%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP001-5 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:06:47 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP001-5 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 15:28:02 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(product_type, type, (
% 0.19/0.39 product: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(c_type, type, (
% 0.19/0.39 c: $i)).
% 0.19/0.39 tff(identity_type, type, (
% 0.19/0.39 identity: $i)).
% 0.19/0.39 tff(b_type, type, (
% 0.19/0.39 b: $i)).
% 0.19/0.39 tff(a_type, type, (
% 0.19/0.39 a: $i)).
% 0.19/0.39 tff(1,assumption,(~product(c, c, identity)), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (^[X: $i] : refl(product(X, X, identity) <=> product(X, X, identity))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![X: $i] : product(X, X, identity) <=> ![X: $i] : product(X, X, identity)),
% 0.19/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![X: $i] : product(X, X, identity) <=> ![X: $i] : product(X, X, identity)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(5,axiom,(![X: $i] : product(X, X, identity)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','square_element')).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (![X: $i] : product(X, X, identity)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.39 tff(7,plain,(
% 0.19/0.39 ![X: $i] : product(X, X, identity)),
% 0.19/0.39 inference(skolemize,[status(sab)],[6])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (![X: $i] : product(X, X, identity)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 ((~![X: $i] : product(X, X, identity)) | product(c, c, identity)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.40 tff(11,plain,(product(c, c, identity)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(12,assumption,(~product(identity, b, b)), introduced(assumption)).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 ((~![X: $i] : product(X, X, identity)) | product(b, b, identity)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (product(b, b, identity)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[13, 8])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (^[X: $i] : refl(product(X, identity, X) <=> product(X, identity, X))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (![X: $i] : product(X, identity, X) <=> ![X: $i] : product(X, identity, X)),
% 0.19/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![X: $i] : product(X, identity, X) <=> ![X: $i] : product(X, identity, X)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(18,axiom,(![X: $i] : product(X, identity, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','right_identity')).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![X: $i] : product(X, identity, X)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.40 tff(20,plain,(
% 0.19/0.40 ![X: $i] : product(X, identity, X)),
% 0.19/0.40 inference(skolemize,[status(sab)],[19])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (![X: $i] : product(X, identity, X)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 ((~![X: $i] : product(X, identity, X)) | product(b, identity, b)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (product(b, identity, b)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.40 tff(29,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/sandbox/benchmark/theBenchmark.p','associativity2')).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.19/0.40 tff(32,plain,(
% 0.19/0.40 ![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)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[31])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (((~![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(b, b, identity)) | (~product(b, identity, b)) | product(identity, b, b))) <=> ((~![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(b, b, identity)) | (~product(b, identity, b)) | product(identity, b, b))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 ((product(identity, b, b) | (~product(b, b, identity)) | (~product(b, b, identity)) | (~product(b, identity, b))) <=> ((~product(b, b, identity)) | (~product(b, identity, b)) | product(identity, b, b))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (((~![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, b) | (~product(b, b, identity)) | (~product(b, b, identity)) | (~product(b, identity, b)))) <=> ((~![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(b, b, identity)) | (~product(b, identity, b)) | product(identity, b, b)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (((~![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, b) | (~product(b, b, identity)) | (~product(b, b, identity)) | (~product(b, identity, b)))) <=> ((~![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(b, b, identity)) | (~product(b, identity, b)) | product(identity, b, b))),
% 0.19/0.40 inference(transitivity,[status(thm)],[36, 34])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 ((~![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, b) | (~product(b, b, identity)) | (~product(b, b, identity)) | (~product(b, identity, b)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(b, b, identity)) | (~product(b, identity, b)) | product(identity, b, b)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[39, 33, 23, 14, 12])).
% 0.19/0.40 tff(41,plain,(product(identity, b, b)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(42,assumption,(~product(c, a, b)), introduced(assumption)).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 ((~![X: $i] : product(X, identity, X)) | product(a, identity, a)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (product(a, identity, a)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[43, 21])).
% 0.19/0.40 tff(45,assumption,(~product(c, b, a)), introduced(assumption)).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (product(a, b, c) <=> product(a, b, c)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(47,axiom,(product(a, b, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a_times_b_is_c')).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (product(a, b, c)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (((~![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, c)) | product(c, b, a) | (~product(a, identity, a)) | (~product(b, b, 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, c)) | product(c, b, a) | (~product(a, identity, a)) | (~product(b, b, identity)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 ((product(c, b, a) | (~product(b, b, identity)) | (~product(a, b, c)) | (~product(a, identity, a))) <=> ((~product(a, b, c)) | product(c, b, a) | (~product(a, identity, a)) | (~product(b, b, identity)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (((~![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(c, b, a) | (~product(b, b, identity)) | (~product(a, b, c)) | (~product(a, identity, a)))) <=> ((~![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, c)) | product(c, b, a) | (~product(a, identity, a)) | (~product(b, b, identity))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[50])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (((~![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(c, b, a) | (~product(b, b, identity)) | (~product(a, b, c)) | (~product(a, identity, a)))) <=> ((~![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, c)) | product(c, b, a) | (~product(a, identity, a)) | (~product(b, b, identity)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[51, 49])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 ((~![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(c, b, a) | (~product(b, b, identity)) | (~product(a, b, c)) | (~product(a, identity, a)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(a, b, c)) | product(c, b, a) | (~product(a, identity, a)) | (~product(b, b, identity))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[54, 33, 48, 45, 44, 14])).
% 0.19/0.40 tff(56,plain,(product(c, b, a)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((product(X, V, W) | (~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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.41 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) <=> ((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W)) <=> (((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) | product(X, V, W)))), rewrite((((~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) | product(X, V, W)) <=> (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W)) <=> (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W)) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.41 tff(62,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(U, Z, W))) | product(X, V, W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','associativity1')).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.19/0.41 tff(65,plain,(
% 0.19/0.41 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[64])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | ((~product(c, b, a)) | (~product(identity, b, b)) | (~product(c, c, identity)) | product(c, a, b))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (~product(c, b, a)) | (~product(identity, b, b)) | (~product(c, c, identity)) | product(c, a, b))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 ((product(c, a, b) | (~product(identity, b, b)) | (~product(c, b, a)) | (~product(c, c, identity))) <=> ((~product(c, b, a)) | (~product(identity, b, b)) | (~product(c, c, identity)) | product(c, a, b))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(c, a, b) | (~product(identity, b, b)) | (~product(c, b, a)) | (~product(c, c, identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | ((~product(c, b, a)) | (~product(identity, b, b)) | (~product(c, c, identity)) | product(c, a, b)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[68])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(c, a, b) | (~product(identity, b, b)) | (~product(c, b, a)) | (~product(c, c, identity)))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (~product(c, b, a)) | (~product(identity, b, b)) | (~product(c, c, identity)) | product(c, a, b))),
% 0.19/0.41 inference(transitivity,[status(thm)],[69, 67])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(c, a, b) | (~product(identity, b, b)) | (~product(c, b, a)) | (~product(c, c, identity)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(X, V, W) | (~product(U, Z, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (~product(c, b, a)) | (~product(identity, b, b)) | (~product(c, c, identity)) | product(c, a, b)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[72, 66, 56, 42, 41, 11])).
% 0.19/0.41 tff(74,plain,(product(c, a, b)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 ((~![X: $i] : product(X, X, identity)) | product(a, a, identity)),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (product(a, a, identity)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[75, 8])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 ((~product(b, a, c)) <=> (~product(b, a, c))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(78,axiom,(~product(b, a, c)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_b_times_a_is_c')).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (~product(b, a, c)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (((~![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(b, a, c) | (~product(c, identity, c)) | (~product(a, a, identity)) | (~product(c, a, b)))) <=> ((~![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(b, a, c) | (~product(c, identity, c)) | (~product(a, a, identity)) | (~product(c, a, b)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 ((product(b, a, c) | (~product(a, a, identity)) | (~product(c, a, b)) | (~product(c, identity, c))) <=> (product(b, a, c) | (~product(c, identity, c)) | (~product(a, a, identity)) | (~product(c, a, b)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (((~![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(b, a, c) | (~product(a, a, identity)) | (~product(c, a, b)) | (~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(b, a, c) | (~product(c, identity, c)) | (~product(a, a, identity)) | (~product(c, a, b))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (((~![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(b, a, c) | (~product(a, a, identity)) | (~product(c, a, b)) | (~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(b, a, c) | (~product(c, identity, c)) | (~product(a, a, identity)) | (~product(c, a, b)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[82, 80])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 ((~![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(b, a, c) | (~product(a, a, identity)) | (~product(c, a, b)) | (~product(c, identity, c)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 ((~![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(b, a, c) | (~product(c, identity, c)) | (~product(a, a, identity)) | (~product(c, a, b))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (~product(c, identity, c)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[85, 33, 79, 76, 74])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (((~![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, c)) | (~product(b, identity, b)) | 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, c)) | (~product(b, identity, b)) | product(c, identity, c))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 ((product(c, identity, c) | (~product(b, identity, b)) | (~product(a, b, c)) | (~product(a, b, c))) <=> ((~product(a, b, c)) | (~product(b, identity, b)) | product(c, identity, c))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (((~![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(c, identity, c) | (~product(b, identity, b)) | (~product(a, b, c)) | (~product(a, b, 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, c)) | (~product(b, identity, b)) | product(c, identity, c)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[88])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 (((~![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(c, identity, c) | (~product(b, identity, b)) | (~product(a, b, c)) | (~product(a, b, 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, c)) | (~product(b, identity, b)) | product(c, identity, c))),
% 0.19/0.41 inference(transitivity,[status(thm)],[89, 87])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 ((~![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(c, identity, c) | (~product(b, identity, b)) | (~product(a, b, c)) | (~product(a, b, c)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(a, b, c)) | (~product(b, identity, b)) | product(c, identity, c)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[92, 33, 48, 23, 86])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------