%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG038-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:23:58 AM UTC 2025
% Result : Unsatisfiable 5.33s 5.49s
% Output : Proof 5.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : RNG038-1 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 03:19:19 EDT 2025
% 0.12/0.34 % CPUTime :
% 5.33/5.49 % SZS status Unsatisfiable
% 5.33/5.49 % SZS output start Proof
% 5.33/5.49 tff(additive_identity_type, type, (
% 5.33/5.49 additive_identity: $i)).
% 5.33/5.49 tff(a_type, type, (
% 5.33/5.49 a: $i)).
% 5.33/5.49 tff(add_type, type, (
% 5.33/5.49 add: ( $i * $i ) > $i)).
% 5.33/5.49 tff(sum_type, type, (
% 5.33/5.49 sum: ( $i * $i * $i ) > $o)).
% 5.33/5.49 tff(additive_inverse_type, type, (
% 5.33/5.49 additive_inverse: $i > $i)).
% 5.33/5.49 tff(product_type, type, (
% 5.33/5.49 product: ( $i * $i * $i ) > $o)).
% 5.33/5.49 tff(h_type, type, (
% 5.33/5.49 h: ( $i * $i ) > $i)).
% 5.33/5.49 tff(1,assumption,(~sum(additive_inverse(a), add(a, additive_identity), add(a, additive_identity))), introduced(assumption)).
% 5.33/5.49 tff(2,assumption,(~sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity))), introduced(assumption)).
% 5.33/5.49 tff(3,plain,
% 5.33/5.49 (^[Y: $i, X: $i] : refl(sum(X, Y, add(X, Y)) <=> sum(X, Y, add(X, Y)))),
% 5.33/5.49 inference(bind,[status(th)],[])).
% 5.33/5.49 tff(4,plain,
% 5.33/5.49 (![Y: $i, X: $i] : sum(X, Y, add(X, Y)) <=> ![Y: $i, X: $i] : sum(X, Y, add(X, Y))),
% 5.33/5.49 inference(quant_intro,[status(thm)],[3])).
% 5.33/5.49 tff(5,plain,
% 5.33/5.49 (![Y: $i, X: $i] : sum(X, Y, add(X, Y)) <=> ![Y: $i, X: $i] : sum(X, Y, add(X, Y))),
% 5.33/5.49 inference(rewrite,[status(thm)],[])).
% 5.33/5.49 tff(6,axiom,(![Y: $i, X: $i] : sum(X, Y, add(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax','closure_of_addition')).
% 5.33/5.49 tff(7,plain,
% 5.33/5.49 (![Y: $i, X: $i] : sum(X, Y, add(X, Y))),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[6, 5])).
% 5.33/5.49 tff(8,plain,(
% 5.33/5.49 ![Y: $i, X: $i] : sum(X, Y, add(X, Y))),
% 5.33/5.49 inference(skolemize,[status(sab)],[7])).
% 5.33/5.49 tff(9,plain,
% 5.33/5.49 (![Y: $i, X: $i] : sum(X, Y, add(X, Y))),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[8, 4])).
% 5.33/5.49 tff(10,plain,
% 5.33/5.49 ((~![Y: $i, X: $i] : sum(X, Y, add(X, Y))) | sum(a, additive_identity, add(a, additive_identity))),
% 5.33/5.49 inference(quant_inst,[status(thm)],[])).
% 5.33/5.49 tff(11,plain,
% 5.33/5.49 (sum(a, additive_identity, add(a, additive_identity))),
% 5.33/5.49 inference(unit_resolution,[status(thm)],[10, 9])).
% 5.33/5.49 tff(12,plain,
% 5.33/5.49 (^[X: $i] : refl(sum(X, additive_identity, X) <=> sum(X, additive_identity, X))),
% 5.33/5.49 inference(bind,[status(th)],[])).
% 5.33/5.49 tff(13,plain,
% 5.33/5.49 (![X: $i] : sum(X, additive_identity, X) <=> ![X: $i] : sum(X, additive_identity, X)),
% 5.33/5.49 inference(quant_intro,[status(thm)],[12])).
% 5.33/5.49 tff(14,plain,
% 5.33/5.49 (![X: $i] : sum(X, additive_identity, X) <=> ![X: $i] : sum(X, additive_identity, X)),
% 5.33/5.49 inference(rewrite,[status(thm)],[])).
% 5.33/5.49 tff(15,axiom,(![X: $i] : sum(X, additive_identity, X)), file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax','additive_identity2')).
% 5.33/5.49 tff(16,plain,
% 5.33/5.49 (![X: $i] : sum(X, additive_identity, X)),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[15, 14])).
% 5.33/5.49 tff(17,plain,(
% 5.33/5.49 ![X: $i] : sum(X, additive_identity, X)),
% 5.33/5.49 inference(skolemize,[status(sab)],[16])).
% 5.33/5.49 tff(18,plain,
% 5.33/5.49 (![X: $i] : sum(X, additive_identity, X)),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[17, 13])).
% 5.33/5.49 tff(19,plain,
% 5.33/5.49 ((~![X: $i] : sum(X, additive_identity, X)) | sum(a, additive_identity, a)),
% 5.33/5.49 inference(quant_inst,[status(thm)],[])).
% 5.33/5.49 tff(20,plain,
% 5.33/5.49 (sum(a, additive_identity, a)),
% 5.33/5.49 inference(unit_resolution,[status(thm)],[19, 18])).
% 5.33/5.49 tff(21,plain,
% 5.33/5.49 (^[V: $i, Y: $i, U: $i, X: $i] : refl(((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V)) <=> ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V)))),
% 5.33/5.49 inference(bind,[status(th)],[])).
% 5.33/5.49 tff(22,plain,
% 5.33/5.49 (![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] : ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V))),
% 5.33/5.49 inference(quant_intro,[status(thm)],[21])).
% 5.33/5.49 tff(23,plain,
% 5.33/5.49 (![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] : ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V))),
% 5.33/5.49 inference(rewrite,[status(thm)],[])).
% 5.33/5.49 tff(24,plain,
% 5.33/5.49 (^[V: $i, Y: $i, U: $i, X: $i] : rewrite((((~sum(X, Y, U)) | (~sum(X, Y, V))) | (U = V)) <=> ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V)))),
% 5.33/5.49 inference(bind,[status(th)],[])).
% 5.33/5.49 tff(25,plain,
% 5.33/5.49 (![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] : ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V))),
% 5.33/5.49 inference(quant_intro,[status(thm)],[24])).
% 5.33/5.49 tff(26,axiom,(![V: $i, Y: $i, U: $i, X: $i] : (((~sum(X, Y, U)) | (~sum(X, Y, V))) | (U = V))), file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax','addition_is_well_defined')).
% 5.33/5.49 tff(27,plain,
% 5.33/5.49 (![V: $i, Y: $i, U: $i, X: $i] : ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V))),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[26, 25])).
% 5.33/5.49 tff(28,plain,
% 5.33/5.49 (![V: $i, Y: $i, U: $i, X: $i] : ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V))),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[27, 23])).
% 5.33/5.49 tff(29,plain,(
% 5.33/5.49 ![V: $i, Y: $i, U: $i, X: $i] : ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V))),
% 5.33/5.49 inference(skolemize,[status(sab)],[28])).
% 5.33/5.49 tff(30,plain,
% 5.33/5.49 (![V: $i, Y: $i, U: $i, X: $i] : ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V))),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[29, 22])).
% 5.33/5.49 tff(31,plain,
% 5.33/5.49 (((~![V: $i, Y: $i, U: $i, X: $i] : ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V))) | ((~sum(a, additive_identity, a)) | (~sum(a, additive_identity, add(a, additive_identity))) | (a = add(a, additive_identity)))) <=> ((~![V: $i, Y: $i, U: $i, X: $i] : ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V))) | (~sum(a, additive_identity, a)) | (~sum(a, additive_identity, add(a, additive_identity))) | (a = add(a, additive_identity)))),
% 5.33/5.49 inference(rewrite,[status(thm)],[])).
% 5.33/5.49 tff(32,plain,
% 5.33/5.49 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V))) | ((~sum(a, additive_identity, a)) | (~sum(a, additive_identity, add(a, additive_identity))) | (a = add(a, additive_identity)))),
% 5.33/5.49 inference(quant_inst,[status(thm)],[])).
% 5.33/5.49 tff(33,plain,
% 5.33/5.49 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V))) | (~sum(a, additive_identity, a)) | (~sum(a, additive_identity, add(a, additive_identity))) | (a = add(a, additive_identity))),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[32, 31])).
% 5.33/5.49 tff(34,plain,
% 5.33/5.49 (a = add(a, additive_identity)),
% 5.33/5.49 inference(unit_resolution,[status(thm)],[33, 30, 20, 11])).
% 5.33/5.49 tff(35,plain,
% 5.33/5.49 (add(a, additive_identity) = a),
% 5.33/5.49 inference(symmetry,[status(thm)],[34])).
% 5.33/5.49 tff(36,plain,
% 5.33/5.49 (product(additive_identity, h(additive_identity, a), add(a, additive_identity)) <=> product(additive_identity, h(additive_identity, a), a)),
% 5.33/5.49 inference(monotonicity,[status(thm)],[35])).
% 5.33/5.49 tff(37,plain,
% 5.33/5.49 (product(additive_identity, h(additive_identity, a), a) <=> product(additive_identity, h(additive_identity, a), add(a, additive_identity))),
% 5.33/5.49 inference(symmetry,[status(thm)],[36])).
% 5.33/5.49 tff(38,plain,
% 5.33/5.49 (^[Y: $i] : refl(product(additive_identity, h(additive_identity, Y), Y) <=> product(additive_identity, h(additive_identity, Y), Y))),
% 5.33/5.49 inference(bind,[status(th)],[])).
% 5.33/5.49 tff(39,plain,
% 5.33/5.49 (![Y: $i] : product(additive_identity, h(additive_identity, Y), Y) <=> ![Y: $i] : product(additive_identity, h(additive_identity, Y), Y)),
% 5.33/5.49 inference(quant_intro,[status(thm)],[38])).
% 5.33/5.49 tff(40,plain,
% 5.33/5.49 (![Y: $i] : product(additive_identity, h(additive_identity, Y), Y) <=> ![Y: $i] : product(additive_identity, h(additive_identity, Y), Y)),
% 5.33/5.49 inference(rewrite,[status(thm)],[])).
% 5.33/5.49 tff(41,plain,
% 5.33/5.49 (![Y: $i, X: $i] : product(additive_identity, h(additive_identity, Y), Y) <=> ![Y: $i] : product(additive_identity, h(additive_identity, Y), Y)),
% 5.33/5.49 inference(elim_unused_vars,[status(thm)],[])).
% 5.33/5.49 tff(42,plain,
% 5.33/5.49 (![Y: $i, X: $i] : ((~(X = additive_identity)) | product(X, h(X, Y), Y)) <=> ![Y: $i, X: $i] : product(additive_identity, h(additive_identity, Y), Y)),
% 5.33/5.49 inference(destructive_equality_resolution,[status(thm)],[])).
% 5.33/5.49 tff(43,plain,
% 5.33/5.49 (![Y: $i, X: $i] : ((~(X = additive_identity)) | product(X, h(X, Y), Y)) <=> ![Y: $i] : product(additive_identity, h(additive_identity, Y), Y)),
% 5.33/5.49 inference(transitivity,[status(thm)],[42, 41])).
% 5.33/5.49 tff(44,axiom,(![Y: $i, X: $i] : ((~(X = additive_identity)) | product(X, h(X, Y), Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','some_property')).
% 5.33/5.49 tff(45,plain,
% 5.33/5.49 (![Y: $i] : product(additive_identity, h(additive_identity, Y), Y)),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[44, 43])).
% 5.33/5.49 tff(46,plain,
% 5.33/5.49 (![Y: $i] : product(additive_identity, h(additive_identity, Y), Y)),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[45, 40])).
% 5.33/5.49 tff(47,plain,(
% 5.33/5.49 ![Y: $i] : product(additive_identity, h(additive_identity, Y), Y)),
% 5.33/5.49 inference(skolemize,[status(sab)],[46])).
% 5.33/5.49 tff(48,plain,
% 5.33/5.49 (![Y: $i] : product(additive_identity, h(additive_identity, Y), Y)),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[47, 39])).
% 5.33/5.49 tff(49,plain,
% 5.33/5.49 ((~![Y: $i] : product(additive_identity, h(additive_identity, Y), Y)) | product(additive_identity, h(additive_identity, a), a)),
% 5.33/5.49 inference(quant_inst,[status(thm)],[])).
% 5.33/5.49 tff(50,plain,
% 5.33/5.49 (product(additive_identity, h(additive_identity, a), a)),
% 5.33/5.49 inference(unit_resolution,[status(thm)],[49, 48])).
% 5.33/5.49 tff(51,plain,
% 5.33/5.49 (product(additive_identity, h(additive_identity, a), add(a, additive_identity))),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[50, 37])).
% 5.33/5.49 tff(52,plain,
% 5.33/5.49 (^[X: $i] : refl(sum(additive_identity, X, X) <=> sum(additive_identity, X, X))),
% 5.33/5.49 inference(bind,[status(th)],[])).
% 5.33/5.49 tff(53,plain,
% 5.33/5.49 (![X: $i] : sum(additive_identity, X, X) <=> ![X: $i] : sum(additive_identity, X, X)),
% 5.33/5.49 inference(quant_intro,[status(thm)],[52])).
% 5.33/5.49 tff(54,plain,
% 5.33/5.49 (![X: $i] : sum(additive_identity, X, X) <=> ![X: $i] : sum(additive_identity, X, X)),
% 5.33/5.49 inference(rewrite,[status(thm)],[])).
% 5.33/5.49 tff(55,axiom,(![X: $i] : sum(additive_identity, X, X)), file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax','additive_identity1')).
% 5.33/5.49 tff(56,plain,
% 5.33/5.49 (![X: $i] : sum(additive_identity, X, X)),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[55, 54])).
% 5.33/5.49 tff(57,plain,(
% 5.33/5.49 ![X: $i] : sum(additive_identity, X, X)),
% 5.33/5.49 inference(skolemize,[status(sab)],[56])).
% 5.33/5.49 tff(58,plain,
% 5.33/5.49 (![X: $i] : sum(additive_identity, X, X)),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[57, 53])).
% 5.33/5.49 tff(59,plain,
% 5.33/5.49 ((~![X: $i] : sum(additive_identity, X, X)) | sum(additive_identity, additive_identity, additive_identity)),
% 5.33/5.49 inference(quant_inst,[status(thm)],[])).
% 5.33/5.49 tff(60,plain,
% 5.33/5.49 (sum(additive_identity, additive_identity, additive_identity)),
% 5.33/5.49 inference(unit_resolution,[status(thm)],[59, 58])).
% 5.33/5.49 tff(61,plain,
% 5.33/5.49 (^[Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : refl((sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1))) <=> (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1))))),
% 5.33/5.49 inference(bind,[status(th)],[])).
% 5.33/5.49 tff(62,plain,
% 5.33/5.49 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1))) <=> ![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))),
% 5.33/5.49 inference(quant_intro,[status(thm)],[61])).
% 5.33/5.49 tff(63,plain,
% 5.33/5.49 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1))) <=> ![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))),
% 5.33/5.49 inference(rewrite,[status(thm)],[])).
% 5.33/5.49 tff(64,plain,
% 5.33/5.49 (^[Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~product(Y, X, V1)) | (~product(Z, X, V2))) | (~sum(Y, Z, V3))) <=> ((~sum(Y, Z, V3)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))), (((((~product(Y, X, V1)) | (~product(Z, X, V2))) | (~sum(Y, Z, V3))) | (~product(V3, X, V4))) <=> (((~sum(Y, Z, V3)) | (~product(Z, X, V2)) | (~product(Y, X, V1))) | (~product(V3, X, V4))))), rewrite((((~sum(Y, Z, V3)) | (~product(Z, X, V2)) | (~product(Y, X, V1))) | (~product(V3, X, V4))) <=> ((~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))), (((((~product(Y, X, V1)) | (~product(Z, X, V2))) | (~sum(Y, Z, V3))) | (~product(V3, X, V4))) <=> ((~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1))))), ((((((~product(Y, X, V1)) | (~product(Z, X, V2))) | (~sum(Y, Z, V3))) | (~product(V3, X, V4))) | sum(V1, V2, V4)) <=> (((~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1))) | sum(V1, V2, V4)))), rewrite((((~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1))) | sum(V1, V2, V4)) <=> (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))), ((((((~product(Y, X, V1)) | (~product(Z, X, V2))) | (~sum(Y, Z, V3))) | (~product(V3, X, V4))) | sum(V1, V2, V4)) <=> (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))))),
% 5.33/5.49 inference(bind,[status(th)],[])).
% 5.33/5.49 tff(65,plain,
% 5.33/5.49 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (((((~product(Y, X, V1)) | (~product(Z, X, V2))) | (~sum(Y, Z, V3))) | (~product(V3, X, V4))) | sum(V1, V2, V4)) <=> ![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))),
% 5.33/5.49 inference(quant_intro,[status(thm)],[64])).
% 5.33/5.49 tff(66,axiom,(![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (((((~product(Y, X, V1)) | (~product(Z, X, V2))) | (~sum(Y, Z, V3))) | (~product(V3, X, V4))) | sum(V1, V2, V4))), file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax','distributivity3')).
% 5.33/5.49 tff(67,plain,
% 5.33/5.49 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[66, 65])).
% 5.33/5.49 tff(68,plain,
% 5.33/5.49 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[67, 63])).
% 5.33/5.49 tff(69,plain,(
% 5.33/5.49 ![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))),
% 5.33/5.49 inference(skolemize,[status(sab)],[68])).
% 5.33/5.49 tff(70,plain,
% 5.33/5.49 (![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[69, 62])).
% 5.33/5.49 tff(71,plain,
% 5.33/5.49 (((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))) | ((~product(additive_identity, h(additive_identity, a), add(a, additive_identity))) | (~sum(additive_identity, additive_identity, additive_identity)) | sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity)))) <=> ((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))) | (~product(additive_identity, h(additive_identity, a), add(a, additive_identity))) | (~sum(additive_identity, additive_identity, additive_identity)) | sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity)))),
% 5.33/5.49 inference(rewrite,[status(thm)],[])).
% 5.33/5.49 tff(72,plain,
% 5.33/5.49 ((sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity)) | (~sum(additive_identity, additive_identity, additive_identity)) | (~product(additive_identity, h(additive_identity, a), add(a, additive_identity))) | (~product(additive_identity, h(additive_identity, a), add(a, additive_identity))) | (~product(additive_identity, h(additive_identity, a), add(a, additive_identity)))) <=> ((~product(additive_identity, h(additive_identity, a), add(a, additive_identity))) | (~sum(additive_identity, additive_identity, additive_identity)) | sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity)))),
% 5.33/5.49 inference(rewrite,[status(thm)],[])).
% 5.33/5.49 tff(73,plain,
% 5.33/5.49 (((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))) | (sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity)) | (~sum(additive_identity, additive_identity, additive_identity)) | (~product(additive_identity, h(additive_identity, a), add(a, additive_identity))) | (~product(additive_identity, h(additive_identity, a), add(a, additive_identity))) | (~product(additive_identity, h(additive_identity, a), add(a, additive_identity))))) <=> ((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))) | ((~product(additive_identity, h(additive_identity, a), add(a, additive_identity))) | (~sum(additive_identity, additive_identity, additive_identity)) | sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity))))),
% 5.33/5.49 inference(monotonicity,[status(thm)],[72])).
% 5.33/5.49 tff(74,plain,
% 5.33/5.49 (((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))) | (sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity)) | (~sum(additive_identity, additive_identity, additive_identity)) | (~product(additive_identity, h(additive_identity, a), add(a, additive_identity))) | (~product(additive_identity, h(additive_identity, a), add(a, additive_identity))) | (~product(additive_identity, h(additive_identity, a), add(a, additive_identity))))) <=> ((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))) | (~product(additive_identity, h(additive_identity, a), add(a, additive_identity))) | (~sum(additive_identity, additive_identity, additive_identity)) | sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity)))),
% 5.33/5.49 inference(transitivity,[status(thm)],[73, 71])).
% 5.33/5.49 tff(75,plain,
% 5.33/5.49 ((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))) | (sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity)) | (~sum(additive_identity, additive_identity, additive_identity)) | (~product(additive_identity, h(additive_identity, a), add(a, additive_identity))) | (~product(additive_identity, h(additive_identity, a), add(a, additive_identity))) | (~product(additive_identity, h(additive_identity, a), add(a, additive_identity))))),
% 5.33/5.49 inference(quant_inst,[status(thm)],[])).
% 5.33/5.49 tff(76,plain,
% 5.33/5.49 ((~![Z: $i, Y: $i, V1: $i, X: $i, V2: $i, V3: $i, V4: $i] : (sum(V1, V2, V4) | (~sum(Y, Z, V3)) | (~product(V3, X, V4)) | (~product(Z, X, V2)) | (~product(Y, X, V1)))) | (~product(additive_identity, h(additive_identity, a), add(a, additive_identity))) | (~sum(additive_identity, additive_identity, additive_identity)) | sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity))),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[75, 74])).
% 5.33/5.49 tff(77,plain,
% 5.33/5.49 ($false),
% 5.33/5.49 inference(unit_resolution,[status(thm)],[76, 70, 60, 51, 2])).
% 5.33/5.49 tff(78,plain,(sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity))), inference(lemma,lemma(discharge,[]))).
% 5.33/5.49 tff(79,plain,
% 5.33/5.49 (sum(additive_inverse(a), add(a, additive_identity), additive_identity) <=> sum(additive_inverse(a), a, additive_identity)),
% 5.33/5.49 inference(monotonicity,[status(thm)],[35])).
% 5.33/5.49 tff(80,plain,
% 5.33/5.49 (sum(additive_inverse(a), a, additive_identity) <=> sum(additive_inverse(a), add(a, additive_identity), additive_identity)),
% 5.33/5.49 inference(symmetry,[status(thm)],[79])).
% 5.33/5.49 tff(81,plain,
% 5.33/5.49 (^[X: $i] : refl(sum(additive_inverse(X), X, additive_identity) <=> sum(additive_inverse(X), X, additive_identity))),
% 5.33/5.49 inference(bind,[status(th)],[])).
% 5.33/5.49 tff(82,plain,
% 5.33/5.49 (![X: $i] : sum(additive_inverse(X), X, additive_identity) <=> ![X: $i] : sum(additive_inverse(X), X, additive_identity)),
% 5.33/5.49 inference(quant_intro,[status(thm)],[81])).
% 5.33/5.49 tff(83,plain,
% 5.33/5.49 (![X: $i] : sum(additive_inverse(X), X, additive_identity) <=> ![X: $i] : sum(additive_inverse(X), X, additive_identity)),
% 5.33/5.49 inference(rewrite,[status(thm)],[])).
% 5.33/5.49 tff(84,axiom,(![X: $i] : sum(additive_inverse(X), X, additive_identity)), file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax','left_inverse')).
% 5.33/5.49 tff(85,plain,
% 5.33/5.49 (![X: $i] : sum(additive_inverse(X), X, additive_identity)),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[84, 83])).
% 5.33/5.49 tff(86,plain,(
% 5.33/5.49 ![X: $i] : sum(additive_inverse(X), X, additive_identity)),
% 5.33/5.49 inference(skolemize,[status(sab)],[85])).
% 5.33/5.49 tff(87,plain,
% 5.33/5.49 (![X: $i] : sum(additive_inverse(X), X, additive_identity)),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[86, 82])).
% 5.33/5.49 tff(88,plain,
% 5.33/5.49 ((~![X: $i] : sum(additive_inverse(X), X, additive_identity)) | sum(additive_inverse(a), a, additive_identity)),
% 5.33/5.49 inference(quant_inst,[status(thm)],[])).
% 5.33/5.49 tff(89,plain,
% 5.33/5.49 (sum(additive_inverse(a), a, additive_identity)),
% 5.33/5.49 inference(unit_resolution,[status(thm)],[88, 87])).
% 5.33/5.49 tff(90,plain,
% 5.33/5.49 (sum(additive_inverse(a), add(a, additive_identity), additive_identity)),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[89, 80])).
% 5.33/5.49 tff(91,plain,
% 5.33/5.49 (sum(additive_identity, add(a, additive_identity), add(a, additive_identity)) <=> sum(additive_identity, a, a)),
% 5.33/5.49 inference(monotonicity,[status(thm)],[35, 35])).
% 5.33/5.49 tff(92,plain,
% 5.33/5.49 (sum(additive_identity, a, a) <=> sum(additive_identity, add(a, additive_identity), add(a, additive_identity))),
% 5.33/5.49 inference(symmetry,[status(thm)],[91])).
% 5.33/5.49 tff(93,plain,
% 5.33/5.49 ((~![X: $i] : sum(additive_identity, X, X)) | sum(additive_identity, a, a)),
% 5.33/5.49 inference(quant_inst,[status(thm)],[])).
% 5.33/5.49 tff(94,plain,
% 5.33/5.49 (sum(additive_identity, a, a)),
% 5.33/5.49 inference(unit_resolution,[status(thm)],[93, 58])).
% 5.33/5.49 tff(95,plain,
% 5.33/5.49 (sum(additive_identity, add(a, additive_identity), add(a, additive_identity))),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[94, 92])).
% 5.33/5.49 tff(96,plain,
% 5.33/5.49 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U))) <=> (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U))))),
% 5.33/5.49 inference(bind,[status(th)],[])).
% 5.33/5.49 tff(97,plain,
% 5.33/5.49 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))),
% 5.33/5.49 inference(quant_intro,[status(thm)],[96])).
% 5.33/5.49 tff(98,plain,
% 5.33/5.49 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))),
% 5.33/5.49 inference(rewrite,[status(thm)],[])).
% 5.33/5.49 tff(99,plain,
% 5.33/5.49 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~sum(X, Y, U)) | (~sum(Y, Z, V))) | (~sum(U, Z, W))) <=> ((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))), (((((~sum(X, Y, U)) | (~sum(Y, Z, V))) | (~sum(U, Z, W))) | sum(X, V, W)) <=> (((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U))) | sum(X, V, W)))), rewrite((((~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U))) | sum(X, V, W)) <=> (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))), (((((~sum(X, Y, U)) | (~sum(Y, Z, V))) | (~sum(U, Z, W))) | sum(X, V, W)) <=> (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))))),
% 5.33/5.49 inference(bind,[status(th)],[])).
% 5.33/5.49 tff(100,plain,
% 5.33/5.49 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~sum(X, Y, U)) | (~sum(Y, Z, V))) | (~sum(U, Z, W))) | sum(X, V, W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))),
% 5.33/5.49 inference(quant_intro,[status(thm)],[99])).
% 5.33/5.49 tff(101,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~sum(X, Y, U)) | (~sum(Y, Z, V))) | (~sum(U, Z, W))) | sum(X, V, W))), file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax','associativity_of_addition1')).
% 5.33/5.49 tff(102,plain,
% 5.33/5.49 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[101, 100])).
% 5.33/5.49 tff(103,plain,
% 5.33/5.49 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[102, 98])).
% 5.33/5.49 tff(104,plain,(
% 5.33/5.49 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))),
% 5.33/5.49 inference(skolemize,[status(sab)],[103])).
% 5.33/5.49 tff(105,plain,
% 5.33/5.49 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))),
% 5.33/5.49 inference(modus_ponens,[status(thm)],[104, 97])).
% 5.33/5.49 tff(106,plain,
% 5.33/5.49 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))) | ((~sum(additive_inverse(a), add(a, additive_identity), additive_identity)) | (~sum(additive_identity, add(a, additive_identity), add(a, additive_identity))) | sum(additive_inverse(a), add(a, additive_identity), add(a, additive_identity)) | (~sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))) | (~sum(additive_inverse(a), add(a, additive_identity), additive_identity)) | (~sum(additive_identity, add(a, additive_identity), add(a, additive_identity))) | sum(additive_inverse(a), add(a, additive_identity), add(a, additive_identity)) | (~sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity))))),
% 5.33/5.49 inference(rewrite,[status(thm)],[])).
% 5.33/5.49 tff(107,plain,
% 5.33/5.49 ((sum(additive_inverse(a), add(a, additive_identity), add(a, additive_identity)) | (~sum(additive_identity, add(a, additive_identity), add(a, additive_identity))) | (~sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity))) | (~sum(additive_inverse(a), add(a, additive_identity), additive_identity))) <=> ((~sum(additive_inverse(a), add(a, additive_identity), additive_identity)) | (~sum(additive_identity, add(a, additive_identity), add(a, additive_identity))) | sum(additive_inverse(a), add(a, additive_identity), add(a, additive_identity)) | (~sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity))))),
% 5.33/5.49 inference(rewrite,[status(thm)],[])).
% 5.33/5.49 tff(108,plain,
% 5.33/5.49 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))) | (sum(additive_inverse(a), add(a, additive_identity), add(a, additive_identity)) | (~sum(additive_identity, add(a, additive_identity), add(a, additive_identity))) | (~sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity))) | (~sum(additive_inverse(a), add(a, additive_identity), additive_identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))) | ((~sum(additive_inverse(a), add(a, additive_identity), additive_identity)) | (~sum(additive_identity, add(a, additive_identity), add(a, additive_identity))) | sum(additive_inverse(a), add(a, additive_identity), add(a, additive_identity)) | (~sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity)))))),
% 5.33/5.49 inference(monotonicity,[status(thm)],[107])).
% 5.33/5.49 tff(109,plain,
% 5.33/5.49 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))) | (sum(additive_inverse(a), add(a, additive_identity), add(a, additive_identity)) | (~sum(additive_identity, add(a, additive_identity), add(a, additive_identity))) | (~sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity))) | (~sum(additive_inverse(a), add(a, additive_identity), additive_identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))) | (~sum(additive_inverse(a), add(a, additive_identity), additive_identity)) | (~sum(additive_identity, add(a, additive_identity), add(a, additive_identity))) | sum(additive_inverse(a), add(a, additive_identity), add(a, additive_identity)) | (~sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity))))),
% 5.33/5.50 inference(transitivity,[status(thm)],[108, 106])).
% 5.33/5.50 tff(110,plain,
% 5.33/5.50 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))) | (sum(additive_inverse(a), add(a, additive_identity), add(a, additive_identity)) | (~sum(additive_identity, add(a, additive_identity), add(a, additive_identity))) | (~sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity))) | (~sum(additive_inverse(a), add(a, additive_identity), additive_identity)))),
% 5.33/5.50 inference(quant_inst,[status(thm)],[])).
% 5.33/5.50 tff(111,plain,
% 5.33/5.50 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (sum(X, V, W) | (~sum(U, Z, W)) | (~sum(Y, Z, V)) | (~sum(X, Y, U)))) | (~sum(additive_inverse(a), add(a, additive_identity), additive_identity)) | (~sum(additive_identity, add(a, additive_identity), add(a, additive_identity))) | sum(additive_inverse(a), add(a, additive_identity), add(a, additive_identity)) | (~sum(add(a, additive_identity), add(a, additive_identity), add(a, additive_identity)))),
% 5.33/5.50 inference(modus_ponens,[status(thm)],[110, 109])).
% 5.33/5.50 tff(112,plain,
% 5.33/5.50 ($false),
% 5.33/5.50 inference(unit_resolution,[status(thm)],[111, 105, 95, 90, 78, 1])).
% 5.33/5.50 tff(113,plain,(sum(additive_inverse(a), add(a, additive_identity), add(a, additive_identity))), inference(lemma,lemma(discharge,[]))).
% 5.33/5.50 tff(114,plain,
% 5.33/5.50 (((~![V: $i, Y: $i, U: $i, X: $i] : ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V))) | ((~sum(additive_inverse(a), add(a, additive_identity), additive_identity)) | (~sum(additive_inverse(a), add(a, additive_identity), add(a, additive_identity))) | (additive_identity = add(a, additive_identity)))) <=> ((~![V: $i, Y: $i, U: $i, X: $i] : ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V))) | (~sum(additive_inverse(a), add(a, additive_identity), additive_identity)) | (~sum(additive_inverse(a), add(a, additive_identity), add(a, additive_identity))) | (additive_identity = add(a, additive_identity)))),
% 5.33/5.50 inference(rewrite,[status(thm)],[])).
% 5.33/5.50 tff(115,plain,
% 5.33/5.50 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V))) | ((~sum(additive_inverse(a), add(a, additive_identity), additive_identity)) | (~sum(additive_inverse(a), add(a, additive_identity), add(a, additive_identity))) | (additive_identity = add(a, additive_identity)))),
% 5.33/5.50 inference(quant_inst,[status(thm)],[])).
% 5.33/5.50 tff(116,plain,
% 5.33/5.50 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~sum(X, Y, U)) | (~sum(X, Y, V)) | (U = V))) | (~sum(additive_inverse(a), add(a, additive_identity), additive_identity)) | (~sum(additive_inverse(a), add(a, additive_identity), add(a, additive_identity))) | (additive_identity = add(a, additive_identity))),
% 5.33/5.50 inference(modus_ponens,[status(thm)],[115, 114])).
% 5.33/5.50 tff(117,plain,
% 5.33/5.50 (additive_identity = add(a, additive_identity)),
% 5.33/5.50 inference(unit_resolution,[status(thm)],[116, 30, 90, 113])).
% 5.33/5.50 tff(118,plain,
% 5.33/5.50 (add(a, additive_identity) = additive_identity),
% 5.33/5.50 inference(symmetry,[status(thm)],[117])).
% 5.33/5.50 tff(119,plain,
% 5.33/5.50 (a = additive_identity),
% 5.33/5.50 inference(transitivity,[status(thm)],[34, 118])).
% 5.33/5.50 tff(120,plain,
% 5.33/5.50 ((~(a = additive_identity)) <=> (~(a = additive_identity))),
% 5.33/5.50 inference(rewrite,[status(thm)],[])).
% 5.33/5.50 tff(121,axiom,(~(a = additive_identity)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_not_additive_identity')).
% 5.33/5.50 tff(122,plain,
% 5.33/5.50 (~(a = additive_identity)),
% 5.33/5.50 inference(modus_ponens,[status(thm)],[121, 120])).
% 5.33/5.50 tff(123,plain,
% 5.33/5.50 ($false),
% 5.33/5.50 inference(unit_resolution,[status(thm)],[122, 119])).
% 5.33/5.50 % SZS output end Proof
% 5.33/5.51 % E exiting
%------------------------------------------------------------------------------