%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : BOO012-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:00:07 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO012-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 11:39:41 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 tff(product_type, type, (
% 0.20/0.47 product: ( $i * $i * $i ) > $o)).
% 0.20/0.47 tff(inverse_type, type, (
% 0.20/0.47 inverse: $i > $i)).
% 0.20/0.47 tff(x_type, type, (
% 0.20/0.47 x: $i)).
% 0.20/0.47 tff(multiplicative_identity_type, type, (
% 0.20/0.47 multiplicative_identity: $i)).
% 0.20/0.47 tff(add_type, type, (
% 0.20/0.47 add: ( $i * $i ) > $i)).
% 0.20/0.47 tff(sum_type, type, (
% 0.20/0.47 sum: ( $i * $i * $i ) > $o)).
% 0.20/0.47 tff(additive_identity_type, type, (
% 0.20/0.47 additive_identity: $i)).
% 0.20/0.47 tff(1,plain,
% 0.20/0.47 (^[Y: $i, X: $i] : refl(sum(X, Y, add(X, Y)) <=> sum(X, Y, add(X, Y)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(2,plain,
% 0.20/0.47 (![Y: $i, X: $i] : sum(X, Y, add(X, Y)) <=> ![Y: $i, X: $i] : sum(X, Y, add(X, Y))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.47 tff(3,plain,
% 0.20/0.47 (![Y: $i, X: $i] : sum(X, Y, add(X, Y)) <=> ![Y: $i, X: $i] : sum(X, Y, add(X, Y))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(4,axiom,(![Y: $i, X: $i] : sum(X, Y, add(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax','closure_of_addition')).
% 0.20/0.47 tff(5,plain,
% 0.20/0.47 (![Y: $i, X: $i] : sum(X, Y, add(X, Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.47 tff(6,plain,(
% 0.20/0.47 ![Y: $i, X: $i] : sum(X, Y, add(X, Y))),
% 0.20/0.47 inference(skolemize,[status(sab)],[5])).
% 0.20/0.47 tff(7,plain,
% 0.20/0.47 (![Y: $i, X: $i] : sum(X, Y, add(X, Y))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.47 tff(8,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : sum(X, Y, add(X, Y))) | sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(9,plain,
% 0.20/0.47 (sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.47 tff(10,assumption,(~sum(x, additive_identity, x)), introduced(assumption)).
% 0.20/0.47 tff(11,plain,
% 0.20/0.47 (^[X: $i] : refl(sum(X, additive_identity, X) <=> sum(X, additive_identity, X))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(12,plain,
% 0.20/0.47 (![X: $i] : sum(X, additive_identity, X) <=> ![X: $i] : sum(X, additive_identity, X)),
% 0.20/0.47 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.47 tff(13,plain,
% 0.20/0.47 (![X: $i] : sum(X, additive_identity, X) <=> ![X: $i] : sum(X, additive_identity, X)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(14,axiom,(![X: $i] : sum(X, additive_identity, X)), file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax','additive_identity2')).
% 0.20/0.47 tff(15,plain,
% 0.20/0.47 (![X: $i] : sum(X, additive_identity, X)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.47 tff(16,plain,(
% 0.20/0.47 ![X: $i] : sum(X, additive_identity, X)),
% 0.20/0.47 inference(skolemize,[status(sab)],[15])).
% 0.20/0.47 tff(17,plain,
% 0.20/0.47 (![X: $i] : sum(X, additive_identity, X)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.47 tff(18,plain,
% 0.20/0.47 ((~![X: $i] : sum(X, additive_identity, X)) | sum(x, additive_identity, x)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(19,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[18, 17, 10])).
% 0.20/0.47 tff(20,plain,(sum(x, additive_identity, x)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(21,plain,
% 0.20/0.47 ((~(inverse(inverse(x)) = x)) <=> (~(inverse(inverse(x)) = x))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(22,axiom,(~(inverse(inverse(x)) = x)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_inverse_is_an_involution')).
% 0.20/0.47 tff(23,plain,
% 0.20/0.47 (~(inverse(inverse(x)) = x)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (^[V: $i, Y: $i, U: $i, X: $i] : refl(((U = V) | (~sum(X, Y, V)) | (~sum(X, Y, U))) <=> ((U = V) | (~sum(X, Y, V)) | (~sum(X, Y, U))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(25,plain,
% 0.20/0.47 (![V: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~sum(X, Y, V)) | (~sum(X, Y, U))) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~sum(X, Y, V)) | (~sum(X, Y, U)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 (![V: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~sum(X, Y, V)) | (~sum(X, Y, U))) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~sum(X, Y, V)) | (~sum(X, Y, U)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(27,plain,
% 0.20/0.47 (^[V: $i, Y: $i, U: $i, X: $i] : rewrite((((~sum(X, Y, U)) | (~sum(X, Y, V))) | (U = V)) <=> ((U = V) | (~sum(X, Y, V)) | (~sum(X, Y, U))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (![V: $i, Y: $i, U: $i, X: $i] : (((~sum(X, Y, U)) | (~sum(X, Y, V))) | (U = V)) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~sum(X, Y, V)) | (~sum(X, Y, U)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.47 tff(29,axiom,(![V: $i, Y: $i, U: $i, X: $i] : (((~sum(X, Y, U)) | (~sum(X, Y, V))) | (U = V))), file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax','addition_is_well_defined')).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (![V: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~sum(X, Y, V)) | (~sum(X, Y, U)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (![V: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~sum(X, Y, V)) | (~sum(X, Y, U)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.47 tff(32,plain,(
% 0.20/0.47 ![V: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~sum(X, Y, V)) | (~sum(X, Y, U)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[31])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 (![V: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~sum(X, Y, V)) | (~sum(X, Y, U)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (((~![V: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~sum(X, Y, V)) | (~sum(X, Y, U)))) | ((inverse(inverse(x)) = x) | (~sum(x, additive_identity, x)) | (~sum(x, additive_identity, inverse(inverse(x)))))) <=> ((~![V: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~sum(X, Y, V)) | (~sum(X, Y, U)))) | (inverse(inverse(x)) = x) | (~sum(x, additive_identity, x)) | (~sum(x, additive_identity, inverse(inverse(x)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 ((~![V: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~sum(X, Y, V)) | (~sum(X, Y, U)))) | ((inverse(inverse(x)) = x) | (~sum(x, additive_identity, x)) | (~sum(x, additive_identity, inverse(inverse(x)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 ((~![V: $i, Y: $i, U: $i, X: $i] : ((U = V) | (~sum(X, Y, V)) | (~sum(X, Y, U)))) | (inverse(inverse(x)) = x) | (~sum(x, additive_identity, x)) | (~sum(x, additive_identity, inverse(inverse(x))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.47 tff(37,plain,
% 0.20/0.47 ((~sum(x, additive_identity, x)) | (~sum(x, additive_identity, inverse(inverse(x))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[36, 33, 23])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 (~sum(x, additive_identity, inverse(inverse(x)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[37, 20])).
% 0.20/0.47 tff(39,plain,
% 0.20/0.47 (^[X: $i] : refl(product(inverse(X), X, additive_identity) <=> product(inverse(X), X, additive_identity))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 (![X: $i] : product(inverse(X), X, additive_identity) <=> ![X: $i] : product(inverse(X), X, additive_identity)),
% 0.20/0.47 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.47 tff(41,plain,
% 0.20/0.47 (![X: $i] : product(inverse(X), X, additive_identity) <=> ![X: $i] : product(inverse(X), X, additive_identity)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(42,axiom,(![X: $i] : product(inverse(X), X, additive_identity)), file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax','multiplicative_inverse1')).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 (![X: $i] : product(inverse(X), X, additive_identity)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.47 tff(44,plain,(
% 0.20/0.47 ![X: $i] : product(inverse(X), X, additive_identity)),
% 0.20/0.47 inference(skolemize,[status(sab)],[43])).
% 0.20/0.47 tff(45,plain,
% 0.20/0.47 (![X: $i] : product(inverse(X), X, additive_identity)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 ((~![X: $i] : product(inverse(X), X, additive_identity)) | product(inverse(inverse(x)), inverse(x), additive_identity)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 (product(inverse(inverse(x)), inverse(x), additive_identity)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 (^[X: $i] : refl(sum(X, inverse(X), multiplicative_identity) <=> sum(X, inverse(X), multiplicative_identity))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (![X: $i] : sum(X, inverse(X), multiplicative_identity) <=> ![X: $i] : sum(X, inverse(X), multiplicative_identity)),
% 0.20/0.47 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 (![X: $i] : sum(X, inverse(X), multiplicative_identity) <=> ![X: $i] : sum(X, inverse(X), multiplicative_identity)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(51,axiom,(![X: $i] : sum(X, inverse(X), multiplicative_identity)), file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax','additive_inverse2')).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 (![X: $i] : sum(X, inverse(X), multiplicative_identity)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.47 tff(53,plain,(
% 0.20/0.47 ![X: $i] : sum(X, inverse(X), multiplicative_identity)),
% 0.20/0.47 inference(skolemize,[status(sab)],[52])).
% 0.20/0.47 tff(54,plain,
% 0.20/0.47 (![X: $i] : sum(X, inverse(X), multiplicative_identity)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.47 tff(55,plain,
% 0.20/0.47 ((~![X: $i] : sum(X, inverse(X), multiplicative_identity)) | sum(x, inverse(x), multiplicative_identity)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 (sum(x, inverse(x), multiplicative_identity)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 (^[Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : refl((sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4))) <=> (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4))) <=> ![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4))) <=> ![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 (^[Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~sum(X, Y, V1)) | (~sum(X, Z, V2))) | (~product(Y, Z, V3))) <=> ((~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)))), (((((~sum(X, Y, V1)) | (~sum(X, Z, V2))) | (~product(Y, Z, V3))) | (~product(V1, V2, V4))) <=> (((~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1))) | (~product(V1, V2, V4))))), rewrite((((~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1))) | (~product(V1, V2, V4))) <=> ((~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))), (((((~sum(X, Y, V1)) | (~sum(X, Z, V2))) | (~product(Y, Z, V3))) | (~product(V1, V2, V4))) <=> ((~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4))))), ((((((~sum(X, Y, V1)) | (~sum(X, Z, V2))) | (~product(Y, Z, V3))) | (~product(V1, V2, V4))) | sum(X, V3, V4)) <=> (((~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4))) | sum(X, V3, V4)))), rewrite((((~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4))) | sum(X, V3, V4)) <=> (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))), ((((((~sum(X, Y, V1)) | (~sum(X, Z, V2))) | (~product(Y, Z, V3))) | (~product(V1, V2, V4))) | sum(X, V3, V4)) <=> (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(61,plain,
% 0.20/0.47 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (((((~sum(X, Y, V1)) | (~sum(X, Z, V2))) | (~product(Y, Z, V3))) | (~product(V1, V2, V4))) | sum(X, V3, V4)) <=> ![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.47 tff(62,axiom,(![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (((((~sum(X, Y, V1)) | (~sum(X, Z, V2))) | (~product(Y, Z, V3))) | (~product(V1, V2, V4))) | sum(X, V3, V4))), file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax','distributivity6')).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.47 tff(65,plain,(
% 0.20/0.47 ![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[64])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.20/0.47 tff(67,plain,
% 0.20/0.47 (((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))) | ((~product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x)))) | (~product(inverse(inverse(x)), inverse(x), additive_identity)) | (~sum(x, inverse(x), multiplicative_identity)) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))) | sum(x, additive_identity, inverse(inverse(x))))) <=> ((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))) | (~product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x)))) | (~product(inverse(inverse(x)), inverse(x), additive_identity)) | (~sum(x, inverse(x), multiplicative_identity)) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))) | sum(x, additive_identity, inverse(inverse(x))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 ((sum(x, additive_identity, inverse(inverse(x))) | (~product(inverse(inverse(x)), inverse(x), additive_identity)) | (~sum(x, inverse(x), multiplicative_identity)) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))) | (~product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))))) <=> ((~product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x)))) | (~product(inverse(inverse(x)), inverse(x), additive_identity)) | (~sum(x, inverse(x), multiplicative_identity)) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))) | sum(x, additive_identity, inverse(inverse(x))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 (((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))) | (sum(x, additive_identity, inverse(inverse(x))) | (~product(inverse(inverse(x)), inverse(x), additive_identity)) | (~sum(x, inverse(x), multiplicative_identity)) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))) | (~product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x)))))) <=> ((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))) | ((~product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x)))) | (~product(inverse(inverse(x)), inverse(x), additive_identity)) | (~sum(x, inverse(x), multiplicative_identity)) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))) | sum(x, additive_identity, inverse(inverse(x)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[68])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 (((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))) | (sum(x, additive_identity, inverse(inverse(x))) | (~product(inverse(inverse(x)), inverse(x), additive_identity)) | (~sum(x, inverse(x), multiplicative_identity)) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))) | (~product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x)))))) <=> ((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))) | (~product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x)))) | (~product(inverse(inverse(x)), inverse(x), additive_identity)) | (~sum(x, inverse(x), multiplicative_identity)) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))) | sum(x, additive_identity, inverse(inverse(x))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[69, 67])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 ((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))) | (sum(x, additive_identity, inverse(inverse(x))) | (~product(inverse(inverse(x)), inverse(x), additive_identity)) | (~sum(x, inverse(x), multiplicative_identity)) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))) | (~product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(72,plain,
% 0.20/0.48 ((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(X, V3, V4) | (~product(Y, Z, V3)) | (~sum(X, Z, V2)) | (~sum(X, Y, V1)) | (~product(V1, V2, V4)))) | (~product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x)))) | (~product(inverse(inverse(x)), inverse(x), additive_identity)) | (~sum(x, inverse(x), multiplicative_identity)) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))) | sum(x, additive_identity, inverse(inverse(x)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.48 tff(73,plain,
% 0.20/0.48 (~product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[72, 66, 56, 47, 38, 9])).
% 0.20/0.48 tff(74,plain,
% 0.20/0.48 (^[X: $i] : refl(sum(additive_identity, X, X) <=> sum(additive_identity, X, X))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(75,plain,
% 0.20/0.48 (![X: $i] : sum(additive_identity, X, X) <=> ![X: $i] : sum(additive_identity, X, X)),
% 0.20/0.48 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.48 tff(76,plain,
% 0.20/0.48 (![X: $i] : sum(additive_identity, X, X) <=> ![X: $i] : sum(additive_identity, X, X)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(77,axiom,(![X: $i] : sum(additive_identity, X, X)), file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax','additive_identity1')).
% 0.20/0.48 tff(78,plain,
% 0.20/0.48 (![X: $i] : sum(additive_identity, X, X)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.48 tff(79,plain,(
% 0.20/0.48 ![X: $i] : sum(additive_identity, X, X)),
% 0.20/0.48 inference(skolemize,[status(sab)],[78])).
% 0.20/0.48 tff(80,plain,
% 0.20/0.48 (![X: $i] : sum(additive_identity, X, X)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.20/0.48 tff(81,plain,
% 0.20/0.48 ((~![X: $i] : sum(additive_identity, X, X)) | sum(additive_identity, inverse(inverse(x)), inverse(inverse(x)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(82,plain,
% 0.20/0.48 (sum(additive_identity, inverse(inverse(x)), inverse(inverse(x)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.20/0.48 tff(83,plain,
% 0.20/0.48 ((~![X: $i] : sum(X, inverse(X), multiplicative_identity)) | sum(inverse(x), inverse(inverse(x)), multiplicative_identity)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(84,plain,
% 0.20/0.48 (sum(inverse(x), inverse(inverse(x)), multiplicative_identity)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[83, 54])).
% 0.20/0.48 tff(85,plain,
% 0.20/0.48 (^[X: $i] : refl(product(X, inverse(X), additive_identity) <=> product(X, inverse(X), additive_identity))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(86,plain,
% 0.20/0.48 (![X: $i] : product(X, inverse(X), additive_identity) <=> ![X: $i] : product(X, inverse(X), additive_identity)),
% 0.20/0.48 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.48 tff(87,plain,
% 0.20/0.48 (![X: $i] : product(X, inverse(X), additive_identity) <=> ![X: $i] : product(X, inverse(X), additive_identity)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(88,axiom,(![X: $i] : product(X, inverse(X), additive_identity)), file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax','multiplicative_inverse2')).
% 0.20/0.48 tff(89,plain,
% 0.20/0.48 (![X: $i] : product(X, inverse(X), additive_identity)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.48 tff(90,plain,(
% 0.20/0.48 ![X: $i] : product(X, inverse(X), additive_identity)),
% 0.20/0.48 inference(skolemize,[status(sab)],[89])).
% 0.20/0.48 tff(91,plain,
% 0.20/0.48 (![X: $i] : product(X, inverse(X), additive_identity)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.20/0.48 tff(92,plain,
% 0.20/0.48 ((~![X: $i] : product(X, inverse(X), additive_identity)) | product(x, inverse(x), additive_identity)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(93,plain,
% 0.20/0.48 (product(x, inverse(x), additive_identity)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.20/0.48 tff(94,plain,
% 0.20/0.48 (^[Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : refl((product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1))) <=> (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(95,plain,
% 0.20/0.48 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1))) <=> ![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.48 tff(96,plain,
% 0.20/0.48 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1))) <=> ![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(97,plain,
% 0.20/0.48 (^[Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~sum(Y, X, V1)) | (~sum(Z, X, V2))) | (~product(Y, Z, V3))) <=> ((~product(Y, Z, V3)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))), (((((~sum(Y, X, V1)) | (~sum(Z, X, V2))) | (~product(Y, Z, V3))) | (~sum(V3, X, V4))) <=> (((~product(Y, Z, V3)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1))) | (~sum(V3, X, V4))))), rewrite((((~product(Y, Z, V3)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1))) | (~sum(V3, X, V4))) <=> ((~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))), (((((~sum(Y, X, V1)) | (~sum(Z, X, V2))) | (~product(Y, Z, V3))) | (~sum(V3, X, V4))) <=> ((~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1))))), ((((((~sum(Y, X, V1)) | (~sum(Z, X, V2))) | (~product(Y, Z, V3))) | (~sum(V3, X, V4))) | product(V1, V2, V4)) <=> (((~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1))) | product(V1, V2, V4)))), rewrite((((~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1))) | product(V1, V2, V4)) <=> (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))), ((((((~sum(Y, X, V1)) | (~sum(Z, X, V2))) | (~product(Y, Z, V3))) | (~sum(V3, X, V4))) | product(V1, V2, V4)) <=> (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(98,plain,
% 0.20/0.48 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (((((~sum(Y, X, V1)) | (~sum(Z, X, V2))) | (~product(Y, Z, V3))) | (~sum(V3, X, V4))) | product(V1, V2, V4)) <=> ![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.48 tff(99,axiom,(![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (((((~sum(Y, X, V1)) | (~sum(Z, X, V2))) | (~product(Y, Z, V3))) | (~sum(V3, X, V4))) | product(V1, V2, V4))), file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax','distributivity7')).
% 0.20/0.48 tff(100,plain,
% 0.20/0.48 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.48 tff(101,plain,
% 0.20/0.48 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.20/0.48 tff(102,plain,(
% 0.20/0.48 ![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[101])).
% 0.20/0.48 tff(103,plain,
% 0.20/0.48 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.20/0.48 tff(104,plain,
% 0.20/0.48 (((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))) | (product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))) | (~sum(additive_identity, inverse(inverse(x)), inverse(inverse(x)))) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))) | (~product(x, inverse(x), additive_identity)) | (~sum(inverse(x), inverse(inverse(x)), multiplicative_identity)))) <=> ((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))) | product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))) | (~sum(additive_identity, inverse(inverse(x)), inverse(inverse(x)))) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))) | (~product(x, inverse(x), additive_identity)) | (~sum(inverse(x), inverse(inverse(x)), multiplicative_identity)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(105,plain,
% 0.20/0.48 ((product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))) | (~product(x, inverse(x), additive_identity)) | (~sum(additive_identity, inverse(inverse(x)), inverse(inverse(x)))) | (~sum(inverse(x), inverse(inverse(x)), multiplicative_identity)) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x)))))) <=> (product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))) | (~sum(additive_identity, inverse(inverse(x)), inverse(inverse(x)))) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))) | (~product(x, inverse(x), additive_identity)) | (~sum(inverse(x), inverse(inverse(x)), multiplicative_identity)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(106,plain,
% 0.20/0.48 (((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))) | (product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))) | (~product(x, inverse(x), additive_identity)) | (~sum(additive_identity, inverse(inverse(x)), inverse(inverse(x)))) | (~sum(inverse(x), inverse(inverse(x)), multiplicative_identity)) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))))) <=> ((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))) | (product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))) | (~sum(additive_identity, inverse(inverse(x)), inverse(inverse(x)))) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))) | (~product(x, inverse(x), additive_identity)) | (~sum(inverse(x), inverse(inverse(x)), multiplicative_identity))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[105])).
% 0.20/0.48 tff(107,plain,
% 0.20/0.48 (((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))) | (product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))) | (~product(x, inverse(x), additive_identity)) | (~sum(additive_identity, inverse(inverse(x)), inverse(inverse(x)))) | (~sum(inverse(x), inverse(inverse(x)), multiplicative_identity)) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))))) <=> ((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))) | product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))) | (~sum(additive_identity, inverse(inverse(x)), inverse(inverse(x)))) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))) | (~product(x, inverse(x), additive_identity)) | (~sum(inverse(x), inverse(inverse(x)), multiplicative_identity)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[106, 104])).
% 0.20/0.48 tff(108,plain,
% 0.20/0.48 ((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))) | (product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))) | (~product(x, inverse(x), additive_identity)) | (~sum(additive_identity, inverse(inverse(x)), inverse(inverse(x)))) | (~sum(inverse(x), inverse(inverse(x)), multiplicative_identity)) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(109,plain,
% 0.20/0.48 ((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (product(V1, V2, V4) | (~product(Y, Z, V3)) | (~sum(V3, X, V4)) | (~sum(Z, X, V2)) | (~sum(Y, X, V1)))) | product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))) | (~sum(additive_identity, inverse(inverse(x)), inverse(inverse(x)))) | (~sum(x, inverse(inverse(x)), add(x, inverse(inverse(x))))) | (~product(x, inverse(x), additive_identity)) | (~sum(inverse(x), inverse(inverse(x)), multiplicative_identity))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.48 tff(110,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[109, 103, 93, 84, 9, 82, 73])).
% 0.20/0.48 % SZS output end Proof
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------