TSTP Solution File: KLE017+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE017+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:23:50 EDT 2022
% Result : Theorem 270.13s 172.27s
% Output : Proof 270.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : KLE017+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n018.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.16/0.31 % WCLimit : 300
% 0.16/0.31 % DateTime : Thu Sep 1 07:52:12 EDT 2022
% 0.16/0.31 % CPUTime :
% 0.16/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.31 Usage: tptp [options] [-file:]file
% 0.16/0.31 -h, -? prints this message.
% 0.16/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.31 -m, -model generate model.
% 0.16/0.31 -p, -proof generate proof.
% 0.16/0.31 -c, -core generate unsat core of named formulas.
% 0.16/0.31 -st, -statistics display statistics.
% 0.16/0.31 -t:timeout set timeout (in second).
% 0.16/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.31 -<param>:<value> configuration parameter and value.
% 0.16/0.31 -o:<output-file> file to place output in.
% 270.13/172.27 % SZS status Theorem
% 270.13/172.27 % SZS output start Proof
% 270.13/172.27 tff(tptp_fun_X0_3_type, type, (
% 270.13/172.27 tptp_fun_X0_3: $i)).
% 270.13/172.27 tff(addition_type, type, (
% 270.13/172.27 addition: ( $i * $i ) > $i)).
% 270.13/172.27 tff(tptp_fun_X2_1_type, type, (
% 270.13/172.27 tptp_fun_X2_1: $i)).
% 270.13/172.27 tff(multiplication_type, type, (
% 270.13/172.27 multiplication: ( $i * $i ) > $i)).
% 270.13/172.27 tff(one_type, type, (
% 270.13/172.27 one: $i)).
% 270.13/172.27 tff(tptp_fun_X1_2_type, type, (
% 270.13/172.27 tptp_fun_X1_2: $i)).
% 270.13/172.27 tff(tptp_fun_X1_0_type, type, (
% 270.13/172.27 tptp_fun_X1_0: $i > $i)).
% 270.13/172.27 tff(zero_type, type, (
% 270.13/172.27 zero: $i)).
% 270.13/172.27 tff(complement_type, type, (
% 270.13/172.27 complement: ( $i * $i ) > $o)).
% 270.13/172.27 tff(test_type, type, (
% 270.13/172.27 test: $i > $o)).
% 270.13/172.27 tff(leq_type, type, (
% 270.13/172.27 leq: ( $i * $i ) > $o)).
% 270.13/172.27 tff(1,plain,
% 270.13/172.27 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 270.13/172.27 inference(bind,[status(th)],[])).
% 270.13/172.27 tff(2,plain,
% 270.13/172.27 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 270.13/172.27 inference(quant_intro,[status(thm)],[1])).
% 270.13/172.27 tff(3,plain,
% 270.13/172.27 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 270.13/172.27 inference(rewrite,[status(thm)],[])).
% 270.13/172.27 tff(4,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 270.13/172.27 tff(5,plain,
% 270.13/172.27 (![A: $i] : (multiplication(A, one) = A)),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[4, 3])).
% 270.13/172.27 tff(6,plain,(
% 270.13/172.27 ![A: $i] : (multiplication(A, one) = A)),
% 270.13/172.27 inference(skolemize,[status(sab)],[5])).
% 270.13/172.27 tff(7,plain,
% 270.13/172.27 (![A: $i] : (multiplication(A, one) = A)),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[6, 2])).
% 270.13/172.27 tff(8,plain,
% 270.13/172.27 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(X0!3, one) = X0!3)),
% 270.13/172.27 inference(quant_inst,[status(thm)],[])).
% 270.13/172.27 tff(9,plain,
% 270.13/172.27 (multiplication(X0!3, one) = X0!3),
% 270.13/172.27 inference(unit_resolution,[status(thm)],[8, 7])).
% 270.13/172.27 tff(10,plain,
% 270.13/172.27 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 270.13/172.27 inference(bind,[status(th)],[])).
% 270.13/172.27 tff(11,plain,
% 270.13/172.27 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 270.13/172.27 inference(quant_intro,[status(thm)],[10])).
% 270.13/172.27 tff(12,plain,
% 270.13/172.27 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 270.13/172.27 inference(rewrite,[status(thm)],[])).
% 270.13/172.27 tff(13,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 270.13/172.27 tff(14,plain,
% 270.13/172.27 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[13, 12])).
% 270.13/172.27 tff(15,plain,(
% 270.13/172.27 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 270.13/172.27 inference(skolemize,[status(sab)],[14])).
% 270.13/172.27 tff(16,plain,
% 270.13/172.27 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[15, 11])).
% 270.13/172.27 tff(17,plain,
% 270.13/172.27 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))),
% 270.13/172.27 inference(quant_inst,[status(thm)],[])).
% 270.13/172.27 tff(18,plain,
% 270.13/172.27 (addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))),
% 270.13/172.27 inference(unit_resolution,[status(thm)],[17, 16])).
% 270.13/172.27 tff(19,plain,
% 270.13/172.27 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2))) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))),
% 270.13/172.27 inference(monotonicity,[status(thm)],[18])).
% 270.13/172.27 tff(20,plain,
% 270.13/172.27 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2)))),
% 270.13/172.27 inference(symmetry,[status(thm)],[19])).
% 270.13/172.27 tff(21,plain,
% 270.13/172.27 (addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))), addition(X1!2, X2!1)) = addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2))), addition(X1!2, X2!1))),
% 270.13/172.27 inference(monotonicity,[status(thm)],[20])).
% 270.13/172.27 tff(22,plain,
% 270.13/172.27 (addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2))), addition(X1!2, X2!1)) = addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))), addition(X1!2, X2!1))),
% 270.13/172.27 inference(symmetry,[status(thm)],[21])).
% 270.13/172.27 tff(23,plain,
% 270.13/172.27 (^[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)))),
% 270.13/172.27 inference(bind,[status(th)],[])).
% 270.13/172.27 tff(24,plain,
% 270.13/172.27 (![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))),
% 270.13/172.27 inference(quant_intro,[status(thm)],[23])).
% 270.13/172.27 tff(25,plain,
% 270.13/172.27 (![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))),
% 270.13/172.27 inference(rewrite,[status(thm)],[])).
% 270.13/172.27 tff(26,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_associativity')).
% 270.13/172.27 tff(27,plain,
% 270.13/172.27 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[26, 25])).
% 270.13/172.27 tff(28,plain,(
% 270.13/172.27 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 270.13/172.27 inference(skolemize,[status(sab)],[27])).
% 270.13/172.27 tff(29,plain,
% 270.13/172.27 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[28, 24])).
% 270.13/172.27 tff(30,plain,
% 270.13/172.27 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2)), addition(X1!2, X2!1))) = addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2))), addition(X1!2, X2!1)))),
% 270.13/172.27 inference(quant_inst,[status(thm)],[])).
% 270.13/172.27 tff(31,plain,
% 270.13/172.27 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2)), addition(X1!2, X2!1))) = addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2))), addition(X1!2, X2!1))),
% 270.13/172.27 inference(unit_resolution,[status(thm)],[30, 29])).
% 270.13/172.27 tff(32,plain,
% 270.13/172.27 (^[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))))))),
% 270.13/172.27 inference(bind,[status(th)],[])).
% 270.13/172.27 tff(33,plain,
% 270.13/172.27 (![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)))))),
% 270.13/172.27 inference(quant_intro,[status(thm)],[32])).
% 270.13/172.27 tff(34,plain,
% 270.13/172.27 (^[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))))))),
% 270.13/172.27 inference(bind,[status(th)],[])).
% 270.13/172.27 tff(35,plain,
% 270.13/172.27 (![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)))))),
% 270.13/172.27 inference(quant_intro,[status(thm)],[34])).
% 270.13/172.27 tff(36,plain,
% 270.13/172.27 (![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)))),
% 270.13/172.27 inference(rewrite,[status(thm)],[])).
% 270.13/172.27 tff(37,plain,
% 270.13/172.27 (^[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))))),
% 270.13/172.27 inference(bind,[status(th)],[])).
% 270.13/172.27 tff(38,plain,
% 270.13/172.27 (![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)))),
% 270.13/172.27 inference(quant_intro,[status(thm)],[37])).
% 270.13/172.27 tff(39,axiom,(![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_2')).
% 270.13/172.27 tff(40,plain,
% 270.13/172.27 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[39, 38])).
% 270.13/172.27 tff(41,plain,
% 270.13/172.27 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[40, 36])).
% 270.13/172.27 tff(42,plain,(
% 270.13/172.27 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 270.13/172.27 inference(skolemize,[status(sab)],[41])).
% 270.13/172.27 tff(43,plain,
% 270.13/172.27 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[42, 35])).
% 270.13/172.27 tff(44,plain,
% 270.13/172.27 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[43, 33])).
% 270.13/172.27 tff(45,plain,
% 270.13/172.27 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(tptp_fun_X1_0(X2!1), X2!1) <=> (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one)))))),
% 270.13/172.27 inference(quant_inst,[status(thm)],[])).
% 270.13/172.27 tff(46,plain,
% 270.13/172.27 (complement(tptp_fun_X1_0(X2!1), X2!1) <=> (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))))),
% 270.13/172.27 inference(unit_resolution,[status(thm)],[45, 44])).
% 270.13/172.27 tff(47,plain,
% 270.13/172.27 (^[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)))))))),
% 270.13/172.27 inference(bind,[status(th)],[])).
% 270.13/172.27 tff(48,plain,
% 270.13/172.27 (![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))))))),
% 270.13/172.27 inference(quant_intro,[status(thm)],[47])).
% 270.13/172.27 tff(49,plain,
% 270.13/172.27 (^[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)))))))),
% 270.13/172.27 inference(bind,[status(th)],[])).
% 270.13/172.27 tff(50,plain,
% 270.13/172.27 (![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))))))),
% 270.13/172.27 inference(quant_intro,[status(thm)],[49])).
% 270.13/172.27 tff(51,plain,
% 270.13/172.27 (![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))))))),
% 270.13/172.27 inference(transitivity,[status(thm)],[50, 48])).
% 270.13/172.27 tff(52,plain,
% 270.13/172.27 (^[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))))))))),
% 270.13/172.27 inference(bind,[status(th)],[])).
% 270.13/172.27 tff(53,plain,
% 270.13/172.27 (![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))))))),
% 270.13/172.27 inference(quant_intro,[status(thm)],[52])).
% 270.13/172.27 tff(54,plain,
% 270.13/172.27 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 270.13/172.27 inference(rewrite,[status(thm)],[])).
% 270.13/172.27 tff(55,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_1')).
% 270.13/172.27 tff(56,plain,
% 270.13/172.27 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[55, 54])).
% 270.13/172.27 tff(57,plain,(
% 270.13/172.27 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 270.13/172.27 inference(skolemize,[status(sab)],[56])).
% 270.13/172.27 tff(58,plain,
% 270.13/172.27 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[57, 53])).
% 270.13/172.27 tff(59,plain,
% 270.13/172.27 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[58, 51])).
% 270.13/172.27 tff(60,plain,
% 270.13/172.27 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | (~(test(X2!1) | ![X1: $i] : (~complement(X1, X2!1))))))),
% 270.13/172.27 inference(quant_inst,[status(thm)],[])).
% 270.13/172.27 tff(61,plain,
% 270.13/172.27 (~((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | (~(test(X2!1) | ![X1: $i] : (~complement(X1, X2!1)))))),
% 270.13/172.27 inference(unit_resolution,[status(thm)],[60, 59])).
% 270.13/172.27 tff(62,plain,
% 270.13/172.27 (((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | (~(test(X2!1) | ![X1: $i] : (~complement(X1, X2!1))))) | ((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))),
% 270.13/172.27 inference(tautology,[status(thm)],[])).
% 270.13/172.27 tff(63,plain,
% 270.13/172.27 ((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1)),
% 270.13/172.27 inference(unit_resolution,[status(thm)],[62, 61])).
% 270.13/172.27 tff(64,plain,
% 270.13/172.27 ((~![X0: $i, X1: $i, X2: $i] : ((~(test(X0) & test(X1) & test(X2))) | (leq(X2, multiplication(X0, X1)) <=> (leq(X2, X0) & leq(X2, X1))))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~(test(X0) & test(X1) & test(X2))) | (leq(X2, multiplication(X0, X1)) <=> (leq(X2, X0) & leq(X2, X1)))))),
% 270.13/172.27 inference(rewrite,[status(thm)],[])).
% 270.13/172.27 tff(65,plain,
% 270.13/172.27 ((~![X0: $i, X1: $i, X2: $i] : (((test(X0) & test(X1)) & test(X2)) => (leq(X2, multiplication(X0, X1)) <=> (leq(X2, X0) & leq(X2, X1))))) <=> (~![X0: $i, X1: $i, X2: $i] : ((~(test(X0) & test(X1) & test(X2))) | (leq(X2, multiplication(X0, X1)) <=> (leq(X2, X0) & leq(X2, X1)))))),
% 270.13/172.27 inference(rewrite,[status(thm)],[])).
% 270.13/172.27 tff(66,axiom,(~![X0: $i, X1: $i, X2: $i] : (((test(X0) & test(X1)) & test(X2)) => (leq(X2, multiplication(X0, X1)) <=> (leq(X2, X0) & leq(X2, X1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 270.13/172.27 tff(67,plain,
% 270.13/172.27 (~![X0: $i, X1: $i, X2: $i] : ((~(test(X0) & test(X1) & test(X2))) | (leq(X2, multiplication(X0, X1)) <=> (leq(X2, X0) & leq(X2, X1))))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[66, 65])).
% 270.13/172.27 tff(68,plain,
% 270.13/172.27 (~![X0: $i, X1: $i, X2: $i] : ((~(test(X0) & test(X1) & test(X2))) | (leq(X2, multiplication(X0, X1)) <=> (leq(X2, X0) & leq(X2, X1))))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[67, 64])).
% 270.13/172.27 tff(69,plain,
% 270.13/172.27 (~![X0: $i, X1: $i, X2: $i] : ((~(test(X0) & test(X1) & test(X2))) | (leq(X2, multiplication(X0, X1)) <=> (leq(X2, X0) & leq(X2, X1))))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[68, 64])).
% 270.13/172.27 tff(70,plain,
% 270.13/172.27 (~![X0: $i, X1: $i, X2: $i] : ((~(test(X0) & test(X1) & test(X2))) | (leq(X2, multiplication(X0, X1)) <=> (leq(X2, X0) & leq(X2, X1))))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[69, 64])).
% 270.13/172.27 tff(71,plain,
% 270.13/172.27 (~![X0: $i, X1: $i, X2: $i] : ((~(test(X0) & test(X1) & test(X2))) | (leq(X2, multiplication(X0, X1)) <=> (leq(X2, X0) & leq(X2, X1))))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[70, 64])).
% 270.13/172.27 tff(72,plain,
% 270.13/172.27 (~![X0: $i, X1: $i, X2: $i] : ((~(test(X0) & test(X1) & test(X2))) | (leq(X2, multiplication(X0, X1)) <=> (leq(X2, X0) & leq(X2, X1))))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[71, 64])).
% 270.13/172.27 tff(73,plain,
% 270.13/172.27 (~![X0: $i, X1: $i, X2: $i] : ((~(test(X0) & test(X1) & test(X2))) | (leq(X2, multiplication(X0, X1)) <=> (leq(X2, X0) & leq(X2, X1))))),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[72, 64])).
% 270.13/172.27 tff(74,plain,(
% 270.13/172.27 ~((~(test(X0!3) & test(X1!2) & test(X2!1))) | (leq(X2!1, multiplication(X0!3, X1!2)) <=> (leq(X2!1, X0!3) & leq(X2!1, X1!2))))),
% 270.13/172.27 inference(skolemize,[status(sab)],[73])).
% 270.13/172.27 tff(75,plain,
% 270.13/172.27 (test(X0!3) & test(X1!2) & test(X2!1)),
% 270.13/172.27 inference(or_elim,[status(thm)],[74])).
% 270.13/172.27 tff(76,plain,
% 270.13/172.27 (test(X2!1)),
% 270.13/172.27 inference(and_elim,[status(thm)],[75])).
% 270.13/172.27 tff(77,plain,
% 270.13/172.27 ((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | (~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1)),
% 270.13/172.27 inference(tautology,[status(thm)],[])).
% 270.13/172.27 tff(78,plain,
% 270.13/172.27 ((~((~test(X2!1)) | complement(tptp_fun_X1_0(X2!1), X2!1))) | complement(tptp_fun_X1_0(X2!1), X2!1)),
% 270.13/172.27 inference(unit_resolution,[status(thm)],[77, 76])).
% 270.13/172.27 tff(79,plain,
% 270.13/172.27 (complement(tptp_fun_X1_0(X2!1), X2!1)),
% 270.13/172.27 inference(unit_resolution,[status(thm)],[78, 63])).
% 270.13/172.27 tff(80,plain,
% 270.13/172.27 ((~(complement(tptp_fun_X1_0(X2!1), X2!1) <=> (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one)))))) | (~complement(tptp_fun_X1_0(X2!1), X2!1)) | (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))))),
% 270.13/172.27 inference(tautology,[status(thm)],[])).
% 270.13/172.27 tff(81,plain,
% 270.13/172.27 ((~(complement(tptp_fun_X1_0(X2!1), X2!1) <=> (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one)))))) | (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))))),
% 270.13/172.27 inference(unit_resolution,[status(thm)],[80, 79])).
% 270.13/172.27 tff(82,plain,
% 270.13/172.27 (~((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one)))),
% 270.13/172.27 inference(unit_resolution,[status(thm)],[81, 46])).
% 270.13/172.27 tff(83,plain,
% 270.13/172.27 (((~(multiplication(X2!1, tptp_fun_X1_0(X2!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X2!1), X2!1) = zero)) | (~(addition(X2!1, tptp_fun_X1_0(X2!1)) = one))) | (addition(X2!1, tptp_fun_X1_0(X2!1)) = one)),
% 270.13/172.27 inference(tautology,[status(thm)],[])).
% 270.13/172.27 tff(84,plain,
% 270.13/172.27 (addition(X2!1, tptp_fun_X1_0(X2!1)) = one),
% 270.13/172.27 inference(unit_resolution,[status(thm)],[83, 82])).
% 270.13/172.27 tff(85,plain,
% 270.13/172.27 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X2!1, tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), X2!1))),
% 270.13/172.27 inference(quant_inst,[status(thm)],[])).
% 270.13/172.27 tff(86,plain,
% 270.13/172.27 (addition(X2!1, tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), X2!1)),
% 270.13/172.27 inference(unit_resolution,[status(thm)],[85, 16])).
% 270.13/172.27 tff(87,plain,
% 270.13/172.27 (addition(tptp_fun_X1_0(X2!1), X2!1) = addition(X2!1, tptp_fun_X1_0(X2!1))),
% 270.13/172.27 inference(symmetry,[status(thm)],[86])).
% 270.13/172.27 tff(88,plain,
% 270.13/172.27 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 270.13/172.27 inference(bind,[status(th)],[])).
% 270.13/172.27 tff(89,plain,
% 270.13/172.27 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 270.13/172.27 inference(quant_intro,[status(thm)],[88])).
% 270.13/172.27 tff(90,plain,
% 270.13/172.27 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 270.13/172.27 inference(rewrite,[status(thm)],[])).
% 270.13/172.27 tff(91,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 270.13/172.27 tff(92,plain,
% 270.13/172.27 (![A: $i] : (addition(A, A) = A)),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[91, 90])).
% 270.13/172.27 tff(93,plain,(
% 270.13/172.27 ![A: $i] : (addition(A, A) = A)),
% 270.13/172.27 inference(skolemize,[status(sab)],[92])).
% 270.13/172.27 tff(94,plain,
% 270.13/172.27 (![A: $i] : (addition(A, A) = A)),
% 270.13/172.27 inference(modus_ponens,[status(thm)],[93, 89])).
% 270.13/172.27 tff(95,plain,
% 270.13/172.27 ((~![A: $i] : (addition(A, A) = A)) | (addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X2!1)) = tptp_fun_X1_0(X2!1))),
% 270.13/172.27 inference(quant_inst,[status(thm)],[])).
% 270.13/172.27 tff(96,plain,
% 270.13/172.27 (addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X2!1)) = tptp_fun_X1_0(X2!1)),
% 270.13/172.27 inference(unit_resolution,[status(thm)],[95, 94])).
% 270.13/172.27 tff(97,plain,
% 270.13/172.27 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X2!1)), X2!1) = addition(tptp_fun_X1_0(X2!1), X2!1)),
% 270.13/172.27 inference(monotonicity,[status(thm)],[96])).
% 270.13/172.27 tff(98,plain,
% 270.13/172.27 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X2!1), X2!1)) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X2!1)), X2!1))),
% 270.13/172.27 inference(quant_inst,[status(thm)],[])).
% 270.13/172.27 tff(99,plain,
% 270.13/172.27 (addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X2!1), X2!1)) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X2!1)), X2!1)),
% 270.13/172.27 inference(unit_resolution,[status(thm)],[98, 29])).
% 270.13/172.27 tff(100,plain,
% 270.13/172.27 ((~![A: $i] : (addition(A, A) = A)) | (addition(X2!1, X2!1) = X2!1)),
% 270.13/172.27 inference(quant_inst,[status(thm)],[])).
% 270.13/172.27 tff(101,plain,
% 270.13/172.27 (addition(X2!1, X2!1) = X2!1),
% 270.13/172.27 inference(unit_resolution,[status(thm)],[100, 94])).
% 270.13/172.27 tff(102,plain,
% 270.13/172.27 (addition(tptp_fun_X1_0(X2!1), addition(X2!1, X2!1)) = addition(tptp_fun_X1_0(X2!1), X2!1)),
% 270.13/172.27 inference(monotonicity,[status(thm)],[101])).
% 270.13/172.27 tff(103,plain,
% 270.13/172.27 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X2!1), addition(X2!1, X2!1)) = addition(addition(tptp_fun_X1_0(X2!1), X2!1), X2!1))),
% 270.13/172.27 inference(quant_inst,[status(thm)],[])).
% 270.13/172.27 tff(104,plain,
% 270.13/172.27 (addition(tptp_fun_X1_0(X2!1), addition(X2!1, X2!1)) = addition(addition(tptp_fun_X1_0(X2!1), X2!1), X2!1)),
% 270.13/172.27 inference(unit_resolution,[status(thm)],[103, 29])).
% 270.13/172.27 tff(105,plain,
% 270.13/172.27 (addition(addition(tptp_fun_X1_0(X2!1), X2!1), X2!1) = addition(tptp_fun_X1_0(X2!1), addition(X2!1, X2!1))),
% 270.13/172.27 inference(symmetry,[status(thm)],[104])).
% 270.13/172.27 tff(106,plain,
% 270.13/172.27 (one = addition(X2!1, tptp_fun_X1_0(X2!1))),
% 270.13/172.27 inference(symmetry,[status(thm)],[84])).
% 270.13/172.27 tff(107,plain,
% 270.13/172.27 ((~![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!2), X1!2) <=> (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one)))))),
% 270.13/172.27 inference(quant_inst,[status(thm)],[])).
% 270.13/172.27 tff(108,plain,
% 270.13/172.27 (complement(tptp_fun_X1_0(X1!2), X1!2) <=> (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[107, 44])).
% 270.13/172.28 tff(109,plain,
% 270.13/172.28 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | (~(test(X1!2) | ![X1: $i] : (~complement(X1, X1!2))))))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(110,plain,
% 270.13/172.28 (~((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | (~(test(X1!2) | ![X1: $i] : (~complement(X1, X1!2)))))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[109, 59])).
% 270.13/172.28 tff(111,plain,
% 270.13/172.28 (((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | (~(test(X1!2) | ![X1: $i] : (~complement(X1, X1!2))))) | ((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))),
% 270.13/172.28 inference(tautology,[status(thm)],[])).
% 270.13/172.28 tff(112,plain,
% 270.13/172.28 ((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2)),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[111, 110])).
% 270.13/172.28 tff(113,plain,
% 270.13/172.28 (test(X1!2)),
% 270.13/172.28 inference(and_elim,[status(thm)],[75])).
% 270.13/172.28 tff(114,plain,
% 270.13/172.28 ((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | (~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2)),
% 270.13/172.28 inference(tautology,[status(thm)],[])).
% 270.13/172.28 tff(115,plain,
% 270.13/172.28 ((~((~test(X1!2)) | complement(tptp_fun_X1_0(X1!2), X1!2))) | complement(tptp_fun_X1_0(X1!2), X1!2)),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[114, 113])).
% 270.13/172.28 tff(116,plain,
% 270.13/172.28 (complement(tptp_fun_X1_0(X1!2), X1!2)),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[115, 112])).
% 270.13/172.28 tff(117,plain,
% 270.13/172.28 ((~(complement(tptp_fun_X1_0(X1!2), X1!2) <=> (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one)))))) | (~complement(tptp_fun_X1_0(X1!2), X1!2)) | (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))))),
% 270.13/172.28 inference(tautology,[status(thm)],[])).
% 270.13/172.28 tff(118,plain,
% 270.13/172.28 ((~(complement(tptp_fun_X1_0(X1!2), X1!2) <=> (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one)))))) | (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[117, 116])).
% 270.13/172.28 tff(119,plain,
% 270.13/172.28 (~((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one)))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[118, 108])).
% 270.13/172.28 tff(120,plain,
% 270.13/172.28 (((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))) | (addition(X1!2, tptp_fun_X1_0(X1!2)) = one)),
% 270.13/172.28 inference(tautology,[status(thm)],[])).
% 270.13/172.28 tff(121,plain,
% 270.13/172.28 (addition(X1!2, tptp_fun_X1_0(X1!2)) = one),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[120, 119])).
% 270.13/172.28 tff(122,plain,
% 270.13/172.28 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!2, tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), X1!2))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(123,plain,
% 270.13/172.28 (addition(X1!2, tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), X1!2)),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[122, 16])).
% 270.13/172.28 tff(124,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X1!2), X1!2) = addition(X1!2, tptp_fun_X1_0(X1!2))),
% 270.13/172.28 inference(symmetry,[status(thm)],[123])).
% 270.13/172.28 tff(125,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X1!2), X1!2) = addition(tptp_fun_X1_0(X2!1), X2!1)),
% 270.13/172.28 inference(transitivity,[status(thm)],[124, 121, 106, 86])).
% 270.13/172.28 tff(126,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X1!2), X1!2), X2!1) = addition(addition(tptp_fun_X1_0(X2!1), X2!1), X2!1)),
% 270.13/172.28 inference(monotonicity,[status(thm)],[125])).
% 270.13/172.28 tff(127,plain,
% 270.13/172.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X1!2), addition(X1!2, X2!1)) = addition(addition(tptp_fun_X1_0(X1!2), X1!2), X2!1))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(128,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X1!2), addition(X1!2, X2!1)) = addition(addition(tptp_fun_X1_0(X1!2), X1!2), X2!1)),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[127, 29])).
% 270.13/172.28 tff(129,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X1!2), addition(X1!2, X2!1)) = addition(tptp_fun_X1_0(X2!1), X2!1)),
% 270.13/172.28 inference(transitivity,[status(thm)],[128, 126, 105, 102])).
% 270.13/172.28 tff(130,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), addition(X1!2, X2!1))) = addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X2!1), X2!1))),
% 270.13/172.28 inference(monotonicity,[status(thm)],[129])).
% 270.13/172.28 tff(131,plain,
% 270.13/172.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), addition(X1!2, X2!1))) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2)), addition(X1!2, X2!1)))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(132,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), addition(X1!2, X2!1))) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2)), addition(X1!2, X2!1))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[131, 29])).
% 270.13/172.28 tff(133,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2)), addition(X1!2, X2!1)) = addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), addition(X1!2, X2!1)))),
% 270.13/172.28 inference(symmetry,[status(thm)],[132])).
% 270.13/172.28 tff(134,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2)), addition(X1!2, X2!1)) = one),
% 270.13/172.28 inference(transitivity,[status(thm)],[133, 130, 99, 97, 87, 84])).
% 270.13/172.28 tff(135,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2)), addition(X1!2, X2!1))) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), one)),
% 270.13/172.28 inference(monotonicity,[status(thm)],[134])).
% 270.13/172.28 tff(136,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), one) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2)), addition(X1!2, X2!1)))),
% 270.13/172.28 inference(symmetry,[status(thm)],[135])).
% 270.13/172.28 tff(137,plain,
% 270.13/172.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X0!3), one)) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), one))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(138,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X0!3), one)) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), one)),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[137, 29])).
% 270.13/172.28 tff(139,plain,
% 270.13/172.28 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(tptp_fun_X1_0(X0!3), X0!3) <=> (~((~(multiplication(X0!3, tptp_fun_X1_0(X0!3)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!3), X0!3) = zero)) | (~(addition(X0!3, tptp_fun_X1_0(X0!3)) = one)))))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(140,plain,
% 270.13/172.28 (complement(tptp_fun_X1_0(X0!3), X0!3) <=> (~((~(multiplication(X0!3, tptp_fun_X1_0(X0!3)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!3), X0!3) = zero)) | (~(addition(X0!3, tptp_fun_X1_0(X0!3)) = one))))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[139, 44])).
% 270.13/172.28 tff(141,plain,
% 270.13/172.28 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X0!3)) | complement(tptp_fun_X1_0(X0!3), X0!3))) | (~(test(X0!3) | ![X1: $i] : (~complement(X1, X0!3))))))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(142,plain,
% 270.13/172.28 (~((~((~test(X0!3)) | complement(tptp_fun_X1_0(X0!3), X0!3))) | (~(test(X0!3) | ![X1: $i] : (~complement(X1, X0!3)))))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[141, 59])).
% 270.13/172.28 tff(143,plain,
% 270.13/172.28 (((~((~test(X0!3)) | complement(tptp_fun_X1_0(X0!3), X0!3))) | (~(test(X0!3) | ![X1: $i] : (~complement(X1, X0!3))))) | ((~test(X0!3)) | complement(tptp_fun_X1_0(X0!3), X0!3))),
% 270.13/172.28 inference(tautology,[status(thm)],[])).
% 270.13/172.28 tff(144,plain,
% 270.13/172.28 ((~test(X0!3)) | complement(tptp_fun_X1_0(X0!3), X0!3)),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[143, 142])).
% 270.13/172.28 tff(145,plain,
% 270.13/172.28 (test(X0!3)),
% 270.13/172.28 inference(and_elim,[status(thm)],[75])).
% 270.13/172.28 tff(146,plain,
% 270.13/172.28 ((~((~test(X0!3)) | complement(tptp_fun_X1_0(X0!3), X0!3))) | (~test(X0!3)) | complement(tptp_fun_X1_0(X0!3), X0!3)),
% 270.13/172.28 inference(tautology,[status(thm)],[])).
% 270.13/172.28 tff(147,plain,
% 270.13/172.28 ((~((~test(X0!3)) | complement(tptp_fun_X1_0(X0!3), X0!3))) | complement(tptp_fun_X1_0(X0!3), X0!3)),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[146, 145])).
% 270.13/172.28 tff(148,plain,
% 270.13/172.28 (complement(tptp_fun_X1_0(X0!3), X0!3)),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[147, 144])).
% 270.13/172.28 tff(149,plain,
% 270.13/172.28 ((~(complement(tptp_fun_X1_0(X0!3), X0!3) <=> (~((~(multiplication(X0!3, tptp_fun_X1_0(X0!3)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!3), X0!3) = zero)) | (~(addition(X0!3, tptp_fun_X1_0(X0!3)) = one)))))) | (~complement(tptp_fun_X1_0(X0!3), X0!3)) | (~((~(multiplication(X0!3, tptp_fun_X1_0(X0!3)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!3), X0!3) = zero)) | (~(addition(X0!3, tptp_fun_X1_0(X0!3)) = one))))),
% 270.13/172.28 inference(tautology,[status(thm)],[])).
% 270.13/172.28 tff(150,plain,
% 270.13/172.28 ((~(complement(tptp_fun_X1_0(X0!3), X0!3) <=> (~((~(multiplication(X0!3, tptp_fun_X1_0(X0!3)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!3), X0!3) = zero)) | (~(addition(X0!3, tptp_fun_X1_0(X0!3)) = one)))))) | (~((~(multiplication(X0!3, tptp_fun_X1_0(X0!3)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!3), X0!3) = zero)) | (~(addition(X0!3, tptp_fun_X1_0(X0!3)) = one))))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[149, 148])).
% 270.13/172.28 tff(151,plain,
% 270.13/172.28 (~((~(multiplication(X0!3, tptp_fun_X1_0(X0!3)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!3), X0!3) = zero)) | (~(addition(X0!3, tptp_fun_X1_0(X0!3)) = one)))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[150, 140])).
% 270.13/172.28 tff(152,plain,
% 270.13/172.28 (((~(multiplication(X0!3, tptp_fun_X1_0(X0!3)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!3), X0!3) = zero)) | (~(addition(X0!3, tptp_fun_X1_0(X0!3)) = one))) | (addition(X0!3, tptp_fun_X1_0(X0!3)) = one)),
% 270.13/172.28 inference(tautology,[status(thm)],[])).
% 270.13/172.28 tff(153,plain,
% 270.13/172.28 (addition(X0!3, tptp_fun_X1_0(X0!3)) = one),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[152, 151])).
% 270.13/172.28 tff(154,plain,
% 270.13/172.28 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!3, tptp_fun_X1_0(X0!3)) = addition(tptp_fun_X1_0(X0!3), X0!3))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(155,plain,
% 270.13/172.28 (addition(X0!3, tptp_fun_X1_0(X0!3)) = addition(tptp_fun_X1_0(X0!3), X0!3)),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[154, 16])).
% 270.13/172.28 tff(156,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X0!3), X0!3) = addition(X0!3, tptp_fun_X1_0(X0!3))),
% 270.13/172.28 inference(symmetry,[status(thm)],[155])).
% 270.13/172.28 tff(157,plain,
% 270.13/172.28 ((~![A: $i] : (addition(A, A) = A)) | (addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X0!3)) = tptp_fun_X1_0(X0!3))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(158,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X0!3)) = tptp_fun_X1_0(X0!3)),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[157, 94])).
% 270.13/172.28 tff(159,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X0!3)), X0!3) = addition(tptp_fun_X1_0(X0!3), X0!3)),
% 270.13/172.28 inference(monotonicity,[status(thm)],[158])).
% 270.13/172.28 tff(160,plain,
% 270.13/172.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X0!3), addition(tptp_fun_X1_0(X0!3), X0!3)) = addition(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X0!3)), X0!3))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(161,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X0!3), addition(tptp_fun_X1_0(X0!3), X0!3)) = addition(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X0!3)), X0!3)),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[160, 29])).
% 270.13/172.28 tff(162,plain,
% 270.13/172.28 (one = addition(X0!3, tptp_fun_X1_0(X0!3))),
% 270.13/172.28 inference(symmetry,[status(thm)],[153])).
% 270.13/172.28 tff(163,plain,
% 270.13/172.28 (one = addition(tptp_fun_X1_0(X0!3), X0!3)),
% 270.13/172.28 inference(transitivity,[status(thm)],[162, 155])).
% 270.13/172.28 tff(164,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X0!3), one) = addition(tptp_fun_X1_0(X0!3), addition(tptp_fun_X1_0(X0!3), X0!3))),
% 270.13/172.28 inference(monotonicity,[status(thm)],[163])).
% 270.13/172.28 tff(165,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X0!3), one) = addition(tptp_fun_X1_0(X2!1), X2!1)),
% 270.13/172.28 inference(transitivity,[status(thm)],[164, 161, 159, 156, 153, 106, 86])).
% 270.13/172.28 tff(166,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X0!3), one)) = addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X2!1), X2!1))),
% 270.13/172.28 inference(monotonicity,[status(thm)],[165])).
% 270.13/172.28 tff(167,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X2!1), X2!1)) = addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X0!3), one))),
% 270.13/172.28 inference(symmetry,[status(thm)],[166])).
% 270.13/172.28 tff(168,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X2!1)), X2!1) = addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X2!1), X2!1))),
% 270.13/172.28 inference(symmetry,[status(thm)],[99])).
% 270.13/172.28 tff(169,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X2!1), X2!1) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X2!1)), X2!1)),
% 270.13/172.28 inference(symmetry,[status(thm)],[97])).
% 270.13/172.28 tff(170,plain,
% 270.13/172.28 (one = addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))), addition(X1!2, X2!1))),
% 270.13/172.28 inference(transitivity,[status(thm)],[106, 86, 169, 168, 167, 138, 136, 31, 22])).
% 270.13/172.28 tff(171,plain,
% 270.13/172.28 (multiplication(X0!3, one) = multiplication(X0!3, addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))), addition(X1!2, X2!1)))),
% 270.13/172.28 inference(monotonicity,[status(thm)],[170])).
% 270.13/172.28 tff(172,plain,
% 270.13/172.28 (multiplication(X0!3, addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))), addition(X1!2, X2!1))) = multiplication(X0!3, one)),
% 270.13/172.28 inference(symmetry,[status(thm)],[171])).
% 270.13/172.28 tff(173,plain,
% 270.13/172.28 (^[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))))),
% 270.13/172.28 inference(bind,[status(th)],[])).
% 270.13/172.28 tff(174,plain,
% 270.13/172.28 (![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)))),
% 270.13/172.28 inference(quant_intro,[status(thm)],[173])).
% 270.13/172.28 tff(175,plain,
% 270.13/172.28 (![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)))),
% 270.13/172.28 inference(rewrite,[status(thm)],[])).
% 270.13/172.28 tff(176,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','right_distributivity')).
% 270.13/172.28 tff(177,plain,
% 270.13/172.28 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 270.13/172.28 inference(modus_ponens,[status(thm)],[176, 175])).
% 270.13/172.28 tff(178,plain,(
% 270.13/172.28 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 270.13/172.28 inference(skolemize,[status(sab)],[177])).
% 270.13/172.28 tff(179,plain,
% 270.13/172.28 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 270.13/172.28 inference(modus_ponens,[status(thm)],[178, 174])).
% 270.13/172.28 tff(180,plain,
% 270.13/172.28 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!3, addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))), addition(X1!2, X2!1))) = addition(multiplication(X0!3, addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))), multiplication(X0!3, addition(X1!2, X2!1))))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(181,plain,
% 270.13/172.28 (multiplication(X0!3, addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))), addition(X1!2, X2!1))) = addition(multiplication(X0!3, addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))), multiplication(X0!3, addition(X1!2, X2!1)))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[180, 179])).
% 270.13/172.28 tff(182,plain,
% 270.13/172.28 (addition(multiplication(X0!3, addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))), multiplication(X0!3, addition(X1!2, X2!1))) = multiplication(X0!3, addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))), addition(X1!2, X2!1)))),
% 270.13/172.28 inference(symmetry,[status(thm)],[181])).
% 270.13/172.28 tff(183,plain,
% 270.13/172.28 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 270.13/172.28 inference(bind,[status(th)],[])).
% 270.13/172.28 tff(184,plain,
% 270.13/172.28 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 270.13/172.28 inference(quant_intro,[status(thm)],[183])).
% 270.13/172.28 tff(185,plain,
% 270.13/172.28 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 270.13/172.28 inference(rewrite,[status(thm)],[])).
% 270.13/172.28 tff(186,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 270.13/172.28 tff(187,plain,
% 270.13/172.28 (![A: $i] : (multiplication(one, A) = A)),
% 270.13/172.28 inference(modus_ponens,[status(thm)],[186, 185])).
% 270.13/172.28 tff(188,plain,(
% 270.13/172.28 ![A: $i] : (multiplication(one, A) = A)),
% 270.13/172.28 inference(skolemize,[status(sab)],[187])).
% 270.13/172.28 tff(189,plain,
% 270.13/172.28 (![A: $i] : (multiplication(one, A) = A)),
% 270.13/172.28 inference(modus_ponens,[status(thm)],[188, 184])).
% 270.13/172.28 tff(190,plain,
% 270.13/172.28 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X2!1) = X2!1)),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(191,plain,
% 270.13/172.28 (multiplication(one, X2!1) = X2!1),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[190, 189])).
% 270.13/172.28 tff(192,plain,
% 270.13/172.28 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(tptp_fun_X1_0(X2!1), X1!2) = addition(X1!2, tptp_fun_X1_0(X2!1)))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(193,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X2!1), X1!2) = addition(X1!2, tptp_fun_X1_0(X2!1))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[192, 16])).
% 270.13/172.28 tff(194,plain,
% 270.13/172.28 (addition(X1!2, tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), X1!2)),
% 270.13/172.28 inference(symmetry,[status(thm)],[193])).
% 270.13/172.28 tff(195,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(X1!2, tptp_fun_X1_0(X2!1))) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X2!1), X1!2))),
% 270.13/172.28 inference(monotonicity,[status(thm)],[194])).
% 270.13/172.28 tff(196,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X2!1), X1!2)) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(X1!2, tptp_fun_X1_0(X2!1)))),
% 270.13/172.28 inference(symmetry,[status(thm)],[195])).
% 270.13/172.28 tff(197,plain,
% 270.13/172.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X2!1), X1!2)) = addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X2!1)), X1!2))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(198,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X2!1), X1!2)) = addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X2!1)), X1!2)),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[197, 29])).
% 270.13/172.28 tff(199,plain,
% 270.13/172.28 (addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X2!1)), X1!2) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X2!1), X1!2))),
% 270.13/172.28 inference(symmetry,[status(thm)],[198])).
% 270.13/172.28 tff(200,plain,
% 270.13/172.28 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(201,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[200, 16])).
% 270.13/172.28 tff(202,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X0!3), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X2!1))) = addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1))),
% 270.13/172.28 inference(monotonicity,[status(thm)],[96])).
% 270.13/172.28 tff(203,plain,
% 270.13/172.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X0!3), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X2!1))) = addition(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1)))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(204,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X0!3), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X2!1))) = addition(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[203, 29])).
% 270.13/172.28 tff(205,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X0!3), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X2!1)))),
% 270.13/172.28 inference(symmetry,[status(thm)],[204])).
% 270.13/172.28 tff(206,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)) = addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1))),
% 270.13/172.28 inference(symmetry,[status(thm)],[201])).
% 270.13/172.28 tff(207,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X2!1)) = addition(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1))),
% 270.13/172.28 inference(monotonicity,[status(thm)],[206])).
% 270.13/172.28 tff(208,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3))),
% 270.13/172.28 inference(transitivity,[status(thm)],[207, 205, 202, 201])).
% 270.13/172.28 tff(209,plain,
% 270.13/172.28 (addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X2!1)), X1!2) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), X1!2)),
% 270.13/172.28 inference(monotonicity,[status(thm)],[208])).
% 270.13/172.28 tff(210,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), X1!2) = addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X2!1)), X1!2)),
% 270.13/172.28 inference(symmetry,[status(thm)],[209])).
% 270.13/172.28 tff(211,plain,
% 270.13/172.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X0!3), X1!2)) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), X1!2))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(212,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X0!3), X1!2)) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), X1!2)),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[211, 29])).
% 270.13/172.28 tff(213,plain,
% 270.13/172.28 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(tptp_fun_X1_0(X0!3), X1!2) = addition(X1!2, tptp_fun_X1_0(X0!3)))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(214,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X0!3), X1!2) = addition(X1!2, tptp_fun_X1_0(X0!3))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[213, 16])).
% 270.13/172.28 tff(215,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X0!3), X1!2)) = addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3)))),
% 270.13/172.28 inference(monotonicity,[status(thm)],[214])).
% 270.13/172.28 tff(216,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))) = addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X0!3), X1!2))),
% 270.13/172.28 inference(symmetry,[status(thm)],[215])).
% 270.13/172.28 tff(217,plain,
% 270.13/172.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))) = addition(addition(tptp_fun_X1_0(X2!1), X1!2), tptp_fun_X1_0(X0!3)))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(218,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))) = addition(addition(tptp_fun_X1_0(X2!1), X1!2), tptp_fun_X1_0(X0!3))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[217, 29])).
% 270.13/172.28 tff(219,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X2!1), X1!2), tptp_fun_X1_0(X0!3)) = addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3)))),
% 270.13/172.28 inference(symmetry,[status(thm)],[218])).
% 270.13/172.28 tff(220,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X2!1), X1!2), tptp_fun_X1_0(X0!3)) = addition(addition(X1!2, tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X0!3))),
% 270.13/172.28 inference(monotonicity,[status(thm)],[193])).
% 270.13/172.28 tff(221,plain,
% 270.13/172.28 (addition(addition(X1!2, tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X0!3)) = addition(addition(tptp_fun_X1_0(X2!1), X1!2), tptp_fun_X1_0(X0!3))),
% 270.13/172.28 inference(symmetry,[status(thm)],[220])).
% 270.13/172.28 tff(222,plain,
% 270.13/172.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X1!2, addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3))) = addition(addition(X1!2, tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X0!3)))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(223,plain,
% 270.13/172.28 (addition(X1!2, addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3))) = addition(addition(X1!2, tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X0!3))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[222, 29])).
% 270.13/172.28 tff(224,plain,
% 270.13/172.28 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X2!1, X1!2) = addition(X1!2, X2!1))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(225,plain,
% 270.13/172.28 (addition(X2!1, X1!2) = addition(X1!2, X2!1)),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[224, 16])).
% 270.13/172.28 tff(226,assumption,(~(multiplication(one, X1!2) = X1!2)), introduced(assumption)).
% 270.13/172.28 tff(227,plain,
% 270.13/172.28 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X1!2) = X1!2)),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(228,plain,
% 270.13/172.28 ($false),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[227, 189, 226])).
% 270.13/172.28 tff(229,plain,(multiplication(one, X1!2) = X1!2), inference(lemma,lemma(discharge,[]))).
% 270.13/172.28 tff(230,assumption,(multiplication(one, X1!2) = X1!2), introduced(assumption)).
% 270.13/172.28 tff(231,plain,
% 270.13/172.28 (addition(X2!1, addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X2!1))) = addition(X2!1, tptp_fun_X1_0(X2!1))),
% 270.13/172.28 inference(monotonicity,[status(thm)],[96])).
% 270.13/172.28 tff(232,plain,
% 270.13/172.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X2!1, addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X2!1))) = addition(addition(X2!1, tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1)))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(233,plain,
% 270.13/172.28 (addition(X2!1, addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X2!1))) = addition(addition(X2!1, tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[232, 29])).
% 270.13/172.28 tff(234,plain,
% 270.13/172.28 (addition(addition(X2!1, tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1)) = addition(X2!1, addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X2!1)))),
% 270.13/172.28 inference(symmetry,[status(thm)],[233])).
% 270.13/172.28 tff(235,plain,
% 270.13/172.28 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(tptp_fun_X1_0(X1!2), addition(X1!2, X2!1)) = addition(addition(X1!2, X2!1), tptp_fun_X1_0(X1!2)))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(236,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X1!2), addition(X1!2, X2!1)) = addition(addition(X1!2, X2!1), tptp_fun_X1_0(X1!2))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[235, 16])).
% 270.13/172.28 tff(237,plain,
% 270.13/172.28 (addition(addition(X1!2, X2!1), tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), addition(X1!2, X2!1))),
% 270.13/172.28 inference(symmetry,[status(thm)],[236])).
% 270.13/172.28 tff(238,plain,
% 270.13/172.28 ((~![A: $i] : (addition(A, A) = A)) | (addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X1!2)) = tptp_fun_X1_0(X1!2))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(239,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X1!2)) = tptp_fun_X1_0(X1!2)),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[238, 94])).
% 270.13/172.28 tff(240,plain,
% 270.13/172.28 (addition(addition(X1!2, X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X1!2))) = addition(addition(X1!2, X2!1), tptp_fun_X1_0(X1!2))),
% 270.13/172.28 inference(monotonicity,[status(thm)],[239])).
% 270.13/172.28 tff(241,plain,
% 270.13/172.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(X1!2, X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X1!2))) = addition(addition(addition(X1!2, X2!1), tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X1!2)))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(242,plain,
% 270.13/172.28 (addition(addition(X1!2, X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X1!2))) = addition(addition(addition(X1!2, X2!1), tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X1!2))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[241, 29])).
% 270.13/172.28 tff(243,plain,
% 270.13/172.28 (addition(addition(addition(X1!2, X2!1), tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X1!2)) = addition(addition(X1!2, X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X1!2)))),
% 270.13/172.28 inference(symmetry,[status(thm)],[242])).
% 270.13/172.28 tff(244,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X1!2), X1!2), X2!1) = addition(tptp_fun_X1_0(X1!2), addition(X1!2, X2!1))),
% 270.13/172.28 inference(symmetry,[status(thm)],[128])).
% 270.13/172.28 tff(245,plain,
% 270.13/172.28 (addition(addition(tptp_fun_X1_0(X2!1), X2!1), X2!1) = addition(addition(tptp_fun_X1_0(X1!2), X1!2), X2!1)),
% 270.13/172.28 inference(symmetry,[status(thm)],[126])).
% 270.13/172.28 tff(246,plain,
% 270.13/172.28 (addition(tptp_fun_X1_0(X2!1), X2!1) = addition(tptp_fun_X1_0(X2!1), addition(X2!1, X2!1))),
% 270.13/172.28 inference(symmetry,[status(thm)],[102])).
% 270.13/172.28 tff(247,plain,
% 270.13/172.28 (one = addition(addition(X1!2, X2!1), tptp_fun_X1_0(X1!2))),
% 270.13/172.28 inference(transitivity,[status(thm)],[106, 86, 246, 104, 245, 244, 236])).
% 270.13/172.28 tff(248,plain,
% 270.13/172.28 (addition(one, tptp_fun_X1_0(X1!2)) = addition(addition(addition(X1!2, X2!1), tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X1!2))),
% 270.13/172.28 inference(monotonicity,[status(thm)],[247])).
% 270.13/172.28 tff(249,plain,
% 270.13/172.28 (addition(one, tptp_fun_X1_0(X1!2)) = addition(X2!1, tptp_fun_X1_0(X2!1))),
% 270.13/172.28 inference(transitivity,[status(thm)],[248, 243, 240, 237, 128, 126, 105, 102, 87])).
% 270.13/172.28 tff(250,plain,
% 270.13/172.28 (addition(addition(one, tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X2!1)) = addition(addition(X2!1, tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1))),
% 270.13/172.28 inference(monotonicity,[status(thm)],[249])).
% 270.13/172.28 tff(251,plain,
% 270.13/172.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))) = addition(addition(one, tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X2!1)))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(252,plain,
% 270.13/172.28 (addition(one, addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))) = addition(addition(one, tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X2!1))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[251, 29])).
% 270.13/172.28 tff(253,plain,
% 270.13/172.28 (addition(X0!3, tptp_fun_X1_0(X0!3)) = addition(X2!1, tptp_fun_X1_0(X2!1))),
% 270.13/172.28 inference(transitivity,[status(thm)],[153, 106])).
% 270.13/172.28 tff(254,plain,
% 270.13/172.28 (addition(addition(X0!3, tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X2!1)) = addition(addition(X2!1, tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1))),
% 270.13/172.28 inference(monotonicity,[status(thm)],[253])).
% 270.13/172.28 tff(255,plain,
% 270.13/172.28 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!3, addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1))) = addition(addition(X0!3, tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X2!1)))),
% 270.13/172.28 inference(quant_inst,[status(thm)],[])).
% 270.13/172.28 tff(256,plain,
% 270.13/172.28 (addition(X0!3, addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1))) = addition(addition(X0!3, tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X2!1))),
% 270.13/172.28 inference(unit_resolution,[status(thm)],[255, 29])).
% 270.13/172.28 tff(257,plain,
% 270.13/172.28 (addition(X0!3, addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1))) = one),
% 270.13/172.28 inference(transitivity,[status(thm)],[256, 254, 234, 231, 84])).
% 270.13/172.28 tff(258,plain,
% 270.13/172.28 (addition(addition(X0!3, addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1))), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))) = addition(one, addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))),
% 270.13/172.28 inference(monotonicity,[status(thm)],[257])).
% 270.13/172.29 tff(259,plain,
% 270.13/172.29 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!3, addition(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))) = addition(addition(X0!3, addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1))), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))))),
% 270.13/172.29 inference(quant_inst,[status(thm)],[])).
% 270.13/172.29 tff(260,plain,
% 270.13/172.29 (addition(X0!3, addition(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))) = addition(addition(X0!3, addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1))), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))),
% 270.13/172.29 inference(unit_resolution,[status(thm)],[259, 29])).
% 270.13/172.29 tff(261,plain,
% 270.13/172.29 (addition(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))),
% 270.13/172.29 inference(monotonicity,[status(thm)],[201])).
% 270.13/172.29 tff(262,plain,
% 270.13/172.29 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))) = addition(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))),
% 270.13/172.29 inference(symmetry,[status(thm)],[261])).
% 270.13/172.29 tff(263,plain,
% 270.13/172.29 (addition(X0!3, addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))) = addition(X0!3, addition(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))))),
% 270.13/172.29 inference(monotonicity,[status(thm)],[262])).
% 270.13/172.29 tff(264,plain,
% 270.13/172.29 (addition(X0!3, addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))) = one),
% 270.13/172.29 inference(transitivity,[status(thm)],[263, 260, 258, 252, 250, 234, 231, 84])).
% 270.13/172.29 tff(265,plain,
% 270.13/172.29 (multiplication(addition(X0!3, addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))), X1!2) = multiplication(one, X1!2)),
% 270.13/172.29 inference(monotonicity,[status(thm)],[264])).
% 270.13/172.29 tff(266,plain,
% 270.13/172.29 (^[A: $i, B: $i, C: $i] : refl((multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))))),
% 270.13/172.29 inference(bind,[status(th)],[])).
% 270.13/172.29 tff(267,plain,
% 270.13/172.29 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 270.13/172.29 inference(quant_intro,[status(thm)],[266])).
% 270.13/172.29 tff(268,plain,
% 270.13/172.29 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 270.13/172.29 inference(rewrite,[status(thm)],[])).
% 270.13/172.29 tff(269,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','left_distributivity')).
% 270.13/172.29 tff(270,plain,
% 270.13/172.29 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 270.13/172.29 inference(modus_ponens,[status(thm)],[269, 268])).
% 270.13/172.29 tff(271,plain,(
% 270.13/172.29 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 270.13/172.29 inference(skolemize,[status(sab)],[270])).
% 270.13/172.29 tff(272,plain,
% 270.13/172.29 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 270.13/172.29 inference(modus_ponens,[status(thm)],[271, 267])).
% 270.13/172.29 tff(273,plain,
% 270.13/172.29 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X0!3, addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))), X1!2) = addition(multiplication(X0!3, X1!2), multiplication(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))), X1!2)))),
% 270.13/172.29 inference(quant_inst,[status(thm)],[])).
% 270.13/172.29 tff(274,plain,
% 270.13/172.29 (multiplication(addition(X0!3, addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))), X1!2) = addition(multiplication(X0!3, X1!2), multiplication(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))), X1!2))),
% 270.13/172.29 inference(unit_resolution,[status(thm)],[273, 272])).
% 270.13/172.29 tff(275,plain,
% 270.13/172.29 (addition(multiplication(X0!3, X1!2), multiplication(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))), X1!2)) = multiplication(addition(X0!3, addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))), X1!2)),
% 270.13/172.29 inference(symmetry,[status(thm)],[274])).
% 270.13/172.29 tff(276,plain,
% 270.13/172.29 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))),
% 270.13/172.29 inference(quant_inst,[status(thm)],[])).
% 270.13/172.29 tff(277,plain,
% 270.13/172.29 (addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))),
% 270.13/172.29 inference(unit_resolution,[status(thm)],[276, 16])).
% 270.13/172.29 tff(278,plain,
% 270.13/172.29 (addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)) = addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))),
% 270.13/172.29 inference(symmetry,[status(thm)],[277])).
% 270.13/172.29 tff(279,plain,
% 270.13/172.29 (addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))) = addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)))),
% 270.13/172.29 inference(monotonicity,[status(thm)],[278])).
% 270.13/172.29 tff(280,plain,
% 270.13/172.29 (addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))) = addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))),
% 270.13/172.29 inference(symmetry,[status(thm)],[279])).
% 270.13/172.29 tff(281,plain,
% 270.13/172.29 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X1!2)))),
% 270.13/172.29 inference(quant_inst,[status(thm)],[])).
% 270.13/172.29 tff(282,plain,
% 270.13/172.29 (addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X1!2))),
% 270.13/172.29 inference(unit_resolution,[status(thm)],[281, 29])).
% 270.13/172.29 tff(283,plain,
% 270.13/172.29 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)))),
% 270.13/172.29 inference(symmetry,[status(thm)],[282])).
% 270.13/172.29 tff(284,plain,
% 270.13/172.29 (addition(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X2!1)) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X2!1))),
% 270.13/172.29 inference(symmetry,[status(thm)],[207])).
% 270.13/172.29 tff(285,plain,
% 270.13/172.29 (addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X2!1)) = addition(tptp_fun_X1_0(X0!3), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X2!1)))),
% 270.13/172.29 inference(symmetry,[status(thm)],[202])).
% 270.13/172.29 tff(286,plain,
% 270.13/172.29 (addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X2!1))),
% 270.13/172.29 inference(transitivity,[status(thm)],[206, 285, 204, 284])).
% 270.13/172.29 tff(287,plain,
% 270.13/172.29 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X1!2)) = addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X1!2))),
% 270.13/172.29 inference(monotonicity,[status(thm)],[286])).
% 270.13/172.29 tff(288,plain,
% 270.13/172.29 (addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X1!2)) = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X1!2))),
% 270.13/172.29 inference(symmetry,[status(thm)],[287])).
% 270.25/172.29 tff(289,plain,
% 270.25/172.29 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2))) = addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X1!2)))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(290,plain,
% 270.25/172.29 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X1!2))) = addition(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X1!2))),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[289, 29])).
% 270.25/172.29 tff(291,plain,
% 270.25/172.29 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))) = addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))),
% 270.25/172.29 inference(transitivity,[status(thm)],[20, 290, 288, 283, 280])).
% 270.25/172.29 tff(292,plain,
% 270.25/172.29 (multiplication(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))), X1!2) = multiplication(addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))), X1!2)),
% 270.25/172.29 inference(monotonicity,[status(thm)],[291])).
% 270.25/172.29 tff(293,plain,
% 270.25/172.29 (multiplication(addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))), X1!2) = multiplication(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))), X1!2)),
% 270.25/172.29 inference(symmetry,[status(thm)],[292])).
% 270.25/172.29 tff(294,assumption,(~leq(X2!1, multiplication(X0!3, X1!2))), introduced(assumption)).
% 270.25/172.29 tff(295,plain,
% 270.25/172.29 ((~(leq(X2!1, multiplication(X0!3, X1!2)) <=> (~((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2)))))) <=> (leq(X2!1, multiplication(X0!3, X1!2)) <=> ((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2))))),
% 270.25/172.29 inference(rewrite,[status(thm)],[])).
% 270.25/172.29 tff(296,plain,
% 270.25/172.29 ((leq(X2!1, multiplication(X0!3, X1!2)) <=> (leq(X2!1, X0!3) & leq(X2!1, X1!2))) <=> (leq(X2!1, multiplication(X0!3, X1!2)) <=> (~((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2)))))),
% 270.25/172.29 inference(rewrite,[status(thm)],[])).
% 270.25/172.29 tff(297,plain,
% 270.25/172.29 ((~(leq(X2!1, multiplication(X0!3, X1!2)) <=> (leq(X2!1, X0!3) & leq(X2!1, X1!2)))) <=> (~(leq(X2!1, multiplication(X0!3, X1!2)) <=> (~((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2))))))),
% 270.25/172.29 inference(monotonicity,[status(thm)],[296])).
% 270.25/172.29 tff(298,plain,
% 270.25/172.29 ((~(leq(X2!1, multiplication(X0!3, X1!2)) <=> (leq(X2!1, X0!3) & leq(X2!1, X1!2)))) <=> (leq(X2!1, multiplication(X0!3, X1!2)) <=> ((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2))))),
% 270.25/172.29 inference(transitivity,[status(thm)],[297, 295])).
% 270.25/172.29 tff(299,plain,
% 270.25/172.29 (~(leq(X2!1, multiplication(X0!3, X1!2)) <=> (leq(X2!1, X0!3) & leq(X2!1, X1!2)))),
% 270.25/172.29 inference(or_elim,[status(thm)],[74])).
% 270.25/172.29 tff(300,plain,
% 270.25/172.29 (leq(X2!1, multiplication(X0!3, X1!2)) <=> ((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2)))),
% 270.25/172.29 inference(modus_ponens,[status(thm)],[299, 298])).
% 270.25/172.29 tff(301,plain,
% 270.25/172.29 (leq(X2!1, multiplication(X0!3, X1!2)) | (~((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2)))) | (~(leq(X2!1, multiplication(X0!3, X1!2)) <=> ((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2)))))),
% 270.25/172.29 inference(tautology,[status(thm)],[])).
% 270.25/172.29 tff(302,plain,
% 270.25/172.29 (leq(X2!1, multiplication(X0!3, X1!2)) | (~((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2))))),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[301, 300])).
% 270.25/172.29 tff(303,plain,
% 270.25/172.29 (~((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2)))),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[302, 294])).
% 270.25/172.29 tff(304,plain,
% 270.25/172.29 (((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2))) | leq(X2!1, X0!3)),
% 270.25/172.29 inference(tautology,[status(thm)],[])).
% 270.25/172.29 tff(305,plain,
% 270.25/172.29 (leq(X2!1, X0!3)),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[304, 303])).
% 270.25/172.29 tff(306,plain,
% 270.25/172.29 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 270.25/172.29 inference(bind,[status(th)],[])).
% 270.25/172.29 tff(307,plain,
% 270.25/172.29 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 270.25/172.29 inference(quant_intro,[status(thm)],[306])).
% 270.25/172.29 tff(308,plain,
% 270.25/172.29 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 270.25/172.29 inference(rewrite,[status(thm)],[])).
% 270.25/172.29 tff(309,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','order')).
% 270.25/172.29 tff(310,plain,
% 270.25/172.29 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 270.25/172.29 inference(modus_ponens,[status(thm)],[309, 308])).
% 270.25/172.29 tff(311,plain,(
% 270.25/172.29 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 270.25/172.29 inference(skolemize,[status(sab)],[310])).
% 270.25/172.29 tff(312,plain,
% 270.25/172.29 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 270.25/172.29 inference(modus_ponens,[status(thm)],[311, 307])).
% 270.25/172.29 tff(313,plain,
% 270.25/172.29 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X2!1, X0!3) <=> (addition(X2!1, X0!3) = X0!3))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(314,plain,
% 270.25/172.29 (leq(X2!1, X0!3) <=> (addition(X2!1, X0!3) = X0!3)),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[313, 312])).
% 270.25/172.29 tff(315,plain,
% 270.25/172.29 ((~(leq(X2!1, X0!3) <=> (addition(X2!1, X0!3) = X0!3))) | (~leq(X2!1, X0!3)) | (addition(X2!1, X0!3) = X0!3)),
% 270.25/172.29 inference(tautology,[status(thm)],[])).
% 270.25/172.29 tff(316,plain,
% 270.25/172.29 ((~leq(X2!1, X0!3)) | (addition(X2!1, X0!3) = X0!3)),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[315, 314])).
% 270.25/172.29 tff(317,plain,
% 270.25/172.29 (addition(X2!1, X0!3) = X0!3),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[316, 305])).
% 270.25/172.29 tff(318,plain,
% 270.25/172.29 (((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2))) | leq(X2!1, X1!2)),
% 270.25/172.29 inference(tautology,[status(thm)],[])).
% 270.25/172.29 tff(319,plain,
% 270.25/172.29 (leq(X2!1, X1!2)),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[318, 303])).
% 270.25/172.29 tff(320,plain,
% 270.25/172.29 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X2!1, X1!2) <=> (addition(X2!1, X1!2) = X1!2))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(321,plain,
% 270.25/172.29 (leq(X2!1, X1!2) <=> (addition(X2!1, X1!2) = X1!2)),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[320, 312])).
% 270.25/172.29 tff(322,plain,
% 270.25/172.29 ((~(leq(X2!1, X1!2) <=> (addition(X2!1, X1!2) = X1!2))) | (~leq(X2!1, X1!2)) | (addition(X2!1, X1!2) = X1!2)),
% 270.25/172.29 inference(tautology,[status(thm)],[])).
% 270.25/172.29 tff(323,plain,
% 270.25/172.29 ((~leq(X2!1, X1!2)) | (addition(X2!1, X1!2) = X1!2)),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[322, 321])).
% 270.25/172.29 tff(324,plain,
% 270.25/172.29 (addition(X2!1, X1!2) = X1!2),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[323, 319])).
% 270.25/172.29 tff(325,assumption,(~(addition(addition(multiplication(addition(X2!1, X2!1), X2!1), multiplication(X0!3, X2!1)), zero) = addition(multiplication(addition(X2!1, X2!1), X2!1), multiplication(X0!3, X2!1)))), introduced(assumption)).
% 270.25/172.29 tff(326,plain,
% 270.25/172.29 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 270.25/172.29 inference(bind,[status(th)],[])).
% 270.25/172.29 tff(327,plain,
% 270.25/172.29 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 270.25/172.29 inference(quant_intro,[status(thm)],[326])).
% 270.25/172.29 tff(328,plain,
% 270.25/172.29 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 270.25/172.29 inference(rewrite,[status(thm)],[])).
% 270.25/172.29 tff(329,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 270.25/172.29 tff(330,plain,
% 270.25/172.29 (![A: $i] : (addition(A, zero) = A)),
% 270.25/172.29 inference(modus_ponens,[status(thm)],[329, 328])).
% 270.25/172.29 tff(331,plain,(
% 270.25/172.29 ![A: $i] : (addition(A, zero) = A)),
% 270.25/172.29 inference(skolemize,[status(sab)],[330])).
% 270.25/172.29 tff(332,plain,
% 270.25/172.29 (![A: $i] : (addition(A, zero) = A)),
% 270.25/172.29 inference(modus_ponens,[status(thm)],[331, 327])).
% 270.25/172.29 tff(333,plain,
% 270.25/172.29 ((~![A: $i] : (addition(A, zero) = A)) | (addition(addition(multiplication(addition(X2!1, X2!1), X2!1), multiplication(X0!3, X2!1)), zero) = addition(multiplication(addition(X2!1, X2!1), X2!1), multiplication(X0!3, X2!1)))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(334,plain,
% 270.25/172.29 ($false),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[333, 332, 325])).
% 270.25/172.29 tff(335,plain,(addition(addition(multiplication(addition(X2!1, X2!1), X2!1), multiplication(X0!3, X2!1)), zero) = addition(multiplication(addition(X2!1, X2!1), X2!1), multiplication(X0!3, X2!1))), inference(lemma,lemma(discharge,[]))).
% 270.25/172.29 tff(336,plain,
% 270.25/172.29 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!3, addition(X2!1, X1!2)) = addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2)))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(337,plain,
% 270.25/172.29 (multiplication(X0!3, addition(X2!1, X1!2)) = addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2))),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[336, 179])).
% 270.25/172.29 tff(338,assumption,(addition(X2!1, X1!2) = X1!2), introduced(assumption)).
% 270.25/172.29 tff(339,plain,
% 270.25/172.29 (X1!2 = addition(X2!1, X1!2)),
% 270.25/172.29 inference(symmetry,[status(thm)],[338])).
% 270.25/172.29 tff(340,plain,
% 270.25/172.29 (multiplication(X0!3, X1!2) = multiplication(X0!3, addition(X2!1, X1!2))),
% 270.25/172.29 inference(monotonicity,[status(thm)],[339])).
% 270.25/172.29 tff(341,plain,
% 270.25/172.29 (multiplication(X0!3, X1!2) = addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2))),
% 270.25/172.29 inference(transitivity,[status(thm)],[340, 337])).
% 270.25/172.29 tff(342,plain,
% 270.25/172.29 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X2!1, addition(X2!1, X0!3)) = addition(addition(X2!1, X2!1), X0!3))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(343,plain,
% 270.25/172.29 (addition(X2!1, addition(X2!1, X0!3)) = addition(addition(X2!1, X2!1), X0!3)),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[342, 29])).
% 270.25/172.29 tff(344,assumption,(addition(X2!1, X0!3) = X0!3), introduced(assumption)).
% 270.25/172.29 tff(345,plain,
% 270.25/172.29 (addition(X2!1, addition(X2!1, X0!3)) = addition(X2!1, X0!3)),
% 270.25/172.29 inference(monotonicity,[status(thm)],[344])).
% 270.25/172.29 tff(346,plain,
% 270.25/172.29 (addition(X2!1, X0!3) = addition(X2!1, addition(X2!1, X0!3))),
% 270.25/172.29 inference(symmetry,[status(thm)],[345])).
% 270.25/172.29 tff(347,plain,
% 270.25/172.29 (X0!3 = addition(X2!1, X0!3)),
% 270.25/172.29 inference(symmetry,[status(thm)],[344])).
% 270.25/172.29 tff(348,plain,
% 270.25/172.29 (X0!3 = addition(addition(X2!1, X2!1), X0!3)),
% 270.25/172.29 inference(transitivity,[status(thm)],[347, 346, 343])).
% 270.25/172.29 tff(349,plain,
% 270.25/172.29 (multiplication(X0!3, X2!1) = multiplication(addition(addition(X2!1, X2!1), X0!3), X2!1)),
% 270.25/172.29 inference(monotonicity,[status(thm)],[348])).
% 270.25/172.29 tff(350,plain,
% 270.25/172.29 (multiplication(addition(addition(X2!1, X2!1), X0!3), X2!1) = multiplication(X0!3, X2!1)),
% 270.25/172.29 inference(symmetry,[status(thm)],[349])).
% 270.25/172.29 tff(351,plain,
% 270.25/172.29 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(addition(X2!1, X2!1), X0!3), X2!1) = addition(multiplication(addition(X2!1, X2!1), X2!1), multiplication(X0!3, X2!1)))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(352,plain,
% 270.25/172.29 (multiplication(addition(addition(X2!1, X2!1), X0!3), X2!1) = addition(multiplication(addition(X2!1, X2!1), X2!1), multiplication(X0!3, X2!1))),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[351, 272])).
% 270.25/172.29 tff(353,plain,
% 270.25/172.29 (addition(multiplication(addition(X2!1, X2!1), X2!1), multiplication(X0!3, X2!1)) = multiplication(addition(addition(X2!1, X2!1), X0!3), X2!1)),
% 270.25/172.29 inference(symmetry,[status(thm)],[352])).
% 270.25/172.29 tff(354,assumption,(addition(addition(multiplication(addition(X2!1, X2!1), X2!1), multiplication(X0!3, X2!1)), zero) = addition(multiplication(addition(X2!1, X2!1), X2!1), multiplication(X0!3, X2!1))), introduced(assumption)).
% 270.25/172.29 tff(355,plain,
% 270.25/172.29 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(tptp_fun_X1_0(X1!2), X2!1), zero) = multiplication(tptp_fun_X1_0(X1!2), X2!1))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(356,plain,
% 270.25/172.29 (addition(multiplication(tptp_fun_X1_0(X1!2), X2!1), zero) = multiplication(tptp_fun_X1_0(X1!2), X2!1)),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[355, 332])).
% 270.25/172.29 tff(357,plain,
% 270.25/172.29 (((~(multiplication(X1!2, tptp_fun_X1_0(X1!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)) | (~(addition(X1!2, tptp_fun_X1_0(X1!2)) = one))) | (multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero)),
% 270.25/172.29 inference(tautology,[status(thm)],[])).
% 270.25/172.29 tff(358,plain,
% 270.25/172.29 (multiplication(tptp_fun_X1_0(X1!2), X1!2) = zero),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[357, 119])).
% 270.25/172.29 tff(359,plain,
% 270.25/172.29 (zero = multiplication(tptp_fun_X1_0(X1!2), X1!2)),
% 270.25/172.29 inference(symmetry,[status(thm)],[358])).
% 270.25/172.29 tff(360,plain,
% 270.25/172.29 (addition(multiplication(tptp_fun_X1_0(X1!2), X2!1), zero) = addition(multiplication(tptp_fun_X1_0(X1!2), X2!1), multiplication(tptp_fun_X1_0(X1!2), X1!2))),
% 270.25/172.29 inference(monotonicity,[status(thm)],[359])).
% 270.25/172.29 tff(361,plain,
% 270.25/172.29 (addition(multiplication(tptp_fun_X1_0(X1!2), X2!1), multiplication(tptp_fun_X1_0(X1!2), X1!2)) = addition(multiplication(tptp_fun_X1_0(X1!2), X2!1), zero)),
% 270.25/172.29 inference(symmetry,[status(thm)],[360])).
% 270.25/172.29 tff(362,plain,
% 270.25/172.29 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(tptp_fun_X1_0(X1!2), addition(X2!1, X1!2)) = addition(multiplication(tptp_fun_X1_0(X1!2), X2!1), multiplication(tptp_fun_X1_0(X1!2), X1!2)))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(363,plain,
% 270.25/172.29 (multiplication(tptp_fun_X1_0(X1!2), addition(X2!1, X1!2)) = addition(multiplication(tptp_fun_X1_0(X1!2), X2!1), multiplication(tptp_fun_X1_0(X1!2), X1!2))),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[362, 179])).
% 270.25/172.29 tff(364,plain,
% 270.25/172.29 (multiplication(tptp_fun_X1_0(X1!2), addition(X2!1, X1!2)) = multiplication(tptp_fun_X1_0(X1!2), X1!2)),
% 270.25/172.29 inference(monotonicity,[status(thm)],[338])).
% 270.25/172.29 tff(365,plain,
% 270.25/172.29 (multiplication(tptp_fun_X1_0(X1!2), X1!2) = multiplication(tptp_fun_X1_0(X1!2), addition(X2!1, X1!2))),
% 270.25/172.29 inference(symmetry,[status(thm)],[364])).
% 270.25/172.29 tff(366,plain,
% 270.25/172.29 (zero = multiplication(tptp_fun_X1_0(X1!2), X2!1)),
% 270.25/172.29 inference(transitivity,[status(thm)],[359, 365, 363, 361, 356])).
% 270.25/172.29 tff(367,plain,
% 270.25/172.29 (addition(multiplication(addition(X2!1, X2!1), X2!1), multiplication(X0!3, X2!1)) = multiplication(X0!3, X2!1)),
% 270.25/172.29 inference(transitivity,[status(thm)],[353, 350])).
% 270.25/172.29 tff(368,plain,
% 270.25/172.29 (addition(addition(multiplication(addition(X2!1, X2!1), X2!1), multiplication(X0!3, X2!1)), zero) = addition(multiplication(X0!3, X2!1), multiplication(tptp_fun_X1_0(X1!2), X2!1))),
% 270.25/172.29 inference(monotonicity,[status(thm)],[367, 366])).
% 270.25/172.29 tff(369,plain,
% 270.25/172.29 (addition(multiplication(X0!3, X2!1), multiplication(tptp_fun_X1_0(X1!2), X2!1)) = addition(addition(multiplication(addition(X2!1, X2!1), X2!1), multiplication(X0!3, X2!1)), zero)),
% 270.25/172.29 inference(symmetry,[status(thm)],[368])).
% 270.25/172.29 tff(370,plain,
% 270.25/172.29 (((~(multiplication(X0!3, tptp_fun_X1_0(X0!3)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!3), X0!3) = zero)) | (~(addition(X0!3, tptp_fun_X1_0(X0!3)) = one))) | (multiplication(tptp_fun_X1_0(X0!3), X0!3) = zero)),
% 270.25/172.29 inference(tautology,[status(thm)],[])).
% 270.25/172.29 tff(371,plain,
% 270.25/172.29 (multiplication(tptp_fun_X1_0(X0!3), X0!3) = zero),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[370, 151])).
% 270.25/172.29 tff(372,plain,
% 270.25/172.29 (multiplication(tptp_fun_X1_0(X0!3), addition(X2!1, X0!3)) = multiplication(tptp_fun_X1_0(X0!3), X0!3)),
% 270.25/172.29 inference(monotonicity,[status(thm)],[344])).
% 270.25/172.29 tff(373,plain,
% 270.25/172.29 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(tptp_fun_X1_0(X0!3), addition(X2!1, X0!3)) = addition(multiplication(tptp_fun_X1_0(X0!3), X2!1), multiplication(tptp_fun_X1_0(X0!3), X0!3)))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(374,plain,
% 270.25/172.29 (multiplication(tptp_fun_X1_0(X0!3), addition(X2!1, X0!3)) = addition(multiplication(tptp_fun_X1_0(X0!3), X2!1), multiplication(tptp_fun_X1_0(X0!3), X0!3))),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[373, 179])).
% 270.25/172.29 tff(375,plain,
% 270.25/172.29 (addition(multiplication(tptp_fun_X1_0(X0!3), X2!1), multiplication(tptp_fun_X1_0(X0!3), X0!3)) = multiplication(tptp_fun_X1_0(X0!3), addition(X2!1, X0!3))),
% 270.25/172.29 inference(symmetry,[status(thm)],[374])).
% 270.25/172.29 tff(376,plain,
% 270.25/172.29 (zero = multiplication(tptp_fun_X1_0(X0!3), X0!3)),
% 270.25/172.29 inference(symmetry,[status(thm)],[371])).
% 270.25/172.29 tff(377,plain,
% 270.25/172.29 (addition(multiplication(tptp_fun_X1_0(X1!2), X2!1), multiplication(tptp_fun_X1_0(X1!2), X1!2)) = multiplication(tptp_fun_X1_0(X1!2), addition(X2!1, X1!2))),
% 270.25/172.29 inference(symmetry,[status(thm)],[363])).
% 270.25/172.29 tff(378,plain,
% 270.25/172.29 (multiplication(tptp_fun_X1_0(X1!2), X2!1) = addition(multiplication(tptp_fun_X1_0(X1!2), X2!1), zero)),
% 270.25/172.29 inference(symmetry,[status(thm)],[356])).
% 270.25/172.29 tff(379,plain,
% 270.25/172.29 (multiplication(tptp_fun_X1_0(X1!2), X2!1) = multiplication(tptp_fun_X1_0(X0!3), X0!3)),
% 270.25/172.29 inference(transitivity,[status(thm)],[378, 360, 377, 364, 358, 376])).
% 270.25/172.29 tff(380,plain,
% 270.25/172.29 (addition(multiplication(tptp_fun_X1_0(X0!3), X2!1), multiplication(tptp_fun_X1_0(X1!2), X2!1)) = addition(multiplication(tptp_fun_X1_0(X0!3), X2!1), multiplication(tptp_fun_X1_0(X0!3), X0!3))),
% 270.25/172.29 inference(monotonicity,[status(thm)],[379])).
% 270.25/172.29 tff(381,plain,
% 270.25/172.29 ((~![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!3), tptp_fun_X1_0(X1!2)), X2!1) = addition(multiplication(tptp_fun_X1_0(X0!3), X2!1), multiplication(tptp_fun_X1_0(X1!2), X2!1)))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(382,plain,
% 270.25/172.29 (multiplication(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)), X2!1) = addition(multiplication(tptp_fun_X1_0(X0!3), X2!1), multiplication(tptp_fun_X1_0(X1!2), X2!1))),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[381, 272])).
% 270.25/172.29 tff(383,plain,
% 270.25/172.29 (multiplication(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)), X2!1) = multiplication(tptp_fun_X1_0(X1!2), X1!2)),
% 270.25/172.29 inference(transitivity,[status(thm)],[382, 380, 375, 372, 371, 359])).
% 270.25/172.29 tff(384,plain,
% 270.25/172.29 (addition(multiplication(tptp_fun_X1_0(X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)), X2!1)) = addition(multiplication(tptp_fun_X1_0(X1!2), X2!1), multiplication(tptp_fun_X1_0(X1!2), X1!2))),
% 270.25/172.29 inference(monotonicity,[status(thm)],[383])).
% 270.25/172.29 tff(385,plain,
% 270.25/172.29 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))), X2!1) = addition(multiplication(tptp_fun_X1_0(X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)), X2!1)))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(386,plain,
% 270.25/172.29 (multiplication(addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))), X2!1) = addition(multiplication(tptp_fun_X1_0(X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)), X2!1))),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[385, 272])).
% 270.25/172.29 tff(387,plain,
% 270.25/172.29 (multiplication(addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))), X2!1) = multiplication(tptp_fun_X1_0(X1!2), X2!1)),
% 270.25/172.29 inference(transitivity,[status(thm)],[386, 384, 361, 356])).
% 270.25/172.29 tff(388,plain,
% 270.25/172.29 (addition(multiplication(X0!3, X2!1), multiplication(addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))), X2!1)) = addition(multiplication(X0!3, X2!1), multiplication(tptp_fun_X1_0(X1!2), X2!1))),
% 270.25/172.29 inference(monotonicity,[status(thm)],[387])).
% 270.25/172.29 tff(389,plain,
% 270.25/172.29 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X0!3, addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)))), X2!1) = addition(multiplication(X0!3, X2!1), multiplication(addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))), X2!1)))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(390,plain,
% 270.25/172.29 (multiplication(addition(X0!3, addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)))), X2!1) = addition(multiplication(X0!3, X2!1), multiplication(addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))), X2!1))),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[389, 272])).
% 270.25/172.29 tff(391,plain,
% 270.25/172.29 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)) = addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(392,plain,
% 270.25/172.29 (addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)) = addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[391, 16])).
% 270.25/172.29 tff(393,plain,
% 270.25/172.29 (tptp_fun_X1_0(X1!2) = addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X1!2))),
% 270.25/172.29 inference(symmetry,[status(thm)],[239])).
% 270.25/172.29 tff(394,plain,
% 270.25/172.29 (addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)) = addition(addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X0!3))),
% 270.25/172.29 inference(monotonicity,[status(thm)],[393])).
% 270.25/172.29 tff(395,plain,
% 270.25/172.29 (addition(addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X0!3)) = addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))),
% 270.25/172.29 inference(symmetry,[status(thm)],[394])).
% 270.25/172.29 tff(396,plain,
% 270.25/172.29 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))) = addition(addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X0!3)))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(397,plain,
% 270.25/172.29 (addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))) = addition(addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X0!3))),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[396, 29])).
% 270.25/172.29 tff(398,plain,
% 270.25/172.29 (addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))) = addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)))),
% 270.25/172.29 inference(monotonicity,[status(thm)],[392])).
% 270.25/172.29 tff(399,plain,
% 270.25/172.29 (addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))) = addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))),
% 270.25/172.29 inference(symmetry,[status(thm)],[398])).
% 270.25/172.29 tff(400,plain,
% 270.25/172.29 (addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))) = addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))),
% 270.25/172.29 inference(transitivity,[status(thm)],[399, 397, 395, 392])).
% 270.25/172.29 tff(401,plain,
% 270.25/172.29 (addition(X0!3, addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)))) = addition(X0!3, addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)))),
% 270.25/172.29 inference(monotonicity,[status(thm)],[400])).
% 270.25/172.29 tff(402,plain,
% 270.25/172.29 (addition(X0!3, addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))) = addition(X0!3, addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))))),
% 270.25/172.29 inference(symmetry,[status(thm)],[401])).
% 270.25/172.29 tff(403,plain,
% 270.25/172.29 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!3, addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))) = addition(addition(X0!3, tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X1!2)))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(404,plain,
% 270.25/172.29 (addition(X0!3, addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))) = addition(addition(X0!3, tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X1!2))),
% 270.25/172.29 inference(unit_resolution,[status(thm)],[403, 29])).
% 270.25/172.29 tff(405,plain,
% 270.25/172.29 (addition(addition(X0!3, tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X1!2)) = addition(X0!3, addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)))),
% 270.25/172.29 inference(symmetry,[status(thm)],[404])).
% 270.25/172.29 tff(406,plain,
% 270.25/172.29 (one = addition(X1!2, tptp_fun_X1_0(X1!2))),
% 270.25/172.29 inference(symmetry,[status(thm)],[121])).
% 270.25/172.29 tff(407,plain,
% 270.25/172.29 (addition(X0!3, tptp_fun_X1_0(X0!3)) = addition(X1!2, tptp_fun_X1_0(X1!2))),
% 270.25/172.29 inference(transitivity,[status(thm)],[153, 406])).
% 270.25/172.29 tff(408,plain,
% 270.25/172.29 (addition(addition(X0!3, tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X1!2)) = addition(addition(X1!2, tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X1!2))),
% 270.25/172.29 inference(monotonicity,[status(thm)],[407])).
% 270.25/172.29 tff(409,plain,
% 270.25/172.29 (addition(addition(X1!2, tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X1!2)) = addition(addition(X0!3, tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X1!2))),
% 270.25/172.29 inference(symmetry,[status(thm)],[408])).
% 270.25/172.29 tff(410,plain,
% 270.25/172.29 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X1!2, addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X1!2))) = addition(addition(X1!2, tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X1!2)))),
% 270.25/172.29 inference(quant_inst,[status(thm)],[])).
% 270.25/172.29 tff(411,plain,
% 270.25/172.29 (addition(X1!2, addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X1!2))) = addition(addition(X1!2, tptp_fun_X1_0(X1!2)), tptp_fun_X1_0(X1!2))),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[410, 29])).
% 270.25/172.30 tff(412,plain,
% 270.25/172.30 (addition(X1!2, addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X1!2))) = addition(X1!2, tptp_fun_X1_0(X1!2))),
% 270.25/172.30 inference(monotonicity,[status(thm)],[239])).
% 270.25/172.30 tff(413,plain,
% 270.25/172.30 (addition(X1!2, tptp_fun_X1_0(X1!2)) = addition(X1!2, addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X1!2)))),
% 270.25/172.30 inference(symmetry,[status(thm)],[412])).
% 270.25/172.30 tff(414,plain,
% 270.25/172.30 (one = addition(X0!3, addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2))))),
% 270.25/172.30 inference(transitivity,[status(thm)],[406, 413, 411, 409, 405, 402])).
% 270.25/172.30 tff(415,plain,
% 270.25/172.30 (multiplication(one, X2!1) = multiplication(addition(X0!3, addition(tptp_fun_X1_0(X1!2), addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X1!2)))), X2!1)),
% 270.25/172.30 inference(monotonicity,[status(thm)],[414])).
% 270.25/172.30 tff(416,plain,
% 270.25/172.30 (X2!1 = multiplication(one, X2!1)),
% 270.25/172.30 inference(symmetry,[status(thm)],[191])).
% 270.25/172.30 tff(417,plain,
% 270.25/172.30 (X2!1 = multiplication(X0!3, X2!1)),
% 270.25/172.30 inference(transitivity,[status(thm)],[416, 415, 390, 388, 369, 354, 353, 350])).
% 270.25/172.30 tff(418,plain,
% 270.25/172.30 (leq(X2!1, multiplication(X0!3, X1!2)) <=> leq(multiplication(X0!3, X2!1), addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2)))),
% 270.25/172.30 inference(monotonicity,[status(thm)],[417, 341])).
% 270.25/172.30 tff(419,plain,
% 270.25/172.30 (leq(multiplication(X0!3, X2!1), addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2))) <=> leq(X2!1, multiplication(X0!3, X1!2))),
% 270.25/172.30 inference(symmetry,[status(thm)],[418])).
% 270.25/172.30 tff(420,plain,
% 270.25/172.30 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(multiplication(X0!3, X2!1), addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2))) <=> (addition(multiplication(X0!3, X2!1), addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2))) = addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2))))),
% 270.25/172.30 inference(quant_inst,[status(thm)],[])).
% 270.25/172.30 tff(421,plain,
% 270.25/172.30 (leq(multiplication(X0!3, X2!1), addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2))) <=> (addition(multiplication(X0!3, X2!1), addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2))) = addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2)))),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[420, 312])).
% 270.25/172.30 tff(422,plain,
% 270.25/172.30 (multiplication(X0!3, addition(X2!1, X1!2)) = multiplication(X0!3, X1!2)),
% 270.25/172.30 inference(symmetry,[status(thm)],[340])).
% 270.25/172.30 tff(423,plain,
% 270.25/172.30 (addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2)) = multiplication(X0!3, addition(X2!1, X1!2))),
% 270.25/172.30 inference(symmetry,[status(thm)],[337])).
% 270.25/172.30 tff(424,plain,
% 270.25/172.30 (addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2)) = multiplication(X0!3, X1!2)),
% 270.25/172.30 inference(transitivity,[status(thm)],[423, 422])).
% 270.25/172.30 tff(425,plain,
% 270.25/172.30 (addition(multiplication(X0!3, X2!1), addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2))) = addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2))),
% 270.25/172.30 inference(monotonicity,[status(thm)],[424])).
% 270.25/172.30 tff(426,plain,
% 270.25/172.30 ((~(leq(multiplication(X0!3, X2!1), addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2))) <=> (addition(multiplication(X0!3, X2!1), addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2))) = addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2))))) | leq(multiplication(X0!3, X2!1), addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2))) | (~(addition(multiplication(X0!3, X2!1), addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2))) = addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2))))),
% 270.25/172.30 inference(tautology,[status(thm)],[])).
% 270.25/172.30 tff(427,plain,
% 270.25/172.30 (leq(multiplication(X0!3, X2!1), addition(multiplication(X0!3, X2!1), multiplication(X0!3, X1!2)))),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[426, 425, 421])).
% 270.25/172.30 tff(428,plain,
% 270.25/172.30 (leq(X2!1, multiplication(X0!3, X1!2))),
% 270.25/172.30 inference(modus_ponens,[status(thm)],[427, 419])).
% 270.25/172.30 tff(429,plain,
% 270.25/172.30 ($false),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[294, 428])).
% 270.25/172.30 tff(430,plain,((~(addition(addition(multiplication(addition(X2!1, X2!1), X2!1), multiplication(X0!3, X2!1)), zero) = addition(multiplication(addition(X2!1, X2!1), X2!1), multiplication(X0!3, X2!1)))) | leq(X2!1, multiplication(X0!3, X1!2)) | (~(addition(X2!1, X1!2) = X1!2)) | (~(addition(X2!1, X0!3) = X0!3))), inference(lemma,lemma(discharge,[]))).
% 270.25/172.30 tff(431,plain,
% 270.25/172.30 (leq(X2!1, multiplication(X0!3, X1!2)) | (~(addition(X2!1, X1!2) = X1!2)) | (~(addition(X2!1, X0!3) = X0!3))),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[430, 335])).
% 270.25/172.30 tff(432,plain,
% 270.25/172.30 ($false),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[431, 324, 317, 294])).
% 270.25/172.30 tff(433,plain,(leq(X2!1, multiplication(X0!3, X1!2))), inference(lemma,lemma(discharge,[]))).
% 270.25/172.30 tff(434,plain,
% 270.25/172.30 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X2!1, multiplication(X0!3, X1!2)) <=> (addition(X2!1, multiplication(X0!3, X1!2)) = multiplication(X0!3, X1!2)))),
% 270.25/172.30 inference(quant_inst,[status(thm)],[])).
% 270.25/172.30 tff(435,plain,
% 270.25/172.30 (leq(X2!1, multiplication(X0!3, X1!2)) <=> (addition(X2!1, multiplication(X0!3, X1!2)) = multiplication(X0!3, X1!2))),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[434, 312])).
% 270.25/172.30 tff(436,plain,
% 270.25/172.30 ((~(leq(X2!1, multiplication(X0!3, X1!2)) <=> (addition(X2!1, multiplication(X0!3, X1!2)) = multiplication(X0!3, X1!2)))) | (~leq(X2!1, multiplication(X0!3, X1!2))) | (addition(X2!1, multiplication(X0!3, X1!2)) = multiplication(X0!3, X1!2))),
% 270.25/172.30 inference(tautology,[status(thm)],[])).
% 270.25/172.30 tff(437,plain,
% 270.25/172.30 ((~leq(X2!1, multiplication(X0!3, X1!2))) | (addition(X2!1, multiplication(X0!3, X1!2)) = multiplication(X0!3, X1!2))),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[436, 435])).
% 270.25/172.30 tff(438,plain,
% 270.25/172.30 (addition(X2!1, multiplication(X0!3, X1!2)) = multiplication(X0!3, X1!2)),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[437, 433])).
% 270.25/172.30 tff(439,plain,
% 270.25/172.30 (addition(addition(X2!1, X2!1), multiplication(X0!3, X1!2)) = addition(X2!1, multiplication(X0!3, X1!2))),
% 270.25/172.30 inference(monotonicity,[status(thm)],[101])).
% 270.25/172.30 tff(440,plain,
% 270.25/172.30 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X2!1, addition(X2!1, multiplication(X0!3, X1!2))) = addition(addition(X2!1, X2!1), multiplication(X0!3, X1!2)))),
% 270.25/172.30 inference(quant_inst,[status(thm)],[])).
% 270.25/172.30 tff(441,plain,
% 270.25/172.30 (addition(X2!1, addition(X2!1, multiplication(X0!3, X1!2))) = addition(addition(X2!1, X2!1), multiplication(X0!3, X1!2))),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[440, 29])).
% 270.25/172.30 tff(442,plain,
% 270.25/172.30 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X2!1, multiplication(X0!3, X1!2)) = addition(multiplication(X0!3, X1!2), X2!1))),
% 270.25/172.30 inference(quant_inst,[status(thm)],[])).
% 270.25/172.30 tff(443,plain,
% 270.25/172.30 (addition(X2!1, multiplication(X0!3, X1!2)) = addition(multiplication(X0!3, X1!2), X2!1)),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[442, 16])).
% 270.25/172.30 tff(444,plain,
% 270.25/172.30 (addition(multiplication(X0!3, X1!2), X2!1) = addition(X2!1, multiplication(X0!3, X1!2))),
% 270.25/172.30 inference(symmetry,[status(thm)],[443])).
% 270.25/172.30 tff(445,plain,
% 270.25/172.30 (addition(X2!1, addition(multiplication(X0!3, X1!2), X2!1)) = addition(X2!1, addition(X2!1, multiplication(X0!3, X1!2)))),
% 270.25/172.30 inference(monotonicity,[status(thm)],[444])).
% 270.25/172.30 tff(446,plain,
% 270.25/172.30 (addition(X2!1, addition(multiplication(X0!3, X1!2), X2!1)) = multiplication(X0!3, X1!2)),
% 270.25/172.30 inference(transitivity,[status(thm)],[445, 441, 439, 438])).
% 270.25/172.30 tff(447,plain,
% 270.25/172.30 (addition(addition(X2!1, addition(multiplication(X0!3, X1!2), X2!1)), multiplication(addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))), X1!2)) = addition(multiplication(X0!3, X1!2), multiplication(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))), X1!2))),
% 270.25/172.30 inference(monotonicity,[status(thm)],[446, 293])).
% 270.25/172.30 tff(448,plain,
% 270.25/172.30 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X2!1, addition(addition(multiplication(X0!3, X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))), X1!2))) = addition(addition(X2!1, addition(multiplication(X0!3, X1!2), X2!1)), multiplication(addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))), X1!2)))),
% 270.25/172.30 inference(quant_inst,[status(thm)],[])).
% 270.25/172.30 tff(449,plain,
% 270.25/172.30 (addition(X2!1, addition(addition(multiplication(X0!3, X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))), X1!2))) = addition(addition(X2!1, addition(multiplication(X0!3, X1!2), X2!1)), multiplication(addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))), X1!2))),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[448, 29])).
% 270.25/172.30 tff(450,plain,
% 270.25/172.30 (addition(multiplication(X0!3, X1!2), X2!1) = multiplication(X0!3, X1!2)),
% 270.25/172.30 inference(transitivity,[status(thm)],[444, 438])).
% 270.25/172.30 tff(451,plain,
% 270.25/172.30 (addition(addition(multiplication(X0!3, X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))), X1!2)) = addition(multiplication(X0!3, X1!2), multiplication(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))), X1!2))),
% 270.25/172.30 inference(monotonicity,[status(thm)],[450, 293])).
% 270.25/172.30 tff(452,plain,
% 270.25/172.30 (addition(multiplication(X0!3, X1!2), multiplication(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))), X1!2)) = addition(addition(multiplication(X0!3, X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))), X1!2))),
% 270.25/172.30 inference(symmetry,[status(thm)],[451])).
% 270.25/172.30 tff(453,plain,
% 270.25/172.30 (multiplication(one, X1!2) = multiplication(addition(X0!3, addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))), X1!2)),
% 270.25/172.30 inference(symmetry,[status(thm)],[265])).
% 270.25/172.30 tff(454,plain,
% 270.25/172.30 (X1!2 = multiplication(one, X1!2)),
% 270.25/172.30 inference(symmetry,[status(thm)],[230])).
% 270.25/172.30 tff(455,plain,
% 270.25/172.30 (X1!2 = addition(addition(multiplication(X0!3, X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))), X1!2))),
% 270.25/172.30 inference(transitivity,[status(thm)],[454, 453, 274, 452])).
% 270.25/172.30 tff(456,plain,
% 270.25/172.30 (addition(X2!1, X1!2) = addition(X2!1, addition(addition(multiplication(X0!3, X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))), X1!2)))),
% 270.25/172.30 inference(monotonicity,[status(thm)],[455])).
% 270.25/172.30 tff(457,plain,
% 270.25/172.30 (addition(X2!1, X1!2) = X1!2),
% 270.25/172.30 inference(transitivity,[status(thm)],[456, 449, 447, 275, 265, 230])).
% 270.25/172.30 tff(458,assumption,(~(addition(X2!1, X1!2) = X1!2)), introduced(assumption)).
% 270.25/172.30 tff(459,plain,
% 270.25/172.30 ($false),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[458, 457])).
% 270.25/172.30 tff(460,plain,((~(multiplication(one, X1!2) = X1!2)) | (addition(X2!1, X1!2) = X1!2)), inference(lemma,lemma(discharge,[]))).
% 270.25/172.30 tff(461,plain,
% 270.25/172.30 (addition(X2!1, X1!2) = X1!2),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[460, 229])).
% 270.25/172.30 tff(462,plain,
% 270.25/172.30 (X1!2 = addition(X2!1, X1!2)),
% 270.25/172.30 inference(symmetry,[status(thm)],[461])).
% 270.25/172.30 tff(463,plain,
% 270.25/172.30 (X1!2 = addition(X1!2, X2!1)),
% 270.25/172.30 inference(transitivity,[status(thm)],[462, 225])).
% 270.25/172.30 tff(464,plain,
% 270.25/172.30 (addition(X1!2, addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3))) = addition(addition(X1!2, X2!1), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)))),
% 270.25/172.30 inference(monotonicity,[status(thm)],[463])).
% 270.25/172.30 tff(465,plain,
% 270.25/172.30 (addition(addition(X1!2, X2!1), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3))) = addition(X1!2, addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)))),
% 270.25/172.30 inference(symmetry,[status(thm)],[464])).
% 270.25/172.30 tff(466,plain,
% 270.25/172.30 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X1!2, addition(X2!1, X2!1)) = addition(addition(X1!2, X2!1), X2!1))),
% 270.25/172.30 inference(quant_inst,[status(thm)],[])).
% 270.25/172.30 tff(467,plain,
% 270.25/172.30 (addition(X1!2, addition(X2!1, X2!1)) = addition(addition(X1!2, X2!1), X2!1)),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[466, 29])).
% 270.25/172.30 tff(468,plain,
% 270.25/172.30 (addition(X1!2, addition(X2!1, X2!1)) = addition(X1!2, X2!1)),
% 270.25/172.30 inference(monotonicity,[status(thm)],[101])).
% 270.25/172.30 tff(469,plain,
% 270.25/172.30 (addition(X1!2, X2!1) = addition(X1!2, addition(X2!1, X2!1))),
% 270.25/172.30 inference(symmetry,[status(thm)],[468])).
% 270.25/172.30 tff(470,plain,
% 270.25/172.30 (addition(X1!2, X2!1) = addition(addition(X1!2, X2!1), X2!1)),
% 270.25/172.30 inference(transitivity,[status(thm)],[469, 467])).
% 270.25/172.30 tff(471,plain,
% 270.25/172.30 (addition(addition(X1!2, X2!1), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3))) = addition(addition(addition(X1!2, X2!1), X2!1), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)))),
% 270.25/172.30 inference(monotonicity,[status(thm)],[470])).
% 270.25/172.30 tff(472,plain,
% 270.25/172.30 (addition(addition(addition(X1!2, X2!1), X2!1), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3))) = addition(addition(X1!2, X2!1), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)))),
% 270.25/172.30 inference(symmetry,[status(thm)],[471])).
% 270.25/172.30 tff(473,plain,
% 270.25/172.30 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(X1!2, X2!1), addition(X2!1, addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)))) = addition(addition(addition(X1!2, X2!1), X2!1), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3))))),
% 270.25/172.30 inference(quant_inst,[status(thm)],[])).
% 270.25/172.30 tff(474,plain,
% 270.25/172.30 (addition(addition(X1!2, X2!1), addition(X2!1, addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)))) = addition(addition(addition(X1!2, X2!1), X2!1), addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)))),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[473, 29])).
% 270.25/172.30 tff(475,plain,
% 270.25/172.30 (addition(X0!3, addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X0!3))) = addition(X0!3, tptp_fun_X1_0(X0!3))),
% 270.25/172.30 inference(monotonicity,[status(thm)],[158])).
% 270.25/172.30 tff(476,plain,
% 270.25/172.30 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X0!3, addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X0!3))) = addition(addition(X0!3, tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X0!3)))),
% 270.25/172.30 inference(quant_inst,[status(thm)],[])).
% 270.25/172.30 tff(477,plain,
% 270.25/172.30 (addition(X0!3, addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X0!3))) = addition(addition(X0!3, tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X0!3))),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[476, 29])).
% 270.25/172.30 tff(478,plain,
% 270.25/172.30 (addition(addition(X0!3, tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X0!3)) = addition(X0!3, addition(tptp_fun_X1_0(X0!3), tptp_fun_X1_0(X0!3)))),
% 270.25/172.30 inference(symmetry,[status(thm)],[477])).
% 270.25/172.30 tff(479,plain,
% 270.25/172.30 (addition(X2!1, tptp_fun_X1_0(X2!1)) = addition(X0!3, tptp_fun_X1_0(X0!3))),
% 270.25/172.30 inference(transitivity,[status(thm)],[84, 162])).
% 270.25/172.30 tff(480,plain,
% 270.25/172.30 (addition(addition(X2!1, tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X0!3)) = addition(addition(X0!3, tptp_fun_X1_0(X0!3)), tptp_fun_X1_0(X0!3))),
% 270.25/172.30 inference(monotonicity,[status(thm)],[479])).
% 270.25/172.30 tff(481,plain,
% 270.25/172.30 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X2!1, addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3))) = addition(addition(X2!1, tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X0!3)))),
% 270.25/172.30 inference(quant_inst,[status(thm)],[])).
% 270.25/172.30 tff(482,plain,
% 270.25/172.30 (addition(X2!1, addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3))) = addition(addition(X2!1, tptp_fun_X1_0(X2!1)), tptp_fun_X1_0(X0!3))),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[481, 29])).
% 270.25/172.30 tff(483,plain,
% 270.25/172.30 (addition(X2!1, addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3))) = addition(tptp_fun_X1_0(X1!2), X1!2)),
% 270.25/172.30 inference(transitivity,[status(thm)],[482, 480, 478, 475, 153, 406, 123])).
% 270.25/172.30 tff(484,plain,
% 270.25/172.30 (addition(addition(X1!2, X2!1), addition(X2!1, addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)))) = addition(addition(X1!2, X2!1), addition(tptp_fun_X1_0(X1!2), X1!2))),
% 270.25/172.30 inference(monotonicity,[status(thm)],[483])).
% 270.25/172.30 tff(485,plain,
% 270.25/172.30 (addition(addition(X1!2, X2!1), addition(tptp_fun_X1_0(X1!2), X1!2)) = addition(addition(X1!2, X2!1), addition(X2!1, addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3))))),
% 270.25/172.30 inference(symmetry,[status(thm)],[484])).
% 270.25/172.30 tff(486,plain,
% 270.25/172.30 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(X1!2, X2!1), addition(tptp_fun_X1_0(X1!2), X1!2)) = addition(addition(addition(X1!2, X2!1), tptp_fun_X1_0(X1!2)), X1!2))),
% 270.25/172.30 inference(quant_inst,[status(thm)],[])).
% 270.25/172.30 tff(487,plain,
% 270.25/172.30 (addition(addition(X1!2, X2!1), addition(tptp_fun_X1_0(X1!2), X1!2)) = addition(addition(addition(X1!2, X2!1), tptp_fun_X1_0(X1!2)), X1!2)),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[486, 29])).
% 270.25/172.30 tff(488,plain,
% 270.25/172.30 (addition(addition(addition(X1!2, X2!1), tptp_fun_X1_0(X1!2)), X1!2) = addition(addition(X1!2, X2!1), addition(tptp_fun_X1_0(X1!2), X1!2))),
% 270.25/172.30 inference(symmetry,[status(thm)],[487])).
% 270.25/172.30 tff(489,plain,
% 270.25/172.30 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!2, addition(tptp_fun_X1_0(X1!2), X2!1)) = addition(addition(tptp_fun_X1_0(X1!2), X2!1), X1!2))),
% 270.25/172.30 inference(quant_inst,[status(thm)],[])).
% 270.25/172.30 tff(490,plain,
% 270.25/172.30 (addition(X1!2, addition(tptp_fun_X1_0(X1!2), X2!1)) = addition(addition(tptp_fun_X1_0(X1!2), X2!1), X1!2)),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[489, 16])).
% 270.25/172.30 tff(491,plain,
% 270.25/172.30 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X1!2, addition(tptp_fun_X1_0(X1!2), X2!1)) = addition(addition(X1!2, tptp_fun_X1_0(X1!2)), X2!1))),
% 270.25/172.30 inference(quant_inst,[status(thm)],[])).
% 270.25/172.30 tff(492,plain,
% 270.25/172.30 (addition(X1!2, addition(tptp_fun_X1_0(X1!2), X2!1)) = addition(addition(X1!2, tptp_fun_X1_0(X1!2)), X2!1)),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[491, 29])).
% 270.25/172.30 tff(493,plain,
% 270.25/172.30 (addition(addition(X1!2, tptp_fun_X1_0(X1!2)), X2!1) = addition(X1!2, addition(tptp_fun_X1_0(X1!2), X2!1))),
% 270.25/172.30 inference(symmetry,[status(thm)],[492])).
% 270.25/172.30 tff(494,plain,
% 270.25/172.30 (addition(X1!2, tptp_fun_X1_0(X1!2)) = addition(tptp_fun_X1_0(X2!1), X2!1)),
% 270.25/172.30 inference(transitivity,[status(thm)],[121, 106, 86])).
% 270.25/172.30 tff(495,plain,
% 270.25/172.30 (addition(addition(X1!2, tptp_fun_X1_0(X1!2)), X2!1) = addition(addition(tptp_fun_X1_0(X2!1), X2!1), X2!1)),
% 270.25/172.30 inference(monotonicity,[status(thm)],[494])).
% 270.25/172.30 tff(496,plain,
% 270.25/172.30 (addition(addition(tptp_fun_X1_0(X2!1), X2!1), X2!1) = addition(addition(X1!2, tptp_fun_X1_0(X1!2)), X2!1)),
% 270.25/172.30 inference(symmetry,[status(thm)],[495])).
% 270.25/172.30 tff(497,plain,
% 270.25/172.30 (addition(addition(X1!2, X2!1), tptp_fun_X1_0(X1!2)) = addition(addition(tptp_fun_X1_0(X1!2), X2!1), X1!2)),
% 270.25/172.30 inference(transitivity,[status(thm)],[237, 128, 126, 496, 493, 490])).
% 270.25/172.30 tff(498,plain,
% 270.25/172.30 (addition(addition(addition(X1!2, X2!1), tptp_fun_X1_0(X1!2)), X1!2) = addition(addition(addition(tptp_fun_X1_0(X1!2), X2!1), X1!2), X1!2)),
% 270.25/172.30 inference(monotonicity,[status(thm)],[497])).
% 270.25/172.30 tff(499,plain,
% 270.25/172.30 (addition(addition(addition(tptp_fun_X1_0(X1!2), X2!1), X1!2), X1!2) = addition(addition(addition(X1!2, X2!1), tptp_fun_X1_0(X1!2)), X1!2)),
% 270.25/172.30 inference(symmetry,[status(thm)],[498])).
% 270.25/172.30 tff(500,plain,
% 270.25/172.30 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(tptp_fun_X1_0(X1!2), X2!1), addition(X1!2, X1!2)) = addition(addition(addition(tptp_fun_X1_0(X1!2), X2!1), X1!2), X1!2))),
% 270.25/172.30 inference(quant_inst,[status(thm)],[])).
% 270.25/172.30 tff(501,plain,
% 270.25/172.30 (addition(addition(tptp_fun_X1_0(X1!2), X2!1), addition(X1!2, X1!2)) = addition(addition(addition(tptp_fun_X1_0(X1!2), X2!1), X1!2), X1!2)),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[500, 29])).
% 270.25/172.30 tff(502,plain,
% 270.25/172.30 ((~![A: $i] : (addition(A, A) = A)) | (addition(X1!2, X1!2) = X1!2)),
% 270.25/172.30 inference(quant_inst,[status(thm)],[])).
% 270.25/172.30 tff(503,plain,
% 270.25/172.30 (addition(X1!2, X1!2) = X1!2),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[502, 94])).
% 270.25/172.30 tff(504,plain,
% 270.25/172.30 (addition(addition(tptp_fun_X1_0(X1!2), X2!1), addition(X1!2, X1!2)) = addition(addition(tptp_fun_X1_0(X1!2), X2!1), X1!2)),
% 270.25/172.30 inference(monotonicity,[status(thm)],[503])).
% 270.25/172.30 tff(505,plain,
% 270.25/172.30 (addition(addition(tptp_fun_X1_0(X1!2), X2!1), X1!2) = addition(addition(tptp_fun_X1_0(X1!2), X2!1), addition(X1!2, X1!2))),
% 270.25/172.30 inference(symmetry,[status(thm)],[504])).
% 270.25/172.30 tff(506,plain,
% 270.25/172.30 (one = addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(X1!2, tptp_fun_X1_0(X2!1)))),
% 270.25/172.30 inference(transitivity,[status(thm)],[106, 86, 246, 104, 496, 493, 490, 505, 501, 499, 488, 485, 474, 472, 465, 223, 221, 219, 216, 212, 210, 199, 196])).
% 270.25/172.30 tff(507,plain,
% 270.25/172.30 (multiplication(one, X2!1) = multiplication(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(X1!2, tptp_fun_X1_0(X2!1))), X2!1)),
% 270.25/172.30 inference(monotonicity,[status(thm)],[506])).
% 270.25/172.30 tff(508,plain,
% 270.25/172.30 (multiplication(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(X1!2, tptp_fun_X1_0(X2!1))), X2!1) = multiplication(one, X2!1)),
% 270.25/172.30 inference(symmetry,[status(thm)],[507])).
% 270.25/172.30 tff(509,plain,
% 270.25/172.30 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), X1!2) = addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X0!3), X1!2))),
% 270.25/172.30 inference(symmetry,[status(thm)],[212])).
% 270.25/172.30 tff(510,plain,
% 270.25/172.30 (addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(X1!2, tptp_fun_X1_0(X2!1))) = addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3)))),
% 270.25/172.30 inference(transitivity,[status(thm)],[195, 198, 209, 509, 215])).
% 270.25/172.30 tff(511,plain,
% 270.25/172.30 (multiplication(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(X1!2, tptp_fun_X1_0(X2!1))), X2!1) = multiplication(addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))), X2!1)),
% 270.25/172.30 inference(monotonicity,[status(thm)],[510])).
% 270.25/172.30 tff(512,plain,
% 270.25/172.30 (multiplication(addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))), X2!1) = multiplication(addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(X1!2, tptp_fun_X1_0(X2!1))), X2!1)),
% 270.25/172.30 inference(symmetry,[status(thm)],[511])).
% 270.25/172.30 tff(513,plain,
% 270.25/172.30 (multiplication(addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))), X2!1) = X2!1),
% 270.25/172.30 inference(transitivity,[status(thm)],[512, 508, 191])).
% 270.25/172.30 tff(514,plain,
% 270.25/172.30 (addition(addition(multiplication(X0!3, X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))), X2!1)) = addition(addition(multiplication(X0!3, X1!2), X2!1), X2!1)),
% 270.25/172.30 inference(monotonicity,[status(thm)],[513])).
% 270.25/172.30 tff(515,plain,
% 270.25/172.30 (addition(addition(multiplication(X0!3, X1!2), X2!1), X2!1) = addition(addition(multiplication(X0!3, X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))), X2!1))),
% 270.25/172.30 inference(symmetry,[status(thm)],[514])).
% 270.25/172.30 tff(516,plain,
% 270.25/172.30 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X0!3, X1!2), addition(X2!1, X2!1)) = addition(addition(multiplication(X0!3, X1!2), X2!1), X2!1))),
% 270.25/172.30 inference(quant_inst,[status(thm)],[])).
% 270.25/172.30 tff(517,plain,
% 270.25/172.30 (addition(multiplication(X0!3, X1!2), addition(X2!1, X2!1)) = addition(addition(multiplication(X0!3, X1!2), X2!1), X2!1)),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[516, 29])).
% 270.25/172.30 tff(518,plain,
% 270.25/172.30 (addition(multiplication(X0!3, X1!2), addition(X2!1, X2!1)) = addition(multiplication(X0!3, X1!2), X2!1)),
% 270.25/172.30 inference(monotonicity,[status(thm)],[101])).
% 270.25/172.30 tff(519,plain,
% 270.25/172.30 (addition(multiplication(X0!3, X1!2), X2!1) = addition(multiplication(X0!3, X1!2), addition(X2!1, X2!1))),
% 270.25/172.30 inference(symmetry,[status(thm)],[518])).
% 270.25/172.30 tff(520,plain,
% 270.25/172.30 (multiplication(X0!3, X1!2) = addition(X2!1, multiplication(X0!3, X1!2))),
% 270.25/172.30 inference(symmetry,[status(thm)],[438])).
% 270.25/172.30 tff(521,plain,
% 270.25/172.30 (addition(X1!2, X2!1) = addition(X2!1, X1!2)),
% 270.25/172.30 inference(symmetry,[status(thm)],[225])).
% 270.25/172.30 tff(522,plain,
% 270.25/172.30 (addition(X1!2, X2!1) = X1!2),
% 270.25/172.30 inference(transitivity,[status(thm)],[521, 461])).
% 270.25/172.30 tff(523,plain,
% 270.25/172.30 (multiplication(X0!3, addition(X1!2, X2!1)) = multiplication(X0!3, X1!2)),
% 270.25/172.30 inference(monotonicity,[status(thm)],[522])).
% 270.25/172.30 tff(524,plain,
% 270.25/172.30 (multiplication(X0!3, addition(X1!2, X2!1)) = addition(addition(multiplication(X0!3, X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))), X2!1))),
% 270.25/172.30 inference(transitivity,[status(thm)],[523, 520, 443, 519, 517, 515])).
% 270.25/172.30 tff(525,plain,
% 270.25/172.30 (multiplication(X0!3, addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))) = multiplication(X0!3, addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3))))),
% 270.25/172.30 inference(monotonicity,[status(thm)],[291])).
% 270.25/172.30 tff(526,plain,
% 270.25/172.30 (addition(multiplication(X0!3, addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))), multiplication(X0!3, addition(X1!2, X2!1))) = addition(multiplication(X0!3, addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))), addition(addition(multiplication(X0!3, X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))), X2!1)))),
% 270.25/172.30 inference(monotonicity,[status(thm)],[525, 524])).
% 270.25/172.30 tff(527,plain,
% 270.25/172.30 (addition(multiplication(X0!3, addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))), addition(addition(multiplication(X0!3, X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))), X2!1))) = addition(multiplication(X0!3, addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))), multiplication(X0!3, addition(X1!2, X2!1)))),
% 270.25/172.30 inference(symmetry,[status(thm)],[526])).
% 270.25/172.30 tff(528,plain,
% 270.25/172.30 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X0!3, addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))), addition(addition(multiplication(X0!3, X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))), X2!1))) = addition(addition(multiplication(X0!3, addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))), addition(multiplication(X0!3, X1!2), X2!1)), multiplication(addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))), X2!1)))),
% 270.25/172.30 inference(quant_inst,[status(thm)],[])).
% 270.25/172.30 tff(529,plain,
% 270.25/172.30 (addition(multiplication(X0!3, addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))), addition(addition(multiplication(X0!3, X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))), X2!1))) = addition(addition(multiplication(X0!3, addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))), addition(multiplication(X0!3, X1!2), X2!1)), multiplication(addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))), X2!1))),
% 270.25/172.30 inference(unit_resolution,[status(thm)],[528, 29])).
% 270.25/172.30 tff(530,plain,
% 270.25/172.30 (addition(addition(multiplication(X0!3, addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))), addition(multiplication(X0!3, X1!2), X2!1)), multiplication(addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))), X2!1)) = addition(multiplication(X0!3, addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))), addition(addition(multiplication(X0!3, X1!2), X2!1), multiplication(addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))), X2!1)))),
% 270.25/172.30 inference(symmetry,[status(thm)],[529])).
% 270.25/172.30 tff(531,plain,
% 270.25/172.30 (multiplication(X0!3, X1!2) = multiplication(X0!3, addition(X1!2, X2!1))),
% 270.25/172.30 inference(symmetry,[status(thm)],[523])).
% 270.25/172.30 tff(532,plain,
% 270.25/172.30 (addition(multiplication(X0!3, X1!2), X2!1) = multiplication(X0!3, addition(X1!2, X2!1))),
% 270.25/172.30 inference(transitivity,[status(thm)],[444, 438, 531])).
% 270.25/172.30 tff(533,plain,
% 270.25/172.30 (multiplication(X0!3, addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))) = multiplication(X0!3, addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1))))),
% 270.25/172.30 inference(symmetry,[status(thm)],[525])).
% 270.25/172.30 tff(534,plain,
% 270.25/172.30 (addition(multiplication(X0!3, addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))), addition(multiplication(X0!3, X1!2), X2!1)) = addition(multiplication(X0!3, addition(addition(tptp_fun_X1_0(X2!1), tptp_fun_X1_0(X0!3)), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X2!1)))), multiplication(X0!3, addition(X1!2, X2!1)))),
% 270.25/172.30 inference(monotonicity,[status(thm)],[533, 532])).
% 270.25/172.30 tff(535,plain,
% 270.25/172.30 (addition(multiplication(X0!3, addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))), addition(multiplication(X0!3, X1!2), X2!1)) = X0!3),
% 270.25/172.31 inference(transitivity,[status(thm)],[534, 182, 172, 9])).
% 270.25/172.31 tff(536,plain,
% 270.25/172.31 (addition(addition(multiplication(X0!3, addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))), addition(multiplication(X0!3, X1!2), X2!1)), multiplication(addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))), X2!1)) = addition(X0!3, X2!1)),
% 270.25/172.31 inference(monotonicity,[status(thm)],[535, 513])).
% 270.25/172.31 tff(537,plain,
% 270.25/172.31 (addition(X0!3, X2!1) = addition(addition(multiplication(X0!3, addition(tptp_fun_X1_0(X2!1), addition(tptp_fun_X1_0(X1!2), tptp_fun_X1_0(X0!3)))), addition(multiplication(X0!3, X1!2), X2!1)), multiplication(addition(tptp_fun_X1_0(X2!1), addition(X1!2, tptp_fun_X1_0(X0!3))), X2!1))),
% 270.25/172.31 inference(symmetry,[status(thm)],[536])).
% 270.25/172.31 tff(538,plain,
% 270.25/172.31 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X2!1, X0!3) = addition(X0!3, X2!1))),
% 270.25/172.31 inference(quant_inst,[status(thm)],[])).
% 270.25/172.31 tff(539,plain,
% 270.25/172.31 (addition(X2!1, X0!3) = addition(X0!3, X2!1)),
% 270.25/172.31 inference(unit_resolution,[status(thm)],[538, 16])).
% 270.25/172.31 tff(540,plain,
% 270.25/172.31 (addition(X2!1, X0!3) = X0!3),
% 270.25/172.31 inference(transitivity,[status(thm)],[539, 537, 530, 527, 182, 172, 9])).
% 270.25/172.31 tff(541,plain,
% 270.25/172.31 ((~leq(X2!1, multiplication(X0!3, X1!2))) | ((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2))) | (~(leq(X2!1, multiplication(X0!3, X1!2)) <=> ((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2)))))),
% 270.25/172.31 inference(tautology,[status(thm)],[])).
% 270.25/172.31 tff(542,plain,
% 270.25/172.31 ((~leq(X2!1, multiplication(X0!3, X1!2))) | ((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2)))),
% 270.25/172.31 inference(unit_resolution,[status(thm)],[541, 300])).
% 270.25/172.31 tff(543,plain,
% 270.25/172.31 ((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2))),
% 270.25/172.31 inference(unit_resolution,[status(thm)],[542, 433])).
% 270.25/172.31 tff(544,plain,
% 270.25/172.31 ((~(leq(X2!1, X1!2) <=> (addition(X2!1, X1!2) = X1!2))) | leq(X2!1, X1!2) | (~(addition(X2!1, X1!2) = X1!2))),
% 270.25/172.31 inference(tautology,[status(thm)],[])).
% 270.25/172.31 tff(545,plain,
% 270.25/172.31 (leq(X2!1, X1!2) | (~(addition(X2!1, X1!2) = X1!2))),
% 270.25/172.31 inference(unit_resolution,[status(thm)],[544, 321])).
% 270.25/172.31 tff(546,plain,
% 270.25/172.31 (leq(X2!1, X1!2)),
% 270.25/172.31 inference(unit_resolution,[status(thm)],[545, 461])).
% 270.25/172.31 tff(547,plain,
% 270.25/172.31 ((~((~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2)))) | (~leq(X2!1, X0!3)) | (~leq(X2!1, X1!2))),
% 270.25/172.31 inference(tautology,[status(thm)],[])).
% 270.25/172.31 tff(548,plain,
% 270.25/172.31 (~leq(X2!1, X0!3)),
% 270.25/172.31 inference(unit_resolution,[status(thm)],[547, 546, 543])).
% 270.25/172.31 tff(549,plain,
% 270.25/172.31 ((~(leq(X2!1, X0!3) <=> (addition(X2!1, X0!3) = X0!3))) | leq(X2!1, X0!3) | (~(addition(X2!1, X0!3) = X0!3))),
% 270.25/172.31 inference(tautology,[status(thm)],[])).
% 270.25/172.31 tff(550,plain,
% 270.25/172.31 (leq(X2!1, X0!3) | (~(addition(X2!1, X0!3) = X0!3))),
% 270.25/172.31 inference(unit_resolution,[status(thm)],[549, 314])).
% 270.25/172.31 tff(551,plain,
% 270.25/172.31 (~(addition(X2!1, X0!3) = X0!3)),
% 270.25/172.31 inference(unit_resolution,[status(thm)],[550, 548])).
% 270.25/172.31 tff(552,plain,
% 270.25/172.31 ($false),
% 270.25/172.31 inference(unit_resolution,[status(thm)],[551, 540])).
% 270.25/172.31 % SZS output end Proof
%------------------------------------------------------------------------------