TSTP Solution File: KLE010+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE010+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 17:23:47 EDT 2022
% Result : Theorem 3.51s 2.55s
% Output : Proof 3.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE010+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Sep 1 07:53:36 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 3.51/2.55 % SZS status Theorem
% 3.51/2.55 % SZS output start Proof
% 3.51/2.55 tff(addition_type, type, (
% 3.51/2.55 addition: ( $i * $i ) > $i)).
% 3.51/2.55 tff(multiplication_type, type, (
% 3.51/2.55 multiplication: ( $i * $i ) > $i)).
% 3.51/2.55 tff(c_type, type, (
% 3.51/2.55 c: $i > $i)).
% 3.51/2.55 tff(tptp_fun_X1_1_type, type, (
% 3.51/2.55 tptp_fun_X1_1: $i)).
% 3.51/2.55 tff(tptp_fun_X0_2_type, type, (
% 3.51/2.55 tptp_fun_X0_2: $i)).
% 3.51/2.55 tff(tptp_fun_X1_0_type, type, (
% 3.51/2.55 tptp_fun_X1_0: $i > $i)).
% 3.51/2.55 tff(one_type, type, (
% 3.51/2.55 one: $i)).
% 3.51/2.55 tff(complement_type, type, (
% 3.51/2.55 complement: ( $i * $i ) > $o)).
% 3.51/2.55 tff(test_type, type, (
% 3.51/2.55 test: $i > $o)).
% 3.51/2.55 tff(zero_type, type, (
% 3.51/2.55 zero: $i)).
% 3.51/2.55 tff(1,plain,
% 3.51/2.55 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 3.51/2.55 inference(bind,[status(th)],[])).
% 3.51/2.55 tff(2,plain,
% 3.51/2.55 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 3.51/2.55 inference(quant_intro,[status(thm)],[1])).
% 3.51/2.55 tff(3,plain,
% 3.51/2.55 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 3.51/2.55 inference(rewrite,[status(thm)],[])).
% 3.51/2.55 tff(4,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 3.51/2.55 tff(5,plain,
% 3.51/2.55 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[4, 3])).
% 3.51/2.55 tff(6,plain,(
% 3.51/2.55 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 3.51/2.55 inference(skolemize,[status(sab)],[5])).
% 3.51/2.55 tff(7,plain,
% 3.51/2.55 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.51/2.55 tff(8,plain,
% 3.51/2.55 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)))),
% 3.51/2.55 inference(quant_inst,[status(thm)],[])).
% 3.51/2.55 tff(9,plain,
% 3.51/2.55 (addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2))),
% 3.51/2.55 inference(unit_resolution,[status(thm)],[8, 7])).
% 3.51/2.55 tff(10,plain,
% 3.51/2.55 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 3.51/2.55 inference(monotonicity,[status(thm)],[9])).
% 3.51/2.55 tff(11,plain,
% 3.51/2.55 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 3.51/2.55 inference(symmetry,[status(thm)],[10])).
% 3.51/2.55 tff(12,plain,
% 3.51/2.55 (^[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)))),
% 3.51/2.55 inference(bind,[status(th)],[])).
% 3.51/2.55 tff(13,plain,
% 3.51/2.55 (![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))),
% 3.51/2.55 inference(quant_intro,[status(thm)],[12])).
% 3.51/2.55 tff(14,plain,
% 3.51/2.55 (![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))),
% 3.51/2.55 inference(rewrite,[status(thm)],[])).
% 3.51/2.55 tff(15,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')).
% 3.51/2.55 tff(16,plain,
% 3.51/2.55 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[15, 14])).
% 3.51/2.55 tff(17,plain,(
% 3.51/2.55 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 3.51/2.55 inference(skolemize,[status(sab)],[16])).
% 3.51/2.55 tff(18,plain,
% 3.51/2.55 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[17, 13])).
% 3.51/2.55 tff(19,plain,
% 3.51/2.55 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 3.51/2.55 inference(quant_inst,[status(thm)],[])).
% 3.51/2.55 tff(20,plain,
% 3.51/2.55 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 3.51/2.55 inference(unit_resolution,[status(thm)],[19, 18])).
% 3.51/2.55 tff(21,plain,
% 3.51/2.55 (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 3.51/2.55 inference(symmetry,[status(thm)],[20])).
% 3.51/2.55 tff(22,plain,
% 3.51/2.55 (addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1))),
% 3.51/2.55 inference(symmetry,[status(thm)],[9])).
% 3.51/2.55 tff(23,plain,
% 3.51/2.55 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1)) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))),
% 3.51/2.55 inference(monotonicity,[status(thm)],[22])).
% 3.51/2.55 tff(24,plain,
% 3.51/2.55 (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 3.51/2.55 inference(monotonicity,[status(thm)],[23])).
% 3.51/2.55 tff(25,plain,
% 3.51/2.55 (addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 3.51/2.55 inference(symmetry,[status(thm)],[24])).
% 3.51/2.55 tff(26,plain,
% 3.51/2.55 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X1!1), X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X1!1), X0!2)))),
% 3.51/2.55 inference(quant_inst,[status(thm)],[])).
% 3.51/2.55 tff(27,plain,
% 3.51/2.55 (addition(multiplication(c(X1!1), X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X1!1), X0!2))),
% 3.51/2.55 inference(unit_resolution,[status(thm)],[26, 7])).
% 3.51/2.55 tff(28,plain,
% 3.51/2.55 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X1!1), X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)))),
% 3.51/2.55 inference(quant_inst,[status(thm)],[])).
% 3.51/2.55 tff(29,plain,
% 3.51/2.55 (addition(multiplication(c(X1!1), X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1))),
% 3.51/2.55 inference(unit_resolution,[status(thm)],[28, 18])).
% 3.51/2.55 tff(30,plain,
% 3.51/2.55 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X1!1), X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 3.51/2.55 inference(symmetry,[status(thm)],[29])).
% 3.51/2.55 tff(31,plain,
% 3.51/2.55 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X1!1), X0!2))),
% 3.51/2.55 inference(transitivity,[status(thm)],[30, 27])).
% 3.51/2.55 tff(32,plain,
% 3.51/2.55 (addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1)))),
% 3.51/2.55 inference(monotonicity,[status(thm)],[31])).
% 3.51/2.55 tff(33,plain,
% 3.51/2.55 (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1))) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 3.51/2.55 inference(symmetry,[status(thm)],[32])).
% 3.51/2.55 tff(34,plain,
% 3.51/2.55 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1))))),
% 3.51/2.55 inference(quant_inst,[status(thm)],[])).
% 3.51/2.55 tff(35,plain,
% 3.51/2.55 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1)))),
% 3.51/2.55 inference(unit_resolution,[status(thm)],[34, 18])).
% 3.51/2.55 tff(36,plain,
% 3.51/2.55 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 3.51/2.55 inference(bind,[status(th)],[])).
% 3.51/2.55 tff(37,plain,
% 3.51/2.55 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 3.51/2.55 inference(quant_intro,[status(thm)],[36])).
% 3.51/2.55 tff(38,plain,
% 3.51/2.55 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 3.51/2.55 inference(rewrite,[status(thm)],[])).
% 3.51/2.55 tff(39,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 3.51/2.55 tff(40,plain,
% 3.51/2.55 (![A: $i] : (multiplication(A, one) = A)),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[39, 38])).
% 3.51/2.55 tff(41,plain,(
% 3.51/2.55 ![A: $i] : (multiplication(A, one) = A)),
% 3.51/2.55 inference(skolemize,[status(sab)],[40])).
% 3.51/2.55 tff(42,plain,
% 3.51/2.55 (![A: $i] : (multiplication(A, one) = A)),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[41, 37])).
% 3.51/2.55 tff(43,plain,
% 3.51/2.55 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(tptp_fun_X1_0(X1!1), one) = tptp_fun_X1_0(X1!1))),
% 3.51/2.55 inference(quant_inst,[status(thm)],[])).
% 3.51/2.55 tff(44,plain,
% 3.51/2.55 (multiplication(tptp_fun_X1_0(X1!1), one) = tptp_fun_X1_0(X1!1)),
% 3.51/2.55 inference(unit_resolution,[status(thm)],[43, 42])).
% 3.51/2.55 tff(45,plain,
% 3.51/2.55 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, c(X0!2)) = addition(c(X0!2), X0!2))),
% 3.51/2.55 inference(quant_inst,[status(thm)],[])).
% 3.51/2.55 tff(46,plain,
% 3.51/2.55 (addition(X0!2, c(X0!2)) = addition(c(X0!2), X0!2)),
% 3.51/2.55 inference(unit_resolution,[status(thm)],[45, 7])).
% 3.51/2.55 tff(47,plain,
% 3.51/2.55 ((~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))))))),
% 3.51/2.55 inference(rewrite,[status(thm)],[])).
% 3.51/2.55 tff(48,plain,
% 3.51/2.55 ((~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (one = addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))))))),
% 3.51/2.55 inference(rewrite,[status(thm)],[])).
% 3.51/2.55 tff(49,axiom,(~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (one = addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 3.51/2.55 tff(50,plain,
% 3.51/2.55 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[49, 48])).
% 3.51/2.55 tff(51,plain,
% 3.51/2.55 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[50, 47])).
% 3.51/2.55 tff(52,plain,
% 3.51/2.55 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[51, 47])).
% 3.51/2.55 tff(53,plain,
% 3.51/2.55 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[52, 47])).
% 3.51/2.55 tff(54,plain,
% 3.51/2.55 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[53, 47])).
% 3.51/2.55 tff(55,plain,
% 3.51/2.55 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[54, 47])).
% 3.51/2.55 tff(56,plain,
% 3.51/2.55 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(addition(addition(multiplication(X1, X0), multiplication(c(X1), X0)), multiplication(X0, X1)), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[55, 47])).
% 3.51/2.55 tff(57,plain,(
% 3.51/2.55 ~((~(test(X1!1) & test(X0!2))) | (one = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 3.51/2.55 inference(skolemize,[status(sab)],[56])).
% 3.51/2.55 tff(58,plain,
% 3.51/2.55 (test(X1!1) & test(X0!2)),
% 3.51/2.55 inference(or_elim,[status(thm)],[57])).
% 3.51/2.55 tff(59,plain,
% 3.51/2.55 (test(X0!2)),
% 3.51/2.55 inference(and_elim,[status(thm)],[58])).
% 3.51/2.55 tff(60,plain,
% 3.51/2.55 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 3.51/2.55 inference(bind,[status(th)],[])).
% 3.51/2.55 tff(61,plain,
% 3.51/2.55 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 3.51/2.55 inference(quant_intro,[status(thm)],[60])).
% 3.51/2.55 tff(62,plain,
% 3.51/2.55 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 3.51/2.55 inference(rewrite,[status(thm)],[])).
% 3.51/2.55 tff(63,plain,
% 3.51/2.55 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 3.51/2.55 inference(bind,[status(th)],[])).
% 3.51/2.55 tff(64,plain,
% 3.51/2.55 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 3.51/2.55 inference(quant_intro,[status(thm)],[63])).
% 3.51/2.55 tff(65,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_3')).
% 3.51/2.55 tff(66,plain,
% 3.51/2.55 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[65, 64])).
% 3.51/2.55 tff(67,plain,
% 3.51/2.55 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[66, 62])).
% 3.51/2.55 tff(68,plain,(
% 3.51/2.55 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 3.51/2.55 inference(skolemize,[status(sab)],[67])).
% 3.51/2.55 tff(69,plain,
% 3.51/2.55 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[68, 61])).
% 3.51/2.55 tff(70,plain,
% 3.51/2.55 (((~![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))))),
% 3.51/2.55 inference(rewrite,[status(thm)],[])).
% 3.51/2.55 tff(71,plain,
% 3.51/2.55 ((~![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))))),
% 3.51/2.55 inference(quant_inst,[status(thm)],[])).
% 3.51/2.55 tff(72,plain,
% 3.51/2.55 ((~![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)))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[71, 70])).
% 3.51/2.55 tff(73,plain,
% 3.51/2.55 ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))),
% 3.51/2.55 inference(unit_resolution,[status(thm)],[72, 69, 59])).
% 3.51/2.55 tff(74,plain,
% 3.51/2.55 (^[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))))))),
% 3.51/2.55 inference(bind,[status(th)],[])).
% 3.51/2.55 tff(75,plain,
% 3.51/2.55 (![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)))))),
% 3.51/2.55 inference(quant_intro,[status(thm)],[74])).
% 3.51/2.55 tff(76,plain,
% 3.51/2.55 (^[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))))))),
% 3.51/2.55 inference(bind,[status(th)],[])).
% 3.51/2.55 tff(77,plain,
% 3.51/2.55 (![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)))))),
% 3.51/2.55 inference(quant_intro,[status(thm)],[76])).
% 3.51/2.55 tff(78,plain,
% 3.51/2.55 (![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)))),
% 3.51/2.55 inference(rewrite,[status(thm)],[])).
% 3.51/2.55 tff(79,plain,
% 3.51/2.55 (^[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))))),
% 3.51/2.55 inference(bind,[status(th)],[])).
% 3.51/2.55 tff(80,plain,
% 3.51/2.55 (![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)))),
% 3.51/2.55 inference(quant_intro,[status(thm)],[79])).
% 3.51/2.55 tff(81,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')).
% 3.51/2.55 tff(82,plain,
% 3.51/2.55 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[81, 80])).
% 3.51/2.55 tff(83,plain,
% 3.51/2.55 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[82, 78])).
% 3.51/2.55 tff(84,plain,(
% 3.51/2.55 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 3.51/2.55 inference(skolemize,[status(sab)],[83])).
% 3.51/2.55 tff(85,plain,
% 3.51/2.55 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[84, 77])).
% 3.51/2.55 tff(86,plain,
% 3.51/2.55 (![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[85, 75])).
% 3.51/2.55 tff(87,plain,
% 3.51/2.55 (((~![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))))))),
% 3.51/2.55 inference(rewrite,[status(thm)],[])).
% 3.51/2.55 tff(88,plain,
% 3.51/2.55 ((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)))))),
% 3.51/2.55 inference(rewrite,[status(thm)],[])).
% 3.51/2.55 tff(89,plain,
% 3.51/2.55 (((~![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))))))),
% 3.51/2.55 inference(monotonicity,[status(thm)],[88])).
% 3.51/2.55 tff(90,plain,
% 3.51/2.55 (((~![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))))))),
% 3.51/2.55 inference(transitivity,[status(thm)],[89, 87])).
% 3.51/2.55 tff(91,plain,
% 3.51/2.55 ((~![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)))))),
% 3.51/2.55 inference(quant_inst,[status(thm)],[])).
% 3.51/2.55 tff(92,plain,
% 3.51/2.55 ((~![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)))))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[91, 90])).
% 3.51/2.55 tff(93,plain,
% 3.51/2.55 (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))))),
% 3.51/2.55 inference(unit_resolution,[status(thm)],[92, 86])).
% 3.51/2.55 tff(94,plain,
% 3.51/2.55 ((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))),
% 3.51/2.55 inference(commutativity,[status(thm)],[])).
% 3.51/2.55 tff(95,plain,
% 3.51/2.55 ((~![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)))))),
% 3.51/2.55 inference(quant_inst,[status(thm)],[])).
% 3.51/2.55 tff(96,plain,
% 3.51/2.55 (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))))),
% 3.51/2.55 inference(unit_resolution,[status(thm)],[95, 86])).
% 3.51/2.55 tff(97,plain,
% 3.51/2.55 (^[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)))))))),
% 3.51/2.55 inference(bind,[status(th)],[])).
% 3.51/2.55 tff(98,plain,
% 3.51/2.55 (![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))))))),
% 3.51/2.55 inference(quant_intro,[status(thm)],[97])).
% 3.51/2.55 tff(99,plain,
% 3.51/2.55 (^[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)))))))),
% 3.51/2.55 inference(bind,[status(th)],[])).
% 3.51/2.55 tff(100,plain,
% 3.51/2.55 (![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))))))),
% 3.51/2.55 inference(quant_intro,[status(thm)],[99])).
% 3.51/2.55 tff(101,plain,
% 3.51/2.55 (![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))))))),
% 3.51/2.55 inference(transitivity,[status(thm)],[100, 98])).
% 3.51/2.55 tff(102,plain,
% 3.51/2.55 (^[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))))))))),
% 3.51/2.55 inference(bind,[status(th)],[])).
% 3.51/2.55 tff(103,plain,
% 3.51/2.55 (![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))))))),
% 3.51/2.55 inference(quant_intro,[status(thm)],[102])).
% 3.51/2.55 tff(104,plain,
% 3.51/2.55 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 3.51/2.55 inference(rewrite,[status(thm)],[])).
% 3.51/2.55 tff(105,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_1')).
% 3.51/2.55 tff(106,plain,
% 3.51/2.55 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[105, 104])).
% 3.51/2.55 tff(107,plain,(
% 3.51/2.55 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 3.51/2.55 inference(skolemize,[status(sab)],[106])).
% 3.51/2.55 tff(108,plain,
% 3.51/2.55 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[107, 103])).
% 3.51/2.55 tff(109,plain,
% 3.51/2.55 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 3.51/2.55 inference(modus_ponens,[status(thm)],[108, 101])).
% 3.51/2.55 tff(110,plain,
% 3.51/2.55 ((~![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))))))),
% 3.51/2.55 inference(quant_inst,[status(thm)],[])).
% 3.51/2.55 tff(111,plain,
% 3.51/2.55 (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2)))))),
% 3.51/2.55 inference(unit_resolution,[status(thm)],[110, 109])).
% 3.51/2.55 tff(112,plain,
% 3.51/2.55 (((~((~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))),
% 3.51/2.55 inference(tautology,[status(thm)],[])).
% 3.51/2.55 tff(113,plain,
% 3.51/2.55 ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 3.51/2.55 inference(unit_resolution,[status(thm)],[112, 111])).
% 3.51/2.55 tff(114,plain,
% 3.51/2.55 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 3.51/2.55 inference(tautology,[status(thm)],[])).
% 3.51/2.55 tff(115,plain,
% 3.51/2.55 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 3.51/2.55 inference(unit_resolution,[status(thm)],[114, 59])).
% 3.51/2.55 tff(116,plain,
% 3.51/2.55 (complement(tptp_fun_X1_0(X0!2), X0!2)),
% 3.51/2.55 inference(unit_resolution,[status(thm)],[115, 113])).
% 3.51/2.55 tff(117,plain,
% 3.51/2.55 ((~(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))))),
% 3.60/2.55 inference(tautology,[status(thm)],[])).
% 3.60/2.55 tff(118,plain,
% 3.60/2.55 ((~(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))))),
% 3.60/2.55 inference(unit_resolution,[status(thm)],[117, 116])).
% 3.60/2.55 tff(119,plain,
% 3.60/2.55 (~((~(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)))),
% 3.60/2.55 inference(unit_resolution,[status(thm)],[118, 96])).
% 3.60/2.55 tff(120,plain,
% 3.60/2.55 (((~(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)),
% 3.60/2.55 inference(tautology,[status(thm)],[])).
% 3.60/2.55 tff(121,plain,
% 3.60/2.55 (addition(X0!2, tptp_fun_X1_0(X0!2)) = one),
% 3.60/2.55 inference(unit_resolution,[status(thm)],[120, 119])).
% 3.60/2.55 tff(122,plain,
% 3.60/2.55 (one = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 3.60/2.55 inference(symmetry,[status(thm)],[121])).
% 3.60/2.55 tff(123,plain,
% 3.60/2.55 ((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)))),
% 3.60/2.55 inference(monotonicity,[status(thm)],[122])).
% 3.60/2.55 tff(124,plain,
% 3.60/2.55 ((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))),
% 3.60/2.55 inference(transitivity,[status(thm)],[123, 94])).
% 3.60/2.55 tff(125,plain,
% 3.60/2.55 ((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)),
% 3.60/2.55 inference(symmetry,[status(thm)],[124])).
% 3.60/2.55 tff(126,plain,
% 3.60/2.55 ((~![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))),
% 3.60/2.55 inference(quant_inst,[status(thm)],[])).
% 3.60/2.55 tff(127,plain,
% 3.60/2.55 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 3.60/2.55 inference(unit_resolution,[status(thm)],[126, 7])).
% 3.60/2.55 tff(128,plain,
% 3.60/2.55 (addition(tptp_fun_X1_0(X0!2), X0!2) = one),
% 3.60/2.55 inference(modus_ponens,[status(thm)],[127, 125])).
% 3.60/2.55 tff(129,plain,
% 3.60/2.55 (((~(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)),
% 3.60/2.55 inference(tautology,[status(thm)],[])).
% 3.60/2.55 tff(130,plain,
% 3.60/2.55 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero),
% 3.60/2.55 inference(unit_resolution,[status(thm)],[129, 119])).
% 3.60/2.55 tff(131,plain,
% 3.60/2.55 (((~(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)),
% 3.60/2.55 inference(tautology,[status(thm)],[])).
% 3.60/2.55 tff(132,plain,
% 3.60/2.55 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero),
% 3.60/2.55 inference(unit_resolution,[status(thm)],[131, 119])).
% 3.60/2.55 tff(133,plain,
% 3.60/2.55 ((~((~(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))),
% 3.60/2.55 inference(tautology,[status(thm)],[])).
% 3.60/2.55 tff(134,plain,
% 3.60/2.55 ((~((~(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))),
% 3.60/2.55 inference(unit_resolution,[status(thm)],[133, 132, 130])).
% 3.60/2.55 tff(135,plain,
% 3.60/2.55 (~((~(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)))),
% 3.60/2.55 inference(unit_resolution,[status(thm)],[134, 128])).
% 3.60/2.56 tff(136,plain,
% 3.60/2.56 ((~(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)))),
% 3.60/2.56 inference(tautology,[status(thm)],[])).
% 3.60/2.56 tff(137,plain,
% 3.60/2.56 (complement(X0!2, tptp_fun_X1_0(X0!2))),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[136, 135, 93])).
% 3.60/2.56 tff(138,plain,
% 3.60/2.56 ((~((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)))),
% 3.60/2.56 inference(tautology,[status(thm)],[])).
% 3.60/2.56 tff(139,plain,
% 3.60/2.56 (c(X0!2) = tptp_fun_X1_0(X0!2)),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[138, 137, 73])).
% 3.60/2.56 tff(140,plain,
% 3.60/2.56 (addition(X0!2, c(X0!2)) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 3.60/2.56 inference(monotonicity,[status(thm)],[139])).
% 3.60/2.56 tff(141,plain,
% 3.60/2.56 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(X0!2, c(X0!2))),
% 3.60/2.56 inference(symmetry,[status(thm)],[140])).
% 3.60/2.56 tff(142,plain,
% 3.60/2.56 (one = addition(c(X0!2), X0!2)),
% 3.60/2.56 inference(transitivity,[status(thm)],[122, 141, 46])).
% 3.60/2.56 tff(143,plain,
% 3.60/2.56 (test(X1!1)),
% 3.60/2.56 inference(and_elim,[status(thm)],[58])).
% 3.60/2.56 tff(144,plain,
% 3.60/2.56 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 3.60/2.56 inference(rewrite,[status(thm)],[])).
% 3.60/2.56 tff(145,plain,
% 3.60/2.56 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 3.60/2.56 inference(quant_inst,[status(thm)],[])).
% 3.60/2.56 tff(146,plain,
% 3.60/2.56 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 3.60/2.56 inference(modus_ponens,[status(thm)],[145, 144])).
% 3.60/2.56 tff(147,plain,
% 3.60/2.56 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[146, 69, 143])).
% 3.60/2.56 tff(148,plain,
% 3.60/2.56 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))))))),
% 3.60/2.56 inference(rewrite,[status(thm)],[])).
% 3.60/2.56 tff(149,plain,
% 3.60/2.56 ((complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))))) <=> (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))),
% 3.60/2.56 inference(rewrite,[status(thm)],[])).
% 3.60/2.56 tff(150,plain,
% 3.60/2.56 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))))))),
% 3.60/2.56 inference(monotonicity,[status(thm)],[149])).
% 3.60/2.56 tff(151,plain,
% 3.60/2.56 (((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))) <=> ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))))))),
% 3.60/2.56 inference(transitivity,[status(thm)],[150, 148])).
% 3.60/2.56 tff(152,plain,
% 3.60/2.56 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))),
% 3.60/2.56 inference(quant_inst,[status(thm)],[])).
% 3.60/2.56 tff(153,plain,
% 3.60/2.56 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))),
% 3.60/2.56 inference(modus_ponens,[status(thm)],[152, 151])).
% 3.60/2.56 tff(154,plain,
% 3.60/2.56 (complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))))),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[153, 86])).
% 3.60/2.56 tff(155,plain,
% 3.60/2.56 ((addition(tptp_fun_X1_0(X1!1), X1!1) = addition(X1!1, tptp_fun_X1_0(X1!1))) <=> (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1))),
% 3.60/2.56 inference(commutativity,[status(thm)],[])).
% 3.60/2.56 tff(156,plain,
% 3.60/2.56 ((~![X0: $i, X1: $i] : (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one)))))) | (complement(tptp_fun_X1_0(X1!1), X1!1) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one)))))),
% 3.60/2.56 inference(quant_inst,[status(thm)],[])).
% 3.60/2.56 tff(157,plain,
% 3.60/2.56 (complement(tptp_fun_X1_0(X1!1), X1!1) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))))),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[156, 86])).
% 3.60/2.56 tff(158,plain,
% 3.60/2.56 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1))))))),
% 3.60/2.56 inference(quant_inst,[status(thm)],[])).
% 3.60/2.56 tff(159,plain,
% 3.60/2.56 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[158, 109])).
% 3.60/2.56 tff(160,plain,
% 3.60/2.56 (((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1))))) | ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))),
% 3.60/2.56 inference(tautology,[status(thm)],[])).
% 3.60/2.56 tff(161,plain,
% 3.60/2.56 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[160, 159])).
% 3.60/2.56 tff(162,plain,
% 3.60/2.56 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 3.60/2.56 inference(tautology,[status(thm)],[])).
% 3.60/2.56 tff(163,plain,
% 3.60/2.56 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[162, 143])).
% 3.60/2.56 tff(164,plain,
% 3.60/2.56 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[163, 161])).
% 3.60/2.56 tff(165,plain,
% 3.60/2.56 ((~(complement(tptp_fun_X1_0(X1!1), X1!1) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one)))))) | (~complement(tptp_fun_X1_0(X1!1), X1!1)) | (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))))),
% 3.60/2.56 inference(tautology,[status(thm)],[])).
% 3.60/2.56 tff(166,plain,
% 3.60/2.56 ((~(complement(tptp_fun_X1_0(X1!1), X1!1) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one)))))) | (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))))),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[165, 164])).
% 3.60/2.56 tff(167,plain,
% 3.60/2.56 (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one)))),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[166, 157])).
% 3.60/2.56 tff(168,plain,
% 3.60/2.56 (((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))) | (addition(X1!1, tptp_fun_X1_0(X1!1)) = one)),
% 3.60/2.56 inference(tautology,[status(thm)],[])).
% 3.60/2.56 tff(169,plain,
% 3.60/2.56 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[168, 167])).
% 3.60/2.56 tff(170,plain,
% 3.60/2.56 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 3.60/2.56 inference(symmetry,[status(thm)],[169])).
% 3.60/2.56 tff(171,plain,
% 3.60/2.56 ((addition(tptp_fun_X1_0(X1!1), X1!1) = one) <=> (addition(tptp_fun_X1_0(X1!1), X1!1) = addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 3.60/2.56 inference(monotonicity,[status(thm)],[170])).
% 3.60/2.56 tff(172,plain,
% 3.60/2.56 ((addition(tptp_fun_X1_0(X1!1), X1!1) = one) <=> (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1))),
% 3.60/2.56 inference(transitivity,[status(thm)],[171, 155])).
% 3.60/2.56 tff(173,plain,
% 3.60/2.56 ((addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)) <=> (addition(tptp_fun_X1_0(X1!1), X1!1) = one)),
% 3.60/2.56 inference(symmetry,[status(thm)],[172])).
% 3.60/2.56 tff(174,plain,
% 3.60/2.56 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1))),
% 3.60/2.56 inference(quant_inst,[status(thm)],[])).
% 3.60/2.56 tff(175,plain,
% 3.60/2.56 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[174, 7])).
% 3.60/2.56 tff(176,plain,
% 3.60/2.56 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 3.60/2.56 inference(modus_ponens,[status(thm)],[175, 173])).
% 3.60/2.56 tff(177,plain,
% 3.60/2.56 (((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))) | (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)),
% 3.60/2.56 inference(tautology,[status(thm)],[])).
% 3.60/2.56 tff(178,plain,
% 3.60/2.56 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[177, 167])).
% 3.60/2.56 tff(179,plain,
% 3.60/2.56 (((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(X1!1, tptp_fun_X1_0(X1!1)) = one))) | (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)),
% 3.60/2.56 inference(tautology,[status(thm)],[])).
% 3.60/2.56 tff(180,plain,
% 3.60/2.56 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[179, 167])).
% 3.60/2.56 tff(181,plain,
% 3.60/2.56 ((~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))) | (~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))),
% 3.60/2.56 inference(tautology,[status(thm)],[])).
% 3.60/2.56 tff(182,plain,
% 3.60/2.56 ((~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one))),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[181, 180, 178])).
% 3.60/2.56 tff(183,plain,
% 3.60/2.56 (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[182, 176])).
% 3.60/2.56 tff(184,plain,
% 3.60/2.56 ((~(complement(X1!1, tptp_fun_X1_0(X1!1)) <=> (~((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))))) | complement(X1!1, tptp_fun_X1_0(X1!1)) | ((~(multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero)) | (~(multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero)) | (~(addition(tptp_fun_X1_0(X1!1), X1!1) = one)))),
% 3.60/2.56 inference(tautology,[status(thm)],[])).
% 3.60/2.56 tff(185,plain,
% 3.60/2.56 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[184, 183, 154])).
% 3.60/2.56 tff(186,plain,
% 3.60/2.56 ((~((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))) | (c(X1!1) = tptp_fun_X1_0(X1!1)) | (~complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 3.60/2.56 inference(tautology,[status(thm)],[])).
% 3.60/2.56 tff(187,plain,
% 3.60/2.56 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[186, 185, 147])).
% 3.60/2.56 tff(188,plain,
% 3.60/2.56 (tptp_fun_X1_0(X1!1) = c(X1!1)),
% 3.60/2.56 inference(symmetry,[status(thm)],[187])).
% 3.60/2.56 tff(189,plain,
% 3.60/2.56 (multiplication(tptp_fun_X1_0(X1!1), one) = multiplication(c(X1!1), addition(c(X0!2), X0!2))),
% 3.60/2.56 inference(monotonicity,[status(thm)],[188, 142])).
% 3.60/2.56 tff(190,plain,
% 3.60/2.56 (multiplication(c(X1!1), addition(c(X0!2), X0!2)) = multiplication(tptp_fun_X1_0(X1!1), one)),
% 3.60/2.56 inference(symmetry,[status(thm)],[189])).
% 3.60/2.56 tff(191,plain,
% 3.60/2.56 (^[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))))),
% 3.60/2.56 inference(bind,[status(th)],[])).
% 3.60/2.56 tff(192,plain,
% 3.60/2.56 (![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)))),
% 3.60/2.56 inference(quant_intro,[status(thm)],[191])).
% 3.60/2.56 tff(193,plain,
% 3.60/2.56 (![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)))),
% 3.60/2.56 inference(rewrite,[status(thm)],[])).
% 3.60/2.56 tff(194,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')).
% 3.60/2.56 tff(195,plain,
% 3.60/2.56 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 3.60/2.56 inference(modus_ponens,[status(thm)],[194, 193])).
% 3.60/2.56 tff(196,plain,(
% 3.60/2.56 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 3.60/2.56 inference(skolemize,[status(sab)],[195])).
% 3.60/2.56 tff(197,plain,
% 3.60/2.56 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 3.60/2.56 inference(modus_ponens,[status(thm)],[196, 192])).
% 3.60/2.56 tff(198,plain,
% 3.60/2.56 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(X1!1), addition(c(X0!2), X0!2)) = addition(multiplication(c(X1!1), c(X0!2)), multiplication(c(X1!1), X0!2)))),
% 3.60/2.56 inference(quant_inst,[status(thm)],[])).
% 3.60/2.56 tff(199,plain,
% 3.60/2.56 (multiplication(c(X1!1), addition(c(X0!2), X0!2)) = addition(multiplication(c(X1!1), c(X0!2)), multiplication(c(X1!1), X0!2))),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[198, 197])).
% 3.60/2.56 tff(200,plain,
% 3.60/2.56 (addition(multiplication(c(X1!1), c(X0!2)), multiplication(c(X1!1), X0!2)) = multiplication(c(X1!1), addition(c(X0!2), X0!2))),
% 3.60/2.56 inference(symmetry,[status(thm)],[199])).
% 3.60/2.56 tff(201,plain,
% 3.60/2.56 (^[X0: $i, X1: $i] : refl(((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))))),
% 3.60/2.56 inference(bind,[status(th)],[])).
% 3.60/2.56 tff(202,plain,
% 3.60/2.56 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 3.60/2.56 inference(quant_intro,[status(thm)],[201])).
% 3.60/2.56 tff(203,plain,
% 3.60/2.56 (^[X0: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((test(X0) & test(X1)) <=> (~((~test(X1)) | (~test(X0))))), ((~(test(X0) & test(X1))) <=> (~(~((~test(X1)) | (~test(X0))))))), rewrite((~(~((~test(X1)) | (~test(X0))))) <=> ((~test(X1)) | (~test(X0)))), ((~(test(X0) & test(X1))) <=> ((~test(X1)) | (~test(X0))))), (((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> (((~test(X1)) | (~test(X0))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))))), rewrite((((~test(X1)) | (~test(X0))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))), (((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))))),
% 3.60/2.56 inference(bind,[status(th)],[])).
% 3.60/2.56 tff(204,plain,
% 3.60/2.56 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 3.60/2.56 inference(quant_intro,[status(thm)],[203])).
% 3.60/2.56 tff(205,plain,
% 3.60/2.56 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 3.60/2.56 inference(rewrite,[status(thm)],[])).
% 3.60/2.56 tff(206,plain,
% 3.60/2.56 (^[X0: $i, X1: $i] : rewrite(((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))))),
% 3.60/2.56 inference(bind,[status(th)],[])).
% 3.60/2.56 tff(207,plain,
% 3.60/2.56 (![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 3.60/2.56 inference(quant_intro,[status(thm)],[206])).
% 3.60/2.56 tff(208,axiom,(![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax','test_deMorgan1')).
% 3.60/2.56 tff(209,plain,
% 3.60/2.56 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 3.60/2.56 inference(modus_ponens,[status(thm)],[208, 207])).
% 3.60/2.56 tff(210,plain,
% 3.60/2.56 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 3.60/2.56 inference(modus_ponens,[status(thm)],[209, 205])).
% 3.60/2.56 tff(211,plain,(
% 3.60/2.56 ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 3.60/2.56 inference(skolemize,[status(sab)],[210])).
% 3.60/2.56 tff(212,plain,
% 3.60/2.56 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 3.60/2.56 inference(modus_ponens,[status(thm)],[211, 204])).
% 3.60/2.56 tff(213,plain,
% 3.60/2.56 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 3.60/2.56 inference(modus_ponens,[status(thm)],[212, 202])).
% 3.60/2.56 tff(214,plain,
% 3.60/2.56 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.56 inference(rewrite,[status(thm)],[])).
% 3.60/2.56 tff(215,plain,
% 3.60/2.56 (((~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))) | (~test(X0!2))) <=> ((~test(X0!2)) | (~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.56 inference(rewrite,[status(thm)],[])).
% 3.60/2.56 tff(216,plain,
% 3.60/2.56 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))) | (~test(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1)))))),
% 3.60/2.56 inference(monotonicity,[status(thm)],[215])).
% 3.60/2.56 tff(217,plain,
% 3.60/2.56 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))) | (~test(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.56 inference(transitivity,[status(thm)],[216, 214])).
% 3.60/2.56 tff(218,plain,
% 3.60/2.56 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))) | (~test(X0!2)))),
% 3.60/2.56 inference(quant_inst,[status(thm)],[])).
% 3.60/2.56 tff(219,plain,
% 3.60/2.56 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1)))),
% 3.60/2.56 inference(modus_ponens,[status(thm)],[218, 217])).
% 3.60/2.56 tff(220,plain,
% 3.60/2.56 (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[219, 213, 143, 59])).
% 3.60/2.56 tff(221,plain,
% 3.60/2.56 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, X1!1) = addition(X1!1, X0!2))),
% 3.60/2.56 inference(quant_inst,[status(thm)],[])).
% 3.60/2.56 tff(222,plain,
% 3.60/2.56 (addition(X0!2, X1!1) = addition(X1!1, X0!2)),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[221, 7])).
% 3.60/2.56 tff(223,plain,
% 3.60/2.56 (addition(X1!1, X0!2) = addition(X0!2, X1!1)),
% 3.60/2.56 inference(symmetry,[status(thm)],[222])).
% 3.60/2.56 tff(224,plain,
% 3.60/2.56 (c(addition(X1!1, X0!2)) = c(addition(X0!2, X1!1))),
% 3.60/2.56 inference(monotonicity,[status(thm)],[223])).
% 3.60/2.56 tff(225,plain,
% 3.60/2.56 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(X1!1)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(X1!1)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))))),
% 3.60/2.56 inference(rewrite,[status(thm)],[])).
% 3.60/2.56 tff(226,plain,
% 3.60/2.56 (((~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))) | (~test(X1!1))) <=> ((~test(X0!2)) | (~test(X1!1)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))))),
% 3.60/2.56 inference(rewrite,[status(thm)],[])).
% 3.60/2.56 tff(227,plain,
% 3.60/2.56 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))) | (~test(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(X1!1)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2)))))),
% 3.60/2.56 inference(monotonicity,[status(thm)],[226])).
% 3.60/2.56 tff(228,plain,
% 3.60/2.56 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))) | (~test(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(X1!1)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))))),
% 3.60/2.56 inference(transitivity,[status(thm)],[227, 225])).
% 3.60/2.56 tff(229,plain,
% 3.60/2.56 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))) | (~test(X1!1)))),
% 3.60/2.56 inference(quant_inst,[status(thm)],[])).
% 3.60/2.56 tff(230,plain,
% 3.60/2.56 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(X1!1)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2)))),
% 3.60/2.56 inference(modus_ponens,[status(thm)],[229, 228])).
% 3.60/2.56 tff(231,plain,
% 3.60/2.56 (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[230, 213, 143, 59])).
% 3.60/2.56 tff(232,plain,
% 3.60/2.56 (multiplication(c(X1!1), c(X0!2)) = c(addition(X1!1, X0!2))),
% 3.60/2.56 inference(symmetry,[status(thm)],[231])).
% 3.60/2.56 tff(233,plain,
% 3.60/2.56 (multiplication(c(X1!1), c(X0!2)) = multiplication(c(X0!2), c(X1!1))),
% 3.60/2.56 inference(transitivity,[status(thm)],[232, 224, 220])).
% 3.60/2.56 tff(234,plain,
% 3.60/2.56 (addition(multiplication(c(X1!1), c(X0!2)), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))),
% 3.60/2.56 inference(monotonicity,[status(thm)],[233])).
% 3.60/2.56 tff(235,plain,
% 3.60/2.56 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), c(X0!2)), multiplication(c(X1!1), X0!2))),
% 3.60/2.56 inference(symmetry,[status(thm)],[234])).
% 3.60/2.56 tff(236,plain,
% 3.60/2.56 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.56 inference(quant_inst,[status(thm)],[])).
% 3.60/2.56 tff(237,plain,
% 3.60/2.56 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1)))),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[236, 7])).
% 3.60/2.56 tff(238,plain,
% 3.60/2.56 (addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))),
% 3.60/2.56 inference(symmetry,[status(thm)],[237])).
% 3.60/2.56 tff(239,plain,
% 3.60/2.56 (addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1))) = tptp_fun_X1_0(X1!1)),
% 3.60/2.56 inference(transitivity,[status(thm)],[238, 235, 200, 190, 44])).
% 3.60/2.56 tff(240,plain,
% 3.60/2.56 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 3.60/2.56 inference(bind,[status(th)],[])).
% 3.60/2.56 tff(241,plain,
% 3.60/2.56 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 3.60/2.56 inference(quant_intro,[status(thm)],[240])).
% 3.60/2.56 tff(242,plain,
% 3.60/2.56 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 3.60/2.56 inference(rewrite,[status(thm)],[])).
% 3.60/2.56 tff(243,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 3.60/2.56 tff(244,plain,
% 3.60/2.56 (![A: $i] : (multiplication(one, A) = A)),
% 3.60/2.56 inference(modus_ponens,[status(thm)],[243, 242])).
% 3.60/2.56 tff(245,plain,(
% 3.60/2.56 ![A: $i] : (multiplication(one, A) = A)),
% 3.60/2.56 inference(skolemize,[status(sab)],[244])).
% 3.60/2.56 tff(246,plain,
% 3.60/2.56 (![A: $i] : (multiplication(one, A) = A)),
% 3.60/2.56 inference(modus_ponens,[status(thm)],[245, 241])).
% 3.60/2.56 tff(247,plain,
% 3.60/2.56 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X1!1) = X1!1)),
% 3.60/2.56 inference(quant_inst,[status(thm)],[])).
% 3.60/2.56 tff(248,plain,
% 3.60/2.56 (multiplication(one, X1!1) = X1!1),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[247, 246])).
% 3.60/2.56 tff(249,plain,
% 3.60/2.56 (multiplication(one, X1!1) = multiplication(addition(c(X0!2), X0!2), X1!1)),
% 3.60/2.56 inference(monotonicity,[status(thm)],[142])).
% 3.60/2.56 tff(250,plain,
% 3.60/2.56 (multiplication(addition(c(X0!2), X0!2), X1!1) = multiplication(one, X1!1)),
% 3.60/2.56 inference(symmetry,[status(thm)],[249])).
% 3.60/2.56 tff(251,plain,
% 3.60/2.56 (^[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))))),
% 3.60/2.56 inference(bind,[status(th)],[])).
% 3.60/2.56 tff(252,plain,
% 3.60/2.56 (![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)))),
% 3.60/2.56 inference(quant_intro,[status(thm)],[251])).
% 3.60/2.56 tff(253,plain,
% 3.60/2.56 (![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)))),
% 3.60/2.56 inference(rewrite,[status(thm)],[])).
% 3.60/2.56 tff(254,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')).
% 3.60/2.56 tff(255,plain,
% 3.60/2.56 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 3.60/2.56 inference(modus_ponens,[status(thm)],[254, 253])).
% 3.60/2.56 tff(256,plain,(
% 3.60/2.56 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 3.60/2.56 inference(skolemize,[status(sab)],[255])).
% 3.60/2.56 tff(257,plain,
% 3.60/2.56 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 3.60/2.56 inference(modus_ponens,[status(thm)],[256, 252])).
% 3.60/2.56 tff(258,plain,
% 3.60/2.56 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(c(X0!2), X0!2), X1!1) = addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 3.60/2.56 inference(quant_inst,[status(thm)],[])).
% 3.60/2.56 tff(259,plain,
% 3.60/2.56 (multiplication(addition(c(X0!2), X0!2), X1!1) = addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[258, 257])).
% 3.60/2.56 tff(260,plain,
% 3.60/2.56 (addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)) = multiplication(addition(c(X0!2), X0!2), X1!1)),
% 3.60/2.56 inference(symmetry,[status(thm)],[259])).
% 3.60/2.56 tff(261,plain,
% 3.60/2.56 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)))),
% 3.60/2.56 inference(quant_inst,[status(thm)],[])).
% 3.60/2.56 tff(262,plain,
% 3.60/2.56 (addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1))),
% 3.60/2.56 inference(unit_resolution,[status(thm)],[261, 7])).
% 3.60/2.56 tff(263,plain,
% 3.60/2.56 (addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)) = X1!1),
% 3.60/2.56 inference(transitivity,[status(thm)],[262, 260, 250, 248])).
% 3.60/2.56 tff(264,plain,
% 3.60/2.56 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1)))) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 3.60/2.56 inference(monotonicity,[status(thm)],[263, 239])).
% 3.60/2.56 tff(265,plain,
% 3.60/2.56 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.56 inference(symmetry,[status(thm)],[264])).
% 3.60/2.56 tff(266,plain,
% 3.60/2.56 ((~![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))))),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(267,plain,
% 3.60/2.57 (multiplication(c(X0!2), addition(X1!1, c(X1!1))) = addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[266, 197])).
% 3.60/2.57 tff(268,plain,
% 3.60/2.57 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!1, c(X1!1)) = addition(c(X1!1), X1!1))),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(269,plain,
% 3.60/2.57 (addition(X1!1, c(X1!1)) = addition(c(X1!1), X1!1)),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[268, 7])).
% 3.60/2.57 tff(270,plain,
% 3.60/2.57 (addition(c(X1!1), X1!1) = addition(X1!1, c(X1!1))),
% 3.60/2.57 inference(symmetry,[status(thm)],[269])).
% 3.60/2.57 tff(271,plain,
% 3.60/2.57 (((~![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))))))),
% 3.60/2.57 inference(rewrite,[status(thm)],[])).
% 3.60/2.57 tff(272,plain,
% 3.60/2.57 ((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)))))),
% 3.60/2.57 inference(rewrite,[status(thm)],[])).
% 3.60/2.57 tff(273,plain,
% 3.60/2.57 (((~![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))))))),
% 3.60/2.57 inference(monotonicity,[status(thm)],[272])).
% 3.60/2.57 tff(274,plain,
% 3.60/2.57 (((~![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))))))),
% 3.60/2.57 inference(transitivity,[status(thm)],[273, 271])).
% 3.60/2.57 tff(275,plain,
% 3.60/2.57 ((~![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)))))),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(276,plain,
% 3.60/2.57 ((~![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)))))),
% 3.60/2.57 inference(modus_ponens,[status(thm)],[275, 274])).
% 3.60/2.57 tff(277,plain,
% 3.60/2.57 (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))))),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[276, 86])).
% 3.60/2.57 tff(278,plain,
% 3.60/2.57 (((~![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)))),
% 3.60/2.57 inference(rewrite,[status(thm)],[])).
% 3.60/2.57 tff(279,plain,
% 3.60/2.57 (((~test(X1!1)) | ((c(X1!1) = c(X1!1)) <=> complement(X1!1, c(X1!1)))) <=> ((~test(X1!1)) | complement(X1!1, c(X1!1)))),
% 3.60/2.57 inference(rewrite,[status(thm)],[])).
% 3.60/2.57 tff(280,plain,
% 3.60/2.57 (((~![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))))),
% 3.60/2.57 inference(monotonicity,[status(thm)],[279])).
% 3.60/2.57 tff(281,plain,
% 3.60/2.57 (((~![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)))),
% 3.60/2.57 inference(transitivity,[status(thm)],[280, 278])).
% 3.60/2.57 tff(282,plain,
% 3.60/2.57 ((~![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))))),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(283,plain,
% 3.60/2.57 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | complement(X1!1, c(X1!1))),
% 3.60/2.57 inference(modus_ponens,[status(thm)],[282, 281])).
% 3.60/2.57 tff(284,plain,
% 3.60/2.57 (complement(X1!1, c(X1!1))),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[283, 69, 143])).
% 3.60/2.57 tff(285,plain,
% 3.60/2.57 ((~(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))))),
% 3.60/2.57 inference(tautology,[status(thm)],[])).
% 3.60/2.57 tff(286,plain,
% 3.60/2.57 (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one)))),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[285, 284, 277])).
% 3.60/2.57 tff(287,plain,
% 3.60/2.57 (((~(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)),
% 3.60/2.57 inference(tautology,[status(thm)],[])).
% 3.60/2.57 tff(288,plain,
% 3.60/2.57 (addition(c(X1!1), X1!1) = one),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[287, 286])).
% 3.60/2.57 tff(289,plain,
% 3.60/2.57 (one = addition(c(X1!1), X1!1)),
% 3.60/2.57 inference(symmetry,[status(thm)],[288])).
% 3.60/2.57 tff(290,plain,
% 3.60/2.57 (one = addition(X1!1, c(X1!1))),
% 3.60/2.57 inference(transitivity,[status(thm)],[289, 270])).
% 3.60/2.57 tff(291,plain,
% 3.60/2.57 (tptp_fun_X1_0(X0!2) = c(X0!2)),
% 3.60/2.57 inference(symmetry,[status(thm)],[139])).
% 3.60/2.57 tff(292,plain,
% 3.60/2.57 (multiplication(tptp_fun_X1_0(X0!2), one) = multiplication(c(X0!2), addition(X1!1, c(X1!1)))),
% 3.60/2.57 inference(monotonicity,[status(thm)],[291, 290])).
% 3.60/2.57 tff(293,plain,
% 3.60/2.57 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(tptp_fun_X1_0(X0!2), one) = tptp_fun_X1_0(X0!2))),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(294,plain,
% 3.60/2.57 (multiplication(tptp_fun_X1_0(X0!2), one) = tptp_fun_X1_0(X0!2)),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[293, 42])).
% 3.60/2.57 tff(295,plain,
% 3.60/2.57 (tptp_fun_X1_0(X0!2) = multiplication(tptp_fun_X1_0(X0!2), one)),
% 3.60/2.57 inference(symmetry,[status(thm)],[294])).
% 3.60/2.57 tff(296,plain,
% 3.60/2.57 (tptp_fun_X1_0(X0!2) = addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 3.60/2.57 inference(transitivity,[status(thm)],[295, 292, 267])).
% 3.60/2.57 tff(297,plain,
% 3.60/2.57 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(298,plain,
% 3.60/2.57 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[297, 7])).
% 3.60/2.57 tff(299,plain,
% 3.60/2.57 (addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 3.60/2.57 inference(symmetry,[status(thm)],[298])).
% 3.60/2.57 tff(300,plain,
% 3.60/2.57 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(c(X1!1), X1!1), X0!2) = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(301,plain,
% 3.60/2.57 (multiplication(addition(c(X1!1), X1!1), X0!2) = addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[300, 257])).
% 3.60/2.57 tff(302,plain,
% 3.60/2.57 (multiplication(one, X0!2) = multiplication(addition(c(X1!1), X1!1), X0!2)),
% 3.60/2.57 inference(monotonicity,[status(thm)],[289])).
% 3.60/2.57 tff(303,plain,
% 3.60/2.57 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!2) = X0!2)),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(304,plain,
% 3.60/2.57 (multiplication(one, X0!2) = X0!2),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[303, 246])).
% 3.60/2.57 tff(305,plain,
% 3.60/2.57 (X0!2 = multiplication(one, X0!2)),
% 3.60/2.57 inference(symmetry,[status(thm)],[304])).
% 3.60/2.57 tff(306,plain,
% 3.60/2.57 (X0!2 = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 3.60/2.57 inference(transitivity,[status(thm)],[305, 302, 301, 299])).
% 3.60/2.57 tff(307,plain,
% 3.60/2.57 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.57 inference(monotonicity,[status(thm)],[306, 296])).
% 3.60/2.57 tff(308,plain,
% 3.60/2.57 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 3.60/2.57 inference(symmetry,[status(thm)],[307])).
% 3.60/2.57 tff(309,plain,
% 3.60/2.57 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(310,plain,
% 3.60/2.57 (addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[309, 18])).
% 3.60/2.57 tff(311,plain,
% 3.60/2.57 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(c(X1!1), X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), multiplication(X1!1, X0!2)))),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(312,plain,
% 3.60/2.57 (addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(c(X1!1), X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), multiplication(X1!1, X0!2))),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[311, 7])).
% 3.60/2.57 tff(313,plain,
% 3.60/2.57 (addition(addition(multiplication(c(X1!1), X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 3.60/2.57 inference(symmetry,[status(thm)],[312])).
% 3.60/2.57 tff(314,plain,
% 3.60/2.57 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 3.60/2.57 inference(bind,[status(th)],[])).
% 3.60/2.57 tff(315,plain,
% 3.60/2.57 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 3.60/2.57 inference(quant_intro,[status(thm)],[314])).
% 3.60/2.57 tff(316,plain,
% 3.60/2.57 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 3.60/2.57 inference(rewrite,[status(thm)],[])).
% 3.60/2.57 tff(317,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 3.60/2.57 tff(318,plain,
% 3.60/2.57 (![A: $i] : (addition(A, A) = A)),
% 3.60/2.57 inference(modus_ponens,[status(thm)],[317, 316])).
% 3.60/2.57 tff(319,plain,(
% 3.60/2.57 ![A: $i] : (addition(A, A) = A)),
% 3.60/2.57 inference(skolemize,[status(sab)],[318])).
% 3.60/2.57 tff(320,plain,
% 3.60/2.57 (![A: $i] : (addition(A, A) = A)),
% 3.60/2.57 inference(modus_ponens,[status(thm)],[319, 315])).
% 3.60/2.57 tff(321,plain,
% 3.60/2.57 ((~![A: $i] : (addition(A, A) = A)) | (addition(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(322,plain,
% 3.60/2.57 (addition(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[321, 320])).
% 3.60/2.57 tff(323,plain,
% 3.60/2.57 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 3.60/2.57 inference(symmetry,[status(thm)],[322])).
% 3.60/2.57 tff(324,plain,
% 3.60/2.57 (addition(multiplication(c(X0!2), X1!1), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))),
% 3.60/2.57 inference(symmetry,[status(thm)],[262])).
% 3.60/2.57 tff(325,plain,
% 3.60/2.57 (X1!1 = multiplication(one, X1!1)),
% 3.60/2.57 inference(symmetry,[status(thm)],[248])).
% 3.60/2.57 tff(326,plain,
% 3.60/2.57 (X1!1 = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))),
% 3.60/2.57 inference(transitivity,[status(thm)],[325, 249, 259, 324])).
% 3.60/2.57 tff(327,plain,
% 3.60/2.57 (multiplication(X1!1, X0!2) = multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.60/2.57 inference(monotonicity,[status(thm)],[326, 306])).
% 3.60/2.57 tff(328,plain,
% 3.60/2.57 (multiplication(X1!1, X0!2) = addition(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 3.60/2.57 inference(transitivity,[status(thm)],[327, 323])).
% 3.60/2.57 tff(329,plain,
% 3.60/2.57 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X1!1), X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(330,plain,
% 3.60/2.57 (addition(multiplication(c(X1!1), X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[329, 18])).
% 3.60/2.57 tff(331,plain,
% 3.60/2.57 (addition(addition(multiplication(c(X1!1), X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), multiplication(X1!1, X0!2)) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))))),
% 3.60/2.57 inference(monotonicity,[status(thm)],[330, 328])).
% 3.60/2.57 tff(332,plain,
% 3.60/2.57 (addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) = addition(addition(multiplication(c(X1!1), X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), multiplication(X1!1, X0!2))),
% 3.60/2.57 inference(symmetry,[status(thm)],[331])).
% 3.60/2.57 tff(333,plain,
% 3.60/2.57 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) = addition(addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))))),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(334,plain,
% 3.60/2.57 (addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) = addition(addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[333, 18])).
% 3.60/2.57 tff(335,plain,
% 3.60/2.57 (addition(addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))))),
% 3.60/2.57 inference(symmetry,[status(thm)],[334])).
% 3.60/2.57 tff(336,plain,
% 3.60/2.57 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(X1!1, X0!2)),
% 3.60/2.57 inference(symmetry,[status(thm)],[327])).
% 3.60/2.57 tff(337,plain,
% 3.60/2.57 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2))))),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(338,plain,
% 3.60/2.57 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)))),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[337, 7])).
% 3.60/2.57 tff(339,plain,
% 3.60/2.57 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X1!1), X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.57 inference(symmetry,[status(thm)],[330])).
% 3.60/2.57 tff(340,plain,
% 3.60/2.57 (addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(addition(multiplication(c(X1!1), X0!2), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))), multiplication(X1!1, X0!2))),
% 3.60/2.57 inference(monotonicity,[status(thm)],[339, 336])).
% 3.60/2.57 tff(341,plain,
% 3.60/2.57 (addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)))),
% 3.60/2.57 inference(transitivity,[status(thm)],[340, 313, 310, 308, 121, 170, 265, 35, 33, 25, 21, 338])).
% 3.60/2.57 tff(342,plain,
% 3.60/2.57 (addition(addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2))), multiplication(X1!1, X0!2))),
% 3.60/2.57 inference(monotonicity,[status(thm)],[341, 336])).
% 3.60/2.57 tff(343,plain,
% 3.60/2.57 (addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2))), multiplication(X1!1, X0!2)) = addition(addition(addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 3.60/2.57 inference(symmetry,[status(thm)],[342])).
% 3.60/2.57 tff(344,plain,
% 3.60/2.57 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2))) = addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2))), multiplication(X1!1, X0!2)))),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(345,plain,
% 3.60/2.57 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2))) = addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2))), multiplication(X1!1, X0!2))),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[344, 18])).
% 3.60/2.57 tff(346,plain,
% 3.60/2.57 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(347,plain,
% 3.60/2.57 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[346, 7])).
% 3.60/2.57 tff(348,plain,
% 3.60/2.57 (addition(multiplication(X0!2, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))),
% 3.60/2.57 inference(symmetry,[status(thm)],[347])).
% 3.60/2.57 tff(349,plain,
% 3.60/2.57 (addition(multiplication(X0!2, X1!1), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(multiplication(X0!2, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 3.60/2.57 inference(monotonicity,[status(thm)],[299])).
% 3.60/2.57 tff(350,plain,
% 3.60/2.57 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X0!2, X1!1), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)))),
% 3.60/2.57 inference(quant_inst,[status(thm)],[])).
% 3.60/2.57 tff(351,plain,
% 3.60/2.57 (addition(multiplication(X0!2, X1!1), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2))),
% 3.60/2.57 inference(unit_resolution,[status(thm)],[350, 18])).
% 3.60/2.57 tff(352,plain,
% 3.60/2.57 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)) = addition(multiplication(X0!2, X1!1), addition(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 3.60/2.57 inference(symmetry,[status(thm)],[351])).
% 3.60/2.57 tff(353,plain,
% 3.60/2.57 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))),
% 3.60/2.57 inference(transitivity,[status(thm)],[352, 349, 348])).
% 3.60/2.57 tff(354,plain,
% 3.60/2.57 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))),
% 3.60/2.58 inference(monotonicity,[status(thm)],[353])).
% 3.60/2.58 tff(355,plain,
% 3.60/2.58 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X0!2)))),
% 3.60/2.58 inference(symmetry,[status(thm)],[354])).
% 3.60/2.58 tff(356,plain,
% 3.60/2.58 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))))),
% 3.60/2.58 inference(quant_inst,[status(thm)],[])).
% 3.60/2.58 tff(357,plain,
% 3.60/2.58 (addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))),
% 3.60/2.58 inference(unit_resolution,[status(thm)],[356, 7])).
% 3.60/2.58 tff(358,plain,
% 3.60/2.58 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)))),
% 3.60/2.58 inference(quant_inst,[status(thm)],[])).
% 3.60/2.58 tff(359,plain,
% 3.60/2.58 (addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1))),
% 3.60/2.58 inference(unit_resolution,[status(thm)],[358, 18])).
% 3.60/2.58 tff(360,plain,
% 3.60/2.58 (addition(addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.58 inference(monotonicity,[status(thm)],[359])).
% 3.60/2.58 tff(361,plain,
% 3.60/2.58 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X1!1, X0!2), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 3.60/2.58 inference(quant_inst,[status(thm)],[])).
% 3.60/2.58 tff(362,plain,
% 3.60/2.58 (addition(multiplication(X1!1, X0!2), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.58 inference(unit_resolution,[status(thm)],[361, 18])).
% 3.60/2.58 tff(363,plain,
% 3.60/2.58 (addition(multiplication(X1!1, X0!2), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.58 inference(transitivity,[status(thm)],[362, 360, 357, 355, 345, 343, 335, 332, 313, 310, 308, 121, 170, 265, 35, 33, 25, 21, 11])).
% 3.60/2.58 tff(364,plain,
% 3.60/2.58 ((addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = one) <=> (one = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.58 inference(commutativity,[status(thm)],[])).
% 3.60/2.58 tff(365,plain,
% 3.60/2.58 (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.58 inference(symmetry,[status(thm)],[35])).
% 3.60/2.58 tff(366,plain,
% 3.60/2.58 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = one),
% 3.60/2.58 inference(transitivity,[status(thm)],[10, 20, 24, 32, 365, 264, 169])).
% 3.60/2.58 tff(367,plain,
% 3.60/2.58 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.58 inference(quant_inst,[status(thm)],[])).
% 3.60/2.58 tff(368,plain,
% 3.60/2.58 (addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 3.60/2.58 inference(unit_resolution,[status(thm)],[367, 18])).
% 3.60/2.58 tff(369,plain,
% 3.60/2.58 (addition(multiplication(X1!1, X0!2), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 3.60/2.58 inference(transitivity,[status(thm)],[362, 360, 368])).
% 3.60/2.58 tff(370,plain,
% 3.60/2.58 ((addition(multiplication(X1!1, X0!2), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))) <=> (addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = one)),
% 3.60/2.58 inference(monotonicity,[status(thm)],[369, 366])).
% 3.60/2.58 tff(371,plain,
% 3.60/2.58 ((addition(multiplication(X1!1, X0!2), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))) <=> (one = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.58 inference(transitivity,[status(thm)],[370, 364])).
% 3.60/2.58 tff(372,plain,
% 3.60/2.58 ((one = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(multiplication(X1!1, X0!2), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 3.60/2.58 inference(symmetry,[status(thm)],[371])).
% 3.60/2.58 tff(373,plain,
% 3.60/2.58 ((~(one = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) <=> (~(addition(multiplication(X1!1, X0!2), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))))),
% 3.60/2.58 inference(monotonicity,[status(thm)],[372])).
% 3.60/2.58 tff(374,plain,
% 3.60/2.58 (~(one = addition(addition(addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X0!2, X1!1)), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 3.60/2.58 inference(or_elim,[status(thm)],[57])).
% 3.60/2.58 tff(375,plain,
% 3.60/2.58 (~(addition(multiplication(X1!1, X0!2), addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 3.60/2.58 inference(modus_ponens,[status(thm)],[374, 373])).
% 3.60/2.58 tff(376,plain,
% 3.60/2.58 ($false),
% 3.60/2.58 inference(unit_resolution,[status(thm)],[375, 363])).
% 3.60/2.58 % SZS output end Proof
%------------------------------------------------------------------------------