%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP017-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:06:51 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP017-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.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 : Thu Jun 19 15:27:11 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(product_type, type, (
% 0.20/0.45 product: ( $i * $i * $i ) > $o)).
% 0.20/0.45 tff(b_type, type, (
% 0.20/0.45 b: $i)).
% 0.20/0.45 tff(identity_type, type, (
% 0.20/0.45 identity: $i)).
% 0.20/0.45 tff(c_type, type, (
% 0.20/0.45 c: $i)).
% 0.20/0.45 tff(a_type, type, (
% 0.20/0.45 a: $i)).
% 0.20/0.45 tff(1,plain,
% 0.20/0.45 (^[X: $i] : refl(product(identity, X, X) <=> product(identity, X, X))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(2,plain,
% 0.20/0.45 (![X: $i] : product(identity, X, X) <=> ![X: $i] : product(identity, X, X)),
% 0.20/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.45 tff(3,plain,
% 0.20/0.45 (![X: $i] : product(identity, X, X) <=> ![X: $i] : product(identity, X, X)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(4,axiom,(![X: $i] : product(identity, X, X)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax','left_identity')).
% 0.20/0.45 tff(5,plain,
% 0.20/0.45 (![X: $i] : product(identity, X, X)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.45 tff(6,plain,(
% 0.20/0.45 ![X: $i] : product(identity, X, X)),
% 0.20/0.45 inference(skolemize,[status(sab)],[5])).
% 0.20/0.45 tff(7,plain,
% 0.20/0.45 (![X: $i] : product(identity, X, X)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.45 tff(8,plain,
% 0.20/0.45 ((~![X: $i] : product(identity, X, X)) | product(identity, b, b)),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 (product(identity, b, b)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.45 tff(10,assumption,(~product(c, identity, c)), introduced(assumption)).
% 0.20/0.45 tff(11,plain,
% 0.20/0.45 (^[X: $i] : refl(product(X, identity, X) <=> product(X, identity, X))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(12,plain,
% 0.20/0.45 (![X: $i] : product(X, identity, X) <=> ![X: $i] : product(X, identity, X)),
% 0.20/0.45 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.45 tff(13,plain,
% 0.20/0.45 (![X: $i] : product(X, identity, X) <=> ![X: $i] : product(X, identity, X)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(14,axiom,(![X: $i] : product(X, identity, X)), file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax','right_identity')).
% 0.20/0.45 tff(15,plain,
% 0.20/0.45 (![X: $i] : product(X, identity, X)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.45 tff(16,plain,(
% 0.20/0.45 ![X: $i] : product(X, identity, X)),
% 0.20/0.45 inference(skolemize,[status(sab)],[15])).
% 0.20/0.45 tff(17,plain,
% 0.20/0.45 (![X: $i] : product(X, identity, X)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 ((~![X: $i] : product(X, identity, X)) | product(c, identity, c)),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[18, 17, 10])).
% 0.20/0.45 tff(20,plain,(product(c, identity, c)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(21,assumption,(~product(identity, b, c)), introduced(assumption)).
% 0.20/0.45 tff(22,plain,
% 0.20/0.45 (product(c, a, identity) <=> product(c, a, identity)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(23,axiom,(product(c, a, identity)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_times_a_is_identity')).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 (product(c, a, identity)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 (product(a, b, identity) <=> product(a, b, identity)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(26,axiom,(product(a, b, identity)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_times_b_is_identity')).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 (product(a, b, identity)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) <=> (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(29,plain,
% 0.20/0.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) <=> ((~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W)) <=> (((~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) | product(U, Z, W)))), rewrite((((~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W))) | product(U, Z, W)) <=> (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W)) <=> (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.45 tff(33,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax','associativity2')).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.45 tff(36,plain,(
% 0.20/0.45 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[35])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | ((~product(a, b, identity)) | product(identity, b, c) | (~product(c, identity, c)) | (~product(c, a, identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(a, b, identity)) | product(identity, b, c) | (~product(c, identity, c)) | (~product(c, a, identity)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 ((product(identity, b, c) | (~product(a, b, identity)) | (~product(c, a, identity)) | (~product(c, identity, c))) <=> ((~product(a, b, identity)) | product(identity, b, c) | (~product(c, identity, c)) | (~product(c, a, identity)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(identity, b, c) | (~product(a, b, identity)) | (~product(c, a, identity)) | (~product(c, identity, c)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | ((~product(a, b, identity)) | product(identity, b, c) | (~product(c, identity, c)) | (~product(c, a, identity))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[39])).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(identity, b, c) | (~product(a, b, identity)) | (~product(c, a, identity)) | (~product(c, identity, c)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(a, b, identity)) | product(identity, b, c) | (~product(c, identity, c)) | (~product(c, a, identity)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[40, 38])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(identity, b, c) | (~product(a, b, identity)) | (~product(c, a, identity)) | (~product(c, identity, c)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(a, b, identity)) | product(identity, b, c) | (~product(c, identity, c)) | (~product(c, a, identity))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[43, 37, 27, 24, 21, 20])).
% 0.20/0.45 tff(45,plain,(product(identity, b, c)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 ((~(b = c)) <=> (~(b = c))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(47,axiom,(~(b = c)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_b_equals_c')).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 (~(b = c)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 (^[W: $i, Z: $i, Y: $i, X: $i] : rewrite((((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W)) <=> ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.45 tff(54,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax','total_function2')).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.45 tff(56,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.45 tff(57,plain,(
% 0.20/0.45 ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[56])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((b = c) | (~product(identity, b, c)) | (~product(identity, b, b)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (b = c) | (~product(identity, b, c)) | (~product(identity, b, b)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((b = c) | (~product(identity, b, c)) | (~product(identity, b, b)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (b = c) | (~product(identity, b, c)) | (~product(identity, b, b))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[61, 58, 48, 45, 9])).
% 0.20/0.45 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------