%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE009+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 Jun 21 05:12:50 AM UTC 2025
% Result : Theorem 91.93s 92.15s
% Output : Proof 92.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.13 % Problem : KLE009+4 : TPTP v9.0.0. Released v4.0.0.
% 0.14/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.21/0.35 % WCLimit : 300
% 0.21/0.35 % DateTime : Thu Jun 19 18:52:16 EDT 2025
% 0.21/0.35 % CPUTime :
% 91.93/92.15 % SZS status Theorem
% 91.93/92.15 % SZS output start Proof
% 91.93/92.15 tff(addition_type, type, (
% 91.93/92.15 addition: ( $i * $i ) > $i)).
% 91.93/92.15 tff(multiplication_type, type, (
% 91.93/92.15 multiplication: ( $i * $i ) > $i)).
% 91.93/92.15 tff(c_type, type, (
% 91.93/92.15 c: $i > $i)).
% 91.93/92.15 tff(tptp_fun_X1_1_type, type, (
% 91.93/92.15 tptp_fun_X1_1: $i)).
% 91.93/92.15 tff(tptp_fun_X0_2_type, type, (
% 91.93/92.15 tptp_fun_X0_2: $i)).
% 91.93/92.15 tff(tptp_fun_X1_0_type, type, (
% 91.93/92.15 tptp_fun_X1_0: $i > $i)).
% 91.93/92.15 tff(test_type, type, (
% 91.93/92.15 test: $i > $o)).
% 91.93/92.15 tff(complement_type, type, (
% 91.93/92.15 complement: ( $i * $i ) > $o)).
% 91.93/92.15 tff(leq_type, type, (
% 91.93/92.15 leq: ( $i * $i ) > $o)).
% 91.93/92.15 tff(one_type, type, (
% 91.93/92.15 one: $i)).
% 91.93/92.15 tff(zero_type, type, (
% 91.93/92.15 zero: $i)).
% 91.93/92.15 tff(1,plain,
% 91.93/92.15 (^[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)))),
% 91.93/92.15 inference(bind,[status(th)],[])).
% 91.93/92.15 tff(2,plain,
% 91.93/92.15 (![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))),
% 91.93/92.15 inference(quant_intro,[status(thm)],[1])).
% 91.93/92.15 tff(3,plain,
% 91.93/92.15 (![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))),
% 91.93/92.15 inference(rewrite,[status(thm)],[])).
% 91.93/92.15 tff(4,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')).
% 91.93/92.15 tff(5,plain,
% 91.93/92.15 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 91.93/92.15 inference(modus_ponens,[status(thm)],[4, 3])).
% 91.93/92.15 tff(6,plain,(
% 91.93/92.15 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 91.93/92.15 inference(skolemize,[status(sab)],[5])).
% 91.93/92.15 tff(7,plain,
% 91.93/92.15 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 91.93/92.15 inference(modus_ponens,[status(thm)],[6, 2])).
% 91.93/92.15 tff(8,plain,
% 91.93/92.15 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 91.93/92.15 inference(quant_inst,[status(thm)],[])).
% 91.93/92.15 tff(9,plain,
% 91.93/92.15 (addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 91.93/92.15 inference(unit_resolution,[status(thm)],[8, 7])).
% 91.93/92.15 tff(10,plain,
% 91.93/92.15 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 91.93/92.15 inference(bind,[status(th)],[])).
% 91.93/92.15 tff(11,plain,
% 91.93/92.15 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 91.93/92.15 inference(quant_intro,[status(thm)],[10])).
% 91.93/92.15 tff(12,plain,
% 91.93/92.15 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 91.93/92.15 inference(rewrite,[status(thm)],[])).
% 91.93/92.15 tff(13,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 91.93/92.15 tff(14,plain,
% 91.93/92.15 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 91.93/92.15 inference(modus_ponens,[status(thm)],[13, 12])).
% 91.93/92.15 tff(15,plain,(
% 91.93/92.15 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 91.93/92.15 inference(skolemize,[status(sab)],[14])).
% 91.93/92.15 tff(16,plain,
% 91.93/92.15 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 91.93/92.15 inference(modus_ponens,[status(thm)],[15, 11])).
% 91.93/92.15 tff(17,plain,
% 91.93/92.15 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))) = addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 91.93/92.15 inference(quant_inst,[status(thm)],[])).
% 91.93/92.16 tff(18,plain,
% 91.93/92.16 (addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))) = addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[17, 16])).
% 91.93/92.16 tff(19,plain,
% 91.93/92.16 (addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 91.93/92.16 inference(monotonicity,[status(thm)],[18])).
% 91.93/92.16 tff(20,plain,
% 91.93/92.16 (addition(addition(multiplication(X0!2, c(X1!1)), 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(X0!2, c(X1!1))), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 91.93/92.16 inference(symmetry,[status(thm)],[19])).
% 91.93/92.16 tff(21,plain,
% 91.93/92.16 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X0!2, c(X1!1)), 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(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))))),
% 91.93/92.16 inference(quant_inst,[status(thm)],[])).
% 91.93/92.16 tff(22,plain,
% 91.93/92.16 (addition(addition(multiplication(X0!2, c(X1!1)), 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(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[21, 16])).
% 91.93/92.16 tff(23,plain,
% 91.93/92.16 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))) = addition(addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 91.93/92.16 inference(symmetry,[status(thm)],[22])).
% 91.93/92.16 tff(24,plain,
% 91.93/92.16 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)))),
% 91.93/92.16 inference(quant_inst,[status(thm)],[])).
% 91.93/92.16 tff(25,plain,
% 91.93/92.16 (addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[24, 16])).
% 91.93/92.16 tff(26,plain,
% 91.93/92.16 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 91.93/92.16 inference(monotonicity,[status(thm)],[25])).
% 91.93/92.16 tff(27,plain,
% 91.93/92.16 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 91.93/92.16 inference(symmetry,[status(thm)],[26])).
% 91.93/92.16 tff(28,plain,
% 91.93/92.16 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), X0!2) = addition(X0!2, c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.16 inference(quant_inst,[status(thm)],[])).
% 91.93/92.16 tff(29,plain,
% 91.93/92.16 (addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), X0!2) = addition(X0!2, c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[28, 16])).
% 91.93/92.16 tff(30,plain,
% 91.93/92.16 ((~![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))),
% 91.93/92.16 inference(quant_inst,[status(thm)],[])).
% 91.93/92.16 tff(31,plain,
% 91.93/92.16 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[30, 16])).
% 91.93/92.16 tff(32,plain,
% 91.93/92.16 ((~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one))))),
% 91.93/92.16 inference(rewrite,[status(thm)],[])).
% 91.93/92.16 tff(33,plain,
% 91.93/92.16 ((~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one))))),
% 91.93/92.16 inference(rewrite,[status(thm)],[])).
% 91.93/92.16 tff(34,axiom,(~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 91.93/92.16 tff(35,plain,
% 91.93/92.16 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[34, 33])).
% 91.93/92.16 tff(36,plain,
% 91.93/92.16 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[35, 32])).
% 91.93/92.16 tff(37,plain,
% 91.93/92.16 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[36, 32])).
% 91.93/92.16 tff(38,plain,
% 91.93/92.16 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (leq(one, addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1)))) & leq(addition(addition(addition(multiplication(X0, X1), multiplication(X0, c(X1))), multiplication(c(X0), X1)), multiplication(c(X0), c(X1))), one)))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[37, 32])).
% 91.93/92.16 tff(39,plain,(
% 91.93/92.16 ~((~(test(X1!1) & test(X0!2))) | (leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) & leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)))),
% 91.93/92.16 inference(skolemize,[status(sab)],[38])).
% 91.93/92.16 tff(40,plain,
% 91.93/92.16 (test(X1!1) & test(X0!2)),
% 91.93/92.16 inference(or_elim,[status(thm)],[39])).
% 91.93/92.16 tff(41,plain,
% 91.93/92.16 (test(X0!2)),
% 91.93/92.16 inference(and_elim,[status(thm)],[40])).
% 91.93/92.16 tff(42,plain,
% 91.93/92.16 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 91.93/92.16 inference(bind,[status(th)],[])).
% 91.93/92.16 tff(43,plain,
% 91.93/92.16 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 91.93/92.16 inference(quant_intro,[status(thm)],[42])).
% 91.93/92.16 tff(44,plain,
% 91.93/92.16 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 91.93/92.16 inference(rewrite,[status(thm)],[])).
% 91.93/92.16 tff(45,plain,
% 91.93/92.16 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 91.93/92.16 inference(bind,[status(th)],[])).
% 91.93/92.16 tff(46,plain,
% 91.93/92.16 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 91.93/92.16 inference(quant_intro,[status(thm)],[45])).
% 91.93/92.16 tff(47,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_3')).
% 91.93/92.16 tff(48,plain,
% 91.93/92.16 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[47, 46])).
% 91.93/92.16 tff(49,plain,
% 91.93/92.16 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[48, 44])).
% 91.93/92.16 tff(50,plain,(
% 91.93/92.16 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 91.93/92.16 inference(skolemize,[status(sab)],[49])).
% 91.93/92.16 tff(51,plain,
% 91.93/92.16 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[50, 43])).
% 91.93/92.16 tff(52,plain,
% 91.93/92.16 (((~![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))))),
% 91.93/92.16 inference(rewrite,[status(thm)],[])).
% 91.93/92.16 tff(53,plain,
% 91.93/92.16 ((~![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))))),
% 91.93/92.16 inference(quant_inst,[status(thm)],[])).
% 91.93/92.16 tff(54,plain,
% 91.93/92.16 ((~![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)))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[53, 52])).
% 91.93/92.16 tff(55,plain,
% 91.93/92.16 ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[54, 51, 41])).
% 91.93/92.16 tff(56,plain,
% 91.93/92.16 (^[X0: $i, X1: $i] : refl((~(((~(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))) <=> complement(X1, X0))))),
% 91.93/92.16 inference(bind,[status(th)],[])).
% 91.93/92.16 tff(57,plain,
% 91.93/92.16 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))) <=> ![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 91.93/92.16 inference(quant_intro,[status(thm)],[56])).
% 91.93/92.16 tff(58,plain,
% 91.93/92.16 (^[X0: $i, X1: $i] : trans(trans(monotonicity(rewrite(((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)) <=> (~((~(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))) <=> (complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))))), rewrite((complement(X1, X0) <=> (~((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))), ((complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0))))), rewrite((~(((~(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))) <=> complement(X1, X0)))), ((complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))))),
% 91.93/92.16 inference(bind,[status(th)],[])).
% 91.93/92.16 tff(59,plain,
% 91.93/92.16 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one))) <=> ![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 91.93/92.16 inference(quant_intro,[status(thm)],[58])).
% 91.93/92.16 tff(60,plain,
% 91.93/92.16 (![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)))),
% 91.93/92.16 inference(rewrite,[status(thm)],[])).
% 91.93/92.16 tff(61,plain,
% 91.93/92.16 (^[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))))),
% 91.93/92.16 inference(bind,[status(th)],[])).
% 91.93/92.16 tff(62,plain,
% 91.93/92.16 (![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)))),
% 91.93/92.16 inference(quant_intro,[status(thm)],[61])).
% 91.93/92.16 tff(63,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')).
% 91.93/92.16 tff(64,plain,
% 91.93/92.16 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[63, 62])).
% 91.93/92.16 tff(65,plain,
% 91.93/92.16 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[64, 60])).
% 91.93/92.16 tff(66,plain,(
% 91.93/92.16 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 91.93/92.16 inference(skolemize,[status(sab)],[65])).
% 91.93/92.16 tff(67,plain,
% 91.93/92.16 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[66, 59])).
% 91.93/92.16 tff(68,plain,
% 91.93/92.16 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[67, 57])).
% 91.93/92.16 tff(69,plain,
% 91.93/92.16 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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)))))),
% 91.93/92.16 inference(rewrite,[status(thm)],[])).
% 91.93/92.16 tff(70,plain,
% 91.93/92.16 ((~(((~(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))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 91.93/92.16 inference(rewrite,[status(thm)],[])).
% 91.93/92.16 tff(71,plain,
% 91.93/92.16 ((((~(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))) <=> complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 91.93/92.16 inference(rewrite,[status(thm)],[])).
% 91.93/92.16 tff(72,plain,
% 91.93/92.16 ((~(((~(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))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 91.93/92.16 inference(monotonicity,[status(thm)],[71])).
% 91.93/92.16 tff(73,plain,
% 91.93/92.16 ((~(((~(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))) <=> complement(X0!2, tptp_fun_X1_0(X0!2))))),
% 91.93/92.16 inference(transitivity,[status(thm)],[72, 70])).
% 91.93/92.16 tff(74,plain,
% 91.93/92.16 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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)))))),
% 91.93/92.16 inference(monotonicity,[status(thm)],[73])).
% 91.93/92.16 tff(75,plain,
% 91.93/92.16 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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)))))),
% 91.93/92.16 inference(transitivity,[status(thm)],[74, 69])).
% 91.93/92.16 tff(76,plain,
% 91.93/92.16 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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))))),
% 91.93/92.16 inference(quant_inst,[status(thm)],[])).
% 91.93/92.16 tff(77,plain,
% 91.93/92.16 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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))))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[76, 75])).
% 91.93/92.16 tff(78,plain,
% 91.93/92.16 (~(((~(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)))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[77, 68])).
% 91.93/92.16 tff(79,plain,
% 91.93/92.16 ((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))),
% 91.93/92.16 inference(commutativity,[status(thm)],[])).
% 91.93/92.16 tff(80,plain,
% 91.93/92.16 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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)))),
% 91.93/92.16 inference(quant_inst,[status(thm)],[])).
% 91.93/92.16 tff(81,plain,
% 91.93/92.16 (~(((~(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))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[80, 68])).
% 91.93/92.16 tff(82,plain,
% 91.93/92.16 (^[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)))))))),
% 91.93/92.16 inference(bind,[status(th)],[])).
% 91.93/92.16 tff(83,plain,
% 91.93/92.16 (![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))))))),
% 91.93/92.16 inference(quant_intro,[status(thm)],[82])).
% 91.93/92.16 tff(84,plain,
% 91.93/92.16 (^[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)))))))),
% 91.93/92.16 inference(bind,[status(th)],[])).
% 91.93/92.16 tff(85,plain,
% 91.93/92.16 (![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))))))),
% 91.93/92.16 inference(quant_intro,[status(thm)],[84])).
% 91.93/92.16 tff(86,plain,
% 91.93/92.16 (![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))))))),
% 91.93/92.16 inference(transitivity,[status(thm)],[85, 83])).
% 91.93/92.16 tff(87,plain,
% 91.93/92.16 (^[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))))))))),
% 91.93/92.16 inference(bind,[status(th)],[])).
% 91.93/92.16 tff(88,plain,
% 91.93/92.16 (![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))))))),
% 91.93/92.16 inference(quant_intro,[status(thm)],[87])).
% 91.93/92.16 tff(89,plain,
% 91.93/92.16 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 91.93/92.16 inference(rewrite,[status(thm)],[])).
% 91.93/92.16 tff(90,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_1')).
% 91.93/92.16 tff(91,plain,
% 91.93/92.16 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[90, 89])).
% 91.93/92.16 tff(92,plain,(
% 91.93/92.16 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 91.93/92.16 inference(skolemize,[status(sab)],[91])).
% 91.93/92.16 tff(93,plain,
% 91.93/92.16 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[92, 88])).
% 91.93/92.16 tff(94,plain,
% 91.93/92.16 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[93, 86])).
% 91.93/92.16 tff(95,plain,
% 91.93/92.16 ((~![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))))))),
% 91.93/92.16 inference(quant_inst,[status(thm)],[])).
% 91.93/92.16 tff(96,plain,
% 91.93/92.16 (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2)))))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[95, 94])).
% 91.93/92.16 tff(97,plain,
% 91.93/92.16 (((~((~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))),
% 91.93/92.16 inference(tautology,[status(thm)],[])).
% 91.93/92.16 tff(98,plain,
% 91.93/92.16 ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[97, 96])).
% 91.93/92.16 tff(99,plain,
% 91.93/92.16 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 91.93/92.16 inference(tautology,[status(thm)],[])).
% 91.93/92.16 tff(100,plain,
% 91.93/92.16 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[99, 41])).
% 91.93/92.16 tff(101,plain,
% 91.93/92.16 (complement(tptp_fun_X1_0(X0!2), X0!2)),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[100, 98])).
% 91.93/92.16 tff(102,plain,
% 91.93/92.16 ((((~(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)))) | (~complement(tptp_fun_X1_0(X0!2), X0!2))),
% 91.93/92.16 inference(tautology,[status(thm)],[])).
% 91.93/92.16 tff(103,plain,
% 91.93/92.16 ((((~(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))))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[102, 101])).
% 91.93/92.16 tff(104,plain,
% 91.93/92.16 (~((~(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)))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[103, 81])).
% 91.93/92.16 tff(105,plain,
% 91.93/92.16 (((~(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)),
% 91.93/92.16 inference(tautology,[status(thm)],[])).
% 91.93/92.16 tff(106,plain,
% 91.93/92.16 (addition(X0!2, tptp_fun_X1_0(X0!2)) = one),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[105, 104])).
% 91.93/92.16 tff(107,plain,
% 91.93/92.16 (one = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 91.93/92.16 inference(symmetry,[status(thm)],[106])).
% 91.93/92.16 tff(108,plain,
% 91.93/92.16 ((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)))),
% 91.93/92.16 inference(monotonicity,[status(thm)],[107])).
% 91.93/92.16 tff(109,plain,
% 91.93/92.16 ((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))),
% 91.93/92.16 inference(transitivity,[status(thm)],[108, 79])).
% 91.93/92.16 tff(110,plain,
% 91.93/92.16 ((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)),
% 91.93/92.16 inference(symmetry,[status(thm)],[109])).
% 91.93/92.16 tff(111,plain,
% 91.93/92.16 (addition(tptp_fun_X1_0(X0!2), X0!2) = one),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[31, 110])).
% 91.93/92.16 tff(112,plain,
% 91.93/92.16 (((~(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)),
% 91.93/92.16 inference(tautology,[status(thm)],[])).
% 91.93/92.16 tff(113,plain,
% 91.93/92.16 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[112, 104])).
% 91.93/92.16 tff(114,plain,
% 91.93/92.16 (((~(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)),
% 91.93/92.16 inference(tautology,[status(thm)],[])).
% 91.93/92.16 tff(115,plain,
% 91.93/92.16 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[114, 104])).
% 91.93/92.16 tff(116,plain,
% 91.93/92.16 ((~((~(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))),
% 91.93/92.16 inference(tautology,[status(thm)],[])).
% 91.93/92.16 tff(117,plain,
% 91.93/92.16 ((~((~(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))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[116, 115, 113])).
% 91.93/92.16 tff(118,plain,
% 91.93/92.16 (~((~(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)))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[117, 111])).
% 91.93/92.16 tff(119,plain,
% 91.93/92.16 ((((~(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))) | complement(X0!2, tptp_fun_X1_0(X0!2))),
% 91.93/92.16 inference(tautology,[status(thm)],[])).
% 91.93/92.16 tff(120,plain,
% 91.93/92.16 (complement(X0!2, tptp_fun_X1_0(X0!2))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[119, 118, 78])).
% 91.93/92.16 tff(121,plain,
% 91.93/92.16 ((~((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)))),
% 91.93/92.16 inference(tautology,[status(thm)],[])).
% 91.93/92.16 tff(122,plain,
% 91.93/92.16 (c(X0!2) = tptp_fun_X1_0(X0!2)),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[121, 120, 55])).
% 91.93/92.16 tff(123,plain,
% 91.93/92.16 (tptp_fun_X1_0(X0!2) = c(X0!2)),
% 91.93/92.16 inference(symmetry,[status(thm)],[122])).
% 91.93/92.16 tff(124,assumption,((~((~test(tptp_fun_X1_0(X0!2))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))) | (~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))))), introduced(assumption)).
% 91.93/92.16 tff(125,plain,
% 91.93/92.16 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(tptp_fun_X1_0(X0!2))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))) | (~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))))))),
% 91.93/92.16 inference(quant_inst,[status(thm)],[])).
% 91.93/92.16 tff(126,plain,
% 91.93/92.16 ($false),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[125, 94, 124])).
% 91.93/92.16 tff(127,plain,(~((~((~test(tptp_fun_X1_0(X0!2))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))) | (~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2))))))), inference(lemma,lemma(discharge,[]))).
% 91.93/92.16 tff(128,plain,
% 91.93/92.16 (((~((~test(tptp_fun_X1_0(X0!2))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))) | (~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))))) | (test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2))))),
% 91.93/92.16 inference(tautology,[status(thm)],[])).
% 91.93/92.16 tff(129,plain,
% 91.93/92.16 (test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[128, 127])).
% 91.93/92.16 tff(130,assumption,(![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))), introduced(assumption)).
% 91.93/92.16 tff(131,plain,
% 91.93/92.16 ((~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))) | (~complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 91.93/92.16 inference(quant_inst,[status(thm)],[])).
% 91.93/92.16 tff(132,plain,
% 91.93/92.16 ($false),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[131, 120, 130])).
% 91.93/92.16 tff(133,plain,(~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))), inference(lemma,lemma(discharge,[]))).
% 91.93/92.16 tff(134,plain,
% 91.93/92.16 ((~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2))))) | test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))),
% 91.93/92.16 inference(tautology,[status(thm)],[])).
% 91.93/92.16 tff(135,plain,
% 91.93/92.16 ((~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2))))) | test(tptp_fun_X1_0(X0!2))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[134, 133])).
% 91.93/92.16 tff(136,plain,
% 91.93/92.16 (test(tptp_fun_X1_0(X0!2))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[135, 129])).
% 91.93/92.16 tff(137,plain,
% 91.93/92.16 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X0!2))) | ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X0!2))) | ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2)))),
% 91.93/92.16 inference(rewrite,[status(thm)],[])).
% 91.93/92.16 tff(138,plain,
% 91.93/92.16 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X0!2))) | ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2)))),
% 91.93/92.16 inference(quant_inst,[status(thm)],[])).
% 91.93/92.16 tff(139,plain,
% 91.93/92.16 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X0!2))) | ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2))),
% 91.93/92.16 inference(modus_ponens,[status(thm)],[138, 137])).
% 91.93/92.16 tff(140,plain,
% 91.93/92.16 ((~test(tptp_fun_X1_0(X0!2))) | ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2))),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[139, 51])).
% 91.93/92.16 tff(141,plain,
% 91.93/92.16 ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2)),
% 91.93/92.16 inference(unit_resolution,[status(thm)],[140, 136])).
% 91.93/92.17 tff(142,plain,
% 91.93/92.17 ((~((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2))) | (c(tptp_fun_X1_0(X0!2)) = X0!2) | (~complement(tptp_fun_X1_0(X0!2), X0!2))),
% 91.93/92.17 inference(tautology,[status(thm)],[])).
% 91.93/92.17 tff(143,plain,
% 91.93/92.17 ((~((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2))) | (c(tptp_fun_X1_0(X0!2)) = X0!2)),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[142, 101])).
% 91.93/92.17 tff(144,plain,
% 91.93/92.17 (c(tptp_fun_X1_0(X0!2)) = X0!2),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[143, 141])).
% 91.93/92.17 tff(145,plain,
% 91.93/92.17 (X0!2 = c(tptp_fun_X1_0(X0!2))),
% 91.93/92.17 inference(symmetry,[status(thm)],[144])).
% 91.93/92.17 tff(146,plain,
% 91.93/92.17 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), c(X0!2))),
% 91.93/92.17 inference(monotonicity,[status(thm)],[145, 123])).
% 91.93/92.17 tff(147,plain,
% 91.93/92.17 (addition(c(tptp_fun_X1_0(X0!2)), c(X0!2)) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 91.93/92.17 inference(symmetry,[status(thm)],[146])).
% 91.93/92.17 tff(148,plain,
% 91.93/92.17 (^[X0: $i, X1: $i] : refl(((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0))) <=> ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0))))),
% 91.93/92.17 inference(bind,[status(th)],[])).
% 91.93/92.17 tff(149,plain,
% 91.93/92.17 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 91.93/92.17 inference(quant_intro,[status(thm)],[148])).
% 91.93/92.17 tff(150,plain,
% 91.93/92.17 (^[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(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> (((~test(X1)) | (~test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))))), rewrite((((~test(X1)) | (~test(X0))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))), (((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))))),
% 91.93/92.17 inference(bind,[status(th)],[])).
% 91.93/92.17 tff(151,plain,
% 91.93/92.17 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 91.93/92.17 inference(quant_intro,[status(thm)],[150])).
% 91.93/92.17 tff(152,plain,
% 91.93/92.17 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 91.93/92.17 inference(rewrite,[status(thm)],[])).
% 91.93/92.17 tff(153,plain,
% 91.93/92.17 (^[X0: $i, X1: $i] : rewrite(((test(X0) & test(X1)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))))),
% 91.93/92.17 inference(bind,[status(th)],[])).
% 91.93/92.17 tff(154,plain,
% 91.93/92.17 (![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 91.93/92.17 inference(quant_intro,[status(thm)],[153])).
% 91.93/92.17 tff(155,axiom,(![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax','test_deMorgan2')).
% 91.93/92.17 tff(156,plain,
% 91.93/92.17 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[155, 154])).
% 91.93/92.17 tff(157,plain,
% 91.93/92.17 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[156, 152])).
% 91.93/92.17 tff(158,plain,(
% 91.93/92.17 ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))))),
% 91.93/92.17 inference(skolemize,[status(sab)],[157])).
% 91.93/92.17 tff(159,plain,
% 91.93/92.17 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[158, 151])).
% 91.93/92.17 tff(160,plain,
% 91.93/92.17 (![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[159, 149])).
% 91.93/92.17 tff(161,plain,
% 91.93/92.17 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(tptp_fun_X1_0(X0!2), X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), c(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(tptp_fun_X1_0(X0!2), X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), c(X0!2))))),
% 91.93/92.17 inference(rewrite,[status(thm)],[])).
% 91.93/92.17 tff(162,plain,
% 91.93/92.17 (((~test(X0!2)) | (c(multiplication(tptp_fun_X1_0(X0!2), X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), c(X0!2))) | (~test(tptp_fun_X1_0(X0!2)))) <=> ((~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(tptp_fun_X1_0(X0!2), X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), c(X0!2))))),
% 91.93/92.17 inference(rewrite,[status(thm)],[])).
% 91.93/92.17 tff(163,plain,
% 91.93/92.17 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(multiplication(tptp_fun_X1_0(X0!2), X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), c(X0!2))) | (~test(tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(tptp_fun_X1_0(X0!2), X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), c(X0!2)))))),
% 91.93/92.17 inference(monotonicity,[status(thm)],[162])).
% 91.93/92.17 tff(164,plain,
% 91.93/92.17 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(multiplication(tptp_fun_X1_0(X0!2), X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), c(X0!2))) | (~test(tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(tptp_fun_X1_0(X0!2), X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), c(X0!2))))),
% 91.93/92.17 inference(transitivity,[status(thm)],[163, 161])).
% 91.93/92.17 tff(165,plain,
% 91.93/92.17 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(multiplication(tptp_fun_X1_0(X0!2), X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), c(X0!2))) | (~test(tptp_fun_X1_0(X0!2))))),
% 91.93/92.17 inference(quant_inst,[status(thm)],[])).
% 91.93/92.17 tff(166,plain,
% 91.93/92.17 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(multiplication(X0, X1)) = addition(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(tptp_fun_X1_0(X0!2), X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), c(X0!2)))),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[165, 164])).
% 91.93/92.17 tff(167,plain,
% 91.93/92.17 ((~test(tptp_fun_X1_0(X0!2))) | (c(multiplication(tptp_fun_X1_0(X0!2), X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), c(X0!2)))),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[166, 160, 41])).
% 91.93/92.17 tff(168,plain,
% 91.93/92.17 (c(multiplication(tptp_fun_X1_0(X0!2), X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), c(X0!2))),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[167, 136])).
% 91.93/92.17 tff(169,plain,
% 91.93/92.17 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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)))),
% 91.93/92.17 inference(quant_inst,[status(thm)],[])).
% 91.93/92.17 tff(170,plain,
% 91.93/92.17 (~(((~(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))),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[169, 68])).
% 91.93/92.17 tff(171,plain,
% 91.93/92.17 ((~![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))))))),
% 91.93/92.17 inference(quant_inst,[status(thm)],[])).
% 91.93/92.17 tff(172,plain,
% 91.93/92.17 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[171, 94])).
% 91.93/92.17 tff(173,plain,
% 91.93/92.17 (((~((~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))),
% 91.93/92.17 inference(tautology,[status(thm)],[])).
% 91.93/92.17 tff(174,plain,
% 91.93/92.17 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[173, 172])).
% 91.93/92.17 tff(175,plain,
% 91.93/92.17 (test(X1!1)),
% 91.93/92.17 inference(and_elim,[status(thm)],[40])).
% 91.93/92.17 tff(176,plain,
% 91.93/92.17 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 91.93/92.17 inference(tautology,[status(thm)],[])).
% 91.93/92.17 tff(177,plain,
% 91.93/92.17 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[176, 175])).
% 91.93/92.17 tff(178,plain,
% 91.93/92.17 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[177, 174])).
% 91.93/92.17 tff(179,plain,
% 91.93/92.17 ((((~(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)))) | (~complement(tptp_fun_X1_0(X1!1), X1!1))),
% 91.93/92.17 inference(tautology,[status(thm)],[])).
% 91.93/92.17 tff(180,plain,
% 91.93/92.17 ((((~(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))))),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[179, 178])).
% 91.93/92.17 tff(181,plain,
% 91.93/92.17 (~((~(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)))),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[180, 170])).
% 91.93/92.17 tff(182,plain,
% 91.93/92.17 (((~(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)),
% 91.93/92.17 inference(tautology,[status(thm)],[])).
% 91.93/92.17 tff(183,plain,
% 91.93/92.17 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[182, 181])).
% 91.93/92.17 tff(184,plain,
% 91.93/92.17 (zero = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 91.93/92.17 inference(symmetry,[status(thm)],[183])).
% 91.93/92.17 tff(185,plain,
% 91.93/92.17 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 91.93/92.17 inference(transitivity,[status(thm)],[113, 184])).
% 91.93/92.17 tff(186,plain,
% 91.93/92.17 (c(multiplication(tptp_fun_X1_0(X0!2), X0!2)) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 91.93/92.17 inference(monotonicity,[status(thm)],[185])).
% 91.93/92.17 tff(187,plain,
% 91.93/92.17 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = c(multiplication(tptp_fun_X1_0(X0!2), X0!2))),
% 91.93/92.17 inference(symmetry,[status(thm)],[186])).
% 91.93/92.17 tff(188,plain,
% 91.93/92.17 (((~(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)),
% 91.93/92.17 inference(tautology,[status(thm)],[])).
% 91.93/92.17 tff(189,plain,
% 91.93/92.17 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[188, 181])).
% 91.93/92.17 tff(190,plain,
% 91.93/92.17 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 91.93/92.17 inference(symmetry,[status(thm)],[189])).
% 91.93/92.17 tff(191,plain,
% 91.93/92.17 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 91.93/92.17 inference(transitivity,[status(thm)],[106, 190])).
% 91.93/92.17 tff(192,plain,
% 91.93/92.17 (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 91.93/92.17 inference(monotonicity,[status(thm)],[191])).
% 91.93/92.17 tff(193,plain,
% 91.93/92.17 (^[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))))),
% 91.93/92.17 inference(bind,[status(th)],[])).
% 91.93/92.17 tff(194,plain,
% 91.93/92.17 (![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)))),
% 91.93/92.17 inference(quant_intro,[status(thm)],[193])).
% 91.93/92.17 tff(195,plain,
% 91.93/92.17 (^[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)))))),
% 91.93/92.17 inference(bind,[status(th)],[])).
% 91.93/92.17 tff(196,plain,
% 91.93/92.17 (![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)))),
% 91.93/92.17 inference(quant_intro,[status(thm)],[195])).
% 91.93/92.17 tff(197,plain,
% 91.93/92.17 (![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))))),
% 91.93/92.17 inference(rewrite,[status(thm)],[])).
% 91.93/92.17 tff(198,plain,
% 91.93/92.17 (^[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)))))),
% 91.93/92.17 inference(bind,[status(th)],[])).
% 91.93/92.17 tff(199,plain,
% 91.93/92.17 (![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))))),
% 91.93/92.17 inference(quant_intro,[status(thm)],[198])).
% 91.93/92.17 tff(200,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')).
% 91.93/92.17 tff(201,plain,
% 91.93/92.17 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[200, 199])).
% 91.93/92.17 tff(202,plain,
% 91.93/92.17 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[201, 197])).
% 91.93/92.17 tff(203,plain,(
% 91.93/92.17 ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 91.93/92.17 inference(skolemize,[status(sab)],[202])).
% 91.93/92.17 tff(204,plain,
% 91.93/92.17 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[203, 196])).
% 91.93/92.17 tff(205,plain,
% 91.93/92.17 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[204, 194])).
% 91.93/92.17 tff(206,plain,
% 91.93/92.17 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))))),
% 91.93/92.17 inference(rewrite,[status(thm)],[])).
% 91.93/92.17 tff(207,plain,
% 91.93/92.17 (((~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))) | (~test(X0!2))) <=> ((~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))))),
% 91.93/92.17 inference(rewrite,[status(thm)],[])).
% 91.93/92.17 tff(208,plain,
% 91.93/92.17 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))) | (~test(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2))))))),
% 91.93/92.17 inference(monotonicity,[status(thm)],[207])).
% 91.93/92.17 tff(209,plain,
% 91.93/92.17 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))) | (~test(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))))),
% 91.93/92.17 inference(transitivity,[status(thm)],[208, 206])).
% 91.93/92.17 tff(210,plain,
% 91.93/92.17 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))) | (~test(X0!2)))),
% 91.93/92.17 inference(quant_inst,[status(thm)],[])).
% 91.93/92.17 tff(211,plain,
% 91.93/92.17 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[210, 209])).
% 91.93/92.17 tff(212,plain,
% 91.93/92.17 ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[211, 205, 41])).
% 91.93/92.17 tff(213,plain,
% 91.93/92.17 (c(addition(X0!2, tptp_fun_X1_0(X0!2))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[212, 136])).
% 91.93/92.17 tff(214,plain,
% 91.93/92.17 (multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2))) = c(addition(X0!2, tptp_fun_X1_0(X0!2)))),
% 91.93/92.17 inference(symmetry,[status(thm)],[213])).
% 91.93/92.17 tff(215,plain,
% 91.93/92.17 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 91.93/92.17 inference(monotonicity,[status(thm)],[123, 145])).
% 91.93/92.17 tff(216,plain,
% 91.93/92.17 (zero = multiplication(tptp_fun_X1_0(X0!2), X0!2)),
% 91.93/92.17 inference(symmetry,[status(thm)],[113])).
% 91.93/92.17 tff(217,plain,
% 91.93/92.17 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = c(addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 91.93/92.17 inference(transitivity,[status(thm)],[183, 216, 215, 214, 192])).
% 91.93/92.17 tff(218,plain,
% 91.93/92.17 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = c(c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.17 inference(monotonicity,[status(thm)],[217])).
% 91.93/92.17 tff(219,plain,
% 91.93/92.17 (c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 91.93/92.17 inference(symmetry,[status(thm)],[218])).
% 91.93/92.17 tff(220,assumption,(~test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))), introduced(assumption)).
% 91.93/92.17 tff(221,plain,
% 91.93/92.17 (^[X0: $i] : refl((test(X0) | (c(X0) = zero)) <=> (test(X0) | (c(X0) = zero)))),
% 91.93/92.17 inference(bind,[status(th)],[])).
% 91.93/92.17 tff(222,plain,
% 91.93/92.17 (![X0: $i] : (test(X0) | (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 91.93/92.17 inference(quant_intro,[status(thm)],[221])).
% 91.93/92.17 tff(223,plain,
% 91.93/92.17 (![X0: $i] : (test(X0) | (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 91.93/92.17 inference(rewrite,[status(thm)],[])).
% 91.93/92.17 tff(224,plain,
% 91.93/92.17 (^[X0: $i] : rewrite(((~test(X0)) => (c(X0) = zero)) <=> (test(X0) | (c(X0) = zero)))),
% 91.93/92.17 inference(bind,[status(th)],[])).
% 91.93/92.17 tff(225,plain,
% 91.93/92.17 (![X0: $i] : ((~test(X0)) => (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 91.93/92.17 inference(quant_intro,[status(thm)],[224])).
% 91.93/92.17 tff(226,axiom,(![X0: $i] : ((~test(X0)) => (c(X0) = zero))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_4')).
% 91.93/92.17 tff(227,plain,
% 91.93/92.17 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[226, 225])).
% 91.93/92.17 tff(228,plain,
% 91.93/92.17 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[227, 223])).
% 91.93/92.17 tff(229,plain,(
% 91.93/92.17 ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 91.93/92.17 inference(skolemize,[status(sab)],[228])).
% 91.93/92.17 tff(230,plain,
% 91.93/92.17 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[229, 222])).
% 91.93/92.17 tff(231,plain,
% 91.93/92.17 (((~![X0: $i] : (test(X0) | (c(X0) = zero))) | (test(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) | (c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero))) <=> ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | test(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) | (c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero))),
% 91.93/92.17 inference(rewrite,[status(thm)],[])).
% 91.93/92.17 tff(232,plain,
% 91.93/92.17 ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | (test(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) | (c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero))),
% 91.93/92.17 inference(quant_inst,[status(thm)],[])).
% 91.93/92.17 tff(233,plain,
% 91.93/92.17 ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | test(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) | (c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[232, 231])).
% 91.93/92.17 tff(234,plain,
% 91.93/92.17 (test(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) | (c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[233, 230])).
% 91.93/92.17 tff(235,plain,
% 91.93/92.17 (c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[234, 220])).
% 91.93/92.17 tff(236,plain,
% 91.93/92.17 (zero = c(c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.17 inference(symmetry,[status(thm)],[235])).
% 91.93/92.17 tff(237,plain,
% 91.93/92.17 (multiplication(c(X0!2), c(tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), X0!2)),
% 91.93/92.17 inference(symmetry,[status(thm)],[215])).
% 91.93/92.17 tff(238,plain,
% 91.93/92.17 (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = c(addition(X0!2, tptp_fun_X1_0(X0!2)))),
% 91.93/92.17 inference(symmetry,[status(thm)],[192])).
% 91.93/92.17 tff(239,plain,
% 91.93/92.17 (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 91.93/92.17 inference(transitivity,[status(thm)],[238, 213, 237, 113, 236, 219, 187, 168, 147, 31])).
% 91.93/92.17 tff(240,plain,
% 91.93/92.17 (addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), X0!2) = addition(addition(tptp_fun_X1_0(X0!2), X0!2), X0!2)),
% 91.93/92.17 inference(monotonicity,[status(thm)],[239])).
% 91.93/92.17 tff(241,plain,
% 91.93/92.17 (addition(addition(tptp_fun_X1_0(X0!2), X0!2), X0!2) = addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), X0!2)),
% 91.93/92.17 inference(symmetry,[status(thm)],[240])).
% 91.93/92.17 tff(242,plain,
% 91.93/92.17 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X0!2), addition(X0!2, X0!2)) = addition(addition(tptp_fun_X1_0(X0!2), X0!2), X0!2))),
% 91.93/92.17 inference(quant_inst,[status(thm)],[])).
% 91.93/92.17 tff(243,plain,
% 91.93/92.17 (addition(tptp_fun_X1_0(X0!2), addition(X0!2, X0!2)) = addition(addition(tptp_fun_X1_0(X0!2), X0!2), X0!2)),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[242, 7])).
% 91.93/92.17 tff(244,plain,
% 91.93/92.17 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 91.93/92.17 inference(bind,[status(th)],[])).
% 91.93/92.17 tff(245,plain,
% 91.93/92.17 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 91.93/92.17 inference(quant_intro,[status(thm)],[244])).
% 91.93/92.17 tff(246,plain,
% 91.93/92.17 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 91.93/92.17 inference(rewrite,[status(thm)],[])).
% 91.93/92.17 tff(247,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 91.93/92.17 tff(248,plain,
% 91.93/92.17 (![A: $i] : (addition(A, A) = A)),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[247, 246])).
% 91.93/92.17 tff(249,plain,(
% 91.93/92.17 ![A: $i] : (addition(A, A) = A)),
% 91.93/92.17 inference(skolemize,[status(sab)],[248])).
% 91.93/92.17 tff(250,plain,
% 91.93/92.17 (![A: $i] : (addition(A, A) = A)),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[249, 245])).
% 91.93/92.17 tff(251,plain,
% 91.93/92.17 ((~![A: $i] : (addition(A, A) = A)) | (addition(X0!2, X0!2) = X0!2)),
% 91.93/92.17 inference(quant_inst,[status(thm)],[])).
% 91.93/92.17 tff(252,plain,
% 91.93/92.17 (addition(X0!2, X0!2) = X0!2),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[251, 250])).
% 91.93/92.17 tff(253,plain,
% 91.93/92.17 (addition(tptp_fun_X1_0(X0!2), addition(X0!2, X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 91.93/92.17 inference(monotonicity,[status(thm)],[252])).
% 91.93/92.17 tff(254,plain,
% 91.93/92.17 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(tptp_fun_X1_0(X0!2), addition(X0!2, X0!2))),
% 91.93/92.17 inference(symmetry,[status(thm)],[253])).
% 91.93/92.17 tff(255,plain,
% 91.93/92.17 (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = addition(X0!2, c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.17 inference(transitivity,[status(thm)],[238, 213, 237, 113, 236, 219, 187, 168, 147, 31, 254, 243, 241, 29])).
% 91.93/92.17 tff(256,plain,
% 91.93/92.17 (test(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) <=> test(addition(X0!2, c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.17 inference(monotonicity,[status(thm)],[255])).
% 91.93/92.17 tff(257,plain,
% 91.93/92.17 (test(addition(X0!2, c(addition(X1!1, tptp_fun_X1_0(X1!1))))) <=> test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.17 inference(symmetry,[status(thm)],[256])).
% 91.93/92.17 tff(258,plain,
% 91.93/92.17 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 91.93/92.17 inference(bind,[status(th)],[])).
% 91.93/92.17 tff(259,plain,
% 91.93/92.17 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 91.93/92.17 inference(quant_intro,[status(thm)],[258])).
% 91.93/92.17 tff(260,plain,
% 91.93/92.17 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 91.93/92.17 inference(rewrite,[status(thm)],[])).
% 91.93/92.17 tff(261,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 91.93/92.17 tff(262,plain,
% 91.93/92.17 (![A: $i] : (addition(A, zero) = A)),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[261, 260])).
% 91.93/92.17 tff(263,plain,(
% 91.93/92.17 ![A: $i] : (addition(A, zero) = A)),
% 91.93/92.17 inference(skolemize,[status(sab)],[262])).
% 91.93/92.17 tff(264,plain,
% 91.93/92.17 (![A: $i] : (addition(A, zero) = A)),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[263, 259])).
% 91.93/92.17 tff(265,plain,
% 91.93/92.17 ((~![A: $i] : (addition(A, zero) = A)) | (addition(X0!2, zero) = X0!2)),
% 91.93/92.17 inference(quant_inst,[status(thm)],[])).
% 91.93/92.17 tff(266,plain,
% 91.93/92.17 (addition(X0!2, zero) = X0!2),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[265, 264])).
% 91.93/92.17 tff(267,plain,
% 91.93/92.17 (zero = c(addition(X1!1, tptp_fun_X1_0(X1!1)))),
% 91.93/92.17 inference(transitivity,[status(thm)],[216, 215, 214, 192])).
% 91.93/92.17 tff(268,plain,
% 91.93/92.17 (addition(X0!2, zero) = addition(X0!2, c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.17 inference(monotonicity,[status(thm)],[267])).
% 91.93/92.17 tff(269,plain,
% 91.93/92.17 (addition(X0!2, c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(X0!2, zero)),
% 91.93/92.17 inference(symmetry,[status(thm)],[268])).
% 91.93/92.17 tff(270,plain,
% 91.93/92.17 (addition(X0!2, c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = X0!2),
% 91.93/92.17 inference(transitivity,[status(thm)],[269, 266])).
% 91.93/92.17 tff(271,plain,
% 91.93/92.17 (test(addition(X0!2, c(addition(X1!1, tptp_fun_X1_0(X1!1))))) <=> test(X0!2)),
% 91.93/92.17 inference(monotonicity,[status(thm)],[270])).
% 91.93/92.17 tff(272,plain,
% 91.93/92.17 (test(X0!2) <=> test(addition(X0!2, c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.17 inference(symmetry,[status(thm)],[271])).
% 91.93/92.17 tff(273,plain,
% 91.93/92.17 (test(addition(X0!2, c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[41, 272])).
% 91.93/92.17 tff(274,plain,
% 91.93/92.17 (test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.17 inference(modus_ponens,[status(thm)],[273, 257])).
% 91.93/92.17 tff(275,plain,
% 91.93/92.17 ($false),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[220, 274])).
% 91.93/92.17 tff(276,plain,(test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))), inference(lemma,lemma(discharge,[]))).
% 91.93/92.17 tff(277,plain,
% 91.93/92.17 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = one))) <=> complement(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))))),
% 91.93/92.17 inference(quant_inst,[status(thm)],[])).
% 91.93/92.17 tff(278,plain,
% 91.93/92.17 (~(((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = one))) <=> complement(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 91.93/92.17 inference(unit_resolution,[status(thm)],[277, 68])).
% 91.93/92.17 tff(279,plain,
% 91.93/92.17 ((addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) <=> (addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.17 inference(commutativity,[status(thm)],[])).
% 91.93/92.17 tff(280,plain,
% 91.93/92.17 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))))),
% 91.93/92.17 inference(rewrite,[status(thm)],[])).
% 91.93/92.17 tff(281,plain,
% 91.93/92.17 ((~(((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) <=> (~(((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 91.93/92.17 inference(rewrite,[status(thm)],[])).
% 91.93/92.17 tff(282,plain,
% 91.93/92.17 ((((~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) <=> (((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.17 inference(rewrite,[status(thm)],[])).
% 91.93/92.17 tff(283,plain,
% 91.93/92.17 ((~(((~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) <=> (~(((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 91.93/92.17 inference(monotonicity,[status(thm)],[282])).
% 91.93/92.17 tff(284,plain,
% 91.93/92.17 ((~(((~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) <=> (~(((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 91.93/92.17 inference(transitivity,[status(thm)],[283, 281])).
% 91.93/92.17 tff(285,plain,
% 91.93/92.17 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))))),
% 91.93/92.18 inference(monotonicity,[status(thm)],[284])).
% 91.93/92.18 tff(286,plain,
% 91.93/92.18 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))))),
% 91.93/92.18 inference(transitivity,[status(thm)],[285, 280])).
% 91.93/92.18 tff(287,plain,
% 91.93/92.18 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 91.93/92.18 inference(quant_inst,[status(thm)],[])).
% 91.93/92.18 tff(288,plain,
% 91.93/92.18 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 91.93/92.18 inference(modus_ponens,[status(thm)],[287, 286])).
% 91.93/92.18 tff(289,plain,
% 91.93/92.18 (~(((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[288, 68])).
% 91.93/92.18 tff(290,plain,
% 91.93/92.18 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) | (~(test(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) | ![X1: $i] : (~complement(X1, c(addition(X1!1, tptp_fun_X1_0(X1!1)))))))))),
% 91.93/92.18 inference(quant_inst,[status(thm)],[])).
% 91.93/92.18 tff(291,plain,
% 91.93/92.18 (~((~((~test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) | (~(test(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) | ![X1: $i] : (~complement(X1, c(addition(X1!1, tptp_fun_X1_0(X1!1))))))))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[290, 94])).
% 91.93/92.18 tff(292,plain,
% 91.93/92.18 (((~((~test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) | (~(test(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) | ![X1: $i] : (~complement(X1, c(addition(X1!1, tptp_fun_X1_0(X1!1)))))))) | ((~test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.18 inference(tautology,[status(thm)],[])).
% 91.93/92.18 tff(293,plain,
% 91.93/92.18 ((~test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[292, 291])).
% 91.93/92.18 tff(294,assumption,(test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))), introduced(assumption)).
% 91.93/92.18 tff(295,plain,
% 91.93/92.18 ((~((~test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) | (~test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.18 inference(tautology,[status(thm)],[])).
% 91.93/92.18 tff(296,plain,
% 91.93/92.18 ((~((~test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) | complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[295, 294])).
% 91.93/92.18 tff(297,plain,
% 91.93/92.18 (complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[296, 293])).
% 91.93/92.18 tff(298,plain,
% 91.93/92.18 ((((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | (~((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one)))) | (~complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.18 inference(tautology,[status(thm)],[])).
% 91.93/92.18 tff(299,plain,
% 91.93/92.18 ((((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) <=> complement(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | (~((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[298, 297])).
% 91.93/92.18 tff(300,plain,
% 91.93/92.18 (~((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one)))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[299, 289])).
% 91.93/92.18 tff(301,plain,
% 91.93/92.18 (((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) | (addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one)),
% 91.93/92.18 inference(tautology,[status(thm)],[])).
% 91.93/92.18 tff(302,plain,
% 91.93/92.18 (addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[301, 300])).
% 91.93/92.18 tff(303,plain,
% 91.93/92.18 (one = addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.18 inference(symmetry,[status(thm)],[302])).
% 91.93/92.18 tff(304,plain,
% 91.93/92.18 ((addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = one) <=> (addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 91.93/92.18 inference(monotonicity,[status(thm)],[303])).
% 91.93/92.18 tff(305,plain,
% 91.93/92.18 ((addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = one) <=> (addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.18 inference(transitivity,[status(thm)],[304, 279])).
% 91.93/92.18 tff(306,plain,
% 91.93/92.18 ((addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))) <=> (addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = one)),
% 91.93/92.18 inference(symmetry,[status(thm)],[305])).
% 91.93/92.18 tff(307,plain,
% 91.93/92.18 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.18 inference(quant_inst,[status(thm)],[])).
% 91.93/92.18 tff(308,plain,
% 91.93/92.18 (addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[307, 16])).
% 91.93/92.18 tff(309,plain,
% 91.93/92.18 (addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = one),
% 91.93/92.18 inference(modus_ponens,[status(thm)],[308, 306])).
% 91.93/92.18 tff(310,plain,
% 91.93/92.18 (((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) | (multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)),
% 91.93/92.18 inference(tautology,[status(thm)],[])).
% 91.93/92.18 tff(311,plain,
% 91.93/92.18 (multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[310, 300])).
% 91.93/92.18 tff(312,plain,
% 91.93/92.18 (((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = one))) | (multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)),
% 91.93/92.18 inference(tautology,[status(thm)],[])).
% 91.93/92.18 tff(313,plain,
% 91.93/92.18 (multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[312, 300])).
% 91.93/92.18 tff(314,plain,
% 91.93/92.18 ((~((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = one)))) | (~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = one))),
% 91.93/92.18 inference(tautology,[status(thm)],[])).
% 91.93/92.18 tff(315,plain,
% 91.93/92.18 ((~((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = one)))) | (~(addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = one))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[314, 313, 311])).
% 91.93/92.18 tff(316,plain,
% 91.93/92.18 (~((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = one)))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[315, 309])).
% 91.93/92.18 tff(317,plain,
% 91.93/92.18 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | ((c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) <=> complement(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | ((c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) <=> complement(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))))),
% 91.93/92.18 inference(rewrite,[status(thm)],[])).
% 91.93/92.18 tff(318,plain,
% 91.93/92.18 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | ((c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) <=> complement(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))))),
% 91.93/92.18 inference(quant_inst,[status(thm)],[])).
% 91.93/92.18 tff(319,plain,
% 91.93/92.18 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | ((c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) <=> complement(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 91.93/92.18 inference(modus_ponens,[status(thm)],[318, 317])).
% 91.93/92.18 tff(320,plain,
% 91.93/92.18 ((c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) <=> complement(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[319, 51, 294])).
% 91.93/92.18 tff(321,assumption,(~(c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))), introduced(assumption)).
% 91.93/92.18 tff(322,plain,
% 91.93/92.18 ((~((c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) <=> complement(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))))) | (c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | (~complement(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 91.93/92.18 inference(tautology,[status(thm)],[])).
% 91.93/92.18 tff(323,plain,
% 91.93/92.18 ((~((c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) <=> complement(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))))) | (~complement(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[322, 321])).
% 91.93/92.18 tff(324,plain,
% 91.93/92.18 (~complement(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[323, 320])).
% 91.93/92.18 tff(325,plain,
% 91.93/92.18 ((((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = one))) <=> complement(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) | ((~(multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = zero)) | (~(multiplication(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = zero)) | (~(addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = one))) | complement(c(addition(X1!1, tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.18 inference(tautology,[status(thm)],[])).
% 91.93/92.18 tff(326,plain,
% 91.93/92.18 ($false),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[325, 324, 316, 278])).
% 91.93/92.18 tff(327,plain,((~test(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) | (c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))), inference(lemma,lemma(discharge,[]))).
% 91.93/92.18 tff(328,plain,
% 91.93/92.18 (c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[327, 276])).
% 91.93/92.18 tff(329,plain,
% 91.93/92.18 (c(addition(X1!1, tptp_fun_X1_0(X1!1))) = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 91.93/92.18 inference(transitivity,[status(thm)],[238, 213, 237, 113, 184])).
% 91.93/92.18 tff(330,plain,
% 91.93/92.18 (c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 91.93/92.18 inference(monotonicity,[status(thm)],[329])).
% 91.93/92.18 tff(331,plain,
% 91.93/92.18 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = c(c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.18 inference(symmetry,[status(thm)],[330])).
% 91.93/92.18 tff(332,plain,
% 91.93/92.18 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = multiplication(tptp_fun_X1_0(X0!2), X0!2)),
% 91.93/92.18 inference(transitivity,[status(thm)],[183, 216])).
% 91.93/92.18 tff(333,plain,
% 91.93/92.18 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = c(multiplication(tptp_fun_X1_0(X0!2), X0!2))),
% 91.93/92.18 inference(monotonicity,[status(thm)],[332])).
% 91.93/92.18 tff(334,plain,
% 91.93/92.18 (c(multiplication(tptp_fun_X1_0(X0!2), X0!2)) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 91.93/92.18 inference(symmetry,[status(thm)],[333])).
% 91.93/92.18 tff(335,plain,
% 91.93/92.18 (addition(c(tptp_fun_X1_0(X0!2)), c(X0!2)) = c(multiplication(tptp_fun_X1_0(X0!2), X0!2))),
% 91.93/92.18 inference(symmetry,[status(thm)],[168])).
% 91.93/92.18 tff(336,plain,
% 91.93/92.18 (addition(c(tptp_fun_X1_0(X0!2)), c(X0!2)) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 91.93/92.18 inference(monotonicity,[status(thm)],[144, 122])).
% 91.93/92.18 tff(337,plain,
% 91.93/92.18 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), c(X0!2))),
% 91.93/92.18 inference(symmetry,[status(thm)],[336])).
% 91.93/92.18 tff(338,plain,
% 91.93/92.18 ((~![A: $i] : (addition(A, A) = A)) | (addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 91.93/92.18 inference(quant_inst,[status(thm)],[])).
% 91.93/92.18 tff(339,plain,
% 91.93/92.18 (addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[338, 250])).
% 91.93/92.18 tff(340,assumption,(c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))), introduced(assumption)).
% 91.93/92.18 tff(341,plain,
% 91.93/92.18 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.18 inference(transitivity,[status(thm)],[331, 340])).
% 91.93/92.18 tff(342,plain,
% 91.93/92.18 (addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.18 inference(monotonicity,[status(thm)],[341, 341])).
% 91.93/92.18 tff(343,plain,
% 91.93/92.18 (addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 91.93/92.18 inference(symmetry,[status(thm)],[342])).
% 91.93/92.18 tff(344,plain,
% 91.93/92.18 (tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.18 inference(symmetry,[status(thm)],[340])).
% 91.93/92.18 tff(345,plain,
% 91.93/92.18 (tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 91.93/92.18 inference(transitivity,[status(thm)],[344, 330, 187, 168, 147])).
% 91.93/92.18 tff(346,plain,
% 91.93/92.18 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), X0!2) = multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), X0!2)),
% 91.93/92.18 inference(monotonicity,[status(thm)],[341])).
% 91.93/92.18 tff(347,plain,
% 91.93/92.18 (multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), X0!2) = multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), X0!2)),
% 91.93/92.18 inference(symmetry,[status(thm)],[346])).
% 91.93/92.18 tff(348,plain,
% 91.93/92.18 ((~![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))),
% 91.93/92.18 inference(quant_inst,[status(thm)],[])).
% 91.93/92.18 tff(349,plain,
% 91.93/92.18 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[348, 16])).
% 91.93/92.18 tff(350,plain,
% 91.93/92.18 (addition(tptp_fun_X1_0(X1!1), X1!1) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 91.93/92.18 inference(symmetry,[status(thm)],[349])).
% 91.93/92.18 tff(351,plain,
% 91.93/92.18 (addition(tptp_fun_X1_0(X1!1), X1!1) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.18 inference(transitivity,[status(thm)],[350, 189, 107, 146, 335, 186, 331, 340])).
% 91.93/92.18 tff(352,plain,
% 91.93/92.18 (multiplication(addition(tptp_fun_X1_0(X1!1), X1!1), X0!2) = multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), X0!2)),
% 91.93/92.18 inference(monotonicity,[status(thm)],[351])).
% 91.93/92.18 tff(353,plain,
% 91.93/92.18 (^[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))))),
% 91.93/92.18 inference(bind,[status(th)],[])).
% 91.93/92.18 tff(354,plain,
% 91.93/92.18 (![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)))),
% 91.93/92.18 inference(quant_intro,[status(thm)],[353])).
% 91.93/92.18 tff(355,plain,
% 91.93/92.18 (![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)))),
% 91.93/92.18 inference(rewrite,[status(thm)],[])).
% 91.93/92.18 tff(356,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')).
% 91.93/92.18 tff(357,plain,
% 91.93/92.18 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 91.93/92.18 inference(modus_ponens,[status(thm)],[356, 355])).
% 91.93/92.18 tff(358,plain,(
% 91.93/92.18 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 91.93/92.18 inference(skolemize,[status(sab)],[357])).
% 91.93/92.18 tff(359,plain,
% 91.93/92.18 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 91.93/92.18 inference(modus_ponens,[status(thm)],[358, 354])).
% 91.93/92.18 tff(360,plain,
% 91.93/92.18 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X1!1), X1!1), X0!2) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 91.93/92.18 inference(quant_inst,[status(thm)],[])).
% 91.93/92.18 tff(361,plain,
% 91.93/92.18 (multiplication(addition(tptp_fun_X1_0(X1!1), X1!1), X0!2) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[360, 359])).
% 91.93/92.18 tff(362,plain,
% 91.93/92.18 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2)) = multiplication(addition(tptp_fun_X1_0(X1!1), X1!1), X0!2)),
% 91.93/92.18 inference(symmetry,[status(thm)],[361])).
% 91.93/92.18 tff(363,assumption,((~((~test(tptp_fun_X1_0(X1!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))) | (~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))))), introduced(assumption)).
% 91.93/92.18 tff(364,plain,
% 91.93/92.18 ((~![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))) | (~((~((~test(tptp_fun_X1_0(X1!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))) | (~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))))))),
% 91.93/92.18 inference(quant_inst,[status(thm)],[])).
% 91.93/92.18 tff(365,plain,
% 91.93/92.18 ($false),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[364, 94, 363])).
% 91.93/92.18 tff(366,plain,(~((~((~test(tptp_fun_X1_0(X1!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))) | (~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))))), inference(lemma,lemma(discharge,[]))).
% 91.93/92.18 tff(367,plain,
% 91.93/92.18 (((~((~test(tptp_fun_X1_0(X1!1))) | complement(tptp_fun_X1_0(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))) | (~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))))) | (test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.18 inference(tautology,[status(thm)],[])).
% 91.93/92.18 tff(368,plain,
% 91.93/92.18 (test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))),
% 91.93/92.18 inference(unit_resolution,[status(thm)],[367, 366])).
% 91.93/92.18 tff(369,assumption,(![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))), introduced(assumption)).
% 91.93/92.18 tff(370,plain,
% 91.93/92.18 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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)))))),
% 91.93/92.18 inference(rewrite,[status(thm)],[])).
% 91.93/92.18 tff(371,plain,
% 91.93/92.18 ((~(((~(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))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.18 inference(rewrite,[status(thm)],[])).
% 91.93/92.18 tff(372,plain,
% 91.93/92.18 ((((~(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))) <=> complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 91.93/92.18 inference(rewrite,[status(thm)],[])).
% 91.93/92.18 tff(373,plain,
% 91.93/92.18 ((~(((~(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))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.18 inference(monotonicity,[status(thm)],[372])).
% 91.93/92.18 tff(374,plain,
% 91.93/92.18 ((~(((~(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))) <=> complement(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.18 inference(transitivity,[status(thm)],[373, 371])).
% 91.93/92.18 tff(375,plain,
% 91.93/92.18 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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)))))),
% 91.93/92.18 inference(monotonicity,[status(thm)],[374])).
% 91.93/92.18 tff(376,plain,
% 91.93/92.18 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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)))))),
% 91.93/92.18 inference(transitivity,[status(thm)],[375, 370])).
% 91.93/92.18 tff(377,plain,
% 91.93/92.18 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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))))),
% 91.93/92.19 inference(quant_inst,[status(thm)],[])).
% 91.93/92.19 tff(378,plain,
% 91.93/92.19 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(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))))),
% 91.93/92.19 inference(modus_ponens,[status(thm)],[377, 376])).
% 91.93/92.19 tff(379,plain,
% 91.93/92.19 (~(((~(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)))),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[378, 68])).
% 91.93/92.19 tff(380,plain,
% 91.93/92.19 ((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))),
% 91.93/92.19 inference(commutativity,[status(thm)],[])).
% 91.93/92.19 tff(381,plain,
% 91.93/92.19 ((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)))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[190])).
% 91.93/92.19 tff(382,plain,
% 91.93/92.19 ((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))),
% 91.93/92.19 inference(transitivity,[status(thm)],[381, 380])).
% 91.93/92.19 tff(383,plain,
% 91.93/92.19 ((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)),
% 91.93/92.19 inference(symmetry,[status(thm)],[382])).
% 91.93/92.19 tff(384,plain,
% 91.93/92.19 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 91.93/92.19 inference(modus_ponens,[status(thm)],[349, 383])).
% 91.93/92.19 tff(385,plain,
% 91.93/92.19 (((~(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)),
% 91.93/92.19 inference(tautology,[status(thm)],[])).
% 91.93/92.19 tff(386,plain,
% 91.93/92.19 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[385, 181])).
% 91.93/92.19 tff(387,plain,
% 91.93/92.19 ((~((~(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))),
% 91.93/92.19 inference(tautology,[status(thm)],[])).
% 91.93/92.19 tff(388,plain,
% 91.93/92.19 ((~((~(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))),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[387, 386, 183])).
% 91.93/92.19 tff(389,plain,
% 91.93/92.19 (~((~(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)))),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[388, 384])).
% 91.93/92.19 tff(390,plain,
% 91.93/92.19 ((((~(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))) | complement(X1!1, tptp_fun_X1_0(X1!1))),
% 91.93/92.19 inference(tautology,[status(thm)],[])).
% 91.93/92.19 tff(391,plain,
% 91.93/92.19 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[390, 389, 379])).
% 91.93/92.19 tff(392,plain,
% 91.93/92.19 ((~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))) | (~complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 91.93/92.19 inference(quant_inst,[status(thm)],[])).
% 91.93/92.19 tff(393,plain,
% 91.93/92.19 ($false),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[392, 391, 369])).
% 91.93/92.19 tff(394,plain,(~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))), inference(lemma,lemma(discharge,[]))).
% 91.93/92.19 tff(395,plain,
% 91.93/92.19 ((~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))) | test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))),
% 91.93/92.19 inference(tautology,[status(thm)],[])).
% 91.93/92.19 tff(396,plain,
% 91.93/92.19 ((~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))) | test(tptp_fun_X1_0(X1!1))),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[395, 394])).
% 91.93/92.19 tff(397,plain,
% 91.93/92.19 (test(tptp_fun_X1_0(X1!1))),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[396, 368])).
% 91.93/92.19 tff(398,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)))),
% 91.93/92.19 inference(rewrite,[status(thm)],[])).
% 91.93/92.19 tff(399,plain,
% 91.93/92.19 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)))),
% 91.93/92.19 inference(quant_inst,[status(thm)],[])).
% 91.93/92.19 tff(400,plain,
% 91.93/92.19 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1))),
% 91.93/92.19 inference(modus_ponens,[status(thm)],[399, 398])).
% 91.93/92.19 tff(401,plain,
% 91.93/92.19 ((~test(tptp_fun_X1_0(X1!1))) | ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1))),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[400, 51])).
% 91.93/92.19 tff(402,plain,
% 91.93/92.19 ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[401, 397])).
% 91.93/92.19 tff(403,plain,
% 91.93/92.19 ((~((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1))) | (c(tptp_fun_X1_0(X1!1)) = X1!1) | (~complement(tptp_fun_X1_0(X1!1), X1!1))),
% 91.93/92.19 inference(tautology,[status(thm)],[])).
% 91.93/92.19 tff(404,plain,
% 91.93/92.19 ((~((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1))) | (c(tptp_fun_X1_0(X1!1)) = X1!1)),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[403, 178])).
% 91.93/92.19 tff(405,plain,
% 91.93/92.19 (c(tptp_fun_X1_0(X1!1)) = X1!1),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[404, 402])).
% 91.93/92.19 tff(406,plain,
% 91.93/92.19 (X1!1 = c(tptp_fun_X1_0(X1!1))),
% 91.93/92.19 inference(symmetry,[status(thm)],[405])).
% 91.93/92.19 tff(407,plain,
% 91.93/92.19 (multiplication(X1!1, X0!2) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[406, 145])).
% 91.93/92.19 tff(408,plain,
% 91.93/92.19 (multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))) = multiplication(X1!1, X0!2)),
% 91.93/92.19 inference(symmetry,[status(thm)],[407])).
% 91.93/92.19 tff(409,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X1!1))) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))))),
% 91.93/92.19 inference(rewrite,[status(thm)],[])).
% 91.93/92.19 tff(410,plain,
% 91.93/92.19 (((~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) | (~test(tptp_fun_X1_0(X1!1)))) <=> ((~test(tptp_fun_X1_0(X1!1))) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))))),
% 91.93/92.19 inference(rewrite,[status(thm)],[])).
% 91.93/92.19 tff(411,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) | (~test(tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[410])).
% 91.93/92.19 tff(412,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) | (~test(tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X1!1))) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))))),
% 91.93/92.19 inference(transitivity,[status(thm)],[411, 409])).
% 91.93/92.19 tff(413,plain,
% 91.93/92.19 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))) | (~test(tptp_fun_X1_0(X1!1))))),
% 91.93/92.19 inference(quant_inst,[status(thm)],[])).
% 91.93/92.19 tff(414,plain,
% 91.93/92.19 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X1!1))) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2))))),
% 91.93/92.19 inference(modus_ponens,[status(thm)],[413, 412])).
% 91.93/92.19 tff(415,plain,
% 91.93/92.19 (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), c(tptp_fun_X1_0(X0!2)))),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[414, 205, 397, 136])).
% 91.93/92.19 tff(416,plain,
% 91.93/92.19 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 91.93/92.19 inference(quant_inst,[status(thm)],[])).
% 91.93/92.19 tff(417,plain,
% 91.93/92.19 (addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[416, 16])).
% 91.93/92.19 tff(418,plain,
% 91.93/92.19 (addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 91.93/92.19 inference(symmetry,[status(thm)],[417])).
% 91.93/92.19 tff(419,plain,
% 91.93/92.19 (c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[418])).
% 91.93/92.19 tff(420,plain,
% 91.93/92.19 (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = c(addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 91.93/92.19 inference(symmetry,[status(thm)],[419])).
% 91.93/92.19 tff(421,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X1!1))) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 91.93/92.19 inference(rewrite,[status(thm)],[])).
% 91.93/92.19 tff(422,plain,
% 91.93/92.19 (((~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) | (~test(tptp_fun_X1_0(X0!2)))) <=> ((~test(tptp_fun_X1_0(X1!1))) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 91.93/92.19 inference(rewrite,[status(thm)],[])).
% 91.93/92.19 tff(423,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) | (~test(tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[422])).
% 91.93/92.19 tff(424,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) | (~test(tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X1!1))) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 91.93/92.19 inference(transitivity,[status(thm)],[423, 421])).
% 91.93/92.19 tff(425,plain,
% 91.93/92.19 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) | (~test(tptp_fun_X1_0(X0!2))))),
% 91.93/92.19 inference(quant_inst,[status(thm)],[])).
% 91.93/92.19 tff(426,plain,
% 91.93/92.19 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(tptp_fun_X1_0(X1!1))) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))),
% 91.93/92.19 inference(modus_ponens,[status(thm)],[425, 424])).
% 91.93/92.19 tff(427,plain,
% 91.93/92.19 (c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[426, 205, 397, 136])).
% 91.93/92.19 tff(428,plain,
% 91.93/92.19 (multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))) = c(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 91.93/92.19 inference(symmetry,[status(thm)],[427])).
% 91.93/92.19 tff(429,plain,
% 91.93/92.19 (multiplication(X0!2, X1!1) = multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[145, 406])).
% 91.93/92.19 tff(430,plain,
% 91.93/92.19 (multiplication(X0!2, X1!1) = multiplication(X1!1, X0!2)),
% 91.93/92.19 inference(transitivity,[status(thm)],[429, 428, 420, 415, 408])).
% 91.93/92.19 tff(431,plain,
% 91.93/92.19 (((~![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))))),
% 91.93/92.19 inference(rewrite,[status(thm)],[])).
% 91.93/92.19 tff(432,plain,
% 91.93/92.19 ((~![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))))),
% 91.93/92.19 inference(quant_inst,[status(thm)],[])).
% 91.93/92.19 tff(433,plain,
% 91.93/92.19 ((~![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)))),
% 91.93/92.19 inference(modus_ponens,[status(thm)],[432, 431])).
% 91.93/92.19 tff(434,plain,
% 91.93/92.19 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[433, 51, 175])).
% 91.93/92.19 tff(435,plain,
% 91.93/92.19 ((~((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)))),
% 91.93/92.19 inference(tautology,[status(thm)],[])).
% 91.93/92.19 tff(436,plain,
% 91.93/92.19 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[435, 391, 434])).
% 91.93/92.19 tff(437,plain,
% 91.93/92.19 (tptp_fun_X1_0(X1!1) = c(X1!1)),
% 91.93/92.19 inference(symmetry,[status(thm)],[436])).
% 91.93/92.19 tff(438,plain,
% 91.93/92.19 (multiplication(tptp_fun_X1_0(X1!1), X0!2) = multiplication(c(X1!1), c(tptp_fun_X1_0(X0!2)))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[437, 145])).
% 91.93/92.19 tff(439,plain,
% 91.93/92.19 (multiplication(c(X1!1), c(tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X1!1), X0!2)),
% 91.93/92.19 inference(symmetry,[status(thm)],[438])).
% 91.93/92.19 tff(440,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X1!1, tptp_fun_X1_0(X0!2))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X0!2)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X1!1, tptp_fun_X1_0(X0!2))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X0!2)))))),
% 91.93/92.19 inference(rewrite,[status(thm)],[])).
% 91.93/92.19 tff(441,plain,
% 91.93/92.19 (((~test(tptp_fun_X1_0(X0!2))) | (c(addition(X1!1, tptp_fun_X1_0(X0!2))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X0!2)))) | (~test(X1!1))) <=> ((~test(X1!1)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X1!1, tptp_fun_X1_0(X0!2))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X0!2)))))),
% 91.93/92.19 inference(rewrite,[status(thm)],[])).
% 91.93/92.19 tff(442,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(X1!1, tptp_fun_X1_0(X0!2))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X0!2)))) | (~test(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X1!1, tptp_fun_X1_0(X0!2))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X0!2))))))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[441])).
% 91.93/92.19 tff(443,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(X1!1, tptp_fun_X1_0(X0!2))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X0!2)))) | (~test(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X1!1, tptp_fun_X1_0(X0!2))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X0!2)))))),
% 91.93/92.19 inference(transitivity,[status(thm)],[442, 440])).
% 91.93/92.19 tff(444,plain,
% 91.93/92.19 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X0!2))) | (c(addition(X1!1, tptp_fun_X1_0(X0!2))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X0!2)))) | (~test(X1!1)))),
% 91.93/92.19 inference(quant_inst,[status(thm)],[])).
% 91.93/92.19 tff(445,plain,
% 91.93/92.19 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(X1!1, tptp_fun_X1_0(X0!2))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X0!2))))),
% 91.93/92.19 inference(modus_ponens,[status(thm)],[444, 443])).
% 91.93/92.19 tff(446,plain,
% 91.93/92.19 (c(addition(X1!1, tptp_fun_X1_0(X0!2))) = multiplication(c(X1!1), c(tptp_fun_X1_0(X0!2)))),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[445, 205, 175, 136])).
% 91.93/92.19 tff(447,plain,
% 91.93/92.19 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(tptp_fun_X1_0(X0!2), X1!1) = addition(X1!1, tptp_fun_X1_0(X0!2)))),
% 91.93/92.19 inference(quant_inst,[status(thm)],[])).
% 91.93/92.19 tff(448,plain,
% 91.93/92.19 (addition(tptp_fun_X1_0(X0!2), X1!1) = addition(X1!1, tptp_fun_X1_0(X0!2))),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[447, 16])).
% 91.93/92.19 tff(449,plain,
% 91.93/92.19 (addition(X1!1, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X1!1)),
% 91.93/92.19 inference(symmetry,[status(thm)],[448])).
% 91.93/92.19 tff(450,plain,
% 91.93/92.19 (c(addition(X1!1, tptp_fun_X1_0(X0!2))) = c(addition(tptp_fun_X1_0(X0!2), X1!1))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[449])).
% 91.93/92.19 tff(451,plain,
% 91.93/92.19 (c(addition(tptp_fun_X1_0(X0!2), X1!1)) = c(addition(X1!1, tptp_fun_X1_0(X0!2)))),
% 91.93/92.19 inference(symmetry,[status(thm)],[450])).
% 91.93/92.19 tff(452,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X1!1))))),
% 91.93/92.19 inference(rewrite,[status(thm)],[])).
% 91.93/92.19 tff(453,plain,
% 91.93/92.19 (((~test(X1!1)) | (c(addition(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X1!1))) | (~test(tptp_fun_X1_0(X0!2)))) <=> ((~test(X1!1)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X1!1))))),
% 91.93/92.19 inference(rewrite,[status(thm)],[])).
% 91.93/92.19 tff(454,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(addition(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X1!1))) | (~test(tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X1!1)))))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[453])).
% 91.93/92.19 tff(455,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(addition(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X1!1))) | (~test(tptp_fun_X1_0(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X1!1))))),
% 91.93/92.19 inference(transitivity,[status(thm)],[454, 452])).
% 91.93/92.19 tff(456,plain,
% 91.93/92.19 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (c(addition(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X1!1))) | (~test(tptp_fun_X1_0(X0!2))))),
% 91.93/92.19 inference(quant_inst,[status(thm)],[])).
% 91.93/92.19 tff(457,plain,
% 91.93/92.19 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(tptp_fun_X1_0(X0!2))) | (c(addition(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X1!1)))),
% 91.93/92.19 inference(modus_ponens,[status(thm)],[456, 455])).
% 91.93/92.19 tff(458,plain,
% 91.93/92.19 (c(addition(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X1!1))),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[457, 205, 175, 136])).
% 91.93/92.19 tff(459,plain,
% 91.93/92.19 (multiplication(c(tptp_fun_X1_0(X0!2)), c(X1!1)) = c(addition(tptp_fun_X1_0(X0!2), X1!1))),
% 91.93/92.19 inference(symmetry,[status(thm)],[458])).
% 91.93/92.19 tff(460,plain,
% 91.93/92.19 (multiplication(c(tptp_fun_X1_0(X0!2)), c(X1!1)) = multiplication(X0!2, c(X1!1))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[144])).
% 91.93/92.19 tff(461,plain,
% 91.93/92.19 (multiplication(X0!2, c(X1!1)) = multiplication(c(tptp_fun_X1_0(X0!2)), c(X1!1))),
% 91.93/92.19 inference(symmetry,[status(thm)],[460])).
% 91.93/92.19 tff(462,plain,
% 91.93/92.19 (multiplication(X0!2, c(X1!1)) = multiplication(tptp_fun_X1_0(X1!1), X0!2)),
% 91.93/92.19 inference(transitivity,[status(thm)],[461, 459, 451, 446, 439])).
% 91.93/92.19 tff(463,plain,
% 91.93/92.19 (addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[462, 430])).
% 91.93/92.19 tff(464,plain,
% 91.93/92.19 (addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)) = multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), X0!2)),
% 91.93/92.19 inference(transitivity,[status(thm)],[463, 362, 352, 347])).
% 91.93/92.19 tff(465,plain,
% 91.93/92.19 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X0!2))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[341])).
% 91.93/92.19 tff(466,plain,
% 91.93/92.19 (multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X0!2)) = multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), tptp_fun_X1_0(X0!2))),
% 91.93/92.19 inference(symmetry,[status(thm)],[465])).
% 91.93/92.19 tff(467,plain,
% 91.93/92.19 (multiplication(addition(tptp_fun_X1_0(X1!1), X1!1), tptp_fun_X1_0(X0!2)) = multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(X0!2))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[351])).
% 91.93/92.19 tff(468,plain,
% 91.93/92.19 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X1!1), X1!1), tptp_fun_X1_0(X0!2)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(X1!1, tptp_fun_X1_0(X0!2))))),
% 91.93/92.19 inference(quant_inst,[status(thm)],[])).
% 91.93/92.19 tff(469,plain,
% 91.93/92.19 (multiplication(addition(tptp_fun_X1_0(X1!1), X1!1), tptp_fun_X1_0(X0!2)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(X1!1, tptp_fun_X1_0(X0!2)))),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[468, 359])).
% 91.93/92.19 tff(470,plain,
% 91.93/92.19 (addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(X1!1, tptp_fun_X1_0(X0!2))) = multiplication(addition(tptp_fun_X1_0(X1!1), X1!1), tptp_fun_X1_0(X0!2))),
% 91.93/92.19 inference(symmetry,[status(thm)],[469])).
% 91.93/92.19 tff(471,plain,
% 91.93/92.19 (multiplication(X1!1, tptp_fun_X1_0(X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X0!2))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[406, 123])).
% 91.93/92.19 tff(472,plain,
% 91.93/92.19 (multiplication(c(tptp_fun_X1_0(X1!1)), c(X0!2)) = multiplication(X1!1, tptp_fun_X1_0(X0!2))),
% 91.93/92.19 inference(symmetry,[status(thm)],[471])).
% 91.93/92.19 tff(473,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(c(tptp_fun_X1_0(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(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X0!2))))),
% 91.93/92.19 inference(rewrite,[status(thm)],[])).
% 91.93/92.19 tff(474,plain,
% 91.93/92.19 (((~test(X0!2)) | (c(addition(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X0!2))) | (~test(tptp_fun_X1_0(X1!1)))) <=> ((~test(X0!2)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X0!2))))),
% 91.93/92.19 inference(rewrite,[status(thm)],[])).
% 91.93/92.19 tff(475,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(addition(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X0!2))) | (~test(tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X0!2)))))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[474])).
% 91.93/92.19 tff(476,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(addition(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X0!2))) | (~test(tptp_fun_X1_0(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X0!2))))),
% 91.93/92.19 inference(transitivity,[status(thm)],[475, 473])).
% 91.93/92.19 tff(477,plain,
% 91.93/92.19 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (c(addition(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X0!2))) | (~test(tptp_fun_X1_0(X1!1))))),
% 91.93/92.19 inference(quant_inst,[status(thm)],[])).
% 91.93/92.19 tff(478,plain,
% 91.93/92.19 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X0!2)))),
% 91.93/92.19 inference(modus_ponens,[status(thm)],[477, 476])).
% 91.93/92.19 tff(479,plain,
% 91.93/92.19 (c(addition(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), c(X0!2))),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[478, 205, 41, 397])).
% 91.93/92.19 tff(480,plain,
% 91.93/92.19 (addition(X0!2, tptp_fun_X1_0(X1!1)) = addition(c(tptp_fun_X1_0(X0!2)), c(X1!1))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[145, 437])).
% 91.93/92.19 tff(481,plain,
% 91.93/92.19 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X0!2))),
% 91.93/92.19 inference(quant_inst,[status(thm)],[])).
% 91.93/92.19 tff(482,plain,
% 91.93/92.19 (addition(X0!2, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X0!2)),
% 91.93/92.19 inference(unit_resolution,[status(thm)],[481, 16])).
% 91.93/92.19 tff(483,plain,
% 91.93/92.19 (addition(tptp_fun_X1_0(X1!1), X0!2) = addition(X0!2, tptp_fun_X1_0(X1!1))),
% 91.93/92.19 inference(symmetry,[status(thm)],[482])).
% 91.93/92.19 tff(484,plain,
% 91.93/92.19 (addition(tptp_fun_X1_0(X1!1), X0!2) = addition(c(tptp_fun_X1_0(X0!2)), c(X1!1))),
% 91.93/92.19 inference(transitivity,[status(thm)],[483, 480])).
% 91.93/92.19 tff(485,plain,
% 91.93/92.19 (c(addition(tptp_fun_X1_0(X1!1), X0!2)) = c(addition(c(tptp_fun_X1_0(X0!2)), c(X1!1)))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[484])).
% 91.93/92.19 tff(486,plain,
% 91.93/92.19 (c(addition(c(tptp_fun_X1_0(X0!2)), c(X1!1))) = c(addition(tptp_fun_X1_0(X1!1), X0!2))),
% 91.93/92.19 inference(symmetry,[status(thm)],[485])).
% 91.93/92.19 tff(487,plain,
% 91.93/92.19 (addition(c(tptp_fun_X1_0(X0!2)), c(X1!1)) = addition(X0!2, tptp_fun_X1_0(X1!1))),
% 91.93/92.19 inference(symmetry,[status(thm)],[480])).
% 91.93/92.19 tff(488,plain,
% 91.93/92.19 (c(addition(c(tptp_fun_X1_0(X0!2)), c(X1!1))) = c(addition(X0!2, tptp_fun_X1_0(X1!1)))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[487])).
% 91.93/92.19 tff(489,plain,
% 91.93/92.19 (c(addition(X0!2, tptp_fun_X1_0(X1!1))) = c(addition(c(tptp_fun_X1_0(X0!2)), c(X1!1)))),
% 91.93/92.19 inference(symmetry,[status(thm)],[488])).
% 91.93/92.19 tff(490,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X0!2)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(X0!2, tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(X0!2, tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 91.93/92.19 inference(rewrite,[status(thm)],[])).
% 91.93/92.19 tff(491,plain,
% 91.93/92.19 (((~test(tptp_fun_X1_0(X1!1))) | (c(addition(X0!2, tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X1!1)))) | (~test(X0!2))) <=> ((~test(X0!2)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(X0!2, tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 91.93/92.19 inference(rewrite,[status(thm)],[])).
% 91.93/92.19 tff(492,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(X0!2, tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), c(tptp_fun_X1_0(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(tptp_fun_X1_0(X1!1))) | (c(addition(X0!2, tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 91.93/92.19 inference(monotonicity,[status(thm)],[491])).
% 91.93/92.19 tff(493,plain,
% 91.93/92.19 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(X0!2, tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), c(tptp_fun_X1_0(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(tptp_fun_X1_0(X1!1))) | (c(addition(X0!2, tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 91.93/92.20 inference(transitivity,[status(thm)],[492, 490])).
% 91.93/92.20 tff(494,plain,
% 91.93/92.20 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(tptp_fun_X1_0(X1!1))) | (c(addition(X0!2, tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X1!1)))) | (~test(X0!2)))),
% 91.93/92.20 inference(quant_inst,[status(thm)],[])).
% 91.93/92.20 tff(495,plain,
% 91.93/92.20 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X0!2)) | (~test(tptp_fun_X1_0(X1!1))) | (c(addition(X0!2, tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 91.93/92.20 inference(modus_ponens,[status(thm)],[494, 493])).
% 91.93/92.20 tff(496,plain,
% 91.93/92.20 (c(addition(X0!2, tptp_fun_X1_0(X1!1))) = multiplication(c(X0!2), c(tptp_fun_X1_0(X1!1)))),
% 91.93/92.20 inference(unit_resolution,[status(thm)],[495, 205, 41, 397])).
% 91.93/92.20 tff(497,plain,
% 91.93/92.20 (multiplication(c(X0!2), c(tptp_fun_X1_0(X1!1))) = c(addition(X0!2, tptp_fun_X1_0(X1!1)))),
% 91.93/92.20 inference(symmetry,[status(thm)],[496])).
% 91.93/92.20 tff(498,plain,
% 91.93/92.20 (multiplication(c(X0!2), X1!1) = multiplication(c(X0!2), c(tptp_fun_X1_0(X1!1)))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[406])).
% 91.93/92.20 tff(499,plain,
% 91.93/92.20 (multiplication(c(X0!2), X1!1) = multiplication(X1!1, tptp_fun_X1_0(X0!2))),
% 91.93/92.20 inference(transitivity,[status(thm)],[498, 497, 489, 486, 479, 472])).
% 91.93/92.20 tff(500,plain,
% 91.93/92.20 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(c(X1!1), c(X0!2))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[437, 123])).
% 91.93/92.20 tff(501,plain,
% 91.93/92.20 (multiplication(c(X1!1), c(X0!2)) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))),
% 91.93/92.20 inference(symmetry,[status(thm)],[500])).
% 91.93/92.20 tff(502,plain,
% 91.93/92.20 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(X0!2)) | (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(X1!1)) | (~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))))),
% 91.93/92.20 inference(rewrite,[status(thm)],[])).
% 91.93/92.20 tff(503,plain,
% 91.93/92.20 (((~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))) | (~test(X1!1))) <=> ((~test(X1!1)) | (~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))))),
% 91.93/92.20 inference(rewrite,[status(thm)],[])).
% 91.93/92.20 tff(504,plain,
% 91.93/92.20 (((~![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(X1!1)) | (~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2)))))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[503])).
% 91.93/92.20 tff(505,plain,
% 91.93/92.20 (((~![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(X1!1)) | (~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))))),
% 91.93/92.20 inference(transitivity,[status(thm)],[504, 502])).
% 91.93/92.20 tff(506,plain,
% 91.93/92.20 ((~![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)))),
% 91.93/92.20 inference(quant_inst,[status(thm)],[])).
% 91.93/92.20 tff(507,plain,
% 91.93/92.20 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(X0!2)) | (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2)))),
% 91.93/92.20 inference(modus_ponens,[status(thm)],[506, 505])).
% 91.93/92.20 tff(508,plain,
% 91.93/92.20 (c(addition(X1!1, X0!2)) = multiplication(c(X1!1), c(X0!2))),
% 91.93/92.20 inference(unit_resolution,[status(thm)],[507, 205, 175, 41])).
% 91.93/92.20 tff(509,plain,
% 91.93/92.20 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, X1!1) = addition(X1!1, X0!2))),
% 91.93/92.20 inference(quant_inst,[status(thm)],[])).
% 91.93/92.20 tff(510,plain,
% 91.93/92.20 (addition(X0!2, X1!1) = addition(X1!1, X0!2)),
% 91.93/92.20 inference(unit_resolution,[status(thm)],[509, 16])).
% 91.93/92.20 tff(511,plain,
% 91.93/92.20 (addition(X1!1, X0!2) = addition(X0!2, X1!1)),
% 91.93/92.20 inference(symmetry,[status(thm)],[510])).
% 91.93/92.20 tff(512,plain,
% 91.93/92.20 (c(addition(X1!1, X0!2)) = c(addition(X0!2, X1!1))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[511])).
% 91.93/92.20 tff(513,plain,
% 91.93/92.20 (c(addition(X0!2, X1!1)) = c(addition(X1!1, X0!2))),
% 91.93/92.20 inference(symmetry,[status(thm)],[512])).
% 91.93/92.20 tff(514,plain,
% 91.93/92.20 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(X1!1)) | (~test(X0!2)) | (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(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))))),
% 91.93/92.20 inference(rewrite,[status(thm)],[])).
% 91.93/92.20 tff(515,plain,
% 91.93/92.20 (((~test(X1!1)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))) | (~test(X0!2))) <=> ((~test(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))))),
% 91.93/92.20 inference(rewrite,[status(thm)],[])).
% 91.93/92.20 tff(516,plain,
% 91.93/92.20 (((~![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(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1)))))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[515])).
% 91.93/92.20 tff(517,plain,
% 91.93/92.20 (((~![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(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))))),
% 91.93/92.20 inference(transitivity,[status(thm)],[516, 514])).
% 91.93/92.20 tff(518,plain,
% 91.93/92.20 ((~![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)))),
% 91.93/92.20 inference(quant_inst,[status(thm)],[])).
% 91.93/92.20 tff(519,plain,
% 91.93/92.20 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(X1!1)) | (~test(X0!2)) | (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1)))),
% 91.93/92.20 inference(modus_ponens,[status(thm)],[518, 517])).
% 91.93/92.20 tff(520,plain,
% 91.93/92.20 (c(addition(X0!2, X1!1)) = multiplication(c(X0!2), c(X1!1))),
% 91.93/92.20 inference(unit_resolution,[status(thm)],[519, 205, 175, 41])).
% 91.93/92.20 tff(521,plain,
% 91.93/92.20 (multiplication(c(X0!2), c(X1!1)) = c(addition(X0!2, X1!1))),
% 91.93/92.20 inference(symmetry,[status(thm)],[520])).
% 91.93/92.20 tff(522,plain,
% 91.93/92.20 (multiplication(c(X0!2), c(X1!1)) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))),
% 91.93/92.20 inference(transitivity,[status(thm)],[521, 513, 508, 501])).
% 91.93/92.20 tff(523,plain,
% 91.93/92.20 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(X1!1, tptp_fun_X1_0(X0!2)))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[522, 499])).
% 91.93/92.20 tff(524,plain,
% 91.93/92.20 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)) = multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), tptp_fun_X1_0(X0!2))),
% 91.93/92.20 inference(transitivity,[status(thm)],[523, 470, 467, 466])).
% 91.93/92.20 tff(525,plain,
% 91.93/92.20 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))) = addition(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), X0!2))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[524, 464])).
% 91.93/92.20 tff(526,plain,
% 91.93/92.20 (addition(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), X0!2)) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 91.93/92.20 inference(symmetry,[status(thm)],[525])).
% 91.93/92.20 tff(527,plain,
% 91.93/92.20 (^[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))))),
% 91.93/92.20 inference(bind,[status(th)],[])).
% 91.93/92.20 tff(528,plain,
% 91.93/92.20 (![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)))),
% 91.93/92.20 inference(quant_intro,[status(thm)],[527])).
% 91.93/92.20 tff(529,plain,
% 91.93/92.20 (![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)))),
% 91.93/92.20 inference(rewrite,[status(thm)],[])).
% 91.93/92.20 tff(530,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')).
% 91.93/92.20 tff(531,plain,
% 91.93/92.20 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 91.93/92.20 inference(modus_ponens,[status(thm)],[530, 529])).
% 91.93/92.20 tff(532,plain,(
% 91.93/92.20 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 91.93/92.20 inference(skolemize,[status(sab)],[531])).
% 91.93/92.20 tff(533,plain,
% 91.93/92.20 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 91.93/92.20 inference(modus_ponens,[status(thm)],[532, 528])).
% 91.93/92.20 tff(534,plain,
% 91.93/92.20 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(tptp_fun_X1_0(X0!2), X0!2)) = addition(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), X0!2)))),
% 91.93/92.20 inference(quant_inst,[status(thm)],[])).
% 91.93/92.20 tff(535,plain,
% 91.93/92.20 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(tptp_fun_X1_0(X0!2), X0!2)) = addition(multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), X0!2))),
% 91.93/92.20 inference(unit_resolution,[status(thm)],[534, 533])).
% 91.93/92.20 tff(536,plain,
% 91.93/92.20 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 91.93/92.20 inference(symmetry,[status(thm)],[31])).
% 91.93/92.20 tff(537,plain,
% 91.93/92.20 (addition(tptp_fun_X1_0(X0!2), X0!2) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.20 inference(transitivity,[status(thm)],[536, 146, 335, 186, 331, 340])).
% 91.93/92.20 tff(538,plain,
% 91.93/92.20 (multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[341, 537])).
% 91.93/92.20 tff(539,plain,
% 91.93/92.20 (multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(tptp_fun_X1_0(X0!2), X0!2))),
% 91.93/92.20 inference(symmetry,[status(thm)],[538])).
% 91.93/92.20 tff(540,plain,
% 91.93/92.20 (tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 91.93/92.20 inference(transitivity,[status(thm)],[344, 330])).
% 91.93/92.20 tff(541,plain,
% 91.93/92.20 (tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = one),
% 91.93/92.20 inference(transitivity,[status(thm)],[344, 330, 187, 168, 147, 106])).
% 91.93/92.20 tff(542,plain,
% 91.93/92.20 (multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(one, c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[541, 540])).
% 91.93/92.20 tff(543,plain,
% 91.93/92.20 (multiplication(one, c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.20 inference(symmetry,[status(thm)],[542])).
% 91.93/92.20 tff(544,plain,
% 91.93/92.20 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 91.93/92.20 inference(bind,[status(th)],[])).
% 91.93/92.20 tff(545,plain,
% 91.93/92.20 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 91.93/92.20 inference(quant_intro,[status(thm)],[544])).
% 91.93/92.20 tff(546,plain,
% 91.93/92.20 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 91.93/92.20 inference(rewrite,[status(thm)],[])).
% 91.93/92.20 tff(547,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 91.93/92.20 tff(548,plain,
% 91.93/92.20 (![A: $i] : (multiplication(one, A) = A)),
% 91.93/92.20 inference(modus_ponens,[status(thm)],[547, 546])).
% 91.93/92.20 tff(549,plain,(
% 91.93/92.20 ![A: $i] : (multiplication(one, A) = A)),
% 91.93/92.20 inference(skolemize,[status(sab)],[548])).
% 91.93/92.20 tff(550,plain,
% 91.93/92.20 (![A: $i] : (multiplication(one, A) = A)),
% 91.93/92.20 inference(modus_ponens,[status(thm)],[549, 545])).
% 91.93/92.20 tff(551,plain,
% 91.93/92.20 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 91.93/92.20 inference(quant_inst,[status(thm)],[])).
% 91.93/92.20 tff(552,plain,
% 91.93/92.20 (multiplication(one, c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 91.93/92.20 inference(unit_resolution,[status(thm)],[551, 550])).
% 91.93/92.20 tff(553,plain,
% 91.93/92.20 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(one, c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 91.93/92.20 inference(symmetry,[status(thm)],[552])).
% 91.93/92.20 tff(554,plain,
% 91.93/92.20 (tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 91.93/92.20 inference(transitivity,[status(thm)],[344, 330, 553, 543, 539, 535, 526, 27, 23, 20, 9])).
% 91.93/92.20 tff(555,plain,
% 91.93/92.20 (addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(X0!2, tptp_fun_X1_0(X0!2)))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[554, 345])).
% 91.93/92.20 tff(556,plain,
% 91.93/92.20 (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(X0!2, tptp_fun_X1_0(X0!2))) = addition(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.20 inference(symmetry,[status(thm)],[555])).
% 91.93/92.20 tff(557,plain,
% 91.93/92.20 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(X0!2, tptp_fun_X1_0(X0!2))) = addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)))),
% 91.93/92.20 inference(quant_inst,[status(thm)],[])).
% 91.93/92.20 tff(558,plain,
% 91.93/92.20 (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(X0!2, tptp_fun_X1_0(X0!2))) = addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2))),
% 91.93/92.20 inference(unit_resolution,[status(thm)],[557, 7])).
% 91.93/92.20 tff(559,plain,
% 91.93/92.20 (addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)) = addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(X0!2, tptp_fun_X1_0(X0!2)))),
% 91.93/92.20 inference(symmetry,[status(thm)],[558])).
% 91.93/92.20 tff(560,plain,
% 91.93/92.20 (addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)) = one),
% 91.93/92.20 inference(transitivity,[status(thm)],[559, 556, 343, 339, 187, 168, 147, 106])).
% 91.93/92.20 tff(561,assumption,(~(addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)) = one)), introduced(assumption)).
% 91.93/92.20 tff(562,plain,
% 91.93/92.20 ($false),
% 91.93/92.20 inference(unit_resolution,[status(thm)],[561, 560])).
% 91.93/92.20 tff(563,plain,((~(c(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))) | (addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)) = one)), inference(lemma,lemma(discharge,[]))).
% 91.93/92.20 tff(564,plain,
% 91.93/92.20 (addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)) = one),
% 91.93/92.20 inference(unit_resolution,[status(thm)],[563, 328])).
% 91.93/92.20 tff(565,plain,
% 91.93/92.20 (addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.20 inference(transitivity,[status(thm)],[564, 107, 337, 335, 334, 331, 328])).
% 91.93/92.20 tff(566,plain,
% 91.93/92.20 (multiplication(X0!2, addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2))) = multiplication(X0!2, tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[565])).
% 91.93/92.20 tff(567,plain,
% 91.93/92.20 (multiplication(X0!2, tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(X0!2, addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)))),
% 91.93/92.20 inference(symmetry,[status(thm)],[566])).
% 91.93/92.20 tff(568,plain,
% 91.93/92.20 (addition(tptp_fun_X1_0(X1!1), X1!1) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 91.93/92.20 inference(transitivity,[status(thm)],[350, 189, 107, 337, 335, 334, 331, 328])).
% 91.93/92.20 tff(569,plain,
% 91.93/92.20 (multiplication(X0!2, addition(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(X0!2, tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[568])).
% 91.93/92.20 tff(570,plain,
% 91.93/92.20 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(X0!2, addition(tptp_fun_X1_0(X1!1), X1!1)) = addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1)))),
% 91.93/92.20 inference(quant_inst,[status(thm)],[])).
% 91.93/92.20 tff(571,plain,
% 91.93/92.20 (multiplication(X0!2, addition(tptp_fun_X1_0(X1!1), X1!1)) = addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1))),
% 91.93/92.20 inference(unit_resolution,[status(thm)],[570, 533])).
% 91.93/92.20 tff(572,plain,
% 91.93/92.20 (addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1)) = multiplication(X0!2, addition(tptp_fun_X1_0(X1!1), X1!1))),
% 91.93/92.20 inference(symmetry,[status(thm)],[571])).
% 91.93/92.20 tff(573,plain,
% 91.93/92.20 (multiplication(X0!2, tptp_fun_X1_0(X1!1)) = multiplication(X0!2, c(X1!1))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[437])).
% 91.93/92.20 tff(574,plain,
% 91.93/92.20 (multiplication(X0!2, c(X1!1)) = multiplication(X0!2, tptp_fun_X1_0(X1!1))),
% 91.93/92.20 inference(symmetry,[status(thm)],[573])).
% 91.93/92.20 tff(575,plain,
% 91.93/92.20 (addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, tptp_fun_X1_0(X1!1)), multiplication(X0!2, X1!1))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[574])).
% 91.93/92.20 tff(576,plain,
% 91.93/92.20 (addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)) = multiplication(X0!2, addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)))),
% 91.93/92.20 inference(transitivity,[status(thm)],[575, 572, 569, 567])).
% 91.93/92.20 tff(577,plain,
% 91.93/92.20 (multiplication(tptp_fun_X1_0(X0!2), addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[565])).
% 91.93/92.20 tff(578,plain,
% 91.93/92.20 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(tptp_fun_X1_0(X0!2), addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)))),
% 91.93/92.20 inference(symmetry,[status(thm)],[577])).
% 91.93/92.20 tff(579,plain,
% 91.93/92.20 (multiplication(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), X1!1)) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[568])).
% 91.93/92.20 tff(580,plain,
% 91.93/92.20 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1)))),
% 91.93/92.20 inference(quant_inst,[status(thm)],[])).
% 91.93/92.20 tff(581,plain,
% 91.93/92.20 (multiplication(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 91.93/92.20 inference(unit_resolution,[status(thm)],[580, 533])).
% 91.93/92.20 tff(582,plain,
% 91.93/92.20 (addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), X1!1))),
% 91.93/92.20 inference(symmetry,[status(thm)],[581])).
% 91.93/92.20 tff(583,plain,
% 91.93/92.20 (multiplication(tptp_fun_X1_0(X0!2), X1!1) = multiplication(c(X0!2), X1!1)),
% 91.93/92.20 inference(monotonicity,[status(thm)],[123])).
% 91.93/92.20 tff(584,plain,
% 91.93/92.20 (multiplication(c(X0!2), X1!1) = multiplication(tptp_fun_X1_0(X0!2), X1!1)),
% 91.93/92.20 inference(symmetry,[status(thm)],[583])).
% 91.93/92.20 tff(585,plain,
% 91.93/92.20 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)) = multiplication(c(X0!2), c(X1!1))),
% 91.93/92.20 inference(monotonicity,[status(thm)],[123, 437])).
% 91.93/92.20 tff(586,plain,
% 91.93/92.20 (multiplication(c(X0!2), c(X1!1)) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 91.93/92.20 inference(symmetry,[status(thm)],[585])).
% 91.93/92.20 tff(587,plain,
% 91.93/92.20 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 92.04/92.20 inference(monotonicity,[status(thm)],[586, 584])).
% 92.04/92.20 tff(588,plain,
% 92.04/92.20 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)) = multiplication(tptp_fun_X1_0(X0!2), addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)))),
% 92.04/92.20 inference(transitivity,[status(thm)],[587, 582, 579, 578])).
% 92.04/92.20 tff(589,plain,
% 92.04/92.20 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2))), multiplication(X0!2, addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2))))),
% 92.04/92.20 inference(monotonicity,[status(thm)],[588, 576])).
% 92.04/92.20 tff(590,plain,
% 92.04/92.20 (addition(multiplication(tptp_fun_X1_0(X0!2), addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2))), multiplication(X0!2, addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X0!2), X1!1)), addition(multiplication(X0!2, c(X1!1)), multiplication(X0!2, X1!1)))),
% 92.04/92.20 inference(symmetry,[status(thm)],[589])).
% 92.04/92.20 tff(591,plain,
% 92.04/92.20 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2))), multiplication(X0!2, addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)))))),
% 92.04/92.20 inference(quant_inst,[status(thm)],[])).
% 92.04/92.20 tff(592,plain,
% 92.04/92.20 (multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2))), multiplication(X0!2, addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2))))),
% 92.04/92.20 inference(unit_resolution,[status(thm)],[591, 359])).
% 92.04/92.20 tff(593,plain,
% 92.04/92.20 (addition(tptp_fun_X1_0(X0!2), X0!2) = tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 92.04/92.20 inference(transitivity,[status(thm)],[536, 337, 335, 334, 331, 328])).
% 92.04/92.20 tff(594,plain,
% 92.04/92.20 (multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2))) = multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 92.04/92.21 inference(monotonicity,[status(thm)],[593, 565])).
% 92.04/92.21 tff(595,plain,
% 92.04/92.21 (multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)))),
% 92.04/92.21 inference(symmetry,[status(thm)],[594])).
% 92.04/92.21 tff(596,plain,
% 92.04/92.21 (tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = c(c(addition(X1!1, tptp_fun_X1_0(X1!1))))),
% 92.04/92.21 inference(symmetry,[status(thm)],[328])).
% 92.04/92.21 tff(597,plain,
% 92.04/92.21 (tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = one),
% 92.04/92.21 inference(transitivity,[status(thm)],[596, 330, 333, 168, 336, 106])).
% 92.04/92.21 tff(598,plain,
% 92.04/92.21 (one = addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2))),
% 92.04/92.21 inference(symmetry,[status(thm)],[564])).
% 92.04/92.21 tff(599,plain,
% 92.04/92.21 (tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))) = addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2))),
% 92.04/92.21 inference(transitivity,[status(thm)],[596, 330, 333, 168, 336, 106, 598])).
% 92.04/92.21 tff(600,plain,
% 92.04/92.21 (multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1))))) = multiplication(addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)), one)),
% 92.04/92.21 inference(monotonicity,[status(thm)],[599, 597])).
% 92.04/92.21 tff(601,plain,
% 92.04/92.21 (multiplication(addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)), one) = multiplication(tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))), tptp_fun_X1_0(c(addition(X1!1, tptp_fun_X1_0(X1!1)))))),
% 92.04/92.21 inference(symmetry,[status(thm)],[600])).
% 92.04/92.21 tff(602,plain,
% 92.04/92.21 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 92.04/92.21 inference(bind,[status(th)],[])).
% 92.04/92.21 tff(603,plain,
% 92.04/92.21 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 92.04/92.21 inference(quant_intro,[status(thm)],[602])).
% 92.04/92.21 tff(604,plain,
% 92.04/92.21 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 92.04/92.21 inference(rewrite,[status(thm)],[])).
% 92.04/92.21 tff(605,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 92.04/92.21 tff(606,plain,
% 92.04/92.21 (![A: $i] : (multiplication(A, one) = A)),
% 92.04/92.21 inference(modus_ponens,[status(thm)],[605, 604])).
% 92.04/92.21 tff(607,plain,(
% 92.04/92.21 ![A: $i] : (multiplication(A, one) = A)),
% 92.04/92.21 inference(skolemize,[status(sab)],[606])).
% 92.04/92.21 tff(608,plain,
% 92.04/92.21 (![A: $i] : (multiplication(A, one) = A)),
% 92.04/92.21 inference(modus_ponens,[status(thm)],[607, 603])).
% 92.04/92.21 tff(609,plain,
% 92.04/92.21 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)), one) = addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)))),
% 92.04/92.21 inference(quant_inst,[status(thm)],[])).
% 92.04/92.21 tff(610,plain,
% 92.04/92.21 (multiplication(addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)), one) = addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2))),
% 92.04/92.21 inference(unit_resolution,[status(thm)],[609, 608])).
% 92.04/92.21 tff(611,plain,
% 92.04/92.21 (addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)) = multiplication(addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)), one)),
% 92.04/92.21 inference(symmetry,[status(thm)],[610])).
% 92.04/92.21 tff(612,plain,
% 92.04/92.21 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 92.04/92.21 inference(transitivity,[status(thm)],[333, 168, 336])).
% 92.04/92.21 tff(613,plain,
% 92.04/92.21 (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), addition(X0!2, tptp_fun_X1_0(X0!2)))),
% 92.04/92.21 inference(monotonicity,[status(thm)],[612])).
% 92.04/92.21 tff(614,plain,
% 92.04/92.21 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 92.04/92.21 inference(quant_inst,[status(thm)],[])).
% 92.04/92.21 tff(615,plain,
% 92.04/92.21 (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 92.04/92.21 inference(unit_resolution,[status(thm)],[614, 16])).
% 92.04/92.21 tff(616,plain,
% 92.04/92.21 (addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 92.04/92.21 inference(symmetry,[status(thm)],[615])).
% 92.04/92.21 tff(617,plain,
% 92.04/92.21 (addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 92.04/92.21 inference(transitivity,[status(thm)],[616, 613, 558, 611, 601, 595, 592, 590, 27, 23, 20, 9])).
% 92.04/92.21 tff(618,plain,
% 92.04/92.21 (c(multiplication(tptp_fun_X1_0(X1!1), X1!1)) = one),
% 92.04/92.21 inference(transitivity,[status(thm)],[333, 168, 336, 106])).
% 92.04/92.21 tff(619,plain,
% 92.04/92.21 (leq(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 92.04/92.21 inference(monotonicity,[status(thm)],[618])).
% 92.04/92.21 tff(620,plain,
% 92.04/92.21 (leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> leq(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 92.04/92.21 inference(symmetry,[status(thm)],[619])).
% 92.04/92.21 tff(621,plain,
% 92.04/92.21 ((~leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) <=> (~leq(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 92.04/92.21 inference(monotonicity,[status(thm)],[620])).
% 92.04/92.21 tff(622,plain,
% 92.04/92.21 (leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)),
% 92.04/92.21 inference(monotonicity,[status(thm)],[618])).
% 92.04/92.21 tff(623,plain,
% 92.04/92.21 ((addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = one)),
% 92.04/92.21 inference(monotonicity,[status(thm)],[618])).
% 92.04/92.21 tff(624,plain,
% 92.04/92.21 ((addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = one) <=> (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 92.04/92.21 inference(symmetry,[status(thm)],[623])).
% 92.04/92.21 tff(625,plain,
% 92.04/92.21 (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2))),
% 92.04/92.21 inference(transitivity,[status(thm)],[613, 558])).
% 92.04/92.21 tff(626,plain,
% 92.04/92.21 ((addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = one) <=> (addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)) = one)),
% 92.04/92.21 inference(monotonicity,[status(thm)],[625])).
% 92.04/92.21 tff(627,plain,
% 92.04/92.21 ((addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)) = one) <=> (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = one)),
% 92.04/92.21 inference(symmetry,[status(thm)],[626])).
% 92.04/92.21 tff(628,plain,
% 92.04/92.21 ((addition(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), X0!2), tptp_fun_X1_0(X0!2)) = one) <=> (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 92.04/92.21 inference(transitivity,[status(thm)],[627, 624])).
% 92.04/92.21 tff(629,plain,
% 92.04/92.21 (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))),
% 92.04/92.21 inference(modus_ponens,[status(thm)],[564, 628])).
% 92.04/92.21 tff(630,plain,
% 92.04/92.21 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 92.04/92.21 inference(bind,[status(th)],[])).
% 92.04/92.21 tff(631,plain,
% 92.04/92.21 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 92.04/92.21 inference(quant_intro,[status(thm)],[630])).
% 92.04/92.21 tff(632,plain,
% 92.04/92.21 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 92.04/92.21 inference(rewrite,[status(thm)],[])).
% 92.04/92.21 tff(633,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','order')).
% 92.04/92.21 tff(634,plain,
% 92.04/92.21 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 92.04/92.21 inference(modus_ponens,[status(thm)],[633, 632])).
% 92.04/92.21 tff(635,plain,(
% 92.04/92.21 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 92.04/92.21 inference(skolemize,[status(sab)],[634])).
% 92.04/92.21 tff(636,plain,
% 92.04/92.21 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 92.04/92.21 inference(modus_ponens,[status(thm)],[635, 631])).
% 92.04/92.21 tff(637,plain,
% 92.04/92.21 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))),
% 92.04/92.21 inference(quant_inst,[status(thm)],[])).
% 92.04/92.21 tff(638,plain,
% 92.04/92.21 (leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 92.04/92.21 inference(unit_resolution,[status(thm)],[637, 636])).
% 92.04/92.21 tff(639,plain,
% 92.04/92.21 ((~(leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) <=> (addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))) | leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) | (~(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))),
% 92.04/92.21 inference(tautology,[status(thm)],[])).
% 92.04/92.21 tff(640,plain,
% 92.04/92.21 (leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) | (~(addition(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1))) = c(multiplication(tptp_fun_X1_0(X1!1), X1!1))))),
% 92.04/92.21 inference(unit_resolution,[status(thm)],[639, 638])).
% 92.04/92.21 tff(641,plain,
% 92.04/92.21 (leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), c(multiplication(tptp_fun_X1_0(X1!1), X1!1)))),
% 92.04/92.21 inference(unit_resolution,[status(thm)],[640, 629])).
% 92.04/92.21 tff(642,plain,
% 92.04/92.21 (leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)),
% 92.04/92.21 inference(modus_ponens,[status(thm)],[641, 622])).
% 92.04/92.21 tff(643,plain,
% 92.04/92.21 ((~(~((~leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))))) <=> ((~leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)))),
% 92.04/92.21 inference(rewrite,[status(thm)],[])).
% 92.04/92.21 tff(644,plain,
% 92.04/92.21 ((leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) & leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)) <=> (~((~leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))))),
% 92.04/92.21 inference(rewrite,[status(thm)],[])).
% 92.04/92.21 tff(645,plain,
% 92.04/92.21 ((~(leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) & leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))) <=> (~(~((~leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)))))),
% 92.04/92.21 inference(monotonicity,[status(thm)],[644])).
% 92.04/92.21 tff(646,plain,
% 92.04/92.21 ((~(leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) & leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))) <=> ((~leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one)))),
% 92.04/92.21 inference(transitivity,[status(thm)],[645, 643])).
% 92.04/92.21 tff(647,plain,
% 92.04/92.21 (~(leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) & leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))),
% 92.04/92.21 inference(or_elim,[status(thm)],[39])).
% 92.04/92.21 tff(648,plain,
% 92.04/92.21 ((~leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))) | (~leq(addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))), one))),
% 92.04/92.21 inference(modus_ponens,[status(thm)],[647, 646])).
% 92.04/92.21 tff(649,plain,
% 92.04/92.21 (~leq(one, addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 92.04/92.21 inference(unit_resolution,[status(thm)],[648, 642])).
% 92.04/92.21 tff(650,plain,
% 92.04/92.21 (~leq(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 92.04/92.21 inference(modus_ponens,[status(thm)],[649, 621])).
% 92.04/92.21 tff(651,plain,
% 92.04/92.21 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 92.04/92.21 inference(quant_inst,[status(thm)],[])).
% 92.04/92.21 tff(652,plain,
% 92.04/92.21 (leq(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 92.04/92.21 inference(unit_resolution,[status(thm)],[651, 636])).
% 92.04/92.21 tff(653,plain,
% 92.04/92.21 ((~(leq(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))) | leq(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 92.04/92.21 inference(tautology,[status(thm)],[])).
% 92.04/92.21 tff(654,plain,
% 92.04/92.21 (leq(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) | (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 92.06/92.23 inference(unit_resolution,[status(thm)],[653, 652])).
% 92.06/92.23 tff(655,plain,
% 92.06/92.23 (~(addition(c(multiplication(tptp_fun_X1_0(X1!1), X1!1)), addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(X0!2, c(X1!1))), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 92.06/92.23 inference(unit_resolution,[status(thm)],[654, 650])).
% 92.06/92.23 tff(656,plain,
% 92.06/92.23 ($false),
% 92.06/92.23 inference(unit_resolution,[status(thm)],[655, 617])).
% 92.06/92.23 % SZS output end Proof
% 92.06/92.24 % E exiting
%------------------------------------------------------------------------------