%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE013+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:12:51 AM UTC 2025
% Result : Theorem 19.86s 20.10s
% Output : Proof 19.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE013+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 18:50:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 19.86/20.10 % SZS status Theorem
% 19.86/20.10 % SZS output start Proof
% 19.86/20.10 tff(addition_type, type, (
% 19.86/20.10 addition: ( $i * $i ) > $i)).
% 19.86/20.10 tff(multiplication_type, type, (
% 19.86/20.10 multiplication: ( $i * $i ) > $i)).
% 19.86/20.10 tff(c_type, type, (
% 19.86/20.10 c: $i > $i)).
% 19.86/20.10 tff(tptp_fun_X1_1_type, type, (
% 19.86/20.10 tptp_fun_X1_1: $i)).
% 19.86/20.10 tff(tptp_fun_X0_2_type, type, (
% 19.86/20.10 tptp_fun_X0_2: $i)).
% 19.86/20.10 tff(one_type, type, (
% 19.86/20.10 one: $i)).
% 19.86/20.10 tff(tptp_fun_X1_0_type, type, (
% 19.86/20.10 tptp_fun_X1_0: $i > $i)).
% 19.86/20.10 tff(complement_type, type, (
% 19.86/20.10 complement: ( $i * $i ) > $o)).
% 19.86/20.10 tff(test_type, type, (
% 19.86/20.10 test: $i > $o)).
% 19.86/20.10 tff(zero_type, type, (
% 19.86/20.10 zero: $i)).
% 19.86/20.10 tff(1,plain,
% 19.86/20.10 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 19.86/20.10 inference(bind,[status(th)],[])).
% 19.86/20.10 tff(2,plain,
% 19.86/20.10 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 19.86/20.10 inference(quant_intro,[status(thm)],[1])).
% 19.86/20.10 tff(3,plain,
% 19.86/20.10 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 19.86/20.11 inference(rewrite,[status(thm)],[])).
% 19.86/20.11 tff(4,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 19.86/20.11 tff(5,plain,
% 19.86/20.11 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[4, 3])).
% 19.86/20.11 tff(6,plain,(
% 19.86/20.11 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 19.86/20.11 inference(skolemize,[status(sab)],[5])).
% 19.86/20.11 tff(7,plain,
% 19.86/20.11 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[6, 2])).
% 19.86/20.11 tff(8,plain,
% 19.86/20.11 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, X1!1) = addition(X1!1, X0!2))),
% 19.86/20.11 inference(quant_inst,[status(thm)],[])).
% 19.86/20.11 tff(9,plain,
% 19.86/20.11 (addition(X0!2, X1!1) = addition(X1!1, X0!2)),
% 19.86/20.11 inference(unit_resolution,[status(thm)],[8, 7])).
% 19.86/20.11 tff(10,plain,
% 19.86/20.11 (addition(addition(X0!2, X1!1), multiplication(c(X0!2), c(X1!1))) = addition(addition(X1!1, X0!2), multiplication(c(X0!2), c(X1!1)))),
% 19.86/20.11 inference(monotonicity,[status(thm)],[9])).
% 19.86/20.11 tff(11,plain,
% 19.86/20.11 (addition(addition(X1!1, X0!2), multiplication(c(X0!2), c(X1!1))) = addition(addition(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))),
% 19.86/20.11 inference(symmetry,[status(thm)],[10])).
% 19.86/20.11 tff(12,plain,
% 19.86/20.11 (^[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)))),
% 19.86/20.11 inference(bind,[status(th)],[])).
% 19.86/20.11 tff(13,plain,
% 19.86/20.11 (![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))),
% 19.86/20.11 inference(quant_intro,[status(thm)],[12])).
% 19.86/20.11 tff(14,plain,
% 19.86/20.11 (![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))),
% 19.86/20.11 inference(rewrite,[status(thm)],[])).
% 19.86/20.11 tff(15,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_associativity')).
% 19.86/20.11 tff(16,plain,
% 19.86/20.11 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[15, 14])).
% 19.86/20.11 tff(17,plain,(
% 19.86/20.11 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 19.86/20.11 inference(skolemize,[status(sab)],[16])).
% 19.86/20.11 tff(18,plain,
% 19.86/20.11 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[17, 13])).
% 19.86/20.11 tff(19,plain,
% 19.86/20.11 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(X1!1, addition(X0!2, multiplication(c(X0!2), c(X1!1)))) = addition(addition(X1!1, X0!2), multiplication(c(X0!2), c(X1!1))))),
% 19.86/20.11 inference(quant_inst,[status(thm)],[])).
% 19.86/20.11 tff(20,plain,
% 19.86/20.11 (addition(X1!1, addition(X0!2, multiplication(c(X0!2), c(X1!1)))) = addition(addition(X1!1, X0!2), multiplication(c(X0!2), c(X1!1)))),
% 19.86/20.11 inference(unit_resolution,[status(thm)],[19, 18])).
% 19.86/20.11 tff(21,plain,
% 19.86/20.11 (^[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))))),
% 19.86/20.11 inference(bind,[status(th)],[])).
% 19.86/20.11 tff(22,plain,
% 19.86/20.11 (![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)))),
% 19.86/20.11 inference(quant_intro,[status(thm)],[21])).
% 19.86/20.11 tff(23,plain,
% 19.86/20.11 (![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)))),
% 19.86/20.11 inference(rewrite,[status(thm)],[])).
% 19.86/20.11 tff(24,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')).
% 19.86/20.11 tff(25,plain,
% 19.86/20.11 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[24, 23])).
% 19.86/20.11 tff(26,plain,(
% 19.86/20.11 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 19.86/20.11 inference(skolemize,[status(sab)],[25])).
% 19.86/20.11 tff(27,plain,
% 19.86/20.11 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[26, 22])).
% 19.86/20.11 tff(28,plain,
% 19.86/20.11 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 19.86/20.11 inference(quant_inst,[status(thm)],[])).
% 19.86/20.11 tff(29,plain,
% 19.86/20.11 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))),
% 19.86/20.11 inference(unit_resolution,[status(thm)],[28, 27])).
% 19.86/20.11 tff(30,plain,
% 19.86/20.11 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 19.86/20.11 inference(symmetry,[status(thm)],[29])).
% 19.86/20.11 tff(31,plain,
% 19.86/20.11 ((~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(X0, X1), multiplication(c(X0), c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(X0, X1), multiplication(c(X0), c(X1))))))),
% 19.86/20.11 inference(rewrite,[status(thm)],[])).
% 19.86/20.11 tff(32,plain,
% 19.86/20.11 ((~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (one = addition(addition(X0, X1), multiplication(c(X0), c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(X0, X1), multiplication(c(X0), c(X1))))))),
% 19.86/20.11 inference(rewrite,[status(thm)],[])).
% 19.86/20.11 tff(33,axiom,(~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (one = addition(addition(X0, X1), multiplication(c(X0), c(X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 19.86/20.11 tff(34,plain,
% 19.86/20.11 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(X0, X1), multiplication(c(X0), c(X1)))))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[33, 32])).
% 19.86/20.11 tff(35,plain,
% 19.86/20.11 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(X0, X1), multiplication(c(X0), c(X1)))))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[34, 31])).
% 19.86/20.11 tff(36,plain,
% 19.86/20.11 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(X0, X1), multiplication(c(X0), c(X1)))))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[35, 31])).
% 19.86/20.11 tff(37,plain,
% 19.86/20.11 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(X0, X1), multiplication(c(X0), c(X1)))))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[36, 31])).
% 19.86/20.11 tff(38,plain,(
% 19.86/20.11 ~((~(test(X1!1) & test(X0!2))) | (one = addition(addition(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 19.86/20.11 inference(skolemize,[status(sab)],[37])).
% 19.86/20.11 tff(39,plain,
% 19.86/20.11 (test(X1!1) & test(X0!2)),
% 19.86/20.11 inference(or_elim,[status(thm)],[38])).
% 19.86/20.11 tff(40,plain,
% 19.86/20.11 (test(X1!1)),
% 19.86/20.11 inference(and_elim,[status(thm)],[39])).
% 19.86/20.11 tff(41,plain,
% 19.86/20.11 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 19.86/20.11 inference(bind,[status(th)],[])).
% 19.86/20.11 tff(42,plain,
% 19.86/20.11 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 19.86/20.11 inference(quant_intro,[status(thm)],[41])).
% 19.86/20.11 tff(43,plain,
% 19.86/20.11 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 19.86/20.11 inference(rewrite,[status(thm)],[])).
% 19.86/20.11 tff(44,plain,
% 19.86/20.11 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 19.86/20.11 inference(bind,[status(th)],[])).
% 19.86/20.11 tff(45,plain,
% 19.86/20.11 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 19.86/20.11 inference(quant_intro,[status(thm)],[44])).
% 19.86/20.11 tff(46,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_3')).
% 19.86/20.11 tff(47,plain,
% 19.86/20.11 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[46, 45])).
% 19.86/20.11 tff(48,plain,
% 19.86/20.11 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[47, 43])).
% 19.86/20.11 tff(49,plain,(
% 19.86/20.11 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 19.86/20.11 inference(skolemize,[status(sab)],[48])).
% 19.86/20.11 tff(50,plain,
% 19.86/20.11 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[49, 42])).
% 19.86/20.11 tff(51,plain,
% 19.86/20.11 (((~![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))))),
% 19.86/20.11 inference(rewrite,[status(thm)],[])).
% 19.86/20.11 tff(52,plain,
% 19.86/20.11 ((~![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))))),
% 19.86/20.11 inference(quant_inst,[status(thm)],[])).
% 19.86/20.11 tff(53,plain,
% 19.86/20.11 ((~![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)))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[52, 51])).
% 19.86/20.11 tff(54,plain,
% 19.86/20.11 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 19.86/20.11 inference(unit_resolution,[status(thm)],[53, 50, 40])).
% 19.86/20.11 tff(55,plain,
% 19.86/20.11 (^[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))))),
% 19.86/20.11 inference(bind,[status(th)],[])).
% 19.86/20.11 tff(56,plain,
% 19.86/20.11 (![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)))),
% 19.86/20.11 inference(quant_intro,[status(thm)],[55])).
% 19.86/20.11 tff(57,plain,
% 19.86/20.11 (^[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)))))),
% 19.86/20.11 inference(bind,[status(th)],[])).
% 19.86/20.11 tff(58,plain,
% 19.86/20.11 (![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)))),
% 19.86/20.11 inference(quant_intro,[status(thm)],[57])).
% 19.86/20.11 tff(59,plain,
% 19.86/20.11 (![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)))),
% 19.86/20.11 inference(rewrite,[status(thm)],[])).
% 19.86/20.11 tff(60,plain,
% 19.86/20.11 (^[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))))),
% 19.86/20.11 inference(bind,[status(th)],[])).
% 19.86/20.11 tff(61,plain,
% 19.86/20.11 (![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)))),
% 19.86/20.11 inference(quant_intro,[status(thm)],[60])).
% 19.86/20.11 tff(62,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')).
% 19.86/20.11 tff(63,plain,
% 19.86/20.11 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[62, 61])).
% 19.86/20.11 tff(64,plain,
% 19.86/20.11 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[63, 59])).
% 19.86/20.11 tff(65,plain,(
% 19.86/20.11 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 19.86/20.11 inference(skolemize,[status(sab)],[64])).
% 19.86/20.11 tff(66,plain,
% 19.86/20.11 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[65, 58])).
% 19.86/20.11 tff(67,plain,
% 19.86/20.11 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[66, 56])).
% 19.86/20.11 tff(68,plain,
% 19.86/20.11 (((~![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)))))),
% 19.86/20.11 inference(rewrite,[status(thm)],[])).
% 19.86/20.11 tff(69,plain,
% 19.86/20.11 ((~(((~(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))))),
% 19.86/20.11 inference(rewrite,[status(thm)],[])).
% 19.86/20.11 tff(70,plain,
% 19.86/20.11 ((((~(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)))),
% 19.86/20.11 inference(rewrite,[status(thm)],[])).
% 19.86/20.11 tff(71,plain,
% 19.86/20.11 ((~(((~(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))))),
% 19.86/20.11 inference(monotonicity,[status(thm)],[70])).
% 19.86/20.11 tff(72,plain,
% 19.86/20.11 ((~(((~(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))))),
% 19.86/20.11 inference(transitivity,[status(thm)],[71, 69])).
% 19.86/20.11 tff(73,plain,
% 19.86/20.11 (((~![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)))))),
% 19.86/20.11 inference(monotonicity,[status(thm)],[72])).
% 19.86/20.11 tff(74,plain,
% 19.86/20.11 (((~![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)))))),
% 19.86/20.11 inference(transitivity,[status(thm)],[73, 68])).
% 19.86/20.11 tff(75,plain,
% 19.86/20.11 ((~![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))))),
% 19.86/20.11 inference(quant_inst,[status(thm)],[])).
% 19.86/20.11 tff(76,plain,
% 19.86/20.11 ((~![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))))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[75, 74])).
% 19.86/20.11 tff(77,plain,
% 19.86/20.11 (~(((~(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)))),
% 19.86/20.11 inference(unit_resolution,[status(thm)],[76, 67])).
% 19.86/20.11 tff(78,plain,
% 19.86/20.11 ((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))),
% 19.86/20.11 inference(commutativity,[status(thm)],[])).
% 19.86/20.11 tff(79,plain,
% 19.86/20.11 ((~![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)))),
% 19.86/20.11 inference(quant_inst,[status(thm)],[])).
% 19.86/20.11 tff(80,plain,
% 19.86/20.11 (~(((~(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))),
% 19.86/20.11 inference(unit_resolution,[status(thm)],[79, 67])).
% 19.86/20.11 tff(81,plain,
% 19.86/20.11 (^[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)))))))),
% 19.86/20.11 inference(bind,[status(th)],[])).
% 19.86/20.11 tff(82,plain,
% 19.86/20.11 (![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))))))),
% 19.86/20.11 inference(quant_intro,[status(thm)],[81])).
% 19.86/20.11 tff(83,plain,
% 19.86/20.11 (^[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)))))))),
% 19.86/20.11 inference(bind,[status(th)],[])).
% 19.86/20.11 tff(84,plain,
% 19.86/20.11 (![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))))))),
% 19.86/20.11 inference(quant_intro,[status(thm)],[83])).
% 19.86/20.11 tff(85,plain,
% 19.86/20.11 (![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))))))),
% 19.86/20.11 inference(transitivity,[status(thm)],[84, 82])).
% 19.86/20.11 tff(86,plain,
% 19.86/20.11 (^[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))))))))),
% 19.86/20.11 inference(bind,[status(th)],[])).
% 19.86/20.11 tff(87,plain,
% 19.86/20.11 (![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))))))),
% 19.86/20.11 inference(quant_intro,[status(thm)],[86])).
% 19.86/20.11 tff(88,plain,
% 19.86/20.11 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 19.86/20.11 inference(rewrite,[status(thm)],[])).
% 19.86/20.11 tff(89,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_1')).
% 19.86/20.11 tff(90,plain,
% 19.86/20.11 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 19.86/20.11 inference(modus_ponens,[status(thm)],[89, 88])).
% 19.86/20.11 tff(91,plain,(
% 19.86/20.11 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 19.86/20.11 inference(skolemize,[status(sab)],[90])).
% 19.86/20.11 tff(92,plain,
% 19.86/20.11 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 19.94/20.11 inference(modus_ponens,[status(thm)],[91, 87])).
% 19.94/20.11 tff(93,plain,
% 19.94/20.11 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 19.94/20.11 inference(modus_ponens,[status(thm)],[92, 85])).
% 19.94/20.11 tff(94,plain,
% 19.94/20.11 ((~![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))))))),
% 19.94/20.11 inference(quant_inst,[status(thm)],[])).
% 19.94/20.11 tff(95,plain,
% 19.94/20.11 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 19.94/20.11 inference(unit_resolution,[status(thm)],[94, 93])).
% 19.94/20.11 tff(96,plain,
% 19.94/20.11 (((~((~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))),
% 19.94/20.11 inference(tautology,[status(thm)],[])).
% 19.94/20.11 tff(97,plain,
% 19.94/20.11 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 19.94/20.11 inference(unit_resolution,[status(thm)],[96, 95])).
% 19.94/20.11 tff(98,plain,
% 19.94/20.11 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 19.94/20.11 inference(tautology,[status(thm)],[])).
% 19.94/20.11 tff(99,plain,
% 19.94/20.11 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 19.94/20.11 inference(unit_resolution,[status(thm)],[98, 40])).
% 19.94/20.11 tff(100,plain,
% 19.94/20.11 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 19.94/20.11 inference(unit_resolution,[status(thm)],[99, 97])).
% 19.94/20.11 tff(101,plain,
% 19.94/20.11 ((((~(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))),
% 19.94/20.11 inference(tautology,[status(thm)],[])).
% 19.94/20.11 tff(102,plain,
% 19.94/20.11 ((((~(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))))),
% 19.94/20.11 inference(unit_resolution,[status(thm)],[101, 100])).
% 19.94/20.11 tff(103,plain,
% 19.94/20.11 (~((~(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)))),
% 19.94/20.11 inference(unit_resolution,[status(thm)],[102, 80])).
% 19.94/20.11 tff(104,plain,
% 19.94/20.11 (((~(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)),
% 19.94/20.11 inference(tautology,[status(thm)],[])).
% 19.94/20.11 tff(105,plain,
% 19.94/20.11 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 19.94/20.11 inference(unit_resolution,[status(thm)],[104, 103])).
% 19.94/20.11 tff(106,plain,
% 19.94/20.11 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 19.94/20.11 inference(symmetry,[status(thm)],[105])).
% 19.94/20.11 tff(107,plain,
% 19.94/20.11 ((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)))),
% 19.94/20.11 inference(monotonicity,[status(thm)],[106])).
% 19.94/20.11 tff(108,plain,
% 19.94/20.11 ((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))),
% 19.94/20.11 inference(transitivity,[status(thm)],[107, 78])).
% 19.94/20.11 tff(109,plain,
% 19.94/20.11 ((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)),
% 19.94/20.11 inference(symmetry,[status(thm)],[108])).
% 19.94/20.11 tff(110,plain,
% 19.94/20.11 ((~![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))),
% 19.94/20.11 inference(quant_inst,[status(thm)],[])).
% 19.94/20.11 tff(111,plain,
% 19.94/20.11 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 19.94/20.11 inference(unit_resolution,[status(thm)],[110, 7])).
% 19.94/20.11 tff(112,plain,
% 19.94/20.11 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 19.94/20.11 inference(modus_ponens,[status(thm)],[111, 109])).
% 19.94/20.11 tff(113,plain,
% 19.94/20.11 (((~(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)),
% 19.94/20.11 inference(tautology,[status(thm)],[])).
% 19.94/20.11 tff(114,plain,
% 19.94/20.11 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 19.94/20.11 inference(unit_resolution,[status(thm)],[113, 103])).
% 19.94/20.11 tff(115,plain,
% 19.94/20.11 (((~(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)),
% 19.94/20.11 inference(tautology,[status(thm)],[])).
% 19.94/20.11 tff(116,plain,
% 19.94/20.11 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 19.94/20.11 inference(unit_resolution,[status(thm)],[115, 103])).
% 19.94/20.11 tff(117,plain,
% 19.94/20.11 ((~((~(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))),
% 19.94/20.11 inference(tautology,[status(thm)],[])).
% 19.94/20.11 tff(118,plain,
% 19.94/20.11 ((~((~(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))),
% 19.94/20.11 inference(unit_resolution,[status(thm)],[117, 116, 114])).
% 19.94/20.11 tff(119,plain,
% 19.94/20.11 (~((~(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)))),
% 19.94/20.11 inference(unit_resolution,[status(thm)],[118, 112])).
% 19.94/20.11 tff(120,plain,
% 19.94/20.11 ((((~(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))),
% 19.94/20.11 inference(tautology,[status(thm)],[])).
% 19.94/20.11 tff(121,plain,
% 19.94/20.11 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 19.94/20.11 inference(unit_resolution,[status(thm)],[120, 119, 77])).
% 19.94/20.11 tff(122,plain,
% 19.94/20.11 ((~((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)))),
% 19.94/20.11 inference(tautology,[status(thm)],[])).
% 19.94/20.11 tff(123,plain,
% 19.94/20.11 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 19.94/20.11 inference(unit_resolution,[status(thm)],[122, 121, 54])).
% 19.94/20.11 tff(124,plain,
% 19.94/20.11 (tptp_fun_X1_0(X1!1) = c(X1!1)),
% 19.94/20.11 inference(symmetry,[status(thm)],[123])).
% 19.94/20.11 tff(125,plain,
% 19.94/20.11 (test(X0!2)),
% 19.94/20.11 inference(and_elim,[status(thm)],[39])).
% 19.94/20.11 tff(126,plain,
% 19.94/20.11 (((~![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))))),
% 19.94/20.11 inference(rewrite,[status(thm)],[])).
% 19.94/20.11 tff(127,plain,
% 19.94/20.11 ((~![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))))),
% 19.94/20.11 inference(quant_inst,[status(thm)],[])).
% 19.94/20.11 tff(128,plain,
% 19.94/20.11 ((~![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)))),
% 19.94/20.11 inference(modus_ponens,[status(thm)],[127, 126])).
% 19.94/20.11 tff(129,plain,
% 19.94/20.11 ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))),
% 19.94/20.11 inference(unit_resolution,[status(thm)],[128, 50, 125])).
% 19.94/20.11 tff(130,plain,
% 19.94/20.11 (((~![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)))))),
% 19.94/20.11 inference(rewrite,[status(thm)],[])).
% 19.94/20.11 tff(131,plain,
% 19.94/20.11 ((~(((~(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))))),
% 19.94/20.11 inference(rewrite,[status(thm)],[])).
% 19.94/20.11 tff(132,plain,
% 19.94/20.11 ((((~(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)))),
% 19.94/20.11 inference(rewrite,[status(thm)],[])).
% 19.94/20.11 tff(133,plain,
% 19.94/20.11 ((~(((~(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))))),
% 19.94/20.12 inference(monotonicity,[status(thm)],[132])).
% 19.94/20.12 tff(134,plain,
% 19.94/20.12 ((~(((~(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))))),
% 19.94/20.12 inference(transitivity,[status(thm)],[133, 131])).
% 19.94/20.12 tff(135,plain,
% 19.94/20.12 (((~![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)))))),
% 19.94/20.12 inference(monotonicity,[status(thm)],[134])).
% 19.94/20.12 tff(136,plain,
% 19.94/20.12 (((~![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)))))),
% 19.94/20.12 inference(transitivity,[status(thm)],[135, 130])).
% 19.94/20.12 tff(137,plain,
% 19.94/20.12 ((~![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))))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(138,plain,
% 19.94/20.12 ((~![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))))),
% 19.94/20.12 inference(modus_ponens,[status(thm)],[137, 136])).
% 19.94/20.12 tff(139,plain,
% 19.94/20.12 (~(((~(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)))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[138, 67])).
% 19.94/20.12 tff(140,plain,
% 19.94/20.12 ((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))),
% 19.94/20.12 inference(commutativity,[status(thm)],[])).
% 19.94/20.12 tff(141,plain,
% 19.94/20.12 ((~![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)))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(142,plain,
% 19.94/20.12 (~(((~(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))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[141, 67])).
% 19.94/20.12 tff(143,plain,
% 19.94/20.12 ((~![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))))))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(144,plain,
% 19.94/20.12 (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2)))))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[143, 93])).
% 19.94/20.12 tff(145,plain,
% 19.94/20.12 (((~((~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))),
% 19.94/20.12 inference(tautology,[status(thm)],[])).
% 19.94/20.12 tff(146,plain,
% 19.94/20.12 ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[145, 144])).
% 19.94/20.12 tff(147,plain,
% 19.94/20.12 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 19.94/20.12 inference(tautology,[status(thm)],[])).
% 19.94/20.12 tff(148,plain,
% 19.94/20.12 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[147, 125])).
% 19.94/20.12 tff(149,plain,
% 19.94/20.12 (complement(tptp_fun_X1_0(X0!2), X0!2)),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[148, 146])).
% 19.94/20.12 tff(150,plain,
% 19.94/20.12 ((((~(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))),
% 19.94/20.12 inference(tautology,[status(thm)],[])).
% 19.94/20.12 tff(151,plain,
% 19.94/20.12 ((((~(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))))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[150, 149])).
% 19.94/20.12 tff(152,plain,
% 19.94/20.12 (~((~(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)))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[151, 142])).
% 19.94/20.12 tff(153,plain,
% 19.94/20.12 (((~(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)),
% 19.94/20.12 inference(tautology,[status(thm)],[])).
% 19.94/20.12 tff(154,plain,
% 19.94/20.12 (addition(X0!2, tptp_fun_X1_0(X0!2)) = one),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[153, 152])).
% 19.94/20.12 tff(155,plain,
% 19.94/20.12 (one = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 19.94/20.12 inference(symmetry,[status(thm)],[154])).
% 19.94/20.12 tff(156,plain,
% 19.94/20.12 ((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)))),
% 19.94/20.12 inference(monotonicity,[status(thm)],[155])).
% 19.94/20.12 tff(157,plain,
% 19.94/20.12 ((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))),
% 19.94/20.12 inference(transitivity,[status(thm)],[156, 140])).
% 19.94/20.12 tff(158,plain,
% 19.94/20.12 ((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)),
% 19.94/20.12 inference(symmetry,[status(thm)],[157])).
% 19.94/20.12 tff(159,plain,
% 19.94/20.12 ((~![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))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(160,plain,
% 19.94/20.12 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[159, 7])).
% 19.94/20.12 tff(161,plain,
% 19.94/20.12 (addition(tptp_fun_X1_0(X0!2), X0!2) = one),
% 19.94/20.12 inference(modus_ponens,[status(thm)],[160, 158])).
% 19.94/20.12 tff(162,plain,
% 19.94/20.12 (((~(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)),
% 19.94/20.12 inference(tautology,[status(thm)],[])).
% 19.94/20.12 tff(163,plain,
% 19.94/20.12 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[162, 152])).
% 19.94/20.12 tff(164,plain,
% 19.94/20.12 (((~(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)),
% 19.94/20.12 inference(tautology,[status(thm)],[])).
% 19.94/20.12 tff(165,plain,
% 19.94/20.12 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[164, 152])).
% 19.94/20.12 tff(166,plain,
% 19.94/20.12 ((~((~(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))),
% 19.94/20.12 inference(tautology,[status(thm)],[])).
% 19.94/20.12 tff(167,plain,
% 19.94/20.12 ((~((~(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))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[166, 165, 163])).
% 19.94/20.12 tff(168,plain,
% 19.94/20.12 (~((~(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)))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[167, 161])).
% 19.94/20.12 tff(169,plain,
% 19.94/20.12 ((((~(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))),
% 19.94/20.12 inference(tautology,[status(thm)],[])).
% 19.94/20.12 tff(170,plain,
% 19.94/20.12 (complement(X0!2, tptp_fun_X1_0(X0!2))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[169, 168, 139])).
% 19.94/20.12 tff(171,plain,
% 19.94/20.12 ((~((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)))),
% 19.94/20.12 inference(tautology,[status(thm)],[])).
% 19.94/20.12 tff(172,plain,
% 19.94/20.12 (c(X0!2) = tptp_fun_X1_0(X0!2)),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[171, 170, 129])).
% 19.94/20.12 tff(173,plain,
% 19.94/20.12 (tptp_fun_X1_0(X0!2) = c(X0!2)),
% 19.94/20.12 inference(symmetry,[status(thm)],[172])).
% 19.94/20.12 tff(174,plain,
% 19.94/20.12 (multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)) = multiplication(c(X0!2), c(X1!1))),
% 19.94/20.12 inference(monotonicity,[status(thm)],[173, 124])).
% 19.94/20.12 tff(175,plain,
% 19.94/20.12 (multiplication(c(X0!2), c(X1!1)) = multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 19.94/20.12 inference(symmetry,[status(thm)],[174])).
% 19.94/20.12 tff(176,plain,
% 19.94/20.12 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 19.94/20.12 inference(monotonicity,[status(thm)],[175])).
% 19.94/20.12 tff(177,plain,
% 19.94/20.12 (addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 19.94/20.12 inference(symmetry,[status(thm)],[176])).
% 19.94/20.12 tff(178,plain,
% 19.94/20.12 (^[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))))),
% 19.94/20.12 inference(bind,[status(th)],[])).
% 19.94/20.12 tff(179,plain,
% 19.94/20.12 (![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)))),
% 19.94/20.12 inference(quant_intro,[status(thm)],[178])).
% 19.94/20.12 tff(180,plain,
% 19.94/20.12 (![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)))),
% 19.94/20.12 inference(rewrite,[status(thm)],[])).
% 19.94/20.12 tff(181,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')).
% 19.94/20.12 tff(182,plain,
% 19.94/20.12 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 19.94/20.12 inference(modus_ponens,[status(thm)],[181, 180])).
% 19.94/20.12 tff(183,plain,(
% 19.94/20.12 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 19.94/20.12 inference(skolemize,[status(sab)],[182])).
% 19.94/20.12 tff(184,plain,
% 19.94/20.12 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 19.94/20.12 inference(modus_ponens,[status(thm)],[183, 179])).
% 19.94/20.12 tff(185,plain,
% 19.94/20.12 ((~![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), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(186,plain,
% 19.94/20.12 (multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[185, 184])).
% 19.94/20.12 tff(187,plain,
% 19.94/20.12 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 19.94/20.12 inference(symmetry,[status(thm)],[160])).
% 19.94/20.12 tff(188,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)).
% 19.94/20.12 tff(189,plain,
% 19.94/20.12 ((~![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: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))))))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(190,plain,
% 19.94/20.12 ($false),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[189, 93, 188])).
% 19.94/20.12 tff(191,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,[]))).
% 19.94/20.12 tff(192,plain,
% 19.94/20.12 (((~((~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))))),
% 19.94/20.12 inference(tautology,[status(thm)],[])).
% 19.94/20.12 tff(193,plain,
% 19.94/20.12 (test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[192, 191])).
% 19.94/20.12 tff(194,assumption,(![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))), introduced(assumption)).
% 19.94/20.12 tff(195,plain,
% 19.94/20.12 ((~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))) | (~complement(X0!2, tptp_fun_X1_0(X0!2)))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(196,plain,
% 19.94/20.12 ($false),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[195, 170, 194])).
% 19.94/20.12 tff(197,plain,(~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2)))), inference(lemma,lemma(discharge,[]))).
% 19.94/20.12 tff(198,plain,
% 19.94/20.12 ((~(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)))),
% 19.94/20.12 inference(tautology,[status(thm)],[])).
% 19.94/20.12 tff(199,plain,
% 19.94/20.12 ((~(test(tptp_fun_X1_0(X0!2)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X0!2))))) | test(tptp_fun_X1_0(X0!2))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[198, 197])).
% 19.94/20.12 tff(200,plain,
% 19.94/20.12 (test(tptp_fun_X1_0(X0!2))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[199, 193])).
% 19.94/20.12 tff(201,plain,
% 19.94/20.12 (((~![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)))),
% 19.94/20.12 inference(rewrite,[status(thm)],[])).
% 19.94/20.12 tff(202,plain,
% 19.94/20.12 ((~![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)))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(203,plain,
% 19.94/20.12 ((~![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))),
% 19.94/20.12 inference(modus_ponens,[status(thm)],[202, 201])).
% 19.94/20.12 tff(204,plain,
% 19.94/20.12 ((~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))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[203, 50])).
% 19.94/20.12 tff(205,plain,
% 19.94/20.12 ((c(tptp_fun_X1_0(X0!2)) = X0!2) <=> complement(tptp_fun_X1_0(X0!2), X0!2)),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[204, 200])).
% 19.94/20.12 tff(206,plain,
% 19.94/20.12 ((~((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))),
% 19.94/20.12 inference(tautology,[status(thm)],[])).
% 19.94/20.12 tff(207,plain,
% 19.94/20.12 ((~((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)),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[206, 149])).
% 19.94/20.12 tff(208,plain,
% 19.94/20.12 (c(tptp_fun_X1_0(X0!2)) = X0!2),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[207, 205])).
% 19.94/20.12 tff(209,plain,
% 19.94/20.12 (addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 19.94/20.12 inference(monotonicity,[status(thm)],[208])).
% 19.94/20.12 tff(210,plain,
% 19.94/20.12 (addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))) = one),
% 19.94/20.12 inference(transitivity,[status(thm)],[209, 187, 154])).
% 19.94/20.12 tff(211,plain,
% 19.94/20.12 (multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1)) = multiplication(one, tptp_fun_X1_0(X1!1))),
% 19.94/20.12 inference(monotonicity,[status(thm)],[210])).
% 19.94/20.12 tff(212,plain,
% 19.94/20.12 (multiplication(one, tptp_fun_X1_0(X1!1)) = multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), tptp_fun_X1_0(X1!1))),
% 19.94/20.12 inference(symmetry,[status(thm)],[211])).
% 19.94/20.12 tff(213,plain,
% 19.94/20.12 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 19.94/20.12 inference(bind,[status(th)],[])).
% 19.94/20.12 tff(214,plain,
% 19.94/20.12 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 19.94/20.12 inference(quant_intro,[status(thm)],[213])).
% 19.94/20.12 tff(215,plain,
% 19.94/20.12 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 19.94/20.12 inference(rewrite,[status(thm)],[])).
% 19.94/20.12 tff(216,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 19.94/20.12 tff(217,plain,
% 19.94/20.12 (![A: $i] : (multiplication(one, A) = A)),
% 19.94/20.12 inference(modus_ponens,[status(thm)],[216, 215])).
% 19.94/20.12 tff(218,plain,(
% 19.94/20.12 ![A: $i] : (multiplication(one, A) = A)),
% 19.94/20.12 inference(skolemize,[status(sab)],[217])).
% 19.94/20.12 tff(219,plain,
% 19.94/20.12 (![A: $i] : (multiplication(one, A) = A)),
% 19.94/20.12 inference(modus_ponens,[status(thm)],[218, 214])).
% 19.94/20.12 tff(220,plain,
% 19.94/20.12 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, tptp_fun_X1_0(X1!1)) = tptp_fun_X1_0(X1!1))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(221,plain,
% 19.94/20.12 (multiplication(one, tptp_fun_X1_0(X1!1)) = tptp_fun_X1_0(X1!1)),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[220, 219])).
% 19.94/20.12 tff(222,plain,
% 19.94/20.12 (tptp_fun_X1_0(X1!1) = multiplication(one, tptp_fun_X1_0(X1!1))),
% 19.94/20.12 inference(symmetry,[status(thm)],[221])).
% 19.94/20.12 tff(223,plain,
% 19.94/20.12 (tptp_fun_X1_0(X1!1) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 19.94/20.12 inference(transitivity,[status(thm)],[222, 212, 186, 177])).
% 19.94/20.12 tff(224,plain,
% 19.94/20.12 (addition(tptp_fun_X1_0(X1!1), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.12 inference(monotonicity,[status(thm)],[223, 30])).
% 19.94/20.12 tff(225,plain,
% 19.94/20.12 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = addition(tptp_fun_X1_0(X1!1), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.12 inference(symmetry,[status(thm)],[224])).
% 19.94/20.12 tff(226,plain,
% 19.94/20.12 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(227,plain,
% 19.94/20.12 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[226, 18])).
% 19.94/20.12 tff(228,plain,
% 19.94/20.12 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 19.94/20.12 inference(bind,[status(th)],[])).
% 19.94/20.12 tff(229,plain,
% 19.94/20.12 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 19.94/20.12 inference(quant_intro,[status(thm)],[228])).
% 19.94/20.12 tff(230,plain,
% 19.94/20.12 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 19.94/20.12 inference(rewrite,[status(thm)],[])).
% 19.94/20.12 tff(231,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 19.94/20.12 tff(232,plain,
% 19.94/20.12 (![A: $i] : (multiplication(A, one) = A)),
% 19.94/20.12 inference(modus_ponens,[status(thm)],[231, 230])).
% 19.94/20.12 tff(233,plain,(
% 19.94/20.12 ![A: $i] : (multiplication(A, one) = A)),
% 19.94/20.12 inference(skolemize,[status(sab)],[232])).
% 19.94/20.12 tff(234,plain,
% 19.94/20.12 (![A: $i] : (multiplication(A, one) = A)),
% 19.94/20.12 inference(modus_ponens,[status(thm)],[233, 229])).
% 19.94/20.12 tff(235,plain,
% 19.94/20.12 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(c(tptp_fun_X1_0(X0!2)), one) = c(tptp_fun_X1_0(X0!2)))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(236,plain,
% 19.94/20.12 (multiplication(c(tptp_fun_X1_0(X0!2)), one) = c(tptp_fun_X1_0(X0!2))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[235, 234])).
% 19.94/20.12 tff(237,plain,
% 19.94/20.12 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 19.94/20.12 inference(bind,[status(th)],[])).
% 19.94/20.12 tff(238,plain,
% 19.94/20.12 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 19.94/20.12 inference(quant_intro,[status(thm)],[237])).
% 19.94/20.12 tff(239,plain,
% 19.94/20.12 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 19.94/20.12 inference(rewrite,[status(thm)],[])).
% 19.94/20.12 tff(240,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 19.94/20.12 tff(241,plain,
% 19.94/20.12 (![A: $i] : (addition(A, A) = A)),
% 19.94/20.12 inference(modus_ponens,[status(thm)],[240, 239])).
% 19.94/20.12 tff(242,plain,(
% 19.94/20.12 ![A: $i] : (addition(A, A) = A)),
% 19.94/20.12 inference(skolemize,[status(sab)],[241])).
% 19.94/20.12 tff(243,plain,
% 19.94/20.12 (![A: $i] : (addition(A, A) = A)),
% 19.94/20.12 inference(modus_ponens,[status(thm)],[242, 238])).
% 19.94/20.12 tff(244,plain,
% 19.94/20.12 ((~![A: $i] : (addition(A, A) = A)) | (addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)) = tptp_fun_X1_0(X0!2))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(245,plain,
% 19.94/20.12 (addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)) = tptp_fun_X1_0(X0!2)),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[244, 243])).
% 19.94/20.12 tff(246,plain,
% 19.94/20.12 (addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 19.94/20.12 inference(monotonicity,[status(thm)],[245, 208])).
% 19.94/20.12 tff(247,plain,
% 19.94/20.12 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2))))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(248,plain,
% 19.94/20.12 (addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))) = addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X0!2)))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[247, 18])).
% 19.94/20.12 tff(249,plain,
% 19.94/20.12 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 19.94/20.12 inference(symmetry,[status(thm)],[209])).
% 19.94/20.12 tff(250,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)).
% 19.94/20.12 tff(251,plain,
% 19.94/20.12 ((~![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: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))))))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(252,plain,
% 19.94/20.12 ($false),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[251, 93, 250])).
% 19.94/20.12 tff(253,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,[]))).
% 19.94/20.12 tff(254,plain,
% 19.94/20.12 (((~((~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))))),
% 19.94/20.12 inference(tautology,[status(thm)],[])).
% 19.94/20.12 tff(255,plain,
% 19.94/20.12 (test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[254, 253])).
% 19.94/20.12 tff(256,assumption,(![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))), introduced(assumption)).
% 19.94/20.12 tff(257,plain,
% 19.94/20.12 ((~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))) | (~complement(X1!1, tptp_fun_X1_0(X1!1)))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(258,plain,
% 19.94/20.12 ($false),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[257, 121, 256])).
% 19.94/20.12 tff(259,plain,(~![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1)))), inference(lemma,lemma(discharge,[]))).
% 19.94/20.12 tff(260,plain,
% 19.94/20.12 ((~(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)))),
% 19.94/20.12 inference(tautology,[status(thm)],[])).
% 19.94/20.12 tff(261,plain,
% 19.94/20.12 ((~(test(tptp_fun_X1_0(X1!1)) | ![X1: $i] : (~complement(X1, tptp_fun_X1_0(X1!1))))) | test(tptp_fun_X1_0(X1!1))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[260, 259])).
% 19.94/20.12 tff(262,plain,
% 19.94/20.12 (test(tptp_fun_X1_0(X1!1))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[261, 255])).
% 19.94/20.12 tff(263,plain,
% 19.94/20.12 (((~![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)))),
% 19.94/20.12 inference(rewrite,[status(thm)],[])).
% 19.94/20.12 tff(264,plain,
% 19.94/20.12 ((~![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)))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(265,plain,
% 19.94/20.12 ((~![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))),
% 19.94/20.12 inference(modus_ponens,[status(thm)],[264, 263])).
% 19.94/20.12 tff(266,plain,
% 19.94/20.12 ((~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))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[265, 50])).
% 19.94/20.12 tff(267,plain,
% 19.94/20.12 ((c(tptp_fun_X1_0(X1!1)) = X1!1) <=> complement(tptp_fun_X1_0(X1!1), X1!1)),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[266, 262])).
% 19.94/20.12 tff(268,plain,
% 19.94/20.12 ((~((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))),
% 19.94/20.12 inference(tautology,[status(thm)],[])).
% 19.94/20.12 tff(269,plain,
% 19.94/20.12 ((~((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)),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[268, 100])).
% 19.94/20.12 tff(270,plain,
% 19.94/20.12 (c(tptp_fun_X1_0(X1!1)) = X1!1),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[269, 267])).
% 19.94/20.12 tff(271,plain,
% 19.94/20.12 (addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 19.94/20.12 inference(monotonicity,[status(thm)],[270])).
% 19.94/20.12 tff(272,plain,
% 19.94/20.12 (addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 19.94/20.12 inference(transitivity,[status(thm)],[271, 105, 155, 160, 249])).
% 19.94/20.12 tff(273,plain,
% 19.94/20.12 (addition(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 19.94/20.12 inference(monotonicity,[status(thm)],[272])).
% 19.94/20.12 tff(274,plain,
% 19.94/20.12 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = addition(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(275,plain,
% 19.94/20.12 (addition(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1))) = addition(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[274, 18])).
% 19.94/20.12 tff(276,plain,
% 19.94/20.12 (addition(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)))),
% 19.94/20.12 inference(symmetry,[status(thm)],[275])).
% 19.94/20.12 tff(277,plain,
% 19.94/20.12 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(278,plain,
% 19.94/20.12 (addition(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[277, 7])).
% 19.94/20.12 tff(279,plain,
% 19.94/20.12 (addition(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = addition(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X1!1))),
% 19.94/20.12 inference(symmetry,[status(thm)],[278])).
% 19.94/20.12 tff(280,plain,
% 19.94/20.12 (addition(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = one),
% 19.94/20.12 inference(transitivity,[status(thm)],[279, 276, 273, 248, 246, 187, 154])).
% 19.94/20.12 tff(281,plain,
% 19.94/20.12 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(c(tptp_fun_X1_0(X0!2)), one)),
% 19.94/20.12 inference(monotonicity,[status(thm)],[280])).
% 19.94/20.12 tff(282,plain,
% 19.94/20.12 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(283,plain,
% 19.94/20.12 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[282, 27])).
% 19.94/20.12 tff(284,plain,
% 19.94/20.12 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.12 inference(symmetry,[status(thm)],[283])).
% 19.94/20.12 tff(285,plain,
% 19.94/20.12 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = X0!2),
% 19.94/20.12 inference(transitivity,[status(thm)],[284, 281, 236, 208])).
% 19.94/20.12 tff(286,plain,
% 19.94/20.12 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = addition(multiplication(c(X0!2), c(X1!1)), X0!2)),
% 19.94/20.12 inference(monotonicity,[status(thm)],[285])).
% 19.94/20.12 tff(287,plain,
% 19.94/20.12 (addition(multiplication(c(X0!2), c(X1!1)), X0!2) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 19.94/20.12 inference(symmetry,[status(thm)],[286])).
% 19.94/20.12 tff(288,plain,
% 19.94/20.12 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), c(X1!1)), X0!2) = addition(X0!2, multiplication(c(X0!2), c(X1!1))))),
% 19.94/20.12 inference(quant_inst,[status(thm)],[])).
% 19.94/20.12 tff(289,plain,
% 19.94/20.12 (addition(multiplication(c(X0!2), c(X1!1)), X0!2) = addition(X0!2, multiplication(c(X0!2), c(X1!1)))),
% 19.94/20.12 inference(unit_resolution,[status(thm)],[288, 7])).
% 19.94/20.12 tff(290,plain,
% 19.94/20.12 (addition(X0!2, multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), X0!2)),
% 19.94/20.12 inference(symmetry,[status(thm)],[289])).
% 19.94/20.12 tff(291,plain,
% 19.94/20.12 (addition(X0!2, multiplication(c(X0!2), c(X1!1))) = addition(tptp_fun_X1_0(X1!1), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.12 inference(transitivity,[status(thm)],[290, 287, 227, 225])).
% 19.94/20.12 tff(292,plain,
% 19.94/20.12 (X1!1 = c(tptp_fun_X1_0(X1!1))),
% 19.94/20.12 inference(symmetry,[status(thm)],[270])).
% 19.94/20.12 tff(293,plain,
% 19.94/20.13 (addition(X1!1, addition(X0!2, multiplication(c(X0!2), c(X1!1)))) = addition(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X1!1), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[292, 291])).
% 19.94/20.13 tff(294,plain,
% 19.94/20.13 (addition(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X1!1), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))) = addition(X1!1, addition(X0!2, multiplication(c(X0!2), c(X1!1))))),
% 19.94/20.13 inference(symmetry,[status(thm)],[293])).
% 19.94/20.13 tff(295,plain,
% 19.94/20.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X1!1), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))) = addition(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(296,plain,
% 19.94/20.13 (addition(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X1!1), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))) = addition(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[295, 18])).
% 19.94/20.13 tff(297,plain,
% 19.94/20.13 (addition(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))) = addition(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X1!1), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))))),
% 19.94/20.13 inference(symmetry,[status(thm)],[296])).
% 19.94/20.13 tff(298,plain,
% 19.94/20.13 (addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = one),
% 19.94/20.13 inference(transitivity,[status(thm)],[271, 105])).
% 19.94/20.13 tff(299,plain,
% 19.94/20.13 (addition(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))) = addition(one, addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[298])).
% 19.94/20.13 tff(300,plain,
% 19.94/20.13 (addition(one, addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))) = addition(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.13 inference(symmetry,[status(thm)],[299])).
% 19.94/20.13 tff(301,plain,
% 19.94/20.13 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(302,plain,
% 19.94/20.13 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[301, 27])).
% 19.94/20.13 tff(303,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = addition(c(X1!1), c(X0!2))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[124, 173])).
% 19.94/20.13 tff(304,plain,
% 19.94/20.13 (addition(c(X1!1), c(X0!2)) = addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))),
% 19.94/20.13 inference(symmetry,[status(thm)],[303])).
% 19.94/20.13 tff(305,plain,
% 19.94/20.13 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[304])).
% 19.94/20.13 tff(306,plain,
% 19.94/20.13 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))),
% 19.94/20.13 inference(transitivity,[status(thm)],[305, 302])).
% 19.94/20.13 tff(307,plain,
% 19.94/20.13 ((~![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(c(tptp_fun_X1_0(X1!1)), addition(c(X1!1), c(X0!2)))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2)))))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(308,plain,
% 19.94/20.13 (multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), addition(c(X1!1), c(X0!2)))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[307, 27])).
% 19.94/20.13 tff(309,plain,
% 19.94/20.13 (addition(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[208, 245])).
% 19.94/20.13 tff(310,plain,
% 19.94/20.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = addition(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(311,plain,
% 19.94/20.13 (addition(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2))) = addition(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[310, 18])).
% 19.94/20.13 tff(312,plain,
% 19.94/20.13 (addition(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)))),
% 19.94/20.13 inference(symmetry,[status(thm)],[311])).
% 19.94/20.13 tff(313,plain,
% 19.94/20.13 (addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[208])).
% 19.94/20.13 tff(314,plain,
% 19.94/20.13 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 19.94/20.13 inference(symmetry,[status(thm)],[313])).
% 19.94/20.13 tff(315,plain,
% 19.94/20.13 (addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)) = addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 19.94/20.13 inference(transitivity,[status(thm)],[271, 105, 155, 314])).
% 19.94/20.13 tff(316,plain,
% 19.94/20.13 (addition(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = addition(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[315])).
% 19.94/20.13 tff(317,plain,
% 19.94/20.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = addition(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(318,plain,
% 19.94/20.13 (addition(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = addition(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[317, 18])).
% 19.94/20.13 tff(319,plain,
% 19.94/20.13 (addition(c(tptp_fun_X1_0(X1!1)), addition(c(X1!1), c(X0!2))) = addition(c(tptp_fun_X1_0(X1!1)), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[304])).
% 19.94/20.13 tff(320,plain,
% 19.94/20.13 (addition(c(tptp_fun_X1_0(X1!1)), addition(c(X1!1), c(X0!2))) = one),
% 19.94/20.13 inference(transitivity,[status(thm)],[319, 318, 316, 312, 309, 154])).
% 19.94/20.13 tff(321,plain,
% 19.94/20.13 (multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), addition(c(X1!1), c(X0!2)))) = multiplication(tptp_fun_X1_0(X0!2), one)),
% 19.94/20.13 inference(monotonicity,[status(thm)],[320])).
% 19.94/20.13 tff(322,plain,
% 19.94/20.13 (multiplication(tptp_fun_X1_0(X0!2), one) = multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), addition(c(X1!1), c(X0!2))))),
% 19.94/20.13 inference(symmetry,[status(thm)],[321])).
% 19.94/20.13 tff(323,plain,
% 19.94/20.13 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(tptp_fun_X1_0(X0!2), one) = tptp_fun_X1_0(X0!2))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(324,plain,
% 19.94/20.13 (multiplication(tptp_fun_X1_0(X0!2), one) = tptp_fun_X1_0(X0!2)),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[323, 234])).
% 19.94/20.13 tff(325,plain,
% 19.94/20.13 (tptp_fun_X1_0(X0!2) = multiplication(tptp_fun_X1_0(X0!2), one)),
% 19.94/20.13 inference(symmetry,[status(thm)],[324])).
% 19.94/20.13 tff(326,plain,
% 19.94/20.13 (tptp_fun_X1_0(X0!2) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))))),
% 19.94/20.13 inference(transitivity,[status(thm)],[325, 322, 308])).
% 19.94/20.13 tff(327,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2)))) = addition(addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2)))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[326, 306])).
% 19.94/20.13 tff(328,plain,
% 19.94/20.13 (addition(addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2)))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))) = addition(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2))))),
% 19.94/20.13 inference(symmetry,[status(thm)],[327])).
% 19.94/20.13 tff(329,plain,
% 19.94/20.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))))) = addition(addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2)))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(330,plain,
% 19.94/20.13 (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))))) = addition(addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2)))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[329, 18])).
% 19.94/20.13 tff(331,plain,
% 19.94/20.13 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, addition(c(X1!1), c(X0!2))) = addition(c(X1!1), c(X0!2)))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(332,plain,
% 19.94/20.13 (multiplication(one, addition(c(X1!1), c(X0!2))) = addition(c(X1!1), c(X0!2))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[331, 219])).
% 19.94/20.13 tff(333,plain,
% 19.94/20.13 (multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), addition(c(X1!1), c(X0!2))) = multiplication(one, addition(c(X1!1), c(X0!2)))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[210])).
% 19.94/20.13 tff(334,plain,
% 19.94/20.13 ((~![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), c(tptp_fun_X1_0(X0!2))), addition(c(X1!1), c(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2)))))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(335,plain,
% 19.94/20.13 (multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), addition(c(X1!1), c(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2))))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[334, 184])).
% 19.94/20.13 tff(336,plain,
% 19.94/20.13 (addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2)))) = multiplication(addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))), addition(c(X1!1), c(X0!2)))),
% 19.94/20.13 inference(symmetry,[status(thm)],[335])).
% 19.94/20.13 tff(337,plain,
% 19.94/20.13 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2)))),
% 19.94/20.13 inference(symmetry,[status(thm)],[305])).
% 19.94/20.13 tff(338,plain,
% 19.94/20.13 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 19.94/20.13 inference(symmetry,[status(thm)],[302])).
% 19.94/20.13 tff(339,plain,
% 19.94/20.13 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2)))),
% 19.94/20.13 inference(transitivity,[status(thm)],[338, 337])).
% 19.94/20.13 tff(340,plain,
% 19.94/20.13 (addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))) = addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2))))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[339])).
% 19.94/20.13 tff(341,plain,
% 19.94/20.13 (addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))) = addition(c(X1!1), c(X0!2))),
% 19.94/20.13 inference(transitivity,[status(thm)],[340, 336, 333, 332])).
% 19.94/20.13 tff(342,plain,
% 19.94/20.13 (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), addition(c(X1!1), c(X0!2)))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[341])).
% 19.94/20.13 tff(343,plain,
% 19.94/20.13 (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), addition(c(X1!1), c(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)), multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)))))),
% 19.94/20.13 inference(symmetry,[status(thm)],[342])).
% 19.94/20.13 tff(344,plain,
% 19.94/20.13 (addition(c(X1!1), c(X0!2)) = multiplication(one, addition(c(X1!1), c(X0!2)))),
% 19.94/20.13 inference(symmetry,[status(thm)],[332])).
% 19.94/20.13 tff(345,plain,
% 19.94/20.13 (addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), addition(c(X1!1), c(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), multiplication(one, addition(c(X1!1), c(X0!2))))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[344])).
% 19.94/20.13 tff(346,plain,
% 19.94/20.13 (addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), multiplication(one, addition(c(X1!1), c(X0!2)))) = addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), addition(c(X1!1), c(X0!2)))),
% 19.94/20.13 inference(symmetry,[status(thm)],[345])).
% 19.94/20.13 tff(347,plain,
% 19.94/20.13 ((~![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), one), addition(c(X1!1), c(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), multiplication(one, addition(c(X1!1), c(X0!2)))))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(348,plain,
% 19.94/20.13 (multiplication(addition(tptp_fun_X1_0(X0!2), one), addition(c(X1!1), c(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), multiplication(one, addition(c(X1!1), c(X0!2))))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[347, 184])).
% 19.94/20.13 tff(349,plain,
% 19.94/20.13 (one = addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 19.94/20.13 inference(transitivity,[status(thm)],[155, 160, 249])).
% 19.94/20.13 tff(350,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X0!2), one) = addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[349])).
% 19.94/20.13 tff(351,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X0!2), one) = one),
% 19.94/20.13 inference(transitivity,[status(thm)],[350, 248, 246, 187, 154])).
% 19.94/20.13 tff(352,plain,
% 19.94/20.13 (multiplication(addition(tptp_fun_X1_0(X0!2), one), addition(c(X1!1), c(X0!2))) = multiplication(one, addition(c(X1!1), c(X0!2)))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[351])).
% 19.94/20.13 tff(353,plain,
% 19.94/20.13 (multiplication(one, addition(c(X1!1), c(X0!2))) = multiplication(addition(tptp_fun_X1_0(X0!2), one), addition(c(X1!1), c(X0!2)))),
% 19.94/20.13 inference(symmetry,[status(thm)],[352])).
% 19.94/20.13 tff(354,plain,
% 19.94/20.13 (addition(c(X1!1), c(X0!2)) = addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), addition(c(X1!1), c(X0!2)))),
% 19.94/20.13 inference(transitivity,[status(thm)],[344, 353, 348, 346])).
% 19.94/20.13 tff(355,plain,
% 19.94/20.13 (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), addition(c(X1!1), c(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), addition(c(X1!1), c(X0!2))))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[354])).
% 19.94/20.13 tff(356,plain,
% 19.94/20.13 (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), addition(c(X1!1), c(X0!2)))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), addition(c(X1!1), c(X0!2)))),
% 19.94/20.13 inference(symmetry,[status(thm)],[355])).
% 19.94/20.13 tff(357,plain,
% 19.94/20.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), addition(c(X1!1), c(X0!2)))) = addition(addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2)))), addition(c(X1!1), c(X0!2))))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(358,plain,
% 19.94/20.13 (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), addition(c(X1!1), c(X0!2)))) = addition(addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2)))), addition(c(X1!1), c(X0!2)))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[357, 18])).
% 19.94/20.13 tff(359,plain,
% 19.94/20.13 (addition(addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2)))), addition(c(X1!1), c(X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), addition(multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2))), addition(c(X1!1), c(X0!2))))),
% 19.94/20.13 inference(symmetry,[status(thm)],[358])).
% 19.94/20.13 tff(360,plain,
% 19.94/20.13 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (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)))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(361,plain,
% 19.94/20.13 (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))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[360, 7])).
% 19.94/20.13 tff(362,plain,
% 19.94/20.13 (addition(c(X1!1), c(X0!2)) = addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 19.94/20.13 inference(transitivity,[status(thm)],[304, 361])).
% 19.94/20.13 tff(363,plain,
% 19.94/20.13 (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2)))) = multiplication(tptp_fun_X1_0(X0!2), addition(c(tptp_fun_X1_0(X1!1)), addition(c(X1!1), c(X0!2))))),
% 19.94/20.13 inference(symmetry,[status(thm)],[308])).
% 19.94/20.13 tff(364,plain,
% 19.94/20.13 (addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2)))) = tptp_fun_X1_0(X0!2)),
% 19.94/20.13 inference(transitivity,[status(thm)],[363, 321, 324])).
% 19.94/20.13 tff(365,plain,
% 19.94/20.13 (addition(addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2)))), addition(c(X1!1), c(X0!2))) = addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[364, 362])).
% 19.94/20.13 tff(366,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = addition(addition(multiplication(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))), multiplication(tptp_fun_X1_0(X0!2), addition(c(X1!1), c(X0!2)))), addition(c(X1!1), c(X0!2)))),
% 19.94/20.13 inference(symmetry,[status(thm)],[365])).
% 19.94/20.13 tff(367,plain,
% 19.94/20.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(368,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))) = addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[367, 18])).
% 19.94/20.13 tff(369,plain,
% 19.94/20.13 (addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)))),
% 19.94/20.13 inference(symmetry,[status(thm)],[368])).
% 19.94/20.13 tff(370,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)) = c(X0!2)),
% 19.94/20.13 inference(transitivity,[status(thm)],[245, 173])).
% 19.94/20.13 tff(371,plain,
% 19.94/20.13 (addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(c(X0!2), c(X1!1))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[370, 124])).
% 19.94/20.13 tff(372,plain,
% 19.94/20.13 (addition(c(X0!2), c(X1!1)) = addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 19.94/20.13 inference(symmetry,[status(thm)],[371])).
% 19.94/20.13 tff(373,plain,
% 19.94/20.13 (addition(c(X0!2), c(X1!1)) = addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[172, 123])).
% 19.94/20.13 tff(374,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)) = addition(c(X0!2), c(X1!1))),
% 19.94/20.13 inference(symmetry,[status(thm)],[373])).
% 19.94/20.13 tff(375,plain,
% 19.94/20.13 (addition(c(X1!1), c(X0!2)) = addition(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2))))),
% 19.94/20.13 inference(transitivity,[status(thm)],[304, 361, 374, 372, 369, 366, 359, 356, 343, 330, 328])).
% 19.94/20.13 tff(376,plain,
% 19.94/20.13 (addition(addition(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))) = addition(addition(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2)))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[375, 30])).
% 19.94/20.13 tff(377,plain,
% 19.94/20.13 (addition(addition(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2)))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = addition(addition(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.13 inference(symmetry,[status(thm)],[376])).
% 19.94/20.13 tff(378,plain,
% 19.94/20.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = addition(addition(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2)))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(379,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = addition(addition(tptp_fun_X1_0(X0!2), multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2)))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[378, 18])).
% 19.94/20.13 tff(380,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X1!1), X1!1) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 19.94/20.13 inference(symmetry,[status(thm)],[111])).
% 19.94/20.13 tff(381,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 19.94/20.13 inference(monotonicity,[status(thm)],[270])).
% 19.94/20.13 tff(382,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))) = addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 19.94/20.13 inference(transitivity,[status(thm)],[381, 380, 105, 155, 314])).
% 19.94/20.13 tff(383,plain,
% 19.94/20.13 (addition(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)) = addition(addition(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[382])).
% 19.94/20.13 tff(384,plain,
% 19.94/20.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X1!1), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = addition(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2)))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(385,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X1!1), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = addition(addition(tptp_fun_X1_0(X1!1), c(tptp_fun_X1_0(X1!1))), tptp_fun_X1_0(X0!2))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[384, 18])).
% 19.94/20.13 tff(386,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X1!1), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2)))),
% 19.94/20.13 inference(transitivity,[status(thm)],[385, 383, 312, 309, 160, 249])).
% 19.94/20.13 tff(387,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))) = addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X0!2))))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[386])).
% 19.94/20.13 tff(388,plain,
% 19.94/20.13 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))) = addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(389,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))) = addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[388, 18])).
% 19.94/20.13 tff(390,plain,
% 19.94/20.13 (addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = addition(tptp_fun_X1_0(X0!2), addition(tptp_fun_X1_0(X1!1), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))))),
% 19.94/20.13 inference(symmetry,[status(thm)],[389])).
% 19.94/20.13 tff(391,plain,
% 19.94/20.13 (addition(addition(c(X0!2), c(X1!1)), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))) = addition(addition(tptp_fun_X1_0(X0!2), tptp_fun_X1_0(X1!1)), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[373])).
% 19.94/20.13 tff(392,plain,
% 19.94/20.13 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(393,plain,
% 19.94/20.13 (addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[392, 7])).
% 19.94/20.13 tff(394,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))) = addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 19.94/20.13 inference(symmetry,[status(thm)],[393])).
% 19.94/20.13 tff(395,plain,
% 19.94/20.13 (addition(c(X1!1), c(X0!2)) = addition(c(X0!2), c(X1!1))),
% 19.94/20.13 inference(transitivity,[status(thm)],[304, 361, 374])).
% 19.94/20.13 tff(396,plain,
% 19.94/20.13 (addition(addition(c(X1!1), c(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = addition(addition(c(X0!2), c(X1!1)), addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)))),
% 19.94/20.13 inference(monotonicity,[status(thm)],[395, 394])).
% 19.94/20.13 tff(397,plain,
% 19.94/20.13 (addition(addition(c(X1!1), c(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))) = one),
% 19.94/20.13 inference(transitivity,[status(thm)],[396, 391, 390, 387, 248, 246, 187, 154])).
% 19.94/20.13 tff(398,plain,
% 19.94/20.13 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(addition(c(X1!1), c(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(c(tptp_fun_X1_0(X0!2)), one)),
% 19.94/20.13 inference(monotonicity,[status(thm)],[397])).
% 19.94/20.13 tff(399,plain,
% 19.94/20.13 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(tptp_fun_X1_0(X0!2)), addition(addition(c(X1!1), c(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 19.94/20.13 inference(quant_inst,[status(thm)],[])).
% 19.94/20.13 tff(400,plain,
% 19.94/20.13 (multiplication(c(tptp_fun_X1_0(X0!2)), addition(addition(c(X1!1), c(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.13 inference(unit_resolution,[status(thm)],[399, 27])).
% 19.94/20.13 tff(401,plain,
% 19.94/20.13 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = multiplication(c(tptp_fun_X1_0(X0!2)), addition(addition(c(X1!1), c(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.13 inference(symmetry,[status(thm)],[400])).
% 19.94/20.13 tff(402,plain,
% 19.94/20.13 (addition(multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))) = X0!2),
% 19.94/20.13 inference(transitivity,[status(thm)],[401, 398, 236, 208])).
% 19.94/20.13 tff(403,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1)))))) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 19.94/20.13 inference(monotonicity,[status(thm)],[402])).
% 19.94/20.13 tff(404,plain,
% 19.94/20.13 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(tptp_fun_X1_0(X0!2), addition(multiplication(c(tptp_fun_X1_0(X0!2)), addition(c(X1!1), c(X0!2))), multiplication(c(tptp_fun_X1_0(X0!2)), addition(tptp_fun_X1_0(X0!2), c(tptp_fun_X1_0(X1!1))))))),
% 19.94/20.13 inference(symmetry,[status(thm)],[403])).
% 19.94/20.13 tff(405,plain,
% 19.94/20.13 (one = addition(addition(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.13 inference(transitivity,[status(thm)],[155, 160, 404, 379, 377])).
% 19.94/20.13 tff(406,plain,
% 19.94/20.13 (addition(one, addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))) = addition(addition(addition(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.14 inference(monotonicity,[status(thm)],[405])).
% 19.94/20.14 tff(407,plain,
% 19.94/20.14 (addition(addition(addition(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))) = addition(one, addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.14 inference(symmetry,[status(thm)],[406])).
% 19.94/20.14 tff(408,plain,
% 19.94/20.14 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(c(X1!1), c(X0!2)), addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))) = addition(addition(addition(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))))),
% 19.94/20.14 inference(quant_inst,[status(thm)],[])).
% 19.94/20.14 tff(409,plain,
% 19.94/20.14 (addition(addition(c(X1!1), c(X0!2)), addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))) = addition(addition(addition(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.14 inference(unit_resolution,[status(thm)],[408, 18])).
% 19.94/20.14 tff(410,plain,
% 19.94/20.14 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(tptp_fun_X1_0(X1!1), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)))),
% 19.94/20.14 inference(quant_inst,[status(thm)],[])).
% 19.94/20.14 tff(411,plain,
% 19.94/20.14 (addition(tptp_fun_X1_0(X1!1), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2))) = addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 19.94/20.14 inference(unit_resolution,[status(thm)],[410, 7])).
% 19.94/20.14 tff(412,plain,
% 19.94/20.14 (addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2)))),
% 19.94/20.14 inference(symmetry,[status(thm)],[411])).
% 19.94/20.14 tff(413,plain,
% 19.94/20.14 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)))),
% 19.94/20.14 inference(bind,[status(th)],[])).
% 19.94/20.14 tff(414,plain,
% 19.94/20.14 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 19.94/20.14 inference(quant_intro,[status(thm)],[413])).
% 19.94/20.14 tff(415,plain,
% 19.94/20.14 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C)) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 19.94/20.14 inference(rewrite,[status(thm)],[])).
% 19.94/20.14 tff(416,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_associativity')).
% 19.94/20.14 tff(417,plain,
% 19.94/20.14 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 19.94/20.14 inference(modus_ponens,[status(thm)],[416, 415])).
% 19.94/20.14 tff(418,plain,(
% 19.94/20.14 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 19.94/20.14 inference(skolemize,[status(sab)],[417])).
% 19.94/20.14 tff(419,plain,
% 19.94/20.14 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 19.94/20.14 inference(modus_ponens,[status(thm)],[418, 414])).
% 19.94/20.14 tff(420,plain,
% 19.94/20.14 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(one, multiplication(one, tptp_fun_X1_0(X0!2))) = multiplication(multiplication(one, one), tptp_fun_X1_0(X0!2)))),
% 19.94/20.14 inference(quant_inst,[status(thm)],[])).
% 19.94/20.14 tff(421,plain,
% 19.94/20.14 (multiplication(one, multiplication(one, tptp_fun_X1_0(X0!2))) = multiplication(multiplication(one, one), tptp_fun_X1_0(X0!2))),
% 19.94/20.14 inference(unit_resolution,[status(thm)],[420, 419])).
% 19.94/20.14 tff(422,assumption,(~(multiplication(one, tptp_fun_X1_0(X0!2)) = tptp_fun_X1_0(X0!2))), introduced(assumption)).
% 19.94/20.14 tff(423,plain,
% 19.94/20.14 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, tptp_fun_X1_0(X0!2)) = tptp_fun_X1_0(X0!2))),
% 19.94/20.14 inference(quant_inst,[status(thm)],[])).
% 19.94/20.14 tff(424,plain,
% 19.94/20.14 ($false),
% 19.94/20.14 inference(unit_resolution,[status(thm)],[423, 219, 422])).
% 19.94/20.14 tff(425,plain,(multiplication(one, tptp_fun_X1_0(X0!2)) = tptp_fun_X1_0(X0!2)), inference(lemma,lemma(discharge,[]))).
% 19.94/20.14 tff(426,plain,
% 19.94/20.14 (multiplication(one, multiplication(one, tptp_fun_X1_0(X0!2))) = multiplication(one, tptp_fun_X1_0(X0!2))),
% 19.94/20.14 inference(monotonicity,[status(thm)],[425])).
% 19.94/20.14 tff(427,plain,
% 19.94/20.14 (multiplication(one, tptp_fun_X1_0(X0!2)) = multiplication(one, multiplication(one, tptp_fun_X1_0(X0!2)))),
% 19.94/20.14 inference(symmetry,[status(thm)],[426])).
% 19.94/20.14 tff(428,plain,
% 19.94/20.14 (tptp_fun_X1_0(X0!2) = multiplication(one, tptp_fun_X1_0(X0!2))),
% 19.94/20.14 inference(symmetry,[status(thm)],[425])).
% 19.94/20.14 tff(429,plain,
% 19.94/20.14 (tptp_fun_X1_0(X0!2) = multiplication(multiplication(one, one), tptp_fun_X1_0(X0!2))),
% 19.94/20.14 inference(transitivity,[status(thm)],[428, 427, 421])).
% 19.94/20.14 tff(430,plain,
% 19.94/20.14 (multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(multiplication(one, one), tptp_fun_X1_0(X0!2)))),
% 19.94/20.14 inference(monotonicity,[status(thm)],[429])).
% 19.94/20.14 tff(431,plain,
% 19.94/20.14 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(multiplication(one, one), tptp_fun_X1_0(X0!2))) = multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 19.94/20.14 inference(symmetry,[status(thm)],[430])).
% 19.94/20.14 tff(432,plain,
% 19.94/20.14 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(multiplication(one, one), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2)))),
% 19.94/20.14 inference(quant_inst,[status(thm)],[])).
% 19.94/20.14 tff(433,plain,
% 19.94/20.14 (multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(multiplication(one, one), tptp_fun_X1_0(X0!2))) = multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2))),
% 19.94/20.14 inference(unit_resolution,[status(thm)],[432, 419])).
% 19.94/20.14 tff(434,plain,
% 19.94/20.14 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(multiplication(one, one), tptp_fun_X1_0(X0!2)))),
% 19.94/20.14 inference(symmetry,[status(thm)],[433])).
% 19.94/20.14 tff(435,plain,
% 19.94/20.14 (multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2)) = multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 19.94/20.14 inference(transitivity,[status(thm)],[434, 431])).
% 19.94/20.14 tff(436,plain,
% 19.94/20.14 (addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 19.94/20.14 inference(monotonicity,[status(thm)],[435])).
% 19.94/20.14 tff(437,plain,
% 19.94/20.14 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 19.94/20.14 inference(symmetry,[status(thm)],[436])).
% 19.94/20.14 tff(438,plain,
% 19.94/20.14 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(tptp_fun_X1_0(X1!1), one) = tptp_fun_X1_0(X1!1))),
% 19.94/20.14 inference(quant_inst,[status(thm)],[])).
% 19.94/20.14 tff(439,plain,
% 19.94/20.14 (multiplication(tptp_fun_X1_0(X1!1), one) = tptp_fun_X1_0(X1!1)),
% 19.94/20.14 inference(unit_resolution,[status(thm)],[438, 234])).
% 19.94/20.14 tff(440,plain,
% 19.94/20.14 (tptp_fun_X1_0(X1!1) = multiplication(tptp_fun_X1_0(X1!1), one)),
% 19.94/20.14 inference(symmetry,[status(thm)],[439])).
% 19.94/20.14 tff(441,plain,
% 19.94/20.14 (multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)) = multiplication(c(X1!1), c(X0!2))),
% 19.94/20.14 inference(monotonicity,[status(thm)],[124, 173])).
% 19.94/20.14 tff(442,plain,
% 19.94/20.14 (multiplication(c(X1!1), c(X0!2)) = multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))),
% 19.94/20.14 inference(symmetry,[status(thm)],[441])).
% 19.94/20.14 tff(443,plain,
% 19.94/20.14 (addition(multiplication(c(X1!1), c(X0!2)), tptp_fun_X1_0(X1!1)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), one))),
% 19.94/20.14 inference(monotonicity,[status(thm)],[442, 440])).
% 19.94/20.14 tff(444,plain,
% 19.94/20.14 (addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), one)) = addition(multiplication(c(X1!1), c(X0!2)), tptp_fun_X1_0(X1!1))),
% 19.94/20.14 inference(symmetry,[status(thm)],[443])).
% 19.94/20.14 tff(445,plain,
% 19.94/20.14 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), one)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), one)))),
% 19.94/20.14 inference(quant_inst,[status(thm)],[])).
% 19.94/20.14 tff(446,plain,
% 19.94/20.14 (multiplication(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), one)) = addition(multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), one))),
% 19.94/20.14 inference(unit_resolution,[status(thm)],[445, 27])).
% 19.94/20.14 tff(447,plain,
% 19.94/20.14 (multiplication(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), one)) = multiplication(tptp_fun_X1_0(X1!1), one)),
% 19.94/20.14 inference(monotonicity,[status(thm)],[351])).
% 19.94/20.14 tff(448,plain,
% 19.94/20.14 (multiplication(tptp_fun_X1_0(X1!1), one) = multiplication(tptp_fun_X1_0(X1!1), addition(tptp_fun_X1_0(X0!2), one))),
% 19.94/20.14 inference(symmetry,[status(thm)],[447])).
% 19.94/20.14 tff(449,plain,
% 19.94/20.14 (tptp_fun_X1_0(X1!1) = addition(multiplication(c(X1!1), c(X0!2)), tptp_fun_X1_0(X1!1))),
% 19.94/20.14 inference(transitivity,[status(thm)],[440, 448, 446, 444])).
% 19.94/20.14 tff(450,plain,
% 19.94/20.14 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1)) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(X1!1), c(X0!2)), tptp_fun_X1_0(X1!1)))),
% 19.94/20.14 inference(monotonicity,[status(thm)],[449])).
% 19.94/20.14 tff(451,plain,
% 19.94/20.14 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(X1!1), c(X0!2)), tptp_fun_X1_0(X1!1))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X1!1))),
% 19.94/20.14 inference(symmetry,[status(thm)],[450])).
% 19.94/20.14 tff(452,plain,
% 19.94/20.14 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(X1!1), c(X0!2)), tptp_fun_X1_0(X1!1))) = addition(addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))), tptp_fun_X1_0(X1!1)))),
% 19.94/20.14 inference(quant_inst,[status(thm)],[])).
% 19.94/20.14 tff(453,plain,
% 19.94/20.14 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(X1!1), c(X0!2)), tptp_fun_X1_0(X1!1))) = addition(addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))), tptp_fun_X1_0(X1!1))),
% 19.94/20.14 inference(unit_resolution,[status(thm)],[452, 18])).
% 19.94/20.14 tff(454,plain,
% 19.94/20.14 (addition(addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))), tptp_fun_X1_0(X1!1)) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), addition(multiplication(c(X1!1), c(X0!2)), tptp_fun_X1_0(X1!1)))),
% 19.94/20.14 inference(symmetry,[status(thm)],[453])).
% 19.94/20.14 tff(455,plain,
% 19.94/20.14 (multiplication(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = multiplication(one, tptp_fun_X1_0(X0!2))),
% 19.94/20.14 inference(monotonicity,[status(thm)],[298])).
% 19.94/20.14 tff(456,plain,
% 19.94/20.14 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))))),
% 19.94/20.14 inference(quant_inst,[status(thm)],[])).
% 19.94/20.14 tff(457,plain,
% 19.94/20.14 (multiplication(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 19.94/20.14 inference(unit_resolution,[status(thm)],[456, 184])).
% 19.94/20.14 tff(458,plain,
% 19.94/20.14 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2))) = multiplication(addition(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2))),
% 19.94/20.14 inference(symmetry,[status(thm)],[457])).
% 19.94/20.14 tff(459,plain,
% 19.94/20.14 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))) = addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(tptp_fun_X1_0(X1!1), tptp_fun_X1_0(X0!2)))),
% 19.94/20.14 inference(monotonicity,[status(thm)],[442])).
% 19.94/20.14 tff(460,plain,
% 19.94/20.14 (addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))) = c(X0!2)),
% 19.94/20.14 inference(transitivity,[status(thm)],[459, 458, 455, 425, 173])).
% 19.94/20.14 tff(461,plain,
% 19.94/20.14 (addition(addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))), tptp_fun_X1_0(X1!1)) = addition(c(X0!2), c(X1!1))),
% 19.94/20.14 inference(monotonicity,[status(thm)],[460, 124])).
% 19.94/20.14 tff(462,plain,
% 19.94/20.14 (addition(c(X0!2), c(X1!1)) = addition(addition(multiplication(c(tptp_fun_X1_0(X1!1)), tptp_fun_X1_0(X0!2)), multiplication(c(X1!1), c(X0!2))), tptp_fun_X1_0(X1!1))),
% 19.94/20.14 inference(symmetry,[status(thm)],[461])).
% 19.94/20.14 tff(463,plain,
% 19.94/20.14 (addition(c(X1!1), c(X0!2)) = addition(tptp_fun_X1_0(X1!1), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2)))),
% 19.94/20.14 inference(transitivity,[status(thm)],[304, 361, 374, 462, 454, 451, 437, 412])).
% 19.94/20.14 tff(464,plain,
% 19.94/20.14 (addition(addition(c(X1!1), c(X0!2)), addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))) = addition(addition(tptp_fun_X1_0(X1!1), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2))), addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))))),
% 19.94/20.14 inference(monotonicity,[status(thm)],[463])).
% 19.94/20.14 tff(465,plain,
% 19.94/20.14 (addition(addition(tptp_fun_X1_0(X1!1), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2))), addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))) = addition(addition(c(X1!1), c(X0!2)), addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))))),
% 19.94/20.14 inference(symmetry,[status(thm)],[464])).
% 19.94/20.14 tff(466,plain,
% 19.94/20.14 ((~![A: $i] : (addition(A, A) = A)) | (addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.14 inference(quant_inst,[status(thm)],[])).
% 19.94/20.14 tff(467,plain,
% 19.94/20.14 (addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))) = addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))),
% 19.94/20.14 inference(unit_resolution,[status(thm)],[466, 243])).
% 19.94/20.14 tff(468,plain,
% 19.94/20.14 (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))),
% 19.94/20.14 inference(symmetry,[status(thm)],[361])).
% 19.94/20.14 tff(469,plain,
% 19.94/20.14 (addition(tptp_fun_X1_0(X1!1), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2))) = addition(c(X1!1), c(X0!2))),
% 19.94/20.14 inference(transitivity,[status(thm)],[411, 436, 450, 453, 461, 373, 468, 303])).
% 19.94/20.14 tff(470,plain,
% 19.94/20.14 (addition(addition(tptp_fun_X1_0(X1!1), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2))), addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))) = addition(addition(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))))),
% 19.94/20.14 inference(monotonicity,[status(thm)],[469, 467])).
% 19.94/20.14 tff(471,plain,
% 19.94/20.14 (addition(addition(c(X1!1), c(X0!2)), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))) = addition(addition(tptp_fun_X1_0(X1!1), multiplication(multiplication(c(tptp_fun_X1_0(X1!1)), multiplication(one, one)), tptp_fun_X1_0(X0!2))), addition(addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1)))), addition(multiplication(c(tptp_fun_X1_0(X0!2)), tptp_fun_X1_0(X0!2)), multiplication(c(tptp_fun_X1_0(X0!2)), c(tptp_fun_X1_0(X1!1))))))),
% 19.94/20.14 inference(symmetry,[status(thm)],[470])).
% 19.94/20.14 tff(472,plain,
% 19.94/20.14 (one = addition(addition(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))),
% 19.94/20.14 inference(transitivity,[status(thm)],[155, 160, 404, 379, 377, 471, 465, 409, 407, 300, 297, 294, 20, 11])).
% 19.94/20.14 tff(473,plain,
% 19.94/20.14 (~(one = addition(addition(X0!2, X1!1), multiplication(c(X0!2), c(X1!1))))),
% 19.94/20.15 inference(or_elim,[status(thm)],[38])).
% 19.94/20.15 tff(474,plain,
% 19.94/20.15 ($false),
% 19.94/20.15 inference(unit_resolution,[status(thm)],[473, 472])).
% 19.94/20.15 % SZS output end Proof
% 19.94/20.15 % E exiting
%------------------------------------------------------------------------------