TSTP Solution File: KLE009+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE009+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 17:23:46 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE009+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 07:46:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(addition_type, type, (
% 0.20/0.41 addition: ( $i * $i ) > $i)).
% 0.20/0.41 tff(multiplication_type, type, (
% 0.20/0.41 multiplication: ( $i * $i ) > $i)).
% 0.20/0.41 tff(c_type, type, (
% 0.20/0.41 c: $i > $i)).
% 0.20/0.41 tff(tptp_fun_X1_1_type, type, (
% 0.20/0.41 tptp_fun_X1_1: $i)).
% 0.20/0.41 tff(tptp_fun_X0_2_type, type, (
% 0.20/0.41 tptp_fun_X0_2: $i)).
% 0.20/0.41 tff(one_type, type, (
% 0.20/0.41 one: $i)).
% 0.20/0.41 tff(zero_type, type, (
% 0.20/0.41 zero: $i)).
% 0.20/0.41 tff(complement_type, type, (
% 0.20/0.41 complement: ( $i * $i ) > $o)).
% 0.20/0.41 tff(test_type, type, (
% 0.20/0.41 test: $i > $o)).
% 0.20/0.41 tff(tptp_fun_X1_0_type, type, (
% 0.20/0.41 tptp_fun_X1_0: $i > $i)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (^[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)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (![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))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![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))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(4,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_associativity')).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.41 tff(6,plain,(
% 0.20/0.41 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.20/0.41 inference(skolemize,[status(sab)],[5])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(13,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','right_distributivity')).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.41 tff(15,plain,(
% 0.20/0.41 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[14])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(X0!2), addition(X1!1, c(X1!1))) = addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (multiplication(c(X0!2), addition(X1!1, c(X1!1))) = addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(22,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.42 tff(24,plain,(
% 0.20/0.42 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.42 inference(skolemize,[status(sab)],[23])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!1, c(X1!1)) = addition(c(X1!1), X1!1))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (addition(X1!1, c(X1!1)) = addition(c(X1!1), X1!1)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (addition(c(X1!1), X1!1) = addition(X1!1, c(X1!1))),
% 0.20/0.42 inference(symmetry,[status(thm)],[27])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (multiplication(c(X0!2), addition(c(X1!1), X1!1)) = multiplication(c(X0!2), addition(X1!1, c(X1!1)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[28])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (multiplication(c(X0!2), addition(c(X1!1), X1!1)) = addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[29, 18])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))) = addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))) = addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1)))),
% 0.20/0.42 inference(symmetry,[status(thm)],[32])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!2, addition(c(X1!1), X1!1)) = addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (multiplication(X0!2, addition(c(X1!1), X1!1)) = addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[34, 16])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (multiplication(X0!2, addition(c(X1!1), X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[35, 33])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (addition(multiplication(X0!2, addition(c(X1!1), X1!1)), multiplication(c(X0!2), addition(c(X1!1), X1!1))) = addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[36, 30])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(41,axiom,(![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','left_distributivity')).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.42 tff(43,plain,(
% 0.20/0.42 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[42])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X0!2, c(X0!2)), addition(c(X1!1), X1!1)) = addition(multiplication(X0!2, addition(c(X1!1), X1!1)), multiplication(c(X0!2), addition(c(X1!1), X1!1))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (multiplication(addition(X0!2, c(X0!2)), addition(c(X1!1), X1!1)) = addition(multiplication(X0!2, addition(c(X1!1), X1!1)), multiplication(c(X0!2), addition(c(X1!1), X1!1)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (^[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))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (![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)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (^[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))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (![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)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.42 tff(54,axiom,(![X0: $i, X1: $i] : (complement(X1, X0) <=> (((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero)) & (addition(X0, X1) = one)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_2')).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.42 tff(57,plain,(
% 0.20/0.42 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[56])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 ((complement(X1!1, c(X1!1)) <=> (~((~(multiplication(c(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, c(X1!1)) = zero)) | (~(addition(c(X1!1), X1!1) = one))))) <=> (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(c(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, c(X1!1)) = zero)) | (~(addition(c(X1!1), X1!1) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[61])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(c(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, c(X1!1)) = zero)) | (~(addition(c(X1!1), X1!1) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[62, 60])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(c(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, c(X1!1)) = zero)) | (~(addition(c(X1!1), X1!1) = one)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (complement(X1!1, c(X1!1)) <=> (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[65, 59])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 ((~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 ((~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(69,axiom,(~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[70, 67])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[72, 67])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[73, 67])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[75, 67])).
% 0.20/0.43 tff(77,plain,(
% 0.20/0.43 ~((~(test(X1!1) & test(X0!2))) | (one = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[76])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (test(X1!1) & test(X0!2)),
% 0.20/0.43 inference(or_elim,[status(thm)],[77])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (test(X1!1)),
% 0.20/0.43 inference(and_elim,[status(thm)],[78])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.43 tff(85,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_3')).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.43 tff(88,plain,(
% 0.20/0.43 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[87])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | complement(X1!1, c(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | complement(X1!1, c(X1!1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (((~test(X1!1)) | ((c(X1!1) = c(X1!1)) <=> complement(X1!1, c(X1!1)))) <=> ((~test(X1!1)) | complement(X1!1, c(X1!1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = c(X1!1)) <=> complement(X1!1, c(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | complement(X1!1, c(X1!1))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = c(X1!1)) <=> complement(X1!1, c(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | complement(X1!1, c(X1!1)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[92, 90])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = c(X1!1)) <=> complement(X1!1, c(X1!1))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | complement(X1!1, c(X1!1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (complement(X1!1, c(X1!1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[95, 89, 79])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 ((~(complement(X1!1, c(X1!1)) <=> (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one)))))) | (~complement(X1!1, c(X1!1))) | (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[97, 96, 66])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) | (addition(c(X1!1), X1!1) = one)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (addition(c(X1!1), X1!1) = one),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (one = addition(c(X1!1), X1!1)),
% 0.20/0.43 inference(symmetry,[status(thm)],[100])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(c(X0!2), X0!2) = addition(X0!2, c(X0!2)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (addition(c(X0!2), X0!2) = addition(X0!2, c(X0!2))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[102, 25])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (test(X0!2)),
% 0.20/0.43 inference(and_elim,[status(thm)],[78])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[107, 89, 104])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 ((complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))))) <=> (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[110])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[111, 109])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[114, 59])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 ((addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2))) <=> (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2))),
% 0.20/0.44 inference(commutativity,[status(thm)],[])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(tptp_fun_X1_0(X0!2), X0!2) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 (complement(tptp_fun_X1_0(X0!2), X0!2) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[117, 59])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (^[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)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 (![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))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[119])).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 (^[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)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 (![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))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[121])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 (![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))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[122, 120])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 (^[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))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (![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))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(127,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax','test_1')).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.44 tff(129,plain,(
% 0.20/0.44 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[128])).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.20/0.44 tff(131,plain,
% 0.20/0.44 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.20/0.44 tff(132,plain,
% 0.20/0.44 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(133,plain,
% 0.20/0.44 (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.20/0.44 tff(134,plain,
% 0.20/0.44 (((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2))))) | ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(135,plain,
% 0.20/0.44 ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(137,plain,
% 0.20/0.44 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[136, 104])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 (complement(tptp_fun_X1_0(X0!2), X0!2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[137, 135])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 ((~(complement(tptp_fun_X1_0(X0!2), X0!2) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one)))))) | (~complement(tptp_fun_X1_0(X0!2), X0!2)) | (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 ((~(complement(tptp_fun_X1_0(X0!2), X0!2) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one)))))) | (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[140, 118])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) | (addition(X0!2, tptp_fun_X1_0(X0!2)) = one)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 (addition(X0!2, tptp_fun_X1_0(X0!2)) = one),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.20/0.44 tff(144,plain,
% 0.20/0.44 (one = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 0.20/0.44 inference(symmetry,[status(thm)],[143])).
% 0.20/0.44 tff(145,plain,
% 0.20/0.44 ((addition(tptp_fun_X1_0(X0!2), X0!2) = one) <=> (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[144])).
% 0.20/0.44 tff(146,plain,
% 0.20/0.44 ((addition(tptp_fun_X1_0(X0!2), X0!2) = one) <=> (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2))),
% 0.20/0.44 inference(transitivity,[status(thm)],[145, 116])).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 ((addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)) <=> (addition(tptp_fun_X1_0(X0!2), X0!2) = one)),
% 0.20/0.44 inference(symmetry,[status(thm)],[146])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[148, 25])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 (addition(tptp_fun_X1_0(X0!2), X0!2) = one),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[149, 147])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) | (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[151, 141])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 (((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(X0!2, tptp_fun_X1_0(X0!2)) = one))) | (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[153, 141])).
% 0.20/0.44 tff(155,plain,
% 0.20/0.44 ((~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))) | (~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(156,plain,
% 0.20/0.44 ((~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[155, 154, 152])).
% 0.20/0.44 tff(157,plain,
% 0.20/0.44 (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[156, 150])).
% 0.20/0.44 tff(158,plain,
% 0.20/0.44 ((~(complement(X0!2, tptp_fun_X1_0(X0!2)) <=> (~((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))))) | complement(X0!2, tptp_fun_X1_0(X0!2)) | ((~(multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero)) | (~(multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero)) | (~(addition(tptp_fun_X1_0(X0!2), X0!2) = one)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(159,plain,
% 0.20/0.44 (complement(X0!2, tptp_fun_X1_0(X0!2))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[158, 157, 115])).
% 0.20/0.44 tff(160,plain,
% 0.20/0.44 ((~((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))) | (c(X0!2) = tptp_fun_X1_0(X0!2)) | (~complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(161,plain,
% 0.20/0.44 (c(X0!2) = tptp_fun_X1_0(X0!2)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[160, 159, 108])).
% 0.20/0.44 tff(162,plain,
% 0.20/0.44 (addition(c(X0!2), X0!2) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[161])).
% 0.20/0.44 tff(163,plain,
% 0.20/0.44 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(c(X0!2), X0!2)),
% 0.20/0.44 inference(symmetry,[status(thm)],[162])).
% 0.20/0.44 tff(164,plain,
% 0.20/0.44 (one = addition(X0!2, c(X0!2))),
% 0.20/0.44 inference(transitivity,[status(thm)],[144, 149, 163, 103])).
% 0.20/0.44 tff(165,plain,
% 0.20/0.44 (multiplication(one, one) = multiplication(addition(X0!2, c(X0!2)), addition(c(X1!1), X1!1))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[164, 101])).
% 0.20/0.44 tff(166,plain,
% 0.20/0.44 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(167,plain,
% 0.20/0.44 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.20/0.44 inference(quant_intro,[status(thm)],[166])).
% 0.20/0.44 tff(168,plain,
% 0.20/0.44 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(169,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 0.20/0.44 tff(170,plain,
% 0.20/0.44 (![A: $i] : (multiplication(A, one) = A)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.44 tff(171,plain,(
% 0.20/0.44 ![A: $i] : (multiplication(A, one) = A)),
% 0.20/0.44 inference(skolemize,[status(sab)],[170])).
% 0.20/0.44 tff(172,plain,
% 0.20/0.44 (![A: $i] : (multiplication(A, one) = A)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.20/0.44 tff(173,plain,
% 0.20/0.44 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(one, one) = one)),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(174,plain,
% 0.20/0.44 (multiplication(one, one) = one),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.20/0.44 tff(175,plain,
% 0.20/0.44 (one = multiplication(one, one)),
% 0.20/0.44 inference(symmetry,[status(thm)],[174])).
% 0.20/0.44 tff(176,plain,
% 0.20/0.44 (one = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[175, 165, 46, 37, 9])).
% 0.20/0.45 tff(177,plain,
% 0.20/0.45 (~(one = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 0.20/0.45 inference(or_elim,[status(thm)],[77])).
% 0.20/0.45 tff(178,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.20/0.45 % SZS output end Proof
%------------------------------------------------------------------------------