%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KLE011+3 : 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 1.50s 1.67s
% Output : Proof 1.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE011+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % 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 18:51:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 1.50/1.67 % SZS status Theorem
% 1.50/1.67 % SZS output start Proof
% 1.50/1.67 tff(addition_type, type, (
% 1.50/1.67 addition: ( $i * $i ) > $i)).
% 1.50/1.67 tff(multiplication_type, type, (
% 1.50/1.67 multiplication: ( $i * $i ) > $i)).
% 1.50/1.67 tff(c_type, type, (
% 1.50/1.67 c: $i > $i)).
% 1.50/1.67 tff(tptp_fun_X1_1_type, type, (
% 1.50/1.67 tptp_fun_X1_1: $i)).
% 1.50/1.67 tff(tptp_fun_X0_2_type, type, (
% 1.50/1.67 tptp_fun_X0_2: $i)).
% 1.50/1.67 tff(zero_type, type, (
% 1.50/1.67 zero: $i)).
% 1.50/1.67 tff(tptp_fun_X1_0_type, type, (
% 1.50/1.67 tptp_fun_X1_0: $i > $i)).
% 1.50/1.67 tff(one_type, type, (
% 1.50/1.67 one: $i)).
% 1.50/1.67 tff(complement_type, type, (
% 1.50/1.67 complement: ( $i * $i ) > $o)).
% 1.50/1.67 tff(test_type, type, (
% 1.50/1.67 test: $i > $o)).
% 1.50/1.67 tff(1,plain,
% 1.50/1.67 (^[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))))),
% 1.50/1.67 inference(bind,[status(th)],[])).
% 1.50/1.67 tff(2,plain,
% 1.50/1.67 (![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)))),
% 1.50/1.67 inference(quant_intro,[status(thm)],[1])).
% 1.50/1.67 tff(3,plain,
% 1.50/1.67 (![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)))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(4,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')).
% 1.50/1.67 tff(5,plain,
% 1.50/1.67 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.50/1.67 tff(6,plain,(
% 1.50/1.67 ![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 1.50/1.67 inference(skolemize,[status(sab)],[5])).
% 1.50/1.67 tff(7,plain,
% 1.50/1.67 (![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.50/1.67 tff(8,plain,
% 1.50/1.67 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X0!2, c(X0!2)), X1!1) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(9,plain,
% 1.50/1.67 (multiplication(addition(X0!2, c(X0!2)), X1!1) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.50/1.67 tff(10,plain,
% 1.50/1.67 (addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 1.50/1.67 inference(symmetry,[status(thm)],[9])).
% 1.50/1.67 tff(11,plain,
% 1.50/1.67 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 1.50/1.67 inference(monotonicity,[status(thm)],[10])).
% 1.50/1.67 tff(12,plain,
% 1.50/1.67 (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 1.50/1.67 inference(symmetry,[status(thm)],[11])).
% 1.50/1.67 tff(13,plain,
% 1.50/1.67 (addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(c(X1!1), X0!2), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 1.50/1.67 inference(monotonicity,[status(thm)],[12])).
% 1.50/1.67 tff(14,plain,
% 1.50/1.67 (addition(multiplication(c(X1!1), X0!2), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 1.50/1.67 inference(symmetry,[status(thm)],[13])).
% 1.50/1.67 tff(15,plain,
% 1.50/1.67 (^[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)))),
% 1.50/1.67 inference(bind,[status(th)],[])).
% 1.50/1.67 tff(16,plain,
% 1.50/1.67 (![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))),
% 1.50/1.67 inference(quant_intro,[status(thm)],[15])).
% 1.50/1.67 tff(17,plain,
% 1.50/1.67 (![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))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(18,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')).
% 1.50/1.67 tff(19,plain,
% 1.50/1.67 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.50/1.67 tff(20,plain,(
% 1.50/1.67 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 1.50/1.67 inference(skolemize,[status(sab)],[19])).
% 1.50/1.67 tff(21,plain,
% 1.50/1.67 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[20, 16])).
% 1.50/1.67 tff(22,plain,
% 1.50/1.67 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X1!1), X0!2), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X1!1), X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(c(X0!2), c(X1!1))))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(23,plain,
% 1.50/1.67 (addition(multiplication(c(X1!1), X0!2), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(c(X1!1), X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(c(X0!2), c(X1!1)))),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[22, 21])).
% 1.50/1.67 tff(24,plain,
% 1.50/1.67 (addition(addition(multiplication(c(X1!1), X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X1!1), X0!2), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 1.50/1.67 inference(symmetry,[status(thm)],[23])).
% 1.50/1.67 tff(25,plain,
% 1.50/1.67 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 1.50/1.67 inference(bind,[status(th)],[])).
% 1.50/1.67 tff(26,plain,
% 1.50/1.67 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.50/1.67 inference(quant_intro,[status(thm)],[25])).
% 1.50/1.67 tff(27,plain,
% 1.50/1.67 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(28,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_commutativity')).
% 1.50/1.67 tff(29,plain,
% 1.50/1.67 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.50/1.67 tff(30,plain,(
% 1.50/1.67 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.50/1.67 inference(skolemize,[status(sab)],[29])).
% 1.50/1.67 tff(31,plain,
% 1.50/1.67 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.50/1.67 tff(32,plain,
% 1.50/1.67 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X0!2, c(X0!2)) = addition(c(X0!2), X0!2))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(33,plain,
% 1.50/1.67 (addition(X0!2, c(X0!2)) = addition(c(X0!2), X0!2)),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[32, 31])).
% 1.50/1.67 tff(34,plain,
% 1.50/1.67 (addition(c(X0!2), X0!2) = addition(X0!2, c(X0!2))),
% 1.50/1.67 inference(symmetry,[status(thm)],[33])).
% 1.50/1.67 tff(35,plain,
% 1.50/1.67 (^[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))))),
% 1.50/1.67 inference(bind,[status(th)],[])).
% 1.50/1.67 tff(36,plain,
% 1.50/1.67 (![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)))),
% 1.50/1.67 inference(quant_intro,[status(thm)],[35])).
% 1.50/1.67 tff(37,plain,
% 1.50/1.67 (^[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)))))),
% 1.50/1.67 inference(bind,[status(th)],[])).
% 1.50/1.67 tff(38,plain,
% 1.50/1.67 (![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)))),
% 1.50/1.67 inference(quant_intro,[status(thm)],[37])).
% 1.50/1.67 tff(39,plain,
% 1.50/1.67 (![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)))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(40,plain,
% 1.50/1.67 (^[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))))),
% 1.50/1.67 inference(bind,[status(th)],[])).
% 1.50/1.67 tff(41,plain,
% 1.50/1.67 (![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)))),
% 1.50/1.67 inference(quant_intro,[status(thm)],[40])).
% 1.50/1.67 tff(42,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')).
% 1.50/1.67 tff(43,plain,
% 1.50/1.67 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.50/1.67 tff(44,plain,
% 1.50/1.67 (![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[43, 39])).
% 1.50/1.67 tff(45,plain,(
% 1.50/1.67 ![X0: $i, X1: $i] : (complement(X1, X0) <=> ((multiplication(X0, X1) = zero) & (multiplication(X1, X0) = zero) & (addition(X0, X1) = one)))),
% 1.50/1.67 inference(skolemize,[status(sab)],[44])).
% 1.50/1.67 tff(46,plain,
% 1.50/1.67 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[45, 38])).
% 1.50/1.67 tff(47,plain,
% 1.50/1.67 (![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[46, 36])).
% 1.50/1.67 tff(48,plain,
% 1.50/1.67 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2)))))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(49,plain,
% 1.50/1.67 ((~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2)))) <=> (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(50,plain,
% 1.50/1.67 ((((~(multiplication(c(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, c(X0!2)) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))) <=> (((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2)))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(51,plain,
% 1.50/1.67 ((~(((~(multiplication(c(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, c(X0!2)) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2)))) <=> (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))))),
% 1.50/1.67 inference(monotonicity,[status(thm)],[50])).
% 1.50/1.67 tff(52,plain,
% 1.50/1.67 ((~(((~(multiplication(c(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, c(X0!2)) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2)))) <=> (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))))),
% 1.50/1.67 inference(transitivity,[status(thm)],[51, 49])).
% 1.50/1.67 tff(53,plain,
% 1.50/1.67 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, c(X0!2)) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2)))))),
% 1.50/1.67 inference(monotonicity,[status(thm)],[52])).
% 1.50/1.67 tff(54,plain,
% 1.50/1.67 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, c(X0!2)) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2)))))),
% 1.50/1.67 inference(transitivity,[status(thm)],[53, 48])).
% 1.50/1.67 tff(55,plain,
% 1.50/1.67 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(X0!2), X0!2) = zero)) | (~(multiplication(X0!2, c(X0!2)) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(56,plain,
% 1.50/1.67 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.50/1.67 tff(57,plain,
% 1.50/1.67 (~(((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2)))),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[56, 47])).
% 1.50/1.67 tff(58,plain,
% 1.50/1.67 ((~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1))))))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(59,plain,
% 1.50/1.67 ((~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))) <=> (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1))))))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(60,axiom,(~![X0: $i, X1: $i] : ((test(X1) & test(X0)) => (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 1.50/1.67 tff(61,plain,
% 1.50/1.67 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.50/1.67 tff(62,plain,
% 1.50/1.67 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[61, 58])).
% 1.50/1.67 tff(63,plain,
% 1.50/1.67 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[62, 58])).
% 1.50/1.67 tff(64,plain,
% 1.50/1.67 (~![X0: $i, X1: $i] : ((~(test(X1) & test(X0))) | (one = addition(addition(multiplication(addition(X1, c(X1)), X0), multiplication(addition(X0, c(X0)), X1)), multiplication(c(X0), c(X1)))))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[63, 58])).
% 1.50/1.67 tff(65,plain,(
% 1.50/1.67 ~((~(test(X1!1) & test(X0!2))) | (one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1)))))),
% 1.50/1.67 inference(skolemize,[status(sab)],[64])).
% 1.50/1.67 tff(66,plain,
% 1.50/1.67 (test(X1!1) & test(X0!2)),
% 1.50/1.67 inference(or_elim,[status(thm)],[65])).
% 1.50/1.67 tff(67,plain,
% 1.50/1.67 (test(X0!2)),
% 1.50/1.67 inference(and_elim,[status(thm)],[66])).
% 1.50/1.67 tff(68,plain,
% 1.50/1.67 (^[X0: $i, X1: $i] : refl(((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 1.50/1.67 inference(bind,[status(th)],[])).
% 1.50/1.67 tff(69,plain,
% 1.50/1.67 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 1.50/1.67 inference(quant_intro,[status(thm)],[68])).
% 1.50/1.67 tff(70,plain,
% 1.50/1.67 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(71,plain,
% 1.50/1.67 (^[X0: $i, X1: $i] : rewrite((test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1))))),
% 1.50/1.67 inference(bind,[status(th)],[])).
% 1.50/1.67 tff(72,plain,
% 1.50/1.67 (![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1))) <=> ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 1.50/1.67 inference(quant_intro,[status(thm)],[71])).
% 1.50/1.67 tff(73,axiom,(![X0: $i, X1: $i] : (test(X0) => ((c(X0) = X1) <=> complement(X0, X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_3')).
% 1.50/1.67 tff(74,plain,
% 1.50/1.67 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.50/1.67 tff(75,plain,
% 1.50/1.67 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[74, 70])).
% 1.50/1.67 tff(76,plain,(
% 1.50/1.67 ![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 1.50/1.67 inference(skolemize,[status(sab)],[75])).
% 1.50/1.67 tff(77,plain,
% 1.50/1.67 (![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[76, 69])).
% 1.50/1.67 tff(78,plain,
% 1.50/1.67 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | complement(X0!2, c(X0!2)))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | complement(X0!2, c(X0!2)))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(79,plain,
% 1.50/1.67 (((~test(X0!2)) | ((c(X0!2) = c(X0!2)) <=> complement(X0!2, c(X0!2)))) <=> ((~test(X0!2)) | complement(X0!2, c(X0!2)))),
% 1.50/1.67 inference(rewrite,[status(thm)],[])).
% 1.50/1.67 tff(80,plain,
% 1.50/1.67 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = c(X0!2)) <=> complement(X0!2, c(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | complement(X0!2, c(X0!2))))),
% 1.50/1.67 inference(monotonicity,[status(thm)],[79])).
% 1.50/1.67 tff(81,plain,
% 1.50/1.67 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = c(X0!2)) <=> complement(X0!2, c(X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | complement(X0!2, c(X0!2)))),
% 1.50/1.67 inference(transitivity,[status(thm)],[80, 78])).
% 1.50/1.67 tff(82,plain,
% 1.50/1.67 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X0!2)) | ((c(X0!2) = c(X0!2)) <=> complement(X0!2, c(X0!2))))),
% 1.50/1.67 inference(quant_inst,[status(thm)],[])).
% 1.50/1.67 tff(83,plain,
% 1.50/1.67 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X0!2)) | complement(X0!2, c(X0!2))),
% 1.50/1.67 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.50/1.67 tff(84,plain,
% 1.50/1.67 (complement(X0!2, c(X0!2))),
% 1.50/1.67 inference(unit_resolution,[status(thm)],[83, 77, 67])).
% 1.50/1.67 tff(85,plain,
% 1.50/1.67 ((((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) <=> complement(X0!2, c(X0!2))) | (~((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one)))) | (~complement(X0!2, c(X0!2)))),
% 1.50/1.67 inference(tautology,[status(thm)],[])).
% 1.50/1.67 tff(86,plain,
% 1.50/1.67 (~((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one)))),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[85, 84, 57])).
% 1.50/1.68 tff(87,plain,
% 1.50/1.68 (((~(multiplication(X0!2, c(X0!2)) = zero)) | (~(multiplication(c(X0!2), X0!2) = zero)) | (~(addition(c(X0!2), X0!2) = one))) | (addition(c(X0!2), X0!2) = one)),
% 1.50/1.68 inference(tautology,[status(thm)],[])).
% 1.50/1.68 tff(88,plain,
% 1.50/1.68 (addition(c(X0!2), X0!2) = one),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[87, 86])).
% 1.50/1.68 tff(89,plain,
% 1.50/1.68 (one = addition(c(X0!2), X0!2)),
% 1.50/1.68 inference(symmetry,[status(thm)],[88])).
% 1.50/1.68 tff(90,plain,
% 1.50/1.68 (one = addition(X0!2, c(X0!2))),
% 1.50/1.68 inference(transitivity,[status(thm)],[89, 34])).
% 1.50/1.68 tff(91,plain,
% 1.50/1.68 (multiplication(one, X1!1) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 1.50/1.68 inference(monotonicity,[status(thm)],[90])).
% 1.50/1.68 tff(92,plain,
% 1.50/1.68 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 1.50/1.68 inference(bind,[status(th)],[])).
% 1.50/1.68 tff(93,plain,
% 1.50/1.68 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 1.50/1.68 inference(quant_intro,[status(thm)],[92])).
% 1.50/1.68 tff(94,plain,
% 1.50/1.68 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 1.50/1.68 inference(rewrite,[status(thm)],[])).
% 1.50/1.68 tff(95,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_left_identity')).
% 1.50/1.68 tff(96,plain,
% 1.50/1.68 (![A: $i] : (multiplication(one, A) = A)),
% 1.50/1.68 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.50/1.68 tff(97,plain,(
% 1.50/1.68 ![A: $i] : (multiplication(one, A) = A)),
% 1.50/1.68 inference(skolemize,[status(sab)],[96])).
% 1.50/1.68 tff(98,plain,
% 1.50/1.68 (![A: $i] : (multiplication(one, A) = A)),
% 1.50/1.68 inference(modus_ponens,[status(thm)],[97, 93])).
% 1.50/1.68 tff(99,plain,
% 1.50/1.68 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X1!1) = X1!1)),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(100,plain,
% 1.50/1.68 (multiplication(one, X1!1) = X1!1),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[99, 98])).
% 1.50/1.68 tff(101,plain,
% 1.50/1.68 (X1!1 = multiplication(one, X1!1)),
% 1.50/1.68 inference(symmetry,[status(thm)],[100])).
% 1.50/1.68 tff(102,plain,
% 1.50/1.68 (X1!1 = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 1.50/1.68 inference(transitivity,[status(thm)],[101, 91])).
% 1.50/1.68 tff(103,plain,
% 1.50/1.68 (c(X1!1) = c(multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[102])).
% 1.50/1.68 tff(104,plain,
% 1.50/1.68 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(X1!1, c(X1!1)) = addition(c(X1!1), X1!1))),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(105,plain,
% 1.50/1.68 (addition(X1!1, c(X1!1)) = addition(c(X1!1), X1!1)),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[104, 31])).
% 1.50/1.68 tff(106,plain,
% 1.50/1.68 (addition(c(X1!1), X1!1) = addition(X1!1, c(X1!1))),
% 1.50/1.68 inference(symmetry,[status(thm)],[105])).
% 1.50/1.68 tff(107,plain,
% 1.50/1.68 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1)))))),
% 1.50/1.68 inference(rewrite,[status(thm)],[])).
% 1.50/1.68 tff(108,plain,
% 1.50/1.68 ((~(((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1)))) <=> (~(((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1))))),
% 1.50/1.68 inference(rewrite,[status(thm)],[])).
% 1.50/1.68 tff(109,plain,
% 1.50/1.68 ((((~(multiplication(c(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, c(X1!1)) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1))) <=> (((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1)))),
% 1.50/1.68 inference(rewrite,[status(thm)],[])).
% 1.50/1.68 tff(110,plain,
% 1.50/1.68 ((~(((~(multiplication(c(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, c(X1!1)) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1)))) <=> (~(((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1))))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[109])).
% 1.50/1.68 tff(111,plain,
% 1.50/1.68 ((~(((~(multiplication(c(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, c(X1!1)) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1)))) <=> (~(((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1))))),
% 1.50/1.68 inference(transitivity,[status(thm)],[110, 108])).
% 1.50/1.68 tff(112,plain,
% 1.50/1.68 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, c(X1!1)) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1)))))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[111])).
% 1.50/1.68 tff(113,plain,
% 1.50/1.68 (((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, c(X1!1)) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1))))) <=> ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1)))))),
% 1.50/1.68 inference(transitivity,[status(thm)],[112, 107])).
% 1.50/1.68 tff(114,plain,
% 1.50/1.68 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(c(X1!1), X1!1) = zero)) | (~(multiplication(X1!1, c(X1!1)) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1))))),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(115,plain,
% 1.50/1.68 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1))))),
% 1.50/1.68 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.50/1.68 tff(116,plain,
% 1.50/1.68 (~(((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1)))),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[115, 47])).
% 1.50/1.68 tff(117,plain,
% 1.50/1.68 (test(X1!1)),
% 1.50/1.68 inference(and_elim,[status(thm)],[66])).
% 1.50/1.68 tff(118,plain,
% 1.50/1.68 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | complement(X1!1, c(X1!1)))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | complement(X1!1, c(X1!1)))),
% 1.50/1.68 inference(rewrite,[status(thm)],[])).
% 1.50/1.68 tff(119,plain,
% 1.50/1.68 (((~test(X1!1)) | ((c(X1!1) = c(X1!1)) <=> complement(X1!1, c(X1!1)))) <=> ((~test(X1!1)) | complement(X1!1, c(X1!1)))),
% 1.50/1.68 inference(rewrite,[status(thm)],[])).
% 1.50/1.68 tff(120,plain,
% 1.50/1.68 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = c(X1!1)) <=> complement(X1!1, c(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | complement(X1!1, c(X1!1))))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[119])).
% 1.50/1.68 tff(121,plain,
% 1.50/1.68 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = c(X1!1)) <=> complement(X1!1, c(X1!1))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | complement(X1!1, c(X1!1)))),
% 1.50/1.68 inference(transitivity,[status(thm)],[120, 118])).
% 1.50/1.68 tff(122,plain,
% 1.50/1.68 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(X1!1)) | ((c(X1!1) = c(X1!1)) <=> complement(X1!1, c(X1!1))))),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(123,plain,
% 1.50/1.68 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(X1!1)) | complement(X1!1, c(X1!1))),
% 1.50/1.68 inference(modus_ponens,[status(thm)],[122, 121])).
% 1.50/1.68 tff(124,plain,
% 1.50/1.68 (complement(X1!1, c(X1!1))),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[123, 77, 117])).
% 1.50/1.68 tff(125,plain,
% 1.50/1.68 ((((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) <=> complement(X1!1, c(X1!1))) | (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one)))) | (~complement(X1!1, c(X1!1)))),
% 1.50/1.68 inference(tautology,[status(thm)],[])).
% 1.50/1.68 tff(126,plain,
% 1.50/1.68 (~((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one)))),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[125, 124, 116])).
% 1.50/1.68 tff(127,plain,
% 1.50/1.68 (((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) | (addition(c(X1!1), X1!1) = one)),
% 1.50/1.68 inference(tautology,[status(thm)],[])).
% 1.50/1.68 tff(128,plain,
% 1.50/1.68 (addition(c(X1!1), X1!1) = one),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[127, 126])).
% 1.50/1.68 tff(129,plain,
% 1.50/1.68 (one = addition(c(X1!1), X1!1)),
% 1.50/1.68 inference(symmetry,[status(thm)],[128])).
% 1.50/1.68 tff(130,plain,
% 1.50/1.68 (one = addition(X1!1, c(X1!1))),
% 1.50/1.68 inference(transitivity,[status(thm)],[129, 106])).
% 1.50/1.68 tff(131,plain,
% 1.50/1.68 (multiplication(one, X0!2) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 1.50/1.68 inference(monotonicity,[status(thm)],[130])).
% 1.50/1.68 tff(132,plain,
% 1.50/1.68 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, X0!2) = X0!2)),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(133,plain,
% 1.50/1.68 (multiplication(one, X0!2) = X0!2),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[132, 98])).
% 1.50/1.68 tff(134,plain,
% 1.50/1.68 (X0!2 = multiplication(one, X0!2)),
% 1.50/1.68 inference(symmetry,[status(thm)],[133])).
% 1.50/1.68 tff(135,plain,
% 1.50/1.68 (X0!2 = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 1.50/1.68 inference(transitivity,[status(thm)],[134, 131])).
% 1.50/1.68 tff(136,plain,
% 1.50/1.68 (c(X0!2) = c(multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[135])).
% 1.50/1.68 tff(137,plain,
% 1.50/1.68 (multiplication(c(X0!2), c(X1!1)) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[136, 103])).
% 1.50/1.68 tff(138,plain,
% 1.50/1.68 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(X0!2), c(X1!1))),
% 1.50/1.68 inference(symmetry,[status(thm)],[137])).
% 1.50/1.68 tff(139,plain,
% 1.50/1.68 (test(X0!2) <=> test(multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[135])).
% 1.50/1.68 tff(140,plain,
% 1.50/1.68 (test(multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.50/1.68 inference(modus_ponens,[status(thm)],[67, 139])).
% 1.50/1.68 tff(141,plain,
% 1.50/1.68 (test(X1!1) <=> test(multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[102])).
% 1.50/1.68 tff(142,plain,
% 1.50/1.68 (test(multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 1.50/1.68 inference(modus_ponens,[status(thm)],[117, 141])).
% 1.50/1.68 tff(143,plain,
% 1.50/1.68 (^[X0: $i, X1: $i] : refl(((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))))),
% 1.50/1.68 inference(bind,[status(th)],[])).
% 1.50/1.68 tff(144,plain,
% 1.50/1.68 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 1.50/1.68 inference(quant_intro,[status(thm)],[143])).
% 1.50/1.68 tff(145,plain,
% 1.50/1.68 (^[X0: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((test(X0) & test(X1)) <=> (~((~test(X1)) | (~test(X0))))), ((~(test(X0) & test(X1))) <=> (~(~((~test(X1)) | (~test(X0))))))), rewrite((~(~((~test(X1)) | (~test(X0))))) <=> ((~test(X1)) | (~test(X0)))), ((~(test(X0) & test(X1))) <=> ((~test(X1)) | (~test(X0))))), (((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> (((~test(X1)) | (~test(X0))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))))), rewrite((((~test(X1)) | (~test(X0))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))), (((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))))),
% 1.50/1.68 inference(bind,[status(th)],[])).
% 1.50/1.68 tff(146,plain,
% 1.50/1.68 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 1.50/1.68 inference(quant_intro,[status(thm)],[145])).
% 1.50/1.68 tff(147,plain,
% 1.50/1.68 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 1.50/1.68 inference(rewrite,[status(thm)],[])).
% 1.50/1.68 tff(148,plain,
% 1.50/1.68 (^[X0: $i, X1: $i] : rewrite(((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))))),
% 1.50/1.68 inference(bind,[status(th)],[])).
% 1.50/1.68 tff(149,plain,
% 1.50/1.68 (![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1)))) <=> ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 1.50/1.68 inference(quant_intro,[status(thm)],[148])).
% 1.50/1.68 tff(150,axiom,(![X0: $i, X1: $i] : ((test(X0) & test(X1)) => (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+2.ax','test_deMorgan1')).
% 1.50/1.68 tff(151,plain,
% 1.50/1.68 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 1.50/1.68 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.50/1.68 tff(152,plain,
% 1.50/1.68 (![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 1.50/1.68 inference(modus_ponens,[status(thm)],[151, 147])).
% 1.50/1.68 tff(153,plain,(
% 1.50/1.68 ![X0: $i, X1: $i] : ((~(test(X0) & test(X1))) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))))),
% 1.50/1.68 inference(skolemize,[status(sab)],[152])).
% 1.50/1.68 tff(154,plain,
% 1.50/1.68 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 1.50/1.68 inference(modus_ponens,[status(thm)],[153, 146])).
% 1.50/1.68 tff(155,plain,
% 1.50/1.68 (![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))),
% 1.50/1.68 inference(modus_ponens,[status(thm)],[154, 144])).
% 1.50/1.68 tff(156,plain,
% 1.50/1.68 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(multiplication(addition(X0!2, c(X0!2)), X1!1))) | (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) | (~test(multiplication(addition(X1!1, c(X1!1)), X0!2))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(multiplication(addition(X0!2, c(X0!2)), X1!1))) | (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) | (~test(multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.50/1.68 inference(rewrite,[status(thm)],[])).
% 1.50/1.68 tff(157,plain,
% 1.50/1.68 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(multiplication(addition(X0!2, c(X0!2)), X1!1))) | (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) | (~test(multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(158,plain,
% 1.50/1.68 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(multiplication(addition(X0!2, c(X0!2)), X1!1))) | (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) | (~test(multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.50/1.68 inference(modus_ponens,[status(thm)],[157, 156])).
% 1.50/1.68 tff(159,plain,
% 1.50/1.68 ((~test(multiplication(addition(X0!2, c(X0!2)), X1!1))) | (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) | (~test(multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[158, 155])).
% 1.50/1.68 tff(160,plain,
% 1.50/1.68 (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[159, 142, 140])).
% 1.50/1.68 tff(161,plain,
% 1.50/1.68 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X1!1, c(X1!1)), X0!2) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(162,plain,
% 1.50/1.68 (multiplication(addition(X1!1, c(X1!1)), X0!2) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[161, 7])).
% 1.50/1.68 tff(163,plain,
% 1.50/1.68 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 1.50/1.68 inference(symmetry,[status(thm)],[162])).
% 1.50/1.68 tff(164,plain,
% 1.50/1.68 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[10, 163])).
% 1.50/1.68 tff(165,plain,
% 1.50/1.68 (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.50/1.68 inference(symmetry,[status(thm)],[164])).
% 1.50/1.68 tff(166,plain,
% 1.50/1.68 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(167,plain,
% 1.50/1.68 (addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[166, 31])).
% 1.50/1.68 tff(168,plain,
% 1.50/1.68 (addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.50/1.68 inference(transitivity,[status(thm)],[167, 165])).
% 1.50/1.68 tff(169,plain,
% 1.50/1.68 (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[168])).
% 1.50/1.68 tff(170,plain,
% 1.50/1.68 (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.50/1.68 inference(symmetry,[status(thm)],[169])).
% 1.50/1.68 tff(171,plain,
% 1.50/1.68 (complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))) <=> complement(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1)))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[164])).
% 1.50/1.68 tff(172,plain,
% 1.50/1.68 (complement(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) <=> complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))),
% 1.50/1.68 inference(symmetry,[status(thm)],[171])).
% 1.50/1.68 tff(173,plain,
% 1.50/1.68 ((~complement(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1)))) <=> (~complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[172])).
% 1.50/1.68 tff(174,plain,
% 1.50/1.68 ((~![X0: $i, X1: $i] : (~(((~(multiplication(X0, X1) = zero)) | (~(multiplication(X1, X0) = zero)) | (~(addition(X0, X1) = one))) <=> complement(X1, X0)))) | (~(((~(multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero)) | (~(multiplication(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one))) <=> complement(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1)))))),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(175,plain,
% 1.50/1.68 (~(((~(multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero)) | (~(multiplication(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one))) <=> complement(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))))),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[174, 47])).
% 1.50/1.68 tff(176,plain,
% 1.50/1.68 ((addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))) = one) <=> (one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 1.50/1.68 inference(commutativity,[status(thm)],[])).
% 1.50/1.68 tff(177,plain,
% 1.50/1.68 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.50/1.68 inference(quant_inst,[status(thm)],[])).
% 1.50/1.68 tff(178,plain,
% 1.50/1.68 (addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.50/1.68 inference(unit_resolution,[status(thm)],[177, 31])).
% 1.50/1.68 tff(179,plain,
% 1.50/1.68 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 1.50/1.68 inference(symmetry,[status(thm)],[178])).
% 1.50/1.68 tff(180,plain,
% 1.50/1.68 (addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)) = addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 1.50/1.68 inference(symmetry,[status(thm)],[167])).
% 1.50/1.68 tff(181,plain,
% 1.50/1.68 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[180])).
% 1.50/1.68 tff(182,plain,
% 1.50/1.68 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 1.50/1.68 inference(transitivity,[status(thm)],[181, 179])).
% 1.50/1.68 tff(183,plain,
% 1.50/1.68 ((addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one) <=> (addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))) = one)),
% 1.50/1.68 inference(monotonicity,[status(thm)],[182])).
% 1.50/1.68 tff(184,plain,
% 1.50/1.68 ((addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one) <=> (one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 1.50/1.68 inference(transitivity,[status(thm)],[183, 176])).
% 1.50/1.68 tff(185,plain,
% 1.50/1.68 ((one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one)),
% 1.50/1.68 inference(symmetry,[status(thm)],[184])).
% 1.50/1.68 tff(186,plain,
% 1.50/1.68 ((~(one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))))) <=> (~(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one))),
% 1.50/1.68 inference(monotonicity,[status(thm)],[185])).
% 1.50/1.68 tff(187,plain,
% 1.50/1.68 (~(one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 1.50/1.68 inference(or_elim,[status(thm)],[65])).
% 1.54/1.69 tff(188,plain,
% 1.54/1.69 (~(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one)),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[187, 186])).
% 1.54/1.69 tff(189,plain,
% 1.54/1.69 (((~(multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero)) | (~(multiplication(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one))) | (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one)),
% 1.54/1.69 inference(tautology,[status(thm)],[])).
% 1.54/1.69 tff(190,plain,
% 1.54/1.69 ((~(multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero)) | (~(multiplication(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one))),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[189, 188])).
% 1.54/1.69 tff(191,plain,
% 1.54/1.69 ((((~(multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero)) | (~(multiplication(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one))) <=> complement(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1)))) | (~((~(multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = zero)) | (~(multiplication(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))) = zero)) | (~(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = one)))) | (~complement(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1))))),
% 1.54/1.69 inference(tautology,[status(thm)],[])).
% 1.54/1.69 tff(192,plain,
% 1.54/1.69 (~complement(addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(X0!2), c(X1!1)))),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[191, 190, 175])).
% 1.54/1.69 tff(193,plain,
% 1.54/1.69 (~complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[192, 173])).
% 1.54/1.69 tff(194,plain,
% 1.54/1.69 ((c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))) <=> (c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.54/1.69 inference(monotonicity,[status(thm)],[170, 137])).
% 1.54/1.69 tff(195,plain,
% 1.54/1.69 ((c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) <=> (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1)))),
% 1.54/1.69 inference(symmetry,[status(thm)],[194])).
% 1.54/1.69 tff(196,plain,
% 1.54/1.69 (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[160, 195])).
% 1.54/1.69 tff(197,plain,
% 1.54/1.69 ((~((c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))) <=> complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))))) | (~(c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1)))) | complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))),
% 1.54/1.69 inference(tautology,[status(thm)],[])).
% 1.54/1.69 tff(198,plain,
% 1.54/1.69 (~((c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))) <=> complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))))),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[197, 196, 193])).
% 1.54/1.69 tff(199,plain,
% 1.54/1.69 (((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) | ((c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))) <=> complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) | ((c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))) <=> complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))))),
% 1.54/1.69 inference(rewrite,[status(thm)],[])).
% 1.54/1.69 tff(200,plain,
% 1.54/1.69 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | ((~test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) | ((c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))) <=> complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))))),
% 1.54/1.69 inference(quant_inst,[status(thm)],[])).
% 1.54/1.69 tff(201,plain,
% 1.54/1.69 ((~![X0: $i, X1: $i] : ((~test(X0)) | ((c(X0) = X1) <=> complement(X0, X1)))) | (~test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) | ((c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))) <=> complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))))),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.54/1.69 tff(202,plain,
% 1.54/1.69 ((~test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) | ((c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(X0!2), c(X1!1))) <=> complement(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))))),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[201, 77])).
% 1.54/1.69 tff(203,plain,
% 1.54/1.69 (~test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[202, 198])).
% 1.54/1.69 tff(204,plain,
% 1.54/1.69 (^[X0: $i] : refl((test(X0) | (c(X0) = zero)) <=> (test(X0) | (c(X0) = zero)))),
% 1.54/1.69 inference(bind,[status(th)],[])).
% 1.54/1.69 tff(205,plain,
% 1.54/1.69 (![X0: $i] : (test(X0) | (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 1.54/1.69 inference(quant_intro,[status(thm)],[204])).
% 1.54/1.69 tff(206,plain,
% 1.54/1.69 (![X0: $i] : (test(X0) | (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 1.54/1.69 inference(rewrite,[status(thm)],[])).
% 1.54/1.69 tff(207,plain,
% 1.54/1.69 (^[X0: $i] : rewrite(((~test(X0)) => (c(X0) = zero)) <=> (test(X0) | (c(X0) = zero)))),
% 1.54/1.69 inference(bind,[status(th)],[])).
% 1.54/1.69 tff(208,plain,
% 1.54/1.69 (![X0: $i] : ((~test(X0)) => (c(X0) = zero)) <=> ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 1.54/1.69 inference(quant_intro,[status(thm)],[207])).
% 1.54/1.69 tff(209,axiom,(![X0: $i] : ((~test(X0)) => (c(X0) = zero))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_4')).
% 1.54/1.69 tff(210,plain,
% 1.54/1.69 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[209, 208])).
% 1.54/1.69 tff(211,plain,
% 1.54/1.69 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[210, 206])).
% 1.54/1.69 tff(212,plain,(
% 1.54/1.69 ![X0: $i] : (test(X0) | (c(X0) = zero))),
% 1.54/1.69 inference(skolemize,[status(sab)],[211])).
% 1.54/1.69 tff(213,plain,
% 1.54/1.69 (![X0: $i] : (test(X0) | (c(X0) = zero))),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[212, 205])).
% 1.54/1.69 tff(214,plain,
% 1.54/1.69 (((~![X0: $i] : (test(X0) | (c(X0) = zero))) | (test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = zero))) <=> ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = zero))),
% 1.54/1.69 inference(rewrite,[status(thm)],[])).
% 1.54/1.69 tff(215,plain,
% 1.54/1.69 ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | (test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = zero))),
% 1.54/1.69 inference(quant_inst,[status(thm)],[])).
% 1.54/1.69 tff(216,plain,
% 1.54/1.69 ((~![X0: $i] : (test(X0) | (c(X0) = zero))) | test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = zero)),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.54/1.69 tff(217,plain,
% 1.54/1.69 (test(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = zero)),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[216, 213])).
% 1.54/1.69 tff(218,plain,
% 1.54/1.69 (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = zero),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[217, 203])).
% 1.54/1.69 tff(219,plain,
% 1.54/1.69 (zero = c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.69 inference(symmetry,[status(thm)],[218])).
% 1.54/1.69 tff(220,plain,
% 1.54/1.69 (zero = multiplication(c(X0!2), c(X1!1))),
% 1.54/1.69 inference(transitivity,[status(thm)],[219, 170, 160, 138])).
% 1.54/1.69 tff(221,plain,
% 1.54/1.69 (^[A: $i] : refl((addition(A, zero) = A) <=> (addition(A, zero) = A))),
% 1.54/1.69 inference(bind,[status(th)],[])).
% 1.54/1.69 tff(222,plain,
% 1.54/1.69 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 1.54/1.69 inference(quant_intro,[status(thm)],[221])).
% 1.54/1.69 tff(223,plain,
% 1.54/1.69 (![A: $i] : (addition(A, zero) = A) <=> ![A: $i] : (addition(A, zero) = A)),
% 1.54/1.69 inference(rewrite,[status(thm)],[])).
% 1.54/1.69 tff(224,axiom,(![A: $i] : (addition(A, zero) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_identity')).
% 1.54/1.69 tff(225,plain,
% 1.54/1.69 (![A: $i] : (addition(A, zero) = A)),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[224, 223])).
% 1.54/1.69 tff(226,plain,(
% 1.54/1.69 ![A: $i] : (addition(A, zero) = A)),
% 1.54/1.69 inference(skolemize,[status(sab)],[225])).
% 1.54/1.69 tff(227,plain,
% 1.54/1.69 (![A: $i] : (addition(A, zero) = A)),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[226, 222])).
% 1.54/1.69 tff(228,plain,
% 1.54/1.69 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(X1!1, X1!1), zero) = multiplication(X1!1, X1!1))),
% 1.54/1.69 inference(quant_inst,[status(thm)],[])).
% 1.54/1.69 tff(229,plain,
% 1.54/1.69 (addition(multiplication(X1!1, X1!1), zero) = multiplication(X1!1, X1!1)),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[228, 227])).
% 1.54/1.69 tff(230,plain,
% 1.54/1.69 (((~(multiplication(X1!1, c(X1!1)) = zero)) | (~(multiplication(c(X1!1), X1!1) = zero)) | (~(addition(c(X1!1), X1!1) = one))) | (multiplication(c(X1!1), X1!1) = zero)),
% 1.54/1.69 inference(tautology,[status(thm)],[])).
% 1.54/1.69 tff(231,plain,
% 1.54/1.69 (multiplication(c(X1!1), X1!1) = zero),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[230, 126])).
% 1.54/1.69 tff(232,plain,
% 1.54/1.69 (zero = multiplication(c(X1!1), X1!1)),
% 1.54/1.69 inference(symmetry,[status(thm)],[231])).
% 1.54/1.69 tff(233,plain,
% 1.54/1.69 (addition(multiplication(X1!1, X1!1), zero) = addition(multiplication(X1!1, X1!1), multiplication(c(X1!1), X1!1))),
% 1.54/1.69 inference(monotonicity,[status(thm)],[232])).
% 1.54/1.69 tff(234,plain,
% 1.54/1.69 (addition(multiplication(X1!1, X1!1), multiplication(c(X1!1), X1!1)) = addition(multiplication(X1!1, X1!1), zero)),
% 1.54/1.69 inference(symmetry,[status(thm)],[233])).
% 1.54/1.69 tff(235,plain,
% 1.54/1.69 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X1!1, c(X1!1)), X1!1) = addition(multiplication(X1!1, X1!1), multiplication(c(X1!1), X1!1)))),
% 1.54/1.69 inference(quant_inst,[status(thm)],[])).
% 1.54/1.69 tff(236,plain,
% 1.54/1.69 (multiplication(addition(X1!1, c(X1!1)), X1!1) = addition(multiplication(X1!1, X1!1), multiplication(c(X1!1), X1!1))),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[235, 7])).
% 1.54/1.69 tff(237,plain,
% 1.54/1.69 (addition(X1!1, c(X1!1)) = addition(X0!2, c(X0!2))),
% 1.54/1.69 inference(transitivity,[status(thm)],[105, 128, 89, 34])).
% 1.54/1.69 tff(238,plain,
% 1.54/1.69 (multiplication(addition(X1!1, c(X1!1)), X1!1) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 1.54/1.69 inference(monotonicity,[status(thm)],[237])).
% 1.54/1.69 tff(239,plain,
% 1.54/1.69 (multiplication(addition(X0!2, c(X0!2)), X1!1) = multiplication(addition(X1!1, c(X1!1)), X1!1)),
% 1.54/1.69 inference(symmetry,[status(thm)],[238])).
% 1.54/1.69 tff(240,plain,
% 1.54/1.69 (addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)) = multiplication(X1!1, X1!1)),
% 1.54/1.69 inference(transitivity,[status(thm)],[10, 239, 236, 234, 229])).
% 1.54/1.69 tff(241,plain,
% 1.54/1.69 (((~![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))))),
% 1.54/1.69 inference(rewrite,[status(thm)],[])).
% 1.54/1.69 tff(242,plain,
% 1.54/1.69 ((~![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))))),
% 1.54/1.69 inference(quant_inst,[status(thm)],[])).
% 1.54/1.69 tff(243,plain,
% 1.54/1.69 ((~![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)))),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[242, 241])).
% 1.54/1.69 tff(244,plain,
% 1.54/1.69 ((c(X1!1) = tptp_fun_X1_0(X1!1)) <=> complement(X1!1, tptp_fun_X1_0(X1!1))),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[243, 77, 117])).
% 1.54/1.69 tff(245,plain,
% 1.54/1.69 (((~![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)))))),
% 1.54/1.69 inference(rewrite,[status(thm)],[])).
% 1.54/1.69 tff(246,plain,
% 1.54/1.69 ((~(((~(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))))),
% 1.54/1.69 inference(rewrite,[status(thm)],[])).
% 1.54/1.69 tff(247,plain,
% 1.54/1.69 ((((~(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)))),
% 1.54/1.69 inference(rewrite,[status(thm)],[])).
% 1.54/1.69 tff(248,plain,
% 1.54/1.69 ((~(((~(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))))),
% 1.54/1.69 inference(monotonicity,[status(thm)],[247])).
% 1.54/1.69 tff(249,plain,
% 1.54/1.69 ((~(((~(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))))),
% 1.54/1.69 inference(transitivity,[status(thm)],[248, 246])).
% 1.54/1.69 tff(250,plain,
% 1.54/1.69 (((~![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)))))),
% 1.54/1.69 inference(monotonicity,[status(thm)],[249])).
% 1.54/1.69 tff(251,plain,
% 1.54/1.69 (((~![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)))))),
% 1.54/1.69 inference(transitivity,[status(thm)],[250, 245])).
% 1.54/1.69 tff(252,plain,
% 1.54/1.69 ((~![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))))),
% 1.54/1.69 inference(quant_inst,[status(thm)],[])).
% 1.54/1.69 tff(253,plain,
% 1.54/1.69 ((~![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))))),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[252, 251])).
% 1.54/1.69 tff(254,plain,
% 1.54/1.69 (~(((~(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)))),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[253, 47])).
% 1.54/1.69 tff(255,plain,
% 1.54/1.69 ((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))),
% 1.54/1.69 inference(commutativity,[status(thm)],[])).
% 1.54/1.69 tff(256,plain,
% 1.54/1.69 ((~![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)))),
% 1.54/1.69 inference(quant_inst,[status(thm)],[])).
% 1.54/1.69 tff(257,plain,
% 1.54/1.69 (~(((~(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))),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[256, 47])).
% 1.54/1.69 tff(258,plain,
% 1.54/1.69 (^[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)))))))),
% 1.54/1.69 inference(bind,[status(th)],[])).
% 1.54/1.69 tff(259,plain,
% 1.54/1.69 (![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))))))),
% 1.54/1.69 inference(quant_intro,[status(thm)],[258])).
% 1.54/1.69 tff(260,plain,
% 1.54/1.69 (^[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)))))))),
% 1.54/1.69 inference(bind,[status(th)],[])).
% 1.54/1.69 tff(261,plain,
% 1.54/1.69 (![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))))))),
% 1.54/1.69 inference(quant_intro,[status(thm)],[260])).
% 1.54/1.69 tff(262,plain,
% 1.54/1.69 (![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))))))),
% 1.54/1.69 inference(transitivity,[status(thm)],[261, 259])).
% 1.54/1.69 tff(263,plain,
% 1.54/1.69 (^[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))))))))),
% 1.54/1.69 inference(bind,[status(th)],[])).
% 1.54/1.69 tff(264,plain,
% 1.54/1.69 (![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))))))),
% 1.54/1.69 inference(quant_intro,[status(thm)],[263])).
% 1.54/1.69 tff(265,plain,
% 1.54/1.69 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0)) <=> ![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 1.54/1.69 inference(rewrite,[status(thm)],[])).
% 1.54/1.69 tff(266,axiom,(![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax','test_1')).
% 1.54/1.69 tff(267,plain,
% 1.54/1.69 (![X0: $i] : (test(X0) <=> ?[X1: $i] : complement(X1, X0))),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[266, 265])).
% 1.54/1.69 tff(268,plain,(
% 1.54/1.69 ![X0: $i] : (((~test(X0)) | complement(tptp_fun_X1_0(X0), X0)) & (test(X0) | ![X1: $i] : (~complement(X1, X0))))),
% 1.54/1.69 inference(skolemize,[status(sab)],[267])).
% 1.54/1.69 tff(269,plain,
% 1.54/1.69 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[268, 264])).
% 1.54/1.69 tff(270,plain,
% 1.54/1.69 (![X0: $i] : (~((~((~test(X0)) | complement(tptp_fun_X1_0(X0), X0))) | (~(test(X0) | ![X1: $i] : (~complement(X1, X0))))))),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[269, 262])).
% 1.54/1.69 tff(271,plain,
% 1.54/1.69 ((~![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))))))),
% 1.54/1.69 inference(quant_inst,[status(thm)],[])).
% 1.54/1.69 tff(272,plain,
% 1.54/1.69 (~((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~(test(X1!1) | ![X1: $i] : (~complement(X1, X1!1)))))),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[271, 270])).
% 1.54/1.69 tff(273,plain,
% 1.54/1.69 (((~((~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))),
% 1.54/1.69 inference(tautology,[status(thm)],[])).
% 1.54/1.69 tff(274,plain,
% 1.54/1.69 ((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[273, 272])).
% 1.54/1.69 tff(275,plain,
% 1.54/1.69 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | (~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 1.54/1.69 inference(tautology,[status(thm)],[])).
% 1.54/1.69 tff(276,plain,
% 1.54/1.69 ((~((~test(X1!1)) | complement(tptp_fun_X1_0(X1!1), X1!1))) | complement(tptp_fun_X1_0(X1!1), X1!1)),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[275, 117])).
% 1.54/1.69 tff(277,plain,
% 1.54/1.69 (complement(tptp_fun_X1_0(X1!1), X1!1)),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[276, 274])).
% 1.54/1.69 tff(278,plain,
% 1.54/1.69 ((((~(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))),
% 1.54/1.69 inference(tautology,[status(thm)],[])).
% 1.54/1.69 tff(279,plain,
% 1.54/1.69 ((((~(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))))),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[278, 277])).
% 1.54/1.69 tff(280,plain,
% 1.54/1.69 (~((~(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)))),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[279, 257])).
% 1.54/1.69 tff(281,plain,
% 1.54/1.69 (((~(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)),
% 1.54/1.69 inference(tautology,[status(thm)],[])).
% 1.54/1.69 tff(282,plain,
% 1.54/1.69 (addition(X1!1, tptp_fun_X1_0(X1!1)) = one),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[281, 280])).
% 1.54/1.69 tff(283,plain,
% 1.54/1.69 (one = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 1.54/1.69 inference(symmetry,[status(thm)],[282])).
% 1.54/1.69 tff(284,plain,
% 1.54/1.69 ((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)))),
% 1.54/1.69 inference(monotonicity,[status(thm)],[283])).
% 1.54/1.69 tff(285,plain,
% 1.54/1.69 ((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))),
% 1.54/1.69 inference(transitivity,[status(thm)],[284, 255])).
% 1.54/1.69 tff(286,plain,
% 1.54/1.69 ((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)),
% 1.54/1.69 inference(symmetry,[status(thm)],[285])).
% 1.54/1.69 tff(287,plain,
% 1.54/1.69 ((~![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))),
% 1.54/1.69 inference(quant_inst,[status(thm)],[])).
% 1.54/1.69 tff(288,plain,
% 1.54/1.69 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[287, 31])).
% 1.54/1.69 tff(289,plain,
% 1.54/1.69 (addition(tptp_fun_X1_0(X1!1), X1!1) = one),
% 1.54/1.69 inference(modus_ponens,[status(thm)],[288, 286])).
% 1.54/1.69 tff(290,plain,
% 1.54/1.69 (((~(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)),
% 1.54/1.69 inference(tautology,[status(thm)],[])).
% 1.54/1.69 tff(291,plain,
% 1.54/1.69 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = zero),
% 1.54/1.69 inference(unit_resolution,[status(thm)],[290, 280])).
% 1.54/1.69 tff(292,plain,
% 1.54/1.69 (((~(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)),
% 1.54/1.70 inference(tautology,[status(thm)],[])).
% 1.54/1.70 tff(293,plain,
% 1.54/1.70 (multiplication(X1!1, tptp_fun_X1_0(X1!1)) = zero),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[292, 280])).
% 1.54/1.70 tff(294,plain,
% 1.54/1.70 ((~((~(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))),
% 1.54/1.70 inference(tautology,[status(thm)],[])).
% 1.54/1.70 tff(295,plain,
% 1.54/1.70 ((~((~(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))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[294, 293, 291])).
% 1.54/1.70 tff(296,plain,
% 1.54/1.70 (~((~(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)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[295, 289])).
% 1.54/1.70 tff(297,plain,
% 1.54/1.70 ((((~(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))),
% 1.54/1.70 inference(tautology,[status(thm)],[])).
% 1.54/1.70 tff(298,plain,
% 1.54/1.70 (complement(X1!1, tptp_fun_X1_0(X1!1))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[297, 296, 254])).
% 1.54/1.70 tff(299,plain,
% 1.54/1.70 ((~((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)))),
% 1.54/1.70 inference(tautology,[status(thm)],[])).
% 1.54/1.70 tff(300,plain,
% 1.54/1.70 (c(X1!1) = tptp_fun_X1_0(X1!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[299, 298, 244])).
% 1.54/1.70 tff(301,plain,
% 1.54/1.70 (multiplication(c(X1!1), X0!2) = multiplication(tptp_fun_X1_0(X1!1), X0!2)),
% 1.54/1.70 inference(monotonicity,[status(thm)],[300])).
% 1.54/1.70 tff(302,plain,
% 1.54/1.70 (addition(multiplication(c(X1!1), X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X1!1))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[301, 240])).
% 1.54/1.70 tff(303,plain,
% 1.54/1.70 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X1!1)) = addition(multiplication(c(X1!1), X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.70 inference(symmetry,[status(thm)],[302])).
% 1.54/1.70 tff(304,plain,
% 1.54/1.70 (addition(addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X1!1)), zero) = addition(addition(multiplication(c(X1!1), X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(c(X0!2), c(X1!1)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[303, 220])).
% 1.54/1.70 tff(305,plain,
% 1.54/1.70 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(X1!1, X1!1), zero)) = addition(addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X1!1)), zero))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(306,plain,
% 1.54/1.70 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(X1!1, X1!1), zero)) = addition(addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X1!1)), zero)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[305, 21])).
% 1.54/1.70 tff(307,plain,
% 1.54/1.70 (multiplication(X1!1, X1!1) = addition(multiplication(X1!1, X1!1), zero)),
% 1.54/1.70 inference(symmetry,[status(thm)],[229])).
% 1.54/1.70 tff(308,plain,
% 1.54/1.70 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X1!1)) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(X1!1, X1!1), zero))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[307])).
% 1.54/1.70 tff(309,plain,
% 1.54/1.70 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X1!1), X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X1!1), X0!2)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(310,plain,
% 1.54/1.70 (addition(multiplication(c(X1!1), X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X1!1), X0!2))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[309, 31])).
% 1.54/1.70 tff(311,plain,
% 1.54/1.70 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.70 inference(symmetry,[status(thm)],[310])).
% 1.54/1.70 tff(312,plain,
% 1.54/1.70 (multiplication(tptp_fun_X1_0(X1!1), X0!2) = multiplication(c(X1!1), X0!2)),
% 1.54/1.70 inference(symmetry,[status(thm)],[301])).
% 1.54/1.70 tff(313,plain,
% 1.54/1.70 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), zero) = multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(314,plain,
% 1.54/1.70 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), zero) = multiplication(tptp_fun_X1_0(X1!1), X0!2)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[313, 227])).
% 1.54/1.70 tff(315,plain,
% 1.54/1.70 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))) = c(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.54/1.70 inference(symmetry,[status(thm)],[160])).
% 1.54/1.70 tff(316,plain,
% 1.54/1.70 (multiplication(c(X0!2), c(X1!1)) = zero),
% 1.54/1.70 inference(transitivity,[status(thm)],[137, 315, 169, 218])).
% 1.54/1.70 tff(317,plain,
% 1.54/1.70 (addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), zero)),
% 1.54/1.70 inference(monotonicity,[status(thm)],[301, 316])).
% 1.54/1.70 tff(318,plain,
% 1.54/1.70 (test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) <=> test(multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[163])).
% 1.54/1.70 tff(319,plain,
% 1.54/1.70 (test(multiplication(addition(X1!1, c(X1!1)), X0!2)) <=> test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.70 inference(symmetry,[status(thm)],[318])).
% 1.54/1.70 tff(320,plain,
% 1.54/1.70 (test(X0!2) <=> test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.70 inference(transitivity,[status(thm)],[139, 319])).
% 1.54/1.70 tff(321,plain,
% 1.54/1.70 (test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[67, 320])).
% 1.54/1.70 tff(322,plain,
% 1.54/1.70 (test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) <=> test(multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[10])).
% 1.54/1.70 tff(323,plain,
% 1.54/1.70 (test(multiplication(addition(X0!2, c(X0!2)), X1!1)) <=> test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.70 inference(symmetry,[status(thm)],[322])).
% 1.54/1.70 tff(324,plain,
% 1.54/1.70 (test(X1!1) <=> test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.70 inference(transitivity,[status(thm)],[141, 323])).
% 1.54/1.70 tff(325,plain,
% 1.54/1.70 (test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[117, 324])).
% 1.54/1.70 tff(326,plain,
% 1.54/1.70 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (~test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (~test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(327,plain,
% 1.54/1.70 (((~test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) | (~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))) <=> ((~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (~test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(328,plain,
% 1.54/1.70 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) | (~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (~test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[327])).
% 1.54/1.70 tff(329,plain,
% 1.54/1.70 (((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) | (~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))))) <=> ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (~test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[328, 326])).
% 1.54/1.70 tff(330,plain,
% 1.54/1.70 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | ((~test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) | (~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(331,plain,
% 1.54/1.70 ((~![X0: $i, X1: $i] : ((~test(X1)) | (c(addition(X0, X1)) = multiplication(c(X0), c(X1))) | (~test(X0)))) | (~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (~test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[330, 329])).
% 1.54/1.70 tff(332,plain,
% 1.54/1.70 ((~test(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) | (~test(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) | (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[331, 155])).
% 1.54/1.70 tff(333,plain,
% 1.54/1.70 (c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[332, 325, 321])).
% 1.54/1.70 tff(334,plain,
% 1.54/1.70 (multiplication(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = c(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.70 inference(symmetry,[status(thm)],[333])).
% 1.54/1.70 tff(335,plain,
% 1.54/1.70 (c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = c(multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[163])).
% 1.54/1.70 tff(336,plain,
% 1.54/1.70 (c(multiplication(addition(X1!1, c(X1!1)), X0!2)) = c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.70 inference(symmetry,[status(thm)],[335])).
% 1.54/1.70 tff(337,plain,
% 1.54/1.70 (c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = c(multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[10])).
% 1.54/1.70 tff(338,plain,
% 1.54/1.70 (c(multiplication(addition(X0!2, c(X0!2)), X1!1)) = c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.70 inference(symmetry,[status(thm)],[337])).
% 1.54/1.70 tff(339,plain,
% 1.54/1.70 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), c(multiplication(addition(X1!1, c(X1!1)), X0!2))) = multiplication(c(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), c(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[338, 336])).
% 1.54/1.70 tff(340,plain,
% 1.54/1.70 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), c(multiplication(addition(X1!1, c(X1!1)), X0!2))) = multiplication(c(X0!2), c(X1!1))),
% 1.54/1.70 inference(transitivity,[status(thm)],[339, 334, 170, 160, 138])).
% 1.54/1.70 tff(341,plain,
% 1.54/1.70 (multiplication(addition(X1!1, c(X1!1)), X0!2) = multiplication(one, X0!2)),
% 1.54/1.70 inference(symmetry,[status(thm)],[131])).
% 1.54/1.70 tff(342,plain,
% 1.54/1.70 (addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = X0!2),
% 1.54/1.70 inference(transitivity,[status(thm)],[163, 341, 133])).
% 1.54/1.70 tff(343,plain,
% 1.54/1.70 (c(multiplication(addition(X0!2, c(X0!2)), X1!1)) = c(X1!1)),
% 1.54/1.70 inference(symmetry,[status(thm)],[103])).
% 1.54/1.70 tff(344,plain,
% 1.54/1.70 (c(multiplication(addition(X0!2, c(X0!2)), X1!1)) = tptp_fun_X1_0(X1!1)),
% 1.54/1.70 inference(transitivity,[status(thm)],[343, 300])).
% 1.54/1.70 tff(345,plain,
% 1.54/1.70 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(tptp_fun_X1_0(X1!1), X0!2)),
% 1.54/1.70 inference(monotonicity,[status(thm)],[344, 342])).
% 1.54/1.70 tff(346,plain,
% 1.54/1.70 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(c(X1!1), X0!2)),
% 1.54/1.70 inference(transitivity,[status(thm)],[345, 312])).
% 1.54/1.70 tff(347,plain,
% 1.54/1.70 (addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), c(multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1)))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[346, 340])).
% 1.54/1.70 tff(348,plain,
% 1.54/1.70 (^[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))))),
% 1.54/1.70 inference(bind,[status(th)],[])).
% 1.54/1.70 tff(349,plain,
% 1.54/1.70 (![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)))),
% 1.54/1.70 inference(quant_intro,[status(thm)],[348])).
% 1.54/1.70 tff(350,plain,
% 1.54/1.70 (![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)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(351,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')).
% 1.54/1.70 tff(352,plain,
% 1.54/1.70 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[351, 350])).
% 1.54/1.70 tff(353,plain,(
% 1.54/1.70 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 1.54/1.70 inference(skolemize,[status(sab)],[352])).
% 1.54/1.70 tff(354,plain,
% 1.54/1.70 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[353, 349])).
% 1.54/1.70 tff(355,plain,
% 1.54/1.70 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), c(multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), c(multiplication(addition(X1!1, c(X1!1)), X0!2)))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(356,plain,
% 1.54/1.70 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), c(multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), c(multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[355, 354])).
% 1.54/1.70 tff(357,plain,
% 1.54/1.70 (((~![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))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(358,plain,
% 1.54/1.70 ((~![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))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(359,plain,
% 1.54/1.70 ((~![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)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[358, 357])).
% 1.54/1.70 tff(360,plain,
% 1.54/1.70 ((c(X0!2) = tptp_fun_X1_0(X0!2)) <=> complement(X0!2, tptp_fun_X1_0(X0!2))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[359, 77, 67])).
% 1.54/1.70 tff(361,plain,
% 1.54/1.70 (((~![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)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(362,plain,
% 1.54/1.70 ((~(((~(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))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(363,plain,
% 1.54/1.70 ((((~(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)))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(364,plain,
% 1.54/1.70 ((~(((~(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))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[363])).
% 1.54/1.70 tff(365,plain,
% 1.54/1.70 ((~(((~(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))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[364, 362])).
% 1.54/1.70 tff(366,plain,
% 1.54/1.70 (((~![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)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[365])).
% 1.54/1.70 tff(367,plain,
% 1.54/1.70 (((~![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)))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[366, 361])).
% 1.54/1.70 tff(368,plain,
% 1.54/1.70 ((~![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))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(369,plain,
% 1.54/1.70 ((~![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))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[368, 367])).
% 1.54/1.70 tff(370,plain,
% 1.54/1.70 (~(((~(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)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[369, 47])).
% 1.54/1.70 tff(371,plain,
% 1.54/1.70 ((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))),
% 1.54/1.70 inference(commutativity,[status(thm)],[])).
% 1.54/1.70 tff(372,plain,
% 1.54/1.70 ((~![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)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(373,plain,
% 1.54/1.70 (~(((~(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))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[372, 47])).
% 1.54/1.70 tff(374,plain,
% 1.54/1.70 ((~![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))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(375,plain,
% 1.54/1.70 (~((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~(test(X0!2) | ![X1: $i] : (~complement(X1, X0!2)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[374, 270])).
% 1.54/1.71 tff(376,plain,
% 1.54/1.71 (((~((~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))),
% 1.54/1.71 inference(tautology,[status(thm)],[])).
% 1.54/1.71 tff(377,plain,
% 1.54/1.71 ((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[376, 375])).
% 1.54/1.71 tff(378,plain,
% 1.54/1.71 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | (~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 1.54/1.71 inference(tautology,[status(thm)],[])).
% 1.54/1.71 tff(379,plain,
% 1.54/1.71 ((~((~test(X0!2)) | complement(tptp_fun_X1_0(X0!2), X0!2))) | complement(tptp_fun_X1_0(X0!2), X0!2)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[378, 67])).
% 1.54/1.71 tff(380,plain,
% 1.54/1.71 (complement(tptp_fun_X1_0(X0!2), X0!2)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[379, 377])).
% 1.54/1.71 tff(381,plain,
% 1.54/1.71 ((((~(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))),
% 1.54/1.71 inference(tautology,[status(thm)],[])).
% 1.54/1.71 tff(382,plain,
% 1.54/1.71 ((((~(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))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[381, 380])).
% 1.54/1.71 tff(383,plain,
% 1.54/1.71 (~((~(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)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[382, 373])).
% 1.54/1.71 tff(384,plain,
% 1.54/1.71 (((~(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)),
% 1.54/1.71 inference(tautology,[status(thm)],[])).
% 1.54/1.71 tff(385,plain,
% 1.54/1.71 (addition(X0!2, tptp_fun_X1_0(X0!2)) = one),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[384, 383])).
% 1.54/1.71 tff(386,plain,
% 1.54/1.71 (one = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 1.54/1.71 inference(symmetry,[status(thm)],[385])).
% 1.54/1.71 tff(387,plain,
% 1.54/1.71 ((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)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[386])).
% 1.54/1.71 tff(388,plain,
% 1.54/1.71 ((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))),
% 1.54/1.71 inference(transitivity,[status(thm)],[387, 371])).
% 1.54/1.71 tff(389,plain,
% 1.54/1.71 ((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)),
% 1.54/1.71 inference(symmetry,[status(thm)],[388])).
% 1.54/1.71 tff(390,plain,
% 1.54/1.71 ((~![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))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(391,plain,
% 1.54/1.71 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[390, 31])).
% 1.54/1.71 tff(392,plain,
% 1.54/1.71 (addition(tptp_fun_X1_0(X0!2), X0!2) = one),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[391, 389])).
% 1.54/1.71 tff(393,plain,
% 1.54/1.71 (((~(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)),
% 1.54/1.71 inference(tautology,[status(thm)],[])).
% 1.54/1.71 tff(394,plain,
% 1.54/1.71 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = zero),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[393, 383])).
% 1.54/1.71 tff(395,plain,
% 1.54/1.71 (((~(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)),
% 1.54/1.71 inference(tautology,[status(thm)],[])).
% 1.54/1.71 tff(396,plain,
% 1.54/1.71 (multiplication(X0!2, tptp_fun_X1_0(X0!2)) = zero),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[395, 383])).
% 1.54/1.71 tff(397,plain,
% 1.54/1.71 ((~((~(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))),
% 1.54/1.71 inference(tautology,[status(thm)],[])).
% 1.54/1.71 tff(398,plain,
% 1.54/1.71 ((~((~(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))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[397, 396, 394])).
% 1.54/1.71 tff(399,plain,
% 1.54/1.71 (~((~(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)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[398, 392])).
% 1.54/1.71 tff(400,plain,
% 1.54/1.71 ((((~(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))),
% 1.54/1.71 inference(tautology,[status(thm)],[])).
% 1.54/1.71 tff(401,plain,
% 1.54/1.71 (complement(X0!2, tptp_fun_X1_0(X0!2))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[400, 399, 370])).
% 1.54/1.71 tff(402,plain,
% 1.54/1.71 ((~((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)))),
% 1.54/1.71 inference(tautology,[status(thm)],[])).
% 1.54/1.71 tff(403,plain,
% 1.54/1.71 (c(X0!2) = tptp_fun_X1_0(X0!2)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[402, 401, 360])).
% 1.54/1.71 tff(404,plain,
% 1.54/1.71 (c(multiplication(addition(X1!1, c(X1!1)), X0!2)) = c(X0!2)),
% 1.54/1.71 inference(symmetry,[status(thm)],[136])).
% 1.54/1.71 tff(405,plain,
% 1.54/1.71 (c(multiplication(addition(X1!1, c(X1!1)), X0!2)) = tptp_fun_X1_0(X0!2)),
% 1.54/1.71 inference(transitivity,[status(thm)],[404, 403])).
% 1.54/1.71 tff(406,plain,
% 1.54/1.71 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), c(multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[342, 405])).
% 1.54/1.71 tff(407,plain,
% 1.54/1.71 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), c(multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.71 inference(symmetry,[status(thm)],[406])).
% 1.54/1.71 tff(408,plain,
% 1.54/1.71 (one = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), c(multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[386, 407])).
% 1.54/1.71 tff(409,plain,
% 1.54/1.71 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), c(multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[408])).
% 1.54/1.71 tff(410,plain,
% 1.54/1.71 (^[A: $i] : refl((multiplication(A, one) = A) <=> (multiplication(A, one) = A))),
% 1.54/1.71 inference(bind,[status(th)],[])).
% 1.54/1.71 tff(411,plain,
% 1.54/1.71 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 1.54/1.71 inference(quant_intro,[status(thm)],[410])).
% 1.54/1.71 tff(412,plain,
% 1.54/1.71 (![A: $i] : (multiplication(A, one) = A) <=> ![A: $i] : (multiplication(A, one) = A)),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(413,axiom,(![A: $i] : (multiplication(A, one) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','multiplicative_right_identity')).
% 1.54/1.71 tff(414,plain,
% 1.54/1.71 (![A: $i] : (multiplication(A, one) = A)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[413, 412])).
% 1.54/1.71 tff(415,plain,(
% 1.54/1.71 ![A: $i] : (multiplication(A, one) = A)),
% 1.54/1.71 inference(skolemize,[status(sab)],[414])).
% 1.54/1.71 tff(416,plain,
% 1.54/1.71 (![A: $i] : (multiplication(A, one) = A)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[415, 411])).
% 1.54/1.71 tff(417,plain,
% 1.54/1.71 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one) = c(multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(418,plain,
% 1.54/1.71 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one) = c(multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[417, 416])).
% 1.54/1.71 tff(419,plain,
% 1.54/1.71 (c(multiplication(addition(X0!2, c(X0!2)), X1!1)) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one)),
% 1.54/1.71 inference(symmetry,[status(thm)],[418])).
% 1.54/1.71 tff(420,plain,
% 1.54/1.71 (tptp_fun_X1_0(X1!1) = c(X1!1)),
% 1.54/1.71 inference(symmetry,[status(thm)],[300])).
% 1.54/1.71 tff(421,plain,
% 1.54/1.71 (tptp_fun_X1_0(X1!1) = multiplication(c(X1!1), X0!2)),
% 1.54/1.71 inference(transitivity,[status(thm)],[420, 103, 419, 409, 356, 347, 317, 314, 312])).
% 1.54/1.71 tff(422,plain,
% 1.54/1.71 (X1!1 = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))),
% 1.54/1.71 inference(transitivity,[status(thm)],[101, 91, 9])).
% 1.54/1.71 tff(423,plain,
% 1.54/1.71 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X1!1), X0!2))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[422, 421])).
% 1.54/1.71 tff(424,plain,
% 1.54/1.71 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), one) = c(multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(425,plain,
% 1.54/1.71 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), one) = c(multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[424, 416])).
% 1.54/1.71 tff(426,plain,
% 1.54/1.71 (multiplication(addition(X0!2, c(X0!2)), X1!1) = multiplication(one, X1!1)),
% 1.54/1.71 inference(symmetry,[status(thm)],[91])).
% 1.54/1.71 tff(427,plain,
% 1.54/1.71 (addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)) = X1!1),
% 1.54/1.71 inference(transitivity,[status(thm)],[10, 426, 100])).
% 1.54/1.71 tff(428,plain,
% 1.54/1.71 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[427, 344])).
% 1.54/1.71 tff(429,plain,
% 1.54/1.71 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.54/1.71 inference(symmetry,[status(thm)],[428])).
% 1.54/1.71 tff(430,plain,
% 1.54/1.71 (one = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.54/1.71 inference(transitivity,[status(thm)],[283, 429])).
% 1.54/1.71 tff(431,plain,
% 1.54/1.71 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), one) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[430])).
% 1.54/1.71 tff(432,plain,
% 1.54/1.71 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), one)),
% 1.54/1.71 inference(symmetry,[status(thm)],[431])).
% 1.54/1.71 tff(433,plain,
% 1.54/1.71 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(434,plain,
% 1.54/1.71 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[433, 354])).
% 1.54/1.71 tff(435,plain,
% 1.54/1.71 (addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[434])).
% 1.54/1.71 tff(436,plain,
% 1.54/1.71 (multiplication(c(X0!2), X1!1) = multiplication(tptp_fun_X1_0(X0!2), X1!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[403])).
% 1.54/1.71 tff(437,plain,
% 1.54/1.71 (multiplication(tptp_fun_X1_0(X0!2), X1!1) = multiplication(c(X0!2), X1!1)),
% 1.54/1.71 inference(symmetry,[status(thm)],[436])).
% 1.54/1.71 tff(438,plain,
% 1.54/1.71 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(tptp_fun_X1_0(X0!2), X1!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[405, 427])).
% 1.54/1.71 tff(439,plain,
% 1.54/1.71 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(c(X0!2), X1!1)),
% 1.54/1.71 inference(transitivity,[status(thm)],[438, 437])).
% 1.54/1.71 tff(440,plain,
% 1.54/1.71 (addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[439, 138])).
% 1.54/1.71 tff(441,plain,
% 1.54/1.71 (addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[440])).
% 1.54/1.71 tff(442,plain,
% 1.54/1.71 (addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), zero)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[436, 316])).
% 1.54/1.71 tff(443,plain,
% 1.54/1.71 (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), zero) = addition(multiplication(c(X0!2), X1!1), multiplication(c(X0!2), c(X1!1)))),
% 1.54/1.71 inference(symmetry,[status(thm)],[442])).
% 1.54/1.71 tff(444,plain,
% 1.54/1.71 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), zero) = multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(445,plain,
% 1.54/1.71 (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), zero) = multiplication(tptp_fun_X1_0(X0!2), X1!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[444, 227])).
% 1.54/1.71 tff(446,plain,
% 1.54/1.71 (multiplication(tptp_fun_X1_0(X0!2), X1!1) = addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), zero)),
% 1.54/1.71 inference(symmetry,[status(thm)],[445])).
% 1.54/1.71 tff(447,plain,
% 1.54/1.71 (multiplication(c(X0!2), X1!1) = tptp_fun_X1_0(X0!2)),
% 1.54/1.71 inference(transitivity,[status(thm)],[436, 446, 443, 441, 435, 432, 425, 404, 403])).
% 1.54/1.71 tff(448,plain,
% 1.54/1.71 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1)) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[342, 447])).
% 1.54/1.71 tff(449,plain,
% 1.54/1.71 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(450,plain,
% 1.54/1.71 (addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[449, 31])).
% 1.54/1.71 tff(451,plain,
% 1.54/1.71 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(X1!1, c(X1!1))),
% 1.54/1.71 inference(transitivity,[status(thm)],[385, 129, 106])).
% 1.54/1.71 tff(452,plain,
% 1.54/1.71 (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X0!2) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[451])).
% 1.54/1.71 tff(453,plain,
% 1.54/1.71 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X0!2) = addition(multiplication(X0!2, X0!2), multiplication(tptp_fun_X1_0(X0!2), X0!2)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(454,plain,
% 1.54/1.71 (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X0!2) = addition(multiplication(X0!2, X0!2), multiplication(tptp_fun_X1_0(X0!2), X0!2))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[453, 7])).
% 1.54/1.71 tff(455,plain,
% 1.54/1.71 (addition(multiplication(X0!2, X0!2), multiplication(tptp_fun_X1_0(X0!2), X0!2)) = multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X0!2)),
% 1.54/1.71 inference(symmetry,[status(thm)],[454])).
% 1.54/1.71 tff(456,plain,
% 1.54/1.71 (zero = multiplication(tptp_fun_X1_0(X0!2), X0!2)),
% 1.54/1.71 inference(symmetry,[status(thm)],[394])).
% 1.54/1.71 tff(457,plain,
% 1.54/1.71 (addition(multiplication(X0!2, X0!2), zero) = addition(multiplication(X0!2, X0!2), multiplication(tptp_fun_X1_0(X0!2), X0!2))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[456])).
% 1.54/1.71 tff(458,plain,
% 1.54/1.71 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(X0!2, X0!2), zero) = multiplication(X0!2, X0!2))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(459,plain,
% 1.54/1.71 (addition(multiplication(X0!2, X0!2), zero) = multiplication(X0!2, X0!2)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[458, 227])).
% 1.54/1.71 tff(460,plain,
% 1.54/1.71 (multiplication(X0!2, X0!2) = addition(multiplication(X0!2, X0!2), zero)),
% 1.54/1.71 inference(symmetry,[status(thm)],[459])).
% 1.54/1.71 tff(461,plain,
% 1.54/1.71 (multiplication(X0!2, X0!2) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 1.54/1.71 inference(transitivity,[status(thm)],[460, 457, 455, 452, 162])).
% 1.54/1.71 tff(462,plain,
% 1.54/1.71 (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(X0!2, X0!2)) = addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[437, 461])).
% 1.54/1.71 tff(463,plain,
% 1.54/1.71 (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), addition(multiplication(X0!2, X0!2), zero)) = addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(X0!2, X0!2))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[459])).
% 1.54/1.71 tff(464,plain,
% 1.54/1.71 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), addition(multiplication(X0!2, X0!2), zero)) = addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(X0!2, X0!2)), zero))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(465,plain,
% 1.54/1.71 (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), addition(multiplication(X0!2, X0!2), zero)) = addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(X0!2, X0!2)), zero)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[464, 21])).
% 1.54/1.71 tff(466,plain,
% 1.54/1.71 (addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(X0!2, X0!2)), zero) = addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), addition(multiplication(X0!2, X0!2), zero))),
% 1.54/1.71 inference(symmetry,[status(thm)],[465])).
% 1.54/1.71 tff(467,plain,
% 1.54/1.71 (addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(X0!2, X0!2))),
% 1.54/1.71 inference(symmetry,[status(thm)],[462])).
% 1.54/1.71 tff(468,plain,
% 1.54/1.71 (addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1))) = addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(X0!2, X0!2)), zero)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[467, 316])).
% 1.54/1.71 tff(469,plain,
% 1.54/1.71 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(470,plain,
% 1.54/1.71 (addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[469, 21])).
% 1.54/1.71 tff(471,plain,
% 1.54/1.71 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.71 inference(symmetry,[status(thm)],[470])).
% 1.54/1.71 tff(472,plain,
% 1.54/1.71 (addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1))) = addition(addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(X0!2), c(X1!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[471])).
% 1.54/1.71 tff(473,plain,
% 1.54/1.71 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(474,plain,
% 1.54/1.71 (addition(addition(multiplication(c(X0!2), X1!1), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1)))) = addition(addition(addition(multiplication(c(X0!2), X1!1), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), c(X1!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[473, 21])).
% 1.54/1.71 tff(475,plain,
% 1.54/1.71 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(476,plain,
% 1.54/1.71 (addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[475, 31])).
% 1.54/1.71 tff(477,plain,
% 1.54/1.71 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1)))),
% 1.54/1.71 inference(symmetry,[status(thm)],[476])).
% 1.54/1.71 tff(478,plain,
% 1.54/1.71 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), X1!1), multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(c(X0!2), X1!1)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(479,plain,
% 1.54/1.71 (addition(multiplication(c(X0!2), X1!1), multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(c(X0!2), X1!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[478, 31])).
% 1.54/1.71 tff(480,plain,
% 1.54/1.71 (addition(multiplication(X1!1, X0!2), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), multiplication(X1!1, X0!2))),
% 1.54/1.71 inference(symmetry,[status(thm)],[479])).
% 1.54/1.71 tff(481,plain,
% 1.54/1.71 (multiplication(X1!1, X0!2) = multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[102, 135])).
% 1.54/1.71 tff(482,plain,
% 1.54/1.71 (multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)) = multiplication(X1!1, X0!2)),
% 1.54/1.71 inference(symmetry,[status(thm)],[481])).
% 1.54/1.71 tff(483,plain,
% 1.54/1.71 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X0!2), X1!1)) = addition(multiplication(X1!1, X0!2), multiplication(c(X0!2), X1!1))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[482, 437])).
% 1.54/1.71 tff(484,plain,
% 1.54/1.71 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), multiplication(X1!1, X0!2))),
% 1.54/1.71 inference(transitivity,[status(thm)],[483, 480])).
% 1.54/1.71 tff(485,plain,
% 1.54/1.71 (addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))) = addition(addition(multiplication(c(X0!2), X1!1), multiplication(X1!1, X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[484, 477])).
% 1.54/1.71 tff(486,plain,
% 1.54/1.71 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))) = addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(487,plain,
% 1.54/1.71 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))) = addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X0!2), X1!1)), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[486, 21])).
% 1.54/1.71 tff(488,plain,
% 1.54/1.71 (addition(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))) = addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[436])).
% 1.54/1.71 tff(489,plain,
% 1.54/1.71 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[312, 138])).
% 1.54/1.71 tff(490,plain,
% 1.54/1.71 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))),
% 1.54/1.71 inference(transitivity,[status(thm)],[489, 476])).
% 1.54/1.71 tff(491,plain,
% 1.54/1.71 (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))))) = addition(multiplication(c(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[437, 490])).
% 1.54/1.72 tff(492,plain,
% 1.54/1.72 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))))) = addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(tptp_fun_X1_0(X1!1), X0!2)), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(493,plain,
% 1.54/1.72 (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))))) = addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(tptp_fun_X1_0(X1!1), X0!2)), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[492, 21])).
% 1.54/1.72 tff(494,plain,
% 1.54/1.72 (addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(tptp_fun_X1_0(X1!1), X0!2)), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))))),
% 1.54/1.72 inference(symmetry,[status(thm)],[493])).
% 1.54/1.72 tff(495,plain,
% 1.54/1.72 (addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = addition(multiplication(c(X0!2), X1!1), multiplication(c(X1!1), X0!2))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[437, 312])).
% 1.54/1.72 tff(496,plain,
% 1.54/1.72 (addition(multiplication(c(X0!2), X1!1), multiplication(c(X1!1), X0!2)) = addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 1.54/1.72 inference(symmetry,[status(thm)],[495])).
% 1.54/1.72 tff(497,plain,
% 1.54/1.72 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), X1!1), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(498,plain,
% 1.54/1.72 (addition(multiplication(c(X0!2), X1!1), multiplication(c(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[497, 31])).
% 1.54/1.72 tff(499,plain,
% 1.54/1.72 (addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), multiplication(c(X1!1), X0!2))),
% 1.54/1.72 inference(symmetry,[status(thm)],[498])).
% 1.54/1.72 tff(500,plain,
% 1.54/1.72 (addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)) = addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 1.54/1.72 inference(transitivity,[status(thm)],[499, 496])).
% 1.54/1.72 tff(501,plain,
% 1.54/1.72 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), multiplication(tptp_fun_X1_0(X1!1), X0!2)), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[500])).
% 1.54/1.72 tff(502,plain,
% 1.54/1.72 (zero = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[219, 170, 160])).
% 1.54/1.72 tff(503,plain,
% 1.54/1.72 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), zero) = addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[502])).
% 1.54/1.72 tff(504,plain,
% 1.54/1.72 (addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), zero) = addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[503, 501, 494, 491, 488])).
% 1.54/1.72 tff(505,plain,
% 1.54/1.72 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 1.54/1.72 inference(bind,[status(th)],[])).
% 1.54/1.72 tff(506,plain,
% 1.54/1.72 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 1.54/1.72 inference(quant_intro,[status(thm)],[505])).
% 1.54/1.72 tff(507,plain,
% 1.54/1.72 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(508,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 1.54/1.72 tff(509,plain,
% 1.54/1.72 (![A: $i] : (addition(A, A) = A)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[508, 507])).
% 1.54/1.72 tff(510,plain,(
% 1.54/1.72 ![A: $i] : (addition(A, A) = A)),
% 1.54/1.72 inference(skolemize,[status(sab)],[509])).
% 1.54/1.72 tff(511,plain,
% 1.54/1.72 (![A: $i] : (addition(A, A) = A)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[510, 506])).
% 1.54/1.72 tff(512,plain,
% 1.54/1.72 ((~![A: $i] : (addition(A, A) = A)) | (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(513,plain,
% 1.54/1.72 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[512, 511])).
% 1.54/1.72 tff(514,plain,
% 1.54/1.72 (multiplication(one, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 1.54/1.72 inference(monotonicity,[status(thm)],[90, 427])).
% 1.54/1.72 tff(515,plain,
% 1.54/1.72 (multiplication(multiplication(one, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[514, 163])).
% 1.54/1.72 tff(516,plain,
% 1.54/1.72 (^[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)))),
% 1.54/1.72 inference(bind,[status(th)],[])).
% 1.54/1.72 tff(517,plain,
% 1.54/1.72 (![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))),
% 1.54/1.72 inference(quant_intro,[status(thm)],[516])).
% 1.54/1.72 tff(518,plain,
% 1.54/1.72 (![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))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(519,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')).
% 1.54/1.72 tff(520,plain,
% 1.54/1.72 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[519, 518])).
% 1.54/1.72 tff(521,plain,(
% 1.54/1.72 ![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 1.54/1.72 inference(skolemize,[status(sab)],[520])).
% 1.54/1.72 tff(522,plain,
% 1.54/1.72 (![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[521, 517])).
% 1.54/1.72 tff(523,plain,
% 1.54/1.72 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(one, multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(multiplication(one, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(524,plain,
% 1.54/1.72 (multiplication(one, multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(multiplication(one, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[523, 522])).
% 1.54/1.72 tff(525,plain,
% 1.54/1.72 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[10, 163])).
% 1.54/1.72 tff(526,plain,
% 1.54/1.72 (multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)) = multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.72 inference(symmetry,[status(thm)],[525])).
% 1.54/1.72 tff(527,plain,
% 1.54/1.72 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X0!2, tptp_fun_X1_0(X0!2))),
% 1.54/1.72 inference(symmetry,[status(thm)],[391])).
% 1.54/1.72 tff(528,plain,
% 1.54/1.72 (addition(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(tptp_fun_X1_0(X0!2), X0!2)),
% 1.54/1.72 inference(monotonicity,[status(thm)],[405, 342])).
% 1.54/1.72 tff(529,plain,
% 1.54/1.72 (addition(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = one),
% 1.54/1.72 inference(transitivity,[status(thm)],[528, 527, 385])).
% 1.54/1.72 tff(530,plain,
% 1.54/1.72 (multiplication(addition(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = multiplication(one, multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[529, 526])).
% 1.54/1.72 tff(531,plain,
% 1.54/1.72 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(532,plain,
% 1.54/1.72 (multiplication(addition(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[531, 7])).
% 1.54/1.72 tff(533,plain,
% 1.54/1.72 (addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = multiplication(addition(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.72 inference(symmetry,[status(thm)],[532])).
% 1.54/1.72 tff(534,plain,
% 1.54/1.72 (addition(multiplication(X1!1, X1!1), multiplication(c(X1!1), X1!1)) = multiplication(addition(X1!1, c(X1!1)), X1!1)),
% 1.54/1.72 inference(symmetry,[status(thm)],[236])).
% 1.54/1.72 tff(535,plain,
% 1.54/1.72 (multiplication(X1!1, X1!1) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 1.54/1.72 inference(transitivity,[status(thm)],[307, 233, 534, 238])).
% 1.54/1.72 tff(536,plain,
% 1.54/1.72 (multiplication(multiplication(X1!1, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[535, 163])).
% 1.54/1.72 tff(537,plain,
% 1.54/1.72 (multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)) = multiplication(multiplication(X1!1, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.72 inference(symmetry,[status(thm)],[536])).
% 1.54/1.72 tff(538,plain,
% 1.54/1.72 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(multiplication(multiplication(X1!1, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[537])).
% 1.54/1.72 tff(539,plain,
% 1.54/1.72 (addition(multiplication(multiplication(X1!1, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.72 inference(symmetry,[status(thm)],[538])).
% 1.54/1.72 tff(540,plain,
% 1.54/1.72 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(X1!1, X1!1), zero), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(multiplication(X1!1, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(541,plain,
% 1.54/1.72 (multiplication(addition(multiplication(X1!1, X1!1), zero), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(multiplication(X1!1, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[540, 7])).
% 1.54/1.72 tff(542,plain,
% 1.54/1.72 (multiplication(addition(multiplication(X1!1, X1!1), zero), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(multiplication(X1!1, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[229])).
% 1.54/1.72 tff(543,plain,
% 1.54/1.72 (multiplication(multiplication(X1!1, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(addition(multiplication(X1!1, X1!1), zero), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.72 inference(symmetry,[status(thm)],[542])).
% 1.54/1.72 tff(544,plain,
% 1.54/1.72 (multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)) = addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[537, 543, 541, 539])).
% 1.54/1.72 tff(545,plain,
% 1.54/1.72 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[544])).
% 1.54/1.72 tff(546,plain,
% 1.54/1.72 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.72 inference(symmetry,[status(thm)],[545])).
% 1.54/1.72 tff(547,plain,
% 1.54/1.72 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(548,plain,
% 1.54/1.72 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[547, 354])).
% 1.54/1.72 tff(549,plain,
% 1.54/1.72 (addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))))),
% 1.54/1.72 inference(symmetry,[status(thm)],[548])).
% 1.54/1.72 tff(550,plain,
% 1.54/1.72 (^[A: $i] : refl((multiplication(A, zero) = zero) <=> (multiplication(A, zero) = zero))),
% 1.54/1.72 inference(bind,[status(th)],[])).
% 1.54/1.72 tff(551,plain,
% 1.54/1.72 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 1.54/1.72 inference(quant_intro,[status(thm)],[550])).
% 1.54/1.72 tff(552,plain,
% 1.54/1.72 (![A: $i] : (multiplication(A, zero) = zero) <=> ![A: $i] : (multiplication(A, zero) = zero)),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(553,axiom,(![A: $i] : (multiplication(A, zero) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','right_annihilation')).
% 1.54/1.72 tff(554,plain,
% 1.54/1.72 (![A: $i] : (multiplication(A, zero) = zero)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[553, 552])).
% 1.54/1.72 tff(555,plain,(
% 1.54/1.72 ![A: $i] : (multiplication(A, zero) = zero)),
% 1.54/1.72 inference(skolemize,[status(sab)],[554])).
% 1.54/1.72 tff(556,plain,
% 1.54/1.72 (![A: $i] : (multiplication(A, zero) = zero)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[555, 551])).
% 1.54/1.72 tff(557,plain,
% 1.54/1.72 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), zero) = zero)),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(558,plain,
% 1.54/1.72 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), zero) = zero),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[557, 556])).
% 1.54/1.72 tff(559,plain,
% 1.54/1.72 (zero = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), zero)),
% 1.54/1.72 inference(symmetry,[status(thm)],[558])).
% 1.54/1.72 tff(560,plain,
% 1.54/1.72 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), zero) = zero)),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(561,plain,
% 1.54/1.72 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), zero) = zero),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[560, 556])).
% 1.54/1.72 tff(562,plain,
% 1.54/1.72 (^[A: $i] : refl((multiplication(zero, A) = zero) <=> (multiplication(zero, A) = zero))),
% 1.54/1.72 inference(bind,[status(th)],[])).
% 1.54/1.72 tff(563,plain,
% 1.54/1.72 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 1.54/1.72 inference(quant_intro,[status(thm)],[562])).
% 1.54/1.72 tff(564,plain,
% 1.54/1.72 (![A: $i] : (multiplication(zero, A) = zero) <=> ![A: $i] : (multiplication(zero, A) = zero)),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(565,axiom,(![A: $i] : (multiplication(zero, A) = zero)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','left_annihilation')).
% 1.54/1.72 tff(566,plain,
% 1.54/1.72 (![A: $i] : (multiplication(zero, A) = zero)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[565, 564])).
% 1.54/1.72 tff(567,plain,(
% 1.54/1.72 ![A: $i] : (multiplication(zero, A) = zero)),
% 1.54/1.72 inference(skolemize,[status(sab)],[566])).
% 1.54/1.72 tff(568,plain,
% 1.54/1.72 (![A: $i] : (multiplication(zero, A) = zero)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[567, 563])).
% 1.54/1.72 tff(569,plain,
% 1.54/1.72 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = zero)),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(570,plain,
% 1.54/1.72 (multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = zero),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[569, 568])).
% 1.54/1.72 tff(571,plain,
% 1.54/1.72 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), zero)),
% 1.54/1.72 inference(monotonicity,[status(thm)],[570])).
% 1.54/1.72 tff(572,plain,
% 1.54/1.72 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), zero)),
% 1.54/1.72 inference(transitivity,[status(thm)],[571, 561, 559])).
% 1.54/1.72 tff(573,plain,
% 1.54/1.72 (addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), zero))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[572])).
% 1.54/1.72 tff(574,plain,
% 1.54/1.72 (addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), zero)) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))))),
% 1.54/1.72 inference(symmetry,[status(thm)],[573])).
% 1.54/1.72 tff(575,plain,
% 1.54/1.72 (multiplication(tptp_fun_X1_0(X1!1), X0!2) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.72 inference(symmetry,[status(thm)],[345])).
% 1.54/1.72 tff(576,plain,
% 1.54/1.72 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[575])).
% 1.54/1.72 tff(577,plain,
% 1.54/1.72 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 1.54/1.72 inference(symmetry,[status(thm)],[576])).
% 1.54/1.72 tff(578,plain,
% 1.54/1.72 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(579,plain,
% 1.54/1.72 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[578, 522])).
% 1.54/1.72 tff(580,plain,
% 1.54/1.72 (multiplication(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.72 inference(symmetry,[status(thm)],[579])).
% 1.54/1.72 tff(581,plain,
% 1.54/1.72 (multiplication(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[138])).
% 1.54/1.73 tff(582,plain,
% 1.54/1.73 (multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.73 inference(symmetry,[status(thm)],[581])).
% 1.54/1.73 tff(583,plain,
% 1.54/1.73 (multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[316])).
% 1.54/1.73 tff(584,plain,
% 1.54/1.73 (multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.73 inference(symmetry,[status(thm)],[583])).
% 1.54/1.73 tff(585,plain,
% 1.54/1.73 (zero = multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.73 inference(symmetry,[status(thm)],[570])).
% 1.54/1.73 tff(586,plain,
% 1.54/1.73 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), zero) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 1.54/1.73 inference(transitivity,[status(thm)],[558, 585, 584, 582, 580, 577])).
% 1.54/1.73 tff(587,plain,
% 1.54/1.73 (addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), zero)) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[586])).
% 1.54/1.73 tff(588,plain,
% 1.54/1.73 (addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2))) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), zero))),
% 1.54/1.73 inference(symmetry,[status(thm)],[587])).
% 1.54/1.73 tff(589,plain,
% 1.54/1.73 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2))) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(590,plain,
% 1.54/1.73 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2))) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[589, 354])).
% 1.54/1.73 tff(591,plain,
% 1.54/1.73 (addition(X1!1, tptp_fun_X1_0(X1!1)) = addition(X1!1, c(X1!1))),
% 1.54/1.73 inference(transitivity,[status(thm)],[282, 129, 106])).
% 1.54/1.73 tff(592,plain,
% 1.54/1.73 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 1.54/1.73 inference(monotonicity,[status(thm)],[591])).
% 1.54/1.73 tff(593,plain,
% 1.54/1.73 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(594,plain,
% 1.54/1.73 (multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[593, 7])).
% 1.54/1.73 tff(595,plain,
% 1.54/1.73 (addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(addition(X1!1, tptp_fun_X1_0(X1!1)), X0!2)),
% 1.54/1.73 inference(symmetry,[status(thm)],[594])).
% 1.54/1.73 tff(596,plain,
% 1.54/1.73 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[482])).
% 1.54/1.73 tff(597,plain,
% 1.54/1.73 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = X0!2),
% 1.54/1.73 inference(transitivity,[status(thm)],[596, 595, 592, 341, 133])).
% 1.54/1.73 tff(598,plain,
% 1.54/1.73 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2))) = multiplication(tptp_fun_X1_0(X0!2), X0!2)),
% 1.54/1.73 inference(monotonicity,[status(thm)],[405, 597])).
% 1.54/1.73 tff(599,plain,
% 1.54/1.73 (multiplication(tptp_fun_X1_0(X0!2), X0!2) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)))),
% 1.54/1.73 inference(symmetry,[status(thm)],[598])).
% 1.54/1.73 tff(600,plain,
% 1.54/1.73 (zero = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[456, 599, 590, 588, 574, 549, 546])).
% 1.54/1.73 tff(601,plain,
% 1.54/1.73 (addition(zero, multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[600])).
% 1.54/1.73 tff(602,plain,
% 1.54/1.73 (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[526])).
% 1.54/1.73 tff(603,plain,
% 1.54/1.73 (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.73 inference(symmetry,[status(thm)],[602])).
% 1.54/1.73 tff(604,plain,
% 1.54/1.73 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(605,plain,
% 1.54/1.73 (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[604, 522])).
% 1.54/1.73 tff(606,plain,
% 1.54/1.73 (multiplication(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.73 inference(symmetry,[status(thm)],[605])).
% 1.54/1.73 tff(607,plain,
% 1.54/1.73 (multiplication(X0!2, X1!1) = multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[135, 102])).
% 1.54/1.73 tff(608,plain,
% 1.54/1.73 (multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = multiplication(X0!2, X1!1)),
% 1.54/1.73 inference(symmetry,[status(thm)],[607])).
% 1.54/1.73 tff(609,plain,
% 1.54/1.73 (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[163, 10])).
% 1.54/1.73 tff(610,plain,
% 1.54/1.73 (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(X0!2, X1!1)),
% 1.54/1.73 inference(transitivity,[status(thm)],[609, 608])).
% 1.54/1.73 tff(611,plain,
% 1.54/1.73 (multiplication(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[610])).
% 1.54/1.73 tff(612,plain,
% 1.54/1.73 (multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.73 inference(symmetry,[status(thm)],[611])).
% 1.54/1.73 tff(613,plain,
% 1.54/1.73 (multiplication(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[608])).
% 1.54/1.73 tff(614,plain,
% 1.54/1.73 (multiplication(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[613, 612, 606, 603])).
% 1.54/1.73 tff(615,plain,
% 1.54/1.73 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero) = zero)),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(616,plain,
% 1.54/1.73 (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero) = zero),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[615, 556])).
% 1.54/1.73 tff(617,plain,
% 1.54/1.73 (multiplication(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[616])).
% 1.54/1.73 tff(618,plain,
% 1.54/1.73 (multiplication(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = zero),
% 1.54/1.73 inference(transitivity,[status(thm)],[617, 570])).
% 1.54/1.73 tff(619,plain,
% 1.54/1.73 (addition(multiplication(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(zero, multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[618, 614])).
% 1.54/1.73 tff(620,plain,
% 1.54/1.73 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(621,plain,
% 1.54/1.73 (multiplication(addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[620, 7])).
% 1.54/1.73 tff(622,plain,
% 1.54/1.73 (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1)) = multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[163, 535])).
% 1.54/1.73 tff(623,plain,
% 1.54/1.73 (multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1))),
% 1.54/1.73 inference(symmetry,[status(thm)],[622])).
% 1.54/1.73 tff(624,plain,
% 1.54/1.73 (addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[623])).
% 1.54/1.73 tff(625,plain,
% 1.54/1.73 (addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1))) = addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.54/1.73 inference(symmetry,[status(thm)],[624])).
% 1.54/1.73 tff(626,plain,
% 1.54/1.73 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(zero, multiplication(X1!1, X1!1))) = addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(627,plain,
% 1.54/1.73 (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(zero, multiplication(X1!1, X1!1))) = addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[626, 354])).
% 1.54/1.73 tff(628,plain,
% 1.54/1.73 (addition(c(X1!1), X1!1) = addition(X0!2, c(X0!2))),
% 1.54/1.73 inference(transitivity,[status(thm)],[128, 89, 34])).
% 1.54/1.73 tff(629,plain,
% 1.54/1.73 (multiplication(addition(c(X1!1), X1!1), X1!1) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 1.54/1.73 inference(monotonicity,[status(thm)],[628])).
% 1.54/1.73 tff(630,plain,
% 1.54/1.73 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(c(X1!1), X1!1), X1!1) = addition(multiplication(c(X1!1), X1!1), multiplication(X1!1, X1!1)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(631,plain,
% 1.54/1.73 (multiplication(addition(c(X1!1), X1!1), X1!1) = addition(multiplication(c(X1!1), X1!1), multiplication(X1!1, X1!1))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[630, 7])).
% 1.54/1.73 tff(632,plain,
% 1.54/1.73 (addition(multiplication(c(X1!1), X1!1), multiplication(X1!1, X1!1)) = multiplication(addition(c(X1!1), X1!1), X1!1)),
% 1.54/1.73 inference(symmetry,[status(thm)],[631])).
% 1.54/1.73 tff(633,plain,
% 1.54/1.73 (addition(zero, multiplication(X1!1, X1!1)) = addition(multiplication(c(X1!1), X1!1), multiplication(X1!1, X1!1))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[232])).
% 1.54/1.73 tff(634,plain,
% 1.54/1.73 (addition(zero, multiplication(X1!1, X1!1)) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 1.54/1.73 inference(transitivity,[status(thm)],[633, 632, 629])).
% 1.54/1.73 tff(635,plain,
% 1.54/1.73 (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(zero, multiplication(X1!1, X1!1))) = multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[163, 634])).
% 1.54/1.73 tff(636,plain,
% 1.54/1.73 (multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(zero, multiplication(X1!1, X1!1)))),
% 1.54/1.73 inference(symmetry,[status(thm)],[635])).
% 1.54/1.73 tff(637,plain,
% 1.54/1.73 (multiplication(X0!2, X1!1) = addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[607, 636, 627, 625])).
% 1.54/1.73 tff(638,plain,
% 1.54/1.73 (multiplication(multiplication(X0!2, X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[637])).
% 1.54/1.73 tff(639,plain,
% 1.54/1.73 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 1.54/1.73 inference(transitivity,[status(thm)],[596, 595, 592, 162])).
% 1.54/1.73 tff(640,plain,
% 1.54/1.73 (multiplication(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[639])).
% 1.54/1.73 tff(641,plain,
% 1.54/1.73 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(642,plain,
% 1.54/1.73 (multiplication(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[641, 7])).
% 1.54/1.73 tff(643,plain,
% 1.54/1.73 (addition(multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = multiplication(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.73 inference(symmetry,[status(thm)],[642])).
% 1.54/1.73 tff(644,plain,
% 1.54/1.73 (multiplication(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = multiplication(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[312, 482])).
% 1.54/1.73 tff(645,plain,
% 1.54/1.73 (multiplication(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)) = multiplication(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.73 inference(symmetry,[status(thm)],[644])).
% 1.54/1.73 tff(646,plain,
% 1.54/1.73 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), c(multiplication(addition(X1!1, c(X1!1)), X0!2)))) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one)),
% 1.54/1.73 inference(symmetry,[status(thm)],[409])).
% 1.54/1.73 tff(647,plain,
% 1.54/1.73 (addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), c(multiplication(addition(X1!1, c(X1!1)), X0!2)))) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), c(multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.73 inference(symmetry,[status(thm)],[356])).
% 1.54/1.73 tff(648,plain,
% 1.54/1.73 (addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), c(multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.73 inference(symmetry,[status(thm)],[347])).
% 1.54/1.73 tff(649,plain,
% 1.54/1.73 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), zero) = addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), c(X1!1)))),
% 1.54/1.73 inference(symmetry,[status(thm)],[317])).
% 1.54/1.73 tff(650,plain,
% 1.54/1.73 (multiplication(tptp_fun_X1_0(X1!1), X0!2) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), zero)),
% 1.54/1.73 inference(symmetry,[status(thm)],[314])).
% 1.54/1.73 tff(651,plain,
% 1.54/1.73 (multiplication(c(X1!1), X0!2) = c(multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 1.54/1.73 inference(transitivity,[status(thm)],[301, 650, 649, 648, 647, 646, 418])).
% 1.54/1.73 tff(652,plain,
% 1.54/1.73 (multiplication(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2)) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[651, 481])).
% 1.54/1.73 tff(653,plain,
% 1.54/1.73 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = multiplication(multiplication(c(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 1.54/1.73 inference(symmetry,[status(thm)],[652])).
% 1.54/1.73 tff(654,plain,
% 1.54/1.73 (multiplication(one, multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = multiplication(one, multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[526])).
% 1.54/1.73 tff(655,plain,
% 1.54/1.73 (multiplication(one, multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(one, multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.73 inference(symmetry,[status(thm)],[654])).
% 1.54/1.74 tff(656,plain,
% 1.54/1.74 (multiplication(multiplication(one, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(one, multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.74 inference(symmetry,[status(thm)],[524])).
% 1.54/1.74 tff(657,plain,
% 1.54/1.74 (multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)) = multiplication(multiplication(one, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.74 inference(symmetry,[status(thm)],[515])).
% 1.54/1.74 tff(658,plain,
% 1.54/1.74 (multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)) = multiplication(one, multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[657, 656, 655])).
% 1.54/1.74 tff(659,plain,
% 1.54/1.74 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(one, multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[658])).
% 1.54/1.74 tff(660,plain,
% 1.54/1.74 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(one, multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.74 inference(symmetry,[status(thm)],[659])).
% 1.54/1.74 tff(661,plain,
% 1.54/1.74 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(one, multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(662,plain,
% 1.54/1.74 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(one, multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[661, 522])).
% 1.54/1.74 tff(663,plain,
% 1.54/1.74 (multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(one, multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.74 inference(symmetry,[status(thm)],[662])).
% 1.54/1.74 tff(664,plain,
% 1.54/1.74 (multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[526])).
% 1.54/1.74 tff(665,plain,
% 1.54/1.74 (multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.74 inference(symmetry,[status(thm)],[664])).
% 1.54/1.74 tff(666,plain,
% 1.54/1.74 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(667,plain,
% 1.54/1.74 (multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[666, 522])).
% 1.54/1.74 tff(668,plain,
% 1.54/1.74 (multiplication(multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.74 inference(symmetry,[status(thm)],[667])).
% 1.54/1.74 tff(669,plain,
% 1.54/1.74 (multiplication(one, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = X1!1),
% 1.54/1.74 inference(transitivity,[status(thm)],[514, 426, 100])).
% 1.54/1.74 tff(670,plain,
% 1.54/1.74 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(one, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[344, 669])).
% 1.54/1.74 tff(671,plain,
% 1.54/1.74 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(one, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(672,plain,
% 1.54/1.74 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(one, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[671, 522])).
% 1.54/1.74 tff(673,plain,
% 1.54/1.74 (multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(one, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 1.54/1.74 inference(symmetry,[status(thm)],[672])).
% 1.54/1.74 tff(674,plain,
% 1.54/1.74 (multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = zero),
% 1.54/1.74 inference(transitivity,[status(thm)],[673, 670, 291])).
% 1.54/1.74 tff(675,plain,
% 1.54/1.74 (multiplication(multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[674])).
% 1.54/1.74 tff(676,plain,
% 1.54/1.74 (multiplication(zero, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), one), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.74 inference(symmetry,[status(thm)],[675])).
% 1.54/1.74 tff(677,plain,
% 1.54/1.74 (zero = multiplication(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[585, 676, 668, 665, 663, 660, 653, 645])).
% 1.54/1.74 tff(678,plain,
% 1.54/1.74 (addition(multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), zero) = addition(multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[677])).
% 1.54/1.74 tff(679,plain,
% 1.54/1.74 ((~![A: $i] : (addition(A, zero) = A)) | (addition(multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), zero) = multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(680,plain,
% 1.54/1.74 (addition(multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), zero) = multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[679, 227])).
% 1.54/1.74 tff(681,plain,
% 1.54/1.74 (multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), zero)),
% 1.54/1.74 inference(symmetry,[status(thm)],[680])).
% 1.54/1.74 tff(682,plain,
% 1.54/1.74 (multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.54/1.74 inference(transitivity,[status(thm)],[681, 678, 643, 640, 602, 605, 611, 638, 621, 619, 601, 533, 530, 524, 515])).
% 1.54/1.74 tff(683,plain,
% 1.54/1.74 ((~![A: $i] : (multiplication(A, one) = A)) | (multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), one) = multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(684,plain,
% 1.54/1.74 (multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), one) = multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[683, 416])).
% 1.54/1.74 tff(685,plain,
% 1.54/1.74 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X1!1), X0!2)) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 1.54/1.74 inference(symmetry,[status(thm)],[423])).
% 1.54/1.74 tff(686,plain,
% 1.54/1.74 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(X1!1, X1!1), zero)) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X1!1))),
% 1.54/1.74 inference(symmetry,[status(thm)],[308])).
% 1.54/1.74 tff(687,plain,
% 1.54/1.74 (addition(addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X1!1)), zero) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), addition(multiplication(X1!1, X1!1), zero))),
% 1.54/1.74 inference(symmetry,[status(thm)],[306])).
% 1.54/1.74 tff(688,plain,
% 1.54/1.74 (addition(addition(multiplication(c(X1!1), X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(c(X0!2), c(X1!1))) = addition(addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X1!1)), zero)),
% 1.54/1.74 inference(symmetry,[status(thm)],[304])).
% 1.54/1.74 tff(689,plain,
% 1.54/1.74 (addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))) = one),
% 1.54/1.74 inference(transitivity,[status(thm)],[13, 23, 688, 687, 686, 303, 310, 685, 282])).
% 1.54/1.74 tff(690,plain,
% 1.54/1.74 (multiplication(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))) = multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), one)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[481, 689])).
% 1.54/1.74 tff(691,plain,
% 1.54/1.74 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(c(X1!1), X0!2))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[312])).
% 1.54/1.74 tff(692,plain,
% 1.54/1.74 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[691, 311, 302, 308, 306, 304, 24, 14])).
% 1.54/1.74 tff(693,plain,
% 1.54/1.74 (multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(tptp_fun_X1_0(X1!1), X0!2))) = multiplication(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[482, 692])).
% 1.54/1.74 tff(694,plain,
% 1.54/1.74 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(tptp_fun_X1_0(X1!1), X0!2))) = addition(multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(695,plain,
% 1.54/1.74 (multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(tptp_fun_X1_0(X1!1), X0!2))) = addition(multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[694, 354])).
% 1.54/1.74 tff(696,plain,
% 1.54/1.74 (addition(multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2))) = multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(tptp_fun_X1_0(X1!1), X0!2)))),
% 1.54/1.74 inference(symmetry,[status(thm)],[695])).
% 1.54/1.74 tff(697,plain,
% 1.54/1.74 (multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)) = multiplication(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[482, 312])).
% 1.54/1.74 tff(698,plain,
% 1.54/1.74 (multiplication(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)) = multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2))),
% 1.54/1.74 inference(symmetry,[status(thm)],[697])).
% 1.54/1.74 tff(699,plain,
% 1.54/1.74 (multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(multiplication(X1!1, X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[482])).
% 1.54/1.74 tff(700,plain,
% 1.54/1.74 (multiplication(multiplication(X1!1, X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.74 inference(symmetry,[status(thm)],[699])).
% 1.54/1.74 tff(701,plain,
% 1.54/1.74 (multiplication(X1!1, X0!2) = multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[481, 526])).
% 1.54/1.74 tff(702,plain,
% 1.54/1.74 (multiplication(multiplication(X1!1, X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[701])).
% 1.54/1.74 tff(703,plain,
% 1.54/1.74 (multiplication(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(multiplication(X1!1, X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.74 inference(symmetry,[status(thm)],[702])).
% 1.54/1.74 tff(704,plain,
% 1.54/1.74 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = multiplication(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(705,plain,
% 1.54/1.74 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = multiplication(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[704, 522])).
% 1.54/1.74 tff(706,plain,
% 1.54/1.74 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[609])).
% 1.54/1.74 tff(707,plain,
% 1.54/1.74 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 1.54/1.74 inference(symmetry,[status(thm)],[706])).
% 1.54/1.74 tff(708,plain,
% 1.54/1.74 (multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[636, 627, 625])).
% 1.54/1.74 tff(709,plain,
% 1.54/1.74 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[708])).
% 1.54/1.74 tff(710,plain,
% 1.54/1.74 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))) = multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.54/1.74 inference(symmetry,[status(thm)],[709])).
% 1.54/1.74 tff(711,plain,
% 1.54/1.74 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero)), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(712,plain,
% 1.54/1.74 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero)), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[711, 354])).
% 1.54/1.74 tff(713,plain,
% 1.54/1.74 (addition(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero)), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))) = multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.54/1.74 inference(symmetry,[status(thm)],[712])).
% 1.54/1.74 tff(714,plain,
% 1.54/1.74 ((~![A: $i] : (multiplication(A, zero) = zero)) | (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), zero) = zero)),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(715,plain,
% 1.54/1.74 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), zero) = zero),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[714, 556])).
% 1.54/1.74 tff(716,plain,
% 1.54/1.74 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero)) = multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), zero)),
% 1.54/1.74 inference(monotonicity,[status(thm)],[616])).
% 1.54/1.74 tff(717,plain,
% 1.54/1.74 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero)) = zero),
% 1.54/1.74 inference(transitivity,[status(thm)],[716, 715])).
% 1.54/1.74 tff(718,plain,
% 1.54/1.74 (addition(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero)), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(zero, multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[717])).
% 1.54/1.74 tff(719,plain,
% 1.54/1.74 (addition(zero, multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero)), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.54/1.75 inference(symmetry,[status(thm)],[718])).
% 1.54/1.75 tff(720,plain,
% 1.54/1.75 (addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero)) = addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[623])).
% 1.54/1.75 tff(721,plain,
% 1.54/1.75 (addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero)) = addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero))),
% 1.54/1.75 inference(symmetry,[status(thm)],[720])).
% 1.54/1.75 tff(722,plain,
% 1.54/1.75 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X1!1, X1!1), zero)) = addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(723,plain,
% 1.54/1.75 (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X1!1, X1!1), zero)) = addition(multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[722, 354])).
% 1.54/1.75 tff(724,plain,
% 1.54/1.75 (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X1!1, X1!1), zero)) = multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[229])).
% 1.54/1.75 tff(725,plain,
% 1.54/1.75 (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1)) = multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X1!1, X1!1), zero))),
% 1.54/1.75 inference(symmetry,[status(thm)],[724])).
% 1.54/1.75 tff(726,plain,
% 1.54/1.75 (multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero))),
% 1.54/1.75 inference(transitivity,[status(thm)],[623, 725, 723, 721])).
% 1.54/1.75 tff(727,plain,
% 1.54/1.75 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[726])).
% 1.54/1.75 tff(728,plain,
% 1.54/1.75 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero))) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[727])).
% 1.54/1.75 tff(729,plain,
% 1.54/1.75 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero))) = addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(730,plain,
% 1.54/1.75 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero))) = addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[729, 354])).
% 1.54/1.75 tff(731,plain,
% 1.54/1.75 (addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero))) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[730])).
% 1.54/1.75 tff(732,plain,
% 1.54/1.75 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero)) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), zero)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[616])).
% 1.54/1.75 tff(733,plain,
% 1.54/1.75 (addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero))) = addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), zero))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[732])).
% 1.54/1.75 tff(734,plain,
% 1.54/1.75 (addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), zero)) = addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), zero)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[733])).
% 1.54/1.75 tff(735,plain,
% 1.54/1.75 (multiplication(tptp_fun_X1_0(X0!2), X1!1) = multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[438])).
% 1.54/1.75 tff(736,plain,
% 1.54/1.75 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[735])).
% 1.54/1.75 tff(737,plain,
% 1.54/1.75 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 1.54/1.75 inference(symmetry,[status(thm)],[736])).
% 1.54/1.75 tff(738,plain,
% 1.54/1.75 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), c(multiplication(addition(X1!1, c(X1!1)), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(739,plain,
% 1.54/1.75 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), c(multiplication(addition(X1!1, c(X1!1)), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[738, 522])).
% 1.54/1.75 tff(740,plain,
% 1.54/1.75 (multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), c(multiplication(addition(X1!1, c(X1!1)), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 1.54/1.75 inference(symmetry,[status(thm)],[739])).
% 1.54/1.75 tff(741,plain,
% 1.54/1.75 (multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), c(multiplication(addition(X1!1, c(X1!1)), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[340])).
% 1.54/1.75 tff(742,plain,
% 1.54/1.75 (multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), c(multiplication(addition(X1!1, c(X1!1)), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[741])).
% 1.54/1.75 tff(743,plain,
% 1.54/1.75 (multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[316])).
% 1.54/1.75 tff(744,plain,
% 1.54/1.75 (multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[743])).
% 1.54/1.75 tff(745,plain,
% 1.54/1.75 ((~![A: $i] : (multiplication(zero, A) = zero)) | (multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = zero)),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(746,plain,
% 1.54/1.75 (multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = zero),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[745, 568])).
% 1.54/1.75 tff(747,plain,
% 1.54/1.75 (zero = multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[746])).
% 1.54/1.75 tff(748,plain,
% 1.54/1.75 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), zero) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 1.54/1.75 inference(transitivity,[status(thm)],[558, 747, 744, 742, 740, 737])).
% 1.54/1.75 tff(749,plain,
% 1.54/1.75 (addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), zero)) = addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[748])).
% 1.54/1.75 tff(750,plain,
% 1.54/1.75 (addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1))) = addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), zero))),
% 1.54/1.75 inference(symmetry,[status(thm)],[749])).
% 1.54/1.75 tff(751,plain,
% 1.54/1.75 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1))) = addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(752,plain,
% 1.54/1.75 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1))) = addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[751, 354])).
% 1.54/1.75 tff(753,plain,
% 1.54/1.75 (addition(X0!2, tptp_fun_X1_0(X0!2)) = addition(X0!2, c(X0!2))),
% 1.54/1.75 inference(transitivity,[status(thm)],[385, 89, 34])).
% 1.54/1.75 tff(754,plain,
% 1.54/1.75 (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1) = multiplication(addition(X0!2, c(X0!2)), X1!1)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[753])).
% 1.54/1.75 tff(755,plain,
% 1.54/1.75 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1) = addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(756,plain,
% 1.54/1.75 (multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1) = addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[755, 7])).
% 1.54/1.75 tff(757,plain,
% 1.54/1.75 (addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1)) = multiplication(addition(X0!2, tptp_fun_X1_0(X0!2)), X1!1)),
% 1.54/1.75 inference(symmetry,[status(thm)],[756])).
% 1.54/1.75 tff(758,plain,
% 1.54/1.75 (addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(tptp_fun_X1_0(X0!2), X1!1))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[608])).
% 1.54/1.75 tff(759,plain,
% 1.54/1.75 (addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1)) = X1!1),
% 1.54/1.75 inference(transitivity,[status(thm)],[758, 757, 754, 426, 100])).
% 1.54/1.75 tff(760,plain,
% 1.54/1.75 (multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1))) = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[344, 759])).
% 1.54/1.75 tff(761,plain,
% 1.54/1.75 (multiplication(tptp_fun_X1_0(X1!1), X1!1) = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(tptp_fun_X1_0(X0!2), X1!1)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[760])).
% 1.54/1.75 tff(762,plain,
% 1.54/1.75 (zero = multiplication(tptp_fun_X1_0(X1!1), X1!1)),
% 1.54/1.75 inference(symmetry,[status(thm)],[291])).
% 1.54/1.75 tff(763,plain,
% 1.54/1.75 (zero = multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.54/1.75 inference(transitivity,[status(thm)],[762, 761, 752, 750, 734, 731, 728])).
% 1.54/1.75 tff(764,plain,
% 1.54/1.75 (addition(zero, multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[763])).
% 1.54/1.75 tff(765,plain,
% 1.54/1.75 (addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(zero, multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.54/1.75 inference(symmetry,[status(thm)],[764])).
% 1.54/1.75 tff(766,plain,
% 1.54/1.75 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(767,plain,
% 1.54/1.75 (multiplication(addition(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = addition(multiplication(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[766, 7])).
% 1.54/1.75 tff(768,plain,
% 1.54/1.75 (multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[609])).
% 1.54/1.75 tff(769,plain,
% 1.54/1.75 (addition(tptp_fun_X1_0(X1!1), X1!1) = addition(X1!1, tptp_fun_X1_0(X1!1))),
% 1.54/1.75 inference(symmetry,[status(thm)],[288])).
% 1.54/1.75 tff(770,plain,
% 1.54/1.75 (addition(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(tptp_fun_X1_0(X1!1), X1!1)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[344, 427])).
% 1.54/1.75 tff(771,plain,
% 1.54/1.75 (addition(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = one),
% 1.54/1.75 inference(transitivity,[status(thm)],[770, 769, 282])).
% 1.54/1.75 tff(772,plain,
% 1.54/1.75 (multiplication(addition(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(one, multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[771, 768])).
% 1.54/1.75 tff(773,plain,
% 1.54/1.75 (multiplication(one, multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = multiplication(addition(c(multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[772])).
% 1.54/1.75 tff(774,plain,
% 1.54/1.75 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(one, multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = multiplication(multiplication(one, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(775,plain,
% 1.54/1.75 (multiplication(one, multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = multiplication(multiplication(one, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[774, 522])).
% 1.54/1.75 tff(776,plain,
% 1.54/1.75 (multiplication(multiplication(one, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(one, multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 1.54/1.75 inference(symmetry,[status(thm)],[775])).
% 1.54/1.75 tff(777,plain,
% 1.54/1.75 (multiplication(one, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[130, 342])).
% 1.54/1.76 tff(778,plain,
% 1.54/1.76 (multiplication(multiplication(one, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[777, 10])).
% 1.54/1.76 tff(779,plain,
% 1.54/1.76 (multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = multiplication(multiplication(one, addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[778])).
% 1.54/1.76 tff(780,plain,
% 1.54/1.76 (multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[779, 776, 773, 767, 765, 719, 713, 710, 707, 705, 703, 700])).
% 1.54/1.76 tff(781,plain,
% 1.54/1.76 (addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[780, 698])).
% 1.54/1.76 tff(782,plain,
% 1.54/1.76 (addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.54/1.76 inference(transitivity,[status(thm)],[781, 696, 693, 690, 684])).
% 1.54/1.76 tff(783,plain,
% 1.54/1.76 (addition(addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[782, 682])).
% 1.54/1.76 tff(784,plain,
% 1.54/1.76 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))) = addition(addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(785,plain,
% 1.54/1.76 (addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))) = addition(addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[784, 21])).
% 1.54/1.76 tff(786,plain,
% 1.54/1.76 (addition(multiplication(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[698])).
% 1.54/1.76 tff(787,plain,
% 1.54/1.76 (addition(multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(multiplication(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[786])).
% 1.54/1.76 tff(788,plain,
% 1.54/1.76 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(789,plain,
% 1.54/1.76 (multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(tptp_fun_X1_0(X1!1), X0!2)), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[788, 354])).
% 1.54/1.76 tff(790,plain,
% 1.54/1.76 (addition(tptp_fun_X1_0(X1!1), X1!1) = addition(X1!1, c(X1!1))),
% 1.54/1.76 inference(transitivity,[status(thm)],[769, 282, 129, 106])).
% 1.54/1.76 tff(791,plain,
% 1.54/1.76 (multiplication(addition(tptp_fun_X1_0(X1!1), X1!1), X0!2) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[790])).
% 1.54/1.76 tff(792,plain,
% 1.54/1.76 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X1!1), X1!1), X0!2) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(793,plain,
% 1.54/1.76 (multiplication(addition(tptp_fun_X1_0(X1!1), X1!1), X0!2) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[792, 7])).
% 1.54/1.76 tff(794,plain,
% 1.54/1.76 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2)) = multiplication(addition(tptp_fun_X1_0(X1!1), X1!1), X0!2)),
% 1.54/1.76 inference(symmetry,[status(thm)],[793])).
% 1.54/1.76 tff(795,plain,
% 1.54/1.76 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(X1!1, X0!2))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[482])).
% 1.54/1.76 tff(796,plain,
% 1.54/1.76 (addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))),
% 1.54/1.76 inference(transitivity,[status(thm)],[795, 794, 791, 162])).
% 1.54/1.76 tff(797,plain,
% 1.54/1.76 (multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[796])).
% 1.54/1.76 tff(798,plain,
% 1.54/1.76 (multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(tptp_fun_X1_0(X1!1), X0!2), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[797])).
% 1.54/1.76 tff(799,plain,
% 1.54/1.76 (multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[526])).
% 1.54/1.76 tff(800,plain,
% 1.54/1.76 (multiplication(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[799])).
% 1.54/1.76 tff(801,plain,
% 1.54/1.76 ((~![A: $i, B: $i, C: $i] : (multiplication(A, multiplication(B, C)) = multiplication(multiplication(A, B), C))) | (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(802,plain,
% 1.54/1.76 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[801, 522])).
% 1.54/1.76 tff(803,plain,
% 1.54/1.76 (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(X0!2, X0!2)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[342, 342])).
% 1.54/1.76 tff(804,plain,
% 1.54/1.76 (multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 1.54/1.76 inference(transitivity,[status(thm)],[803, 460, 457, 455, 452])).
% 1.54/1.76 tff(805,plain,
% 1.54/1.76 (multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[10, 804])).
% 1.54/1.76 tff(806,plain,
% 1.54/1.76 (multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)) = multiplication(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), multiplication(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[805])).
% 1.54/1.76 tff(807,plain,
% 1.54/1.76 (multiplication(X1!1, X0!2) = addition(multiplication(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[481, 806, 802, 800, 798, 789, 787])).
% 1.54/1.76 tff(808,plain,
% 1.54/1.76 (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X0!2)) = addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), addition(multiplication(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[607, 807])).
% 1.54/1.76 tff(809,plain,
% 1.54/1.76 (addition(tptp_fun_X1_0(X0!2), X0!2) = addition(X1!1, c(X1!1))),
% 1.54/1.76 inference(transitivity,[status(thm)],[527, 385, 129, 106])).
% 1.54/1.76 tff(810,plain,
% 1.54/1.76 (multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), X0!2) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[809])).
% 1.54/1.76 tff(811,plain,
% 1.54/1.76 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), X0!2) = addition(multiplication(tptp_fun_X1_0(X0!2), X0!2), multiplication(X0!2, X0!2)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(812,plain,
% 1.54/1.76 (multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), X0!2) = addition(multiplication(tptp_fun_X1_0(X0!2), X0!2), multiplication(X0!2, X0!2))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[811, 7])).
% 1.54/1.76 tff(813,plain,
% 1.54/1.76 (addition(multiplication(tptp_fun_X1_0(X0!2), X0!2), multiplication(X0!2, X0!2)) = multiplication(addition(tptp_fun_X1_0(X0!2), X0!2), X0!2)),
% 1.54/1.76 inference(symmetry,[status(thm)],[812])).
% 1.54/1.76 tff(814,plain,
% 1.54/1.76 (addition(zero, multiplication(X0!2, X0!2)) = addition(multiplication(tptp_fun_X1_0(X0!2), X0!2), multiplication(X0!2, X0!2))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[456])).
% 1.54/1.76 tff(815,plain,
% 1.54/1.76 (addition(zero, multiplication(X0!2, X0!2)) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 1.54/1.76 inference(transitivity,[status(thm)],[814, 813, 810])).
% 1.54/1.76 tff(816,plain,
% 1.54/1.76 (multiplication(addition(zero, multiplication(X0!2, X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[815, 10])).
% 1.54/1.76 tff(817,plain,
% 1.54/1.76 ((~![A: $i, B: $i, C: $i] : (multiplication(addition(A, B), C) = addition(multiplication(A, C), multiplication(B, C)))) | (multiplication(addition(zero, multiplication(X0!2, X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(X0!2, X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(818,plain,
% 1.54/1.76 (multiplication(addition(zero, multiplication(X0!2, X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(X0!2, X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[817, 7])).
% 1.54/1.76 tff(819,plain,
% 1.54/1.76 (addition(multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(X0!2, X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = multiplication(addition(zero, multiplication(X0!2, X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[818])).
% 1.54/1.76 tff(820,plain,
% 1.54/1.76 (multiplication(X0!2, X0!2) = multiplication(addition(X1!1, c(X1!1)), X0!2)),
% 1.54/1.76 inference(transitivity,[status(thm)],[460, 457, 455, 452])).
% 1.54/1.76 tff(821,plain,
% 1.54/1.76 (multiplication(multiplication(X0!2, X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[820, 10])).
% 1.54/1.76 tff(822,plain,
% 1.54/1.76 (multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = multiplication(multiplication(X0!2, X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[821])).
% 1.54/1.76 tff(823,plain,
% 1.54/1.76 (addition(multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = addition(multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(X0!2, X0!2), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[822])).
% 1.54/1.76 tff(824,plain,
% 1.54/1.76 (addition(multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = multiplication(X0!2, X1!1)),
% 1.54/1.76 inference(transitivity,[status(thm)],[823, 819, 816, 608])).
% 1.54/1.76 tff(825,plain,
% 1.54/1.76 (addition(addition(multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(multiplication(X0!2, X1!1), multiplication(X1!1, X0!2))),
% 1.62/1.76 inference(monotonicity,[status(thm)],[824, 482])).
% 1.62/1.76 tff(826,plain,
% 1.62/1.76 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(addition(multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.62/1.76 inference(quant_inst,[status(thm)],[])).
% 1.62/1.76 tff(827,plain,
% 1.62/1.76 (addition(multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))) = addition(addition(multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.62/1.76 inference(unit_resolution,[status(thm)],[826, 21])).
% 1.62/1.76 tff(828,plain,
% 1.62/1.76 (addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(multiplication(X0!2, X1!1), multiplication(X1!1, X0!2))),
% 1.62/1.76 inference(monotonicity,[status(thm)],[608, 482])).
% 1.62/1.76 tff(829,plain,
% 1.62/1.76 (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X0!2)) = addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.62/1.76 inference(symmetry,[status(thm)],[828])).
% 1.62/1.76 tff(830,plain,
% 1.62/1.76 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(X0!2, X1!1)))),
% 1.62/1.76 inference(quant_inst,[status(thm)],[])).
% 1.62/1.76 tff(831,plain,
% 1.62/1.76 (addition(multiplication(X0!2, X1!1), multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(X0!2, X1!1))),
% 1.62/1.76 inference(unit_resolution,[status(thm)],[830, 31])).
% 1.62/1.76 tff(832,plain,
% 1.62/1.76 (addition(multiplication(X1!1, X0!2), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(X1!1, X0!2))),
% 1.62/1.76 inference(symmetry,[status(thm)],[831])).
% 1.62/1.76 tff(833,plain,
% 1.62/1.76 (addition(multiplication(X1!1, X0!2), multiplication(X0!2, X1!1)) = addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.62/1.76 inference(transitivity,[status(thm)],[832, 829])).
% 1.62/1.76 tff(834,plain,
% 1.62/1.76 (addition(zero, addition(multiplication(X1!1, X0!2), multiplication(X0!2, X1!1))) = addition(multiplication(zero, addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))), addition(multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))))),
% 1.62/1.76 inference(monotonicity,[status(thm)],[747, 833])).
% 1.62/1.76 tff(835,plain,
% 1.62/1.76 (multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))) = zero),
% 1.62/1.76 inference(transitivity,[status(thm)],[315, 169, 218])).
% 1.62/1.76 tff(836,plain,
% 1.62/1.76 (addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(X0!2, X1!1))) = addition(zero, addition(multiplication(X1!1, X0!2), multiplication(X0!2, X1!1)))),
% 1.62/1.76 inference(monotonicity,[status(thm)],[835])).
% 1.62/1.76 tff(837,plain,
% 1.62/1.76 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = addition(multiplication(X1!1, X0!2), multiplication(X0!2, X1!1))),
% 1.62/1.76 inference(monotonicity,[status(thm)],[482, 608])).
% 1.62/1.76 tff(838,plain,
% 1.62/1.76 (addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), addition(multiplication(X1!1, X0!2), multiplication(X0!2, X1!1)))),
% 1.62/1.76 inference(monotonicity,[status(thm)],[837])).
% 1.62/1.76 tff(839,plain,
% 1.62/1.76 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.62/1.76 inference(quant_inst,[status(thm)],[])).
% 1.62/1.76 tff(840,plain,
% 1.62/1.76 (addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.62/1.76 inference(unit_resolution,[status(thm)],[839, 21])).
% 1.62/1.76 tff(841,plain,
% 1.62/1.76 (addition(addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.62/1.76 inference(symmetry,[status(thm)],[840])).
% 1.62/1.77 tff(842,plain,
% 1.62/1.77 (addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2))),
% 1.62/1.77 inference(monotonicity,[status(thm)],[138, 482])).
% 1.62/1.77 tff(843,plain,
% 1.62/1.77 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.62/1.77 inference(symmetry,[status(thm)],[842])).
% 1.62/1.77 tff(844,plain,
% 1.62/1.77 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(c(X0!2), c(X1!1))))),
% 1.62/1.77 inference(quant_inst,[status(thm)],[])).
% 1.62/1.77 tff(845,plain,
% 1.62/1.77 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)) = addition(multiplication(X1!1, X0!2), multiplication(c(X0!2), c(X1!1)))),
% 1.62/1.77 inference(unit_resolution,[status(thm)],[844, 31])).
% 1.62/1.77 tff(846,plain,
% 1.62/1.77 (addition(multiplication(X1!1, X0!2), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2))),
% 1.62/1.77 inference(symmetry,[status(thm)],[845])).
% 1.62/1.77 tff(847,plain,
% 1.62/1.77 (addition(multiplication(X1!1, X0!2), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.62/1.77 inference(transitivity,[status(thm)],[846, 843])).
% 1.62/1.77 tff(848,plain,
% 1.62/1.77 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(X0!2, X1!1)) = addition(addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.62/1.77 inference(monotonicity,[status(thm)],[847, 607])).
% 1.62/1.77 tff(849,plain,
% 1.62/1.77 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(multiplication(X1!1, X0!2), multiplication(c(X0!2), c(X1!1)))),
% 1.62/1.77 inference(monotonicity,[status(thm)],[482, 138])).
% 1.62/1.77 tff(850,plain,
% 1.62/1.77 (addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X0!2), c(X1!1))), multiplication(X0!2, X1!1))),
% 1.62/1.77 inference(monotonicity,[status(thm)],[849, 608])).
% 1.62/1.77 tff(851,plain,
% 1.62/1.77 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.62/1.77 inference(quant_inst,[status(thm)],[])).
% 1.62/1.77 tff(852,plain,
% 1.62/1.77 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))) = addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1)))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.62/1.77 inference(unit_resolution,[status(thm)],[851, 21])).
% 1.62/1.77 tff(853,plain,
% 1.62/1.77 (addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, X1!1))),
% 1.62/1.77 inference(monotonicity,[status(thm)],[138, 608])).
% 1.62/1.77 tff(854,plain,
% 1.62/1.77 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, X1!1)) = addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)))),
% 1.62/1.77 inference(symmetry,[status(thm)],[853])).
% 1.62/1.77 tff(855,plain,
% 1.62/1.77 (addition(multiplication(X1!1, X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, X1!1))) = addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(c(multiplication(addition(X1!1, c(X1!1)), X0!2)), c(multiplication(addition(X0!2, c(X0!2)), X1!1))), multiplication(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))))),
% 1.62/1.77 inference(monotonicity,[status(thm)],[481, 854])).
% 1.62/1.77 tff(856,plain,
% 1.62/1.77 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1))))),
% 1.62/1.77 inference(quant_inst,[status(thm)],[])).
% 1.62/1.77 tff(857,plain,
% 1.62/1.77 (addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, X1!1)) = addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))),
% 1.62/1.77 inference(unit_resolution,[status(thm)],[856, 31])).
% 1.62/1.77 tff(858,plain,
% 1.62/1.77 (addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, X1!1))),
% 1.62/1.77 inference(symmetry,[status(thm)],[857])).
% 1.62/1.77 tff(859,plain,
% 1.62/1.77 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(X1!1, X0!2), addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, X1!1)))),
% 1.62/1.77 inference(monotonicity,[status(thm)],[482, 858])).
% 1.62/1.77 tff(860,plain,
% 1.62/1.77 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))) = multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))),
% 1.62/1.77 inference(transitivity,[status(thm)],[859, 855, 852, 850, 848, 841, 838, 836, 834, 827, 825, 808, 785, 783, 513])).
% 1.62/1.77 tff(861,plain,
% 1.62/1.77 (addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))), addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), zero)) = addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(tptp_fun_X1_0(X0!2), X1!1), addition(multiplication(c(X0!2), c(X1!1)), multiplication(c(X1!1), X0!2))))),
% 1.62/1.77 inference(monotonicity,[status(thm)],[860, 504])).
% 1.62/1.77 tff(862,plain,
% 1.62/1.77 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))), addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), zero)) = addition(addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1))), zero))),
% 1.62/1.77 inference(quant_inst,[status(thm)],[])).
% 1.62/1.77 tff(863,plain,
% 1.62/1.77 (addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))), addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), zero)) = addition(addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1))), zero)),
% 1.62/1.77 inference(unit_resolution,[status(thm)],[862, 21])).
% 1.62/1.77 tff(864,plain,
% 1.62/1.77 (addition(addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1))), zero) = addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))), addition(addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)), zero))),
% 1.62/1.77 inference(symmetry,[status(thm)],[863])).
% 1.62/1.77 tff(865,plain,
% 1.62/1.77 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 1.62/1.77 inference(quant_inst,[status(thm)],[])).
% 1.62/1.77 tff(866,plain,
% 1.62/1.77 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))) = addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1))))),
% 1.62/1.77 inference(unit_resolution,[status(thm)],[865, 31])).
% 1.62/1.77 tff(867,plain,
% 1.62/1.77 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)))),
% 1.62/1.77 inference(symmetry,[status(thm)],[866])).
% 1.62/1.77 tff(868,plain,
% 1.62/1.77 (addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)))),
% 1.62/1.77 inference(monotonicity,[status(thm)],[867])).
% 1.62/1.77 tff(869,plain,
% 1.62/1.77 (addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)))),
% 1.62/1.77 inference(symmetry,[status(thm)],[868])).
% 1.62/1.77 tff(870,plain,
% 1.62/1.77 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1))))),
% 1.62/1.77 inference(quant_inst,[status(thm)],[])).
% 1.62/1.77 tff(871,plain,
% 1.62/1.77 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)))) = addition(addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1))), multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2))), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)))),
% 1.62/1.77 inference(unit_resolution,[status(thm)],[870, 21])).
% 1.62/1.77 tff(872,plain,
% 1.62/1.77 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1)) = addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.62/1.77 inference(symmetry,[status(thm)],[450])).
% 1.62/1.77 tff(873,plain,
% 1.62/1.77 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1)))),
% 1.62/1.77 inference(quant_inst,[status(thm)],[])).
% 1.62/1.77 tff(874,plain,
% 1.62/1.77 (addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), multiplication(c(X0!2), X1!1))),
% 1.62/1.77 inference(unit_resolution,[status(thm)],[873, 21])).
% 1.62/1.77 tff(875,plain,
% 1.62/1.77 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1))) = addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)))),
% 1.62/1.77 inference(monotonicity,[status(thm)],[482])).
% 1.62/1.77 tff(876,plain,
% 1.62/1.77 (addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1))) = addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.62/1.77 inference(transitivity,[status(thm)],[875, 874, 872])).
% 1.62/1.77 tff(877,plain,
% 1.62/1.77 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.62/1.77 inference(monotonicity,[status(thm)],[858, 876])).
% 1.62/1.77 tff(878,plain,
% 1.62/1.77 (addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1))), addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1))))),
% 1.62/1.77 inference(symmetry,[status(thm)],[877])).
% 1.62/1.77 tff(879,plain,
% 1.62/1.77 ((~![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(X0!2, X1!1), addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))))),
% 1.62/1.77 inference(quant_inst,[status(thm)],[])).
% 1.62/1.77 tff(880,plain,
% 1.62/1.77 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, X1!1), addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X0!2, X1!1)), addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.62/1.77 inference(unit_resolution,[status(thm)],[879, 21])).
% 1.62/1.77 tff(881,plain,
% 1.62/1.77 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X0!2, X1!1), addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.62/1.77 inference(quant_inst,[status(thm)],[])).
% 1.62/1.77 tff(882,plain,
% 1.62/1.77 (addition(multiplication(X0!2, X1!1), addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))),
% 1.62/1.77 inference(unit_resolution,[status(thm)],[881, 21])).
% 1.62/1.77 tff(883,plain,
% 1.62/1.77 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, X1!1), addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.62/1.77 inference(monotonicity,[status(thm)],[882])).
% 1.62/1.77 tff(884,plain,
% 1.62/1.77 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X0!2, X1!1), addition(multiplication(c(X0!2), X1!1), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))))),
% 1.62/1.77 inference(symmetry,[status(thm)],[883])).
% 1.62/1.77 tff(885,plain,
% 1.62/1.77 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))),
% 1.62/1.77 inference(monotonicity,[status(thm)],[163, 10])).
% 1.62/1.77 tff(886,plain,
% 1.62/1.77 (addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.63/1.77 inference(symmetry,[status(thm)],[885])).
% 1.63/1.77 tff(887,plain,
% 1.63/1.77 (addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.63/1.77 inference(transitivity,[status(thm)],[164, 180, 886])).
% 1.63/1.77 tff(888,plain,
% 1.63/1.77 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 1.63/1.77 inference(monotonicity,[status(thm)],[887])).
% 1.63/1.77 tff(889,plain,
% 1.63/1.77 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.63/1.77 inference(symmetry,[status(thm)],[888])).
% 1.63/1.77 tff(890,plain,
% 1.63/1.77 ((~![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(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 1.63/1.77 inference(quant_inst,[status(thm)],[])).
% 1.63/1.77 tff(891,plain,
% 1.63/1.77 (addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.63/1.77 inference(unit_resolution,[status(thm)],[890, 21])).
% 1.63/1.77 tff(892,plain,
% 1.63/1.77 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))))),
% 1.63/1.77 inference(symmetry,[status(thm)],[891])).
% 1.63/1.77 tff(893,plain,
% 1.63/1.77 ((~![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(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)))),
% 1.63/1.77 inference(quant_inst,[status(thm)],[])).
% 1.63/1.77 tff(894,plain,
% 1.63/1.77 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))) = addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2))),
% 1.63/1.77 inference(unit_resolution,[status(thm)],[893, 21])).
% 1.63/1.77 tff(895,plain,
% 1.63/1.77 (addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1))) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1))),
% 1.63/1.77 inference(monotonicity,[status(thm)],[894, 240])).
% 1.63/1.77 tff(896,plain,
% 1.63/1.78 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1)) = addition(addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)))),
% 1.63/1.78 inference(symmetry,[status(thm)],[895])).
% 1.63/1.78 tff(897,plain,
% 1.63/1.78 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1)) = addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1)))),
% 1.63/1.78 inference(transitivity,[status(thm)],[896, 892, 889, 884, 880, 878, 871, 869])).
% 1.63/1.78 tff(898,plain,
% 1.63/1.78 (addition(addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1)), zero) = addition(addition(addition(multiplication(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(addition(X1!1, c(X1!1)), X0!2)), addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), c(X1!1)))), addition(multiplication(c(X1!1), X0!2), multiplication(c(X0!2), X1!1))), zero)),
% 1.63/1.78 inference(monotonicity,[status(thm)],[897])).
% 1.63/1.78 tff(899,plain,
% 1.63/1.78 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), addition(multiplication(X1!1, X1!1), zero)) = addition(addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1)), zero))),
% 1.63/1.78 inference(quant_inst,[status(thm)],[])).
% 1.63/1.78 tff(900,plain,
% 1.63/1.78 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), addition(multiplication(X1!1, X1!1), zero)) = addition(addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1)), zero)),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[899, 21])).
% 1.63/1.78 tff(901,plain,
% 1.63/1.78 (addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), multiplication(X1!1, X1!1)) = addition(addition(addition(multiplication(c(X0!2), c(X1!1)), multiplication(X1!1, X0!2)), multiplication(c(X1!1), X0!2)), addition(multiplication(X1!1, X1!1), zero))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[307])).
% 1.63/1.78 tff(902,plain,
% 1.63/1.78 (addition(multiplication(c(X0!2), c(X1!1)), addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1))) = addition(multiplication(c(X0!2), c(X1!1)), addition(addition(multiplication(X0!2, X1!1), multiplication(c(X0!2), X1!1)), addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2))))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[168])).
% 1.63/1.78 tff(903,plain,
% 1.63/1.78 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(addition(X1!1, c(X1!1)), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 1.63/1.78 inference(quant_inst,[status(thm)],[])).
% 1.63/1.78 tff(904,plain,
% 1.63/1.78 (addition(multiplication(addition(X1!1, c(X1!1)), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[903, 21])).
% 1.63/1.78 tff(905,plain,
% 1.63/1.78 (addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))) = addition(multiplication(addition(X1!1, c(X1!1)), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[163])).
% 1.63/1.78 tff(906,plain,
% 1.63/1.78 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 1.63/1.78 inference(quant_inst,[status(thm)],[])).
% 1.63/1.78 tff(907,plain,
% 1.63/1.78 (addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(X1!1, X0!2), multiplication(c(X1!1), X0!2)), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[906, 21])).
% 1.63/1.78 tff(908,plain,
% 1.63/1.78 (addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))),
% 1.63/1.78 inference(transitivity,[status(thm)],[907, 905, 904, 178, 902, 888, 891, 895, 901, 900, 898, 864, 861, 487, 485, 474, 472, 468, 466, 463, 462, 450, 448, 385, 283, 423, 311, 302, 308, 306, 304, 24, 14])).
% 1.63/1.78 tff(909,plain,
% 1.63/1.78 (addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1)))),
% 1.63/1.78 inference(transitivity,[status(thm)],[907, 905, 904])).
% 1.63/1.78 tff(910,plain,
% 1.63/1.78 ((addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))) <=> (addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))) = one)),
% 1.63/1.78 inference(monotonicity,[status(thm)],[909, 689])).
% 1.63/1.78 tff(911,plain,
% 1.63/1.78 ((addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))) <=> (one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))))),
% 1.63/1.78 inference(transitivity,[status(thm)],[910, 176])).
% 1.63/1.78 tff(912,plain,
% 1.63/1.78 ((one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1)))) <=> (addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 1.63/1.78 inference(symmetry,[status(thm)],[911])).
% 1.63/1.78 tff(913,plain,
% 1.63/1.78 ((~(one = addition(addition(multiplication(addition(X1!1, c(X1!1)), X0!2), multiplication(addition(X0!2, c(X0!2)), X1!1)), multiplication(c(X0!2), c(X1!1))))) <=> (~(addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))))),
% 1.63/1.78 inference(monotonicity,[status(thm)],[912])).
% 1.63/1.78 tff(914,plain,
% 1.63/1.78 (~(addition(multiplication(X1!1, X0!2), addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1))))) = addition(multiplication(c(X1!1), X0!2), addition(multiplication(addition(X0!2, c(X0!2)), X1!1), multiplication(c(X0!2), c(X1!1)))))),
% 1.63/1.78 inference(modus_ponens,[status(thm)],[187, 913])).
% 1.63/1.78 tff(915,plain,
% 1.63/1.78 ($false),
% 1.63/1.78 inference(unit_resolution,[status(thm)],[914, 908])).
% 1.63/1.78 % SZS output end Proof
% 1.63/1.78 % E exiting
%------------------------------------------------------------------------------