmetry,[status(thm)],[134])).
% 1.71/1.36 tff(317,plain,
% 1.71/1.36 (multiplication(one, addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1))) = multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2)),
% 1.71/1.36 inference(monotonicity,[status(thm)],[316, 315])).
% 1.71/1.36 tff(318,plain,
% 1.71/1.36 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(one, addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1))) = addition(multiplication(one, multiplication(X0!2, tptp_fun_X1_0(X1!1))), multiplication(one, multiplication(X0!2, X1!1))))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(319,plain,
% 1.71/1.36 (multiplication(one, addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1))) = addition(multiplication(one, multiplication(X0!2, tptp_fun_X1_0(X1!1))), multiplication(one, multiplication(X0!2, X1!1)))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[318, 159])).
% 1.71/1.36 tff(320,plain,
% 1.71/1.36 (addition(multiplication(one, multiplication(X0!2, tptp_fun_X1_0(X1!1))), multiplication(one, multiplication(X0!2, X1!1))) = multiplication(one, addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1)))),
% 1.71/1.36 inference(symmetry,[status(thm)],[319])).
% 1.71/1.36 tff(321,plain,
% 1.71/1.36 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(one, multiplication(X0!2, X1!1)) = multiplication(multiplication(one, X0!2), X1!1))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(322,plain,
% 1.71/1.36 (multiplication(one, multiplication(X0!2, X1!1)) = multiplication(multiplication(one, X0!2), X1!1)),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[321, 19])).
% 1.71/1.36 tff(323,plain,
% 1.71/1.36 (multiplication(multiplication(one, X0!2), X1!1) = multiplication(one, multiplication(X0!2, X1!1))),
% 1.71/1.36 inference(symmetry,[status(thm)],[322])).
% 1.71/1.36 tff(324,plain,
% 1.71/1.36 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(one, multiplication(X0!2, tptp_fun_X1_0(X1!1))) = multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(325,plain,
% 1.71/1.36 (multiplication(one, multiplication(X0!2, tptp_fun_X1_0(X1!1))) = multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[324, 19])).
% 1.71/1.36 tff(326,plain,
% 1.71/1.36 (multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)) = multiplication(one, multiplication(X0!2, tptp_fun_X1_0(X1!1)))),
% 1.71/1.36 inference(symmetry,[status(thm)],[325])).
% 1.71/1.36 tff(327,plain,
% 1.71/1.36 (multiplication(X0!2, tptp_fun_X1_0(X1!1)) = multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[10])).
% 1.71/1.36 tff(328,plain,
% 1.71/1.36 (multiplication(multiplication(X0!2, one), tptp_fun_X1_0(X1!1)) = multiplication(X0!2, tptp_fun_X1_0(X1!1))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[238])).
% 1.71/1.36 tff(329,plain,
% 1.71/1.36 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(X0!2, multiplication(one, tptp_fun_X1_0(X1!1))) = multiplication(multiplication(X0!2, one), tptp_fun_X1_0(X1!1)))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(330,plain,
% 1.71/1.36 (multiplication(X0!2, multiplication(one, tptp_fun_X1_0(X1!1))) = multiplication(multiplication(X0!2, one), tptp_fun_X1_0(X1!1))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[329, 19])).
% 1.71/1.36 tff(331,plain,
% 1.71/1.36 (multiplication(addition(X0!2, X0!2), multiplication(one, tptp_fun_X1_0(X1!1))) = multiplication(X0!2, multiplication(one, tptp_fun_X1_0(X1!1)))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[119])).
% 1.71/1.36 tff(332,plain,
% 1.71/1.36 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X0!2, X0!2), multiplication(one, tptp_fun_X1_0(X1!1))) = addition(multiplication(X0!2, multiplication(one, tptp_fun_X1_0(X1!1))), multiplication(X0!2, multiplication(one, tptp_fun_X1_0(X1!1)))))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(333,plain,
% 1.71/1.36 (multiplication(addition(X0!2, X0!2), multiplication(one, tptp_fun_X1_0(X1!1))) = addition(multiplication(X0!2, multiplication(one, tptp_fun_X1_0(X1!1))), multiplication(X0!2, multiplication(one, tptp_fun_X1_0(X1!1))))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[332, 101])).
% 1.71/1.36 tff(334,plain,
% 1.71/1.36 (addition(multiplication(X0!2, multiplication(one, tptp_fun_X1_0(X1!1))), multiplication(X0!2, multiplication(one, tptp_fun_X1_0(X1!1)))) = multiplication(addition(X0!2, X0!2), multiplication(one, tptp_fun_X1_0(X1!1)))),
% 1.71/1.36 inference(symmetry,[status(thm)],[333])).
% 1.71/1.36 tff(335,plain,
% 1.71/1.36 (multiplication(multiplication(X0!2, one), tptp_fun_X1_0(X1!1)) = multiplication(X0!2, multiplication(one, tptp_fun_X1_0(X1!1)))),
% 1.71/1.36 inference(symmetry,[status(thm)],[330])).
% 1.71/1.36 tff(336,plain,
% 1.71/1.36 (multiplication(X0!2, tptp_fun_X1_0(X1!1)) = multiplication(multiplication(X0!2, one), tptp_fun_X1_0(X1!1))),
% 1.71/1.36 inference(symmetry,[status(thm)],[328])).
% 1.71/1.36 tff(337,plain,
% 1.71/1.36 (multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)) = multiplication(X0!2, tptp_fun_X1_0(X1!1))),
% 1.71/1.36 inference(symmetry,[status(thm)],[327])).
% 1.71/1.36 tff(338,plain,
% 1.71/1.36 (multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)) = multiplication(X0!2, multiplication(one, tptp_fun_X1_0(X1!1)))),
% 1.71/1.36 inference(transitivity,[status(thm)],[337, 336, 335])).
% 1.71/1.36 tff(339,plain,
% 1.71/1.36 (addition(multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)), multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1))) = addition(multiplication(X0!2, multiplication(one, tptp_fun_X1_0(X1!1))), multiplication(X0!2, multiplication(one, tptp_fun_X1_0(X1!1))))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[338, 338])).
% 1.71/1.36 tff(340,plain,
% 1.71/1.36 (addition(multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)), multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1))) = multiplication(one, multiplication(X0!2, tptp_fun_X1_0(X1!1)))),
% 1.71/1.36 inference(transitivity,[status(thm)],[339, 334, 331, 330, 328, 327, 326])).
% 1.71/1.36 tff(341,plain,
% 1.71/1.36 (addition(addition(multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)), multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1))), multiplication(multiplication(one, X0!2), X1!1)) = addition(multiplication(one, multiplication(X0!2, tptp_fun_X1_0(X1!1))), multiplication(one, multiplication(X0!2, X1!1)))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[340, 323])).
% 1.71/1.36 tff(342,plain,
% 1.71/1.36 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)), addition(multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)), multiplication(multiplication(one, X0!2), X1!1))) = addition(addition(multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)), multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1))), multiplication(multiplication(one, X0!2), X1!1)))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(343,plain,
% 1.71/1.36 (addition(multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)), addition(multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)), multiplication(multiplication(one, X0!2), X1!1))) = addition(addition(multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)), multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1))), multiplication(multiplication(one, X0!2), X1!1))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[342, 147])).
% 1.71/1.36 tff(344,plain,
% 1.71/1.36 (addition(multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)), multiplication(multiplication(one, X0!2), X1!1)) = addition(multiplication(one, multiplication(X0!2, tptp_fun_X1_0(X1!1))), multiplication(one, multiplication(X0!2, X1!1)))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[326, 323])).
% 1.71/1.36 tff(345,plain,
% 1.71/1.36 (addition(multiplication(one, multiplication(X0!2, tptp_fun_X1_0(X1!1))), multiplication(one, multiplication(X0!2, X1!1))) = addition(multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)), multiplication(multiplication(one, X0!2), X1!1))),
% 1.71/1.36 inference(symmetry,[status(thm)],[344])).
% 1.71/1.36 tff(346,plain,
% 1.71/1.36 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = multiplication(one, addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1)))),
% 1.71/1.36 inference(symmetry,[status(thm)],[317])).
% 1.71/1.36 tff(347,plain,
% 1.71/1.36 (multiplication(one, X0!2) = multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2)),
% 1.71/1.36 inference(symmetry,[status(thm)],[135])).
% 1.71/1.36 tff(348,plain,
% 1.71/1.36 (X0!2 = addition(multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)), multiplication(multiplication(one, X0!2), X1!1))),
% 1.71/1.36 inference(transitivity,[status(thm)],[10, 347, 346, 319, 345])).
% 1.71/1.36 tff(349,plain,
% 1.71/1.36 (addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2) = addition(multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)), addition(multiplication(multiplication(one, X0!2), tptp_fun_X1_0(X1!1)), multiplication(multiplication(one, X0!2), X1!1)))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[327, 348])).
% 1.71/1.36 tff(350,plain,
% 1.71/1.36 (addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2) = X0!2),
% 1.71/1.36 inference(transitivity,[status(thm)],[349, 343, 341, 320, 317, 135, 9])).
% 1.71/1.36 tff(351,plain,
% 1.71/1.36 (multiplication(addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2), tptp_fun_X1_0(X0!2)) = multiplication(X0!2, tptp_fun_X1_0(X0!2))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[350])).
% 1.71/1.36 tff(352,plain,
% 1.71/1.36 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = multiplication(addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2), tptp_fun_X1_0(X0!2))),
% 1.71/1.36 inference(symmetry,[status(thm)],[351])).
% 1.71/1.36 tff(353,plain,
% 1.71/1.36 (multiplication(zero, zero) = multiplication(addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2), tptp_fun_X1_0(X0!2))),
% 1.71/1.36 inference(transitivity,[status(thm)],[208, 247, 352])).
% 1.71/1.36 tff(354,plain,
% 1.71/1.36 (addition(multiplication(multiplication(X0!2, X1!1), tptp_fun_X1_0(X0!2)), multiplication(zero, zero)) = addition(multiplication(multiplication(multiplication(one, X0!2), X1!1), tptp_fun_X1_0(X0!2)), multiplication(addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2), tptp_fun_X1_0(X0!2)))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[283, 353])).
% 1.71/1.36 tff(355,plain,
% 1.71/1.36 (addition(multiplication(multiplication(multiplication(one, X0!2), X1!1), tptp_fun_X1_0(X0!2)), multiplication(addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2), tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(X0!2, X1!1), tptp_fun_X1_0(X0!2)), multiplication(zero, zero))),
% 1.71/1.36 inference(symmetry,[status(thm)],[354])).
% 1.71/1.36 tff(356,plain,
% 1.71/1.36 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(multiplication(one, X0!2), X1!1), addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2)), tptp_fun_X1_0(X0!2)) = addition(multiplication(multiplication(multiplication(one, X0!2), X1!1), tptp_fun_X1_0(X0!2)), multiplication(addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2), tptp_fun_X1_0(X0!2))))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(357,plain,
% 1.71/1.36 (multiplication(addition(multiplication(multiplication(one, X0!2), X1!1), addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2)), tptp_fun_X1_0(X0!2)) = addition(multiplication(multiplication(multiplication(one, X0!2), X1!1), tptp_fun_X1_0(X0!2)), multiplication(addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2), tptp_fun_X1_0(X0!2)))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[356, 101])).
% 1.71/1.36 tff(358,plain,
% 1.71/1.36 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 1.71/1.36 inference(transitivity,[status(thm)],[134, 91, 37])).
% 1.71/1.36 tff(359,plain,
% 1.71/1.36 (multiplication(X0!2, addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(X0!2, addition(tptp_fun_X1_0(X0!2), X0!2))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[358])).
% 1.71/1.36 tff(360,plain,
% 1.71/1.36 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!2, addition(X1!1, tptp_fun_X1_0(X1!1))) = addition(multiplication(X0!2, X1!1), multiplication(X0!2, tptp_fun_X1_0(X1!1))))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(361,plain,
% 1.71/1.36 (multiplication(X0!2, addition(X1!1, tptp_fun_X1_0(X1!1))) = addition(multiplication(X0!2, X1!1), multiplication(X0!2, tptp_fun_X1_0(X1!1)))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[360, 159])).
% 1.71/1.36 tff(362,plain,
% 1.71/1.36 (addition(multiplication(X0!2, X1!1), multiplication(X0!2, tptp_fun_X1_0(X1!1))) = multiplication(X0!2, addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 1.71/1.36 inference(symmetry,[status(thm)],[361])).
% 1.71/1.36 tff(363,plain,
% 1.71/1.36 (addition(multiplication(X0!2, X1!1), multiplication(X0!2, tptp_fun_X1_0(X1!1))) = X0!2),
% 1.71/1.36 inference(transitivity,[status(thm)],[362, 359, 241, 238])).
% 1.71/1.36 tff(364,plain,
% 1.71/1.36 (addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, tptp_fun_X1_0(X1!1))), X0!2) = addition(X0!2, X0!2)),
% 1.71/1.36 inference(monotonicity,[status(thm)],[363])).
% 1.71/1.36 tff(365,plain,
% 1.71/1.36 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X0!2, X1!1), addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2)) = addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, tptp_fun_X1_0(X1!1))), X0!2))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(366,plain,
% 1.71/1.36 (addition(multiplication(X0!2, X1!1), addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2)) = addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, tptp_fun_X1_0(X1!1))), X0!2)),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[365, 147])).
% 1.71/1.36 tff(367,plain,
% 1.71/1.36 (addition(multiplication(multiplication(one, X0!2), X1!1), addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2)) = addition(multiplication(X0!2, X1!1), addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[279])).
% 1.71/1.36 tff(368,plain,
% 1.71/1.36 (addition(multiplication(multiplication(one, X0!2), X1!1), addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2)) = X0!2),
% 1.71/1.36 inference(transitivity,[status(thm)],[367, 366, 364, 119])).
% 1.71/1.36 tff(369,plain,
% 1.71/1.36 (multiplication(addition(multiplication(multiplication(one, X0!2), X1!1), addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2)), tptp_fun_X1_0(X0!2)) = multiplication(X0!2, tptp_fun_X1_0(X0!2))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[368])).
% 1.71/1.36 tff(370,plain,
% 1.71/1.36 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = multiplication(addition(multiplication(multiplication(one, X0!2), X1!1), addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), X0!2)), tptp_fun_X1_0(X0!2))),
% 1.71/1.36 inference(symmetry,[status(thm)],[369])).
% 1.71/1.36 tff(371,plain,
% 1.71/1.36 (zero = multiplication(multiplication(multiplication(one, X0!2), X1!1), tptp_fun_X1_0(X0!2))),
% 1.71/1.36 inference(transitivity,[status(thm)],[247, 370, 357, 355, 306, 298, 295, 283])).
% 1.71/1.36 tff(372,plain,
% 1.71/1.36 (addition(zero, multiplication(multiplication(X0!2, X1!1), X0!2)) = addition(multiplication(multiplication(multiplication(one, X0!2), X1!1), tptp_fun_X1_0(X0!2)), multiplication(multiplication(multiplication(one, X0!2), X1!1), X0!2))),
% 1.71/1.36 inference(monotonicity,[status(thm)],[371, 281])).
% 1.71/1.36 tff(373,plain,
% 1.71/1.36 (addition(multiplication(multiplication(multiplication(one, X0!2), X1!1), tptp_fun_X1_0(X0!2)), multiplication(multiplication(multiplication(one, X0!2), X1!1), X0!2)) = addition(zero, multiplication(multiplication(X0!2, X1!1), X0!2))),
% 1.71/1.36 inference(symmetry,[status(thm)],[372])).
% 1.71/1.36 tff(374,plain,
% 1.71/1.36 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(multiplication(multiplication(one, X0!2), X1!1), addition(tptp_fun_X1_0(X0!2), X0!2)) = addition(multiplication(multiplication(multiplication(one, X0!2), X1!1), tptp_fun_X1_0(X0!2)), multiplication(multiplication(multiplication(one, X0!2), X1!1), X0!2)))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(375,plain,
% 1.71/1.36 (multiplication(multiplication(multiplication(one, X0!2), X1!1), addition(tptp_fun_X1_0(X0!2), X0!2)) = addition(multiplication(multiplication(multiplication(one, X0!2), X1!1), tptp_fun_X1_0(X0!2)), multiplication(multiplication(multiplication(one, X0!2), X1!1), X0!2))),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[374, 159])).
% 1.71/1.36 tff(376,plain,
% 1.71/1.36 (multiplication(multiplication(multiplication(one, X0!2), X1!1), addition(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(multiplication(X0!2, X1!1), one)),
% 1.71/1.36 inference(monotonicity,[status(thm)],[279, 240])).
% 1.71/1.36 tff(377,plain,
% 1.71/1.36 (multiplication(multiplication(X0!2, X1!1), one) = multiplication(multiplication(multiplication(one, X0!2), X1!1), addition(tptp_fun_X1_0(X0!2), X0!2))),
% 1.71/1.36 inference(symmetry,[status(thm)],[376])).
% 1.71/1.36 tff(378,plain,
% 1.71/1.36 (multiplication(multiplication(X0!2, X1!1), one) = multiplication(multiplication(multiplication(one, X0!2), X1!1), one)),
% 1.71/1.36 inference(monotonicity,[status(thm)],[278])).
% 1.71/1.36 tff(379,plain,
% 1.71/1.36 (multiplication(multiplication(multiplication(one, X0!2), X1!1), one) = multiplication(multiplication(X0!2, X1!1), one)),
% 1.71/1.36 inference(symmetry,[status(thm)],[378])).
% 1.71/1.36 tff(380,plain,
% 1.71/1.36 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(multiplication(multiplication(one, X0!2), X1!1), one) = multiplication(multiplication(one, X0!2), X1!1))),
% 1.71/1.36 inference(quant_inst,[status(thm)],[])).
% 1.71/1.36 tff(381,plain,
% 1.71/1.36 (multiplication(multiplication(multiplication(one, X0!2), X1!1), one) = multiplication(multiplication(one, X0!2), X1!1)),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[380, 236])).
% 1.71/1.36 tff(382,plain,
% 1.71/1.36 (multiplication(multiplication(one, X0!2), X1!1) = multiplication(multiplication(multiplication(one, X0!2), X1!1), one)),
% 1.71/1.36 inference(symmetry,[status(thm)],[381])).
% 1.71/1.36 tff(383,plain,
% 1.71/1.36 (multiplication(X0!2, X1!1) = multiplication(X1!1, X0!2)),
% 1.71/1.36 inference(transitivity,[status(thm)],[278, 382, 379, 377, 375, 373, 277, 104, 94, 27, 24, 22, 12])).
% 1.71/1.36 tff(384,plain,
% 1.71/1.36 (~(multiplication(X0!2, X1!1) = multiplication(X1!1, X0!2))),
% 1.71/1.36 inference(or_elim,[status(thm)],[80])).
% 1.71/1.36 tff(385,plain,
% 1.71/1.36 ($false),
% 1.71/1.36 inference(unit_resolution,[status(thm)],[384, 383])).
% 1.71/1.36 % SZS output end Proof
%------------------------------------------------------------------------------