%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP028-2 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:06:53 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.50s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP028-2 : TPTP v9.0.0. Released v1.1.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.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 15:27:51 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.50 % SZS status Unsatisfiable
% 0.19/0.50 % SZS output start Proof
% 0.19/0.50 tff(product_type, type, (
% 0.19/0.50 product: ( $i * $i * $i ) > $o)).
% 0.19/0.50 tff(not_identity_type, type, (
% 0.19/0.50 not_identity: $i > $i)).
% 0.19/0.50 tff(right_solution_type, type, (
% 0.19/0.50 right_solution: ( $i * $i ) > $i)).
% 0.19/0.50 tff(elem_0_type, type, (
% 0.19/0.50 elem_0: $i)).
% 0.19/0.50 tff(left_solution_type, type, (
% 0.19/0.50 left_solution: ( $i * $i ) > $i)).
% 0.19/0.50 tff(multiply_type, type, (
% 0.19/0.50 multiply: ( $i * $i ) > $i)).
% 0.19/0.50 tff(1,assumption,(~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), introduced(assumption)).
% 0.19/0.50 tff(2,plain,
% 0.19/0.50 (^[Y: $i, X: $i] : refl(product(left_solution(X, Y), X, Y) <=> product(left_solution(X, Y), X, Y))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(3,plain,
% 0.19/0.50 (![Y: $i, X: $i] : product(left_solution(X, Y), X, Y) <=> ![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 0.19/0.50 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.50 tff(4,plain,
% 0.19/0.50 (![Y: $i, X: $i] : product(left_solution(X, Y), X, Y) <=> ![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(5,axiom,(![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','left_soln')).
% 0.19/0.50 tff(6,plain,
% 0.19/0.50 (![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.50 tff(7,plain,(
% 0.19/0.50 ![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 0.19/0.50 inference(skolemize,[status(sab)],[6])).
% 0.19/0.50 tff(8,plain,
% 0.19/0.50 (![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.50 tff(9,plain,
% 0.19/0.50 ((~![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)) | product(left_solution(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)), multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(10,plain,
% 0.19/0.50 (product(left_solution(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)), multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.19/0.50 tff(11,plain,
% 0.19/0.50 (^[Y: $i, X: $i] : refl(product(X, Y, multiply(X, Y)) <=> product(X, Y, multiply(X, Y)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(12,plain,
% 0.19/0.50 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y)) <=> ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.50 tff(13,plain,
% 0.19/0.50 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y)) <=> ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(14,axiom,(![Y: $i, X: $i] : product(X, Y, multiply(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP002-0.ax','total_function1')).
% 0.19/0.50 tff(15,plain,
% 0.19/0.50 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.50 tff(16,plain,(
% 0.19/0.50 ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 0.19/0.50 inference(skolemize,[status(sab)],[15])).
% 0.19/0.50 tff(17,plain,
% 0.19/0.50 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.50 tff(18,plain,
% 0.19/0.50 ((~![Y: $i, X: $i] : product(X, Y, multiply(X, Y))) | product(elem!0, right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(19,plain,
% 0.19/0.50 (product(elem!0, right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.50 tff(20,plain,
% 0.19/0.50 (^[Y: $i, X: $i] : refl(product(X, right_solution(X, Y), Y) <=> product(X, right_solution(X, Y), Y))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(21,plain,
% 0.19/0.50 (![Y: $i, X: $i] : product(X, right_solution(X, Y), Y) <=> ![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 0.19/0.50 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.50 tff(22,plain,
% 0.19/0.50 (![Y: $i, X: $i] : product(X, right_solution(X, Y), Y) <=> ![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(23,axiom,(![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','right_soln')).
% 0.19/0.50 tff(24,plain,
% 0.19/0.50 (![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.50 tff(25,plain,(
% 0.19/0.50 ![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 0.19/0.50 inference(skolemize,[status(sab)],[24])).
% 0.19/0.50 tff(26,plain,
% 0.19/0.50 (![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.50 tff(27,plain,
% 0.19/0.50 ((~![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)) | product(elem!0, right_solution(elem!0, elem!0), elem!0)),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(28,plain,
% 0.19/0.50 (product(elem!0, right_solution(elem!0, elem!0), elem!0)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.19/0.50 tff(29,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(30,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.50 tff(31,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(32,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(33,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.50 tff(34,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/GRP002-0.ax','total_function2')).
% 0.19/0.50 tff(35,plain,
% 0.19/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.50 tff(36,plain,
% 0.19/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.50 tff(37,plain,(
% 0.19/0.50 ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[36])).
% 0.19/0.50 tff(38,plain,
% 0.19/0.50 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.50 tff(39,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | (elem!0 = multiply(elem!0, right_solution(elem!0, elem!0))) | (~product(elem!0, right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | (elem!0 = multiply(elem!0, right_solution(elem!0, elem!0))) | (~product(elem!0, right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(40,plain,
% 0.19/0.50 (((elem!0 = multiply(elem!0, right_solution(elem!0, elem!0))) | (~product(elem!0, right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0))) <=> ((~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | (elem!0 = multiply(elem!0, right_solution(elem!0, elem!0))) | (~product(elem!0, right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(41,plain,
% 0.19/0.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((elem!0 = multiply(elem!0, right_solution(elem!0, elem!0))) | (~product(elem!0, right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | (elem!0 = multiply(elem!0, right_solution(elem!0, elem!0))) | (~product(elem!0, right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.51 tff(42,plain,
% 0.19/0.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((elem!0 = multiply(elem!0, right_solution(elem!0, elem!0))) | (~product(elem!0, right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | (elem!0 = multiply(elem!0, right_solution(elem!0, elem!0))) | (~product(elem!0, right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[41, 39])).
% 0.19/0.51 tff(43,plain,
% 0.19/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((elem!0 = multiply(elem!0, right_solution(elem!0, elem!0))) | (~product(elem!0, right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(44,plain,
% 0.19/0.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | (elem!0 = multiply(elem!0, right_solution(elem!0, elem!0))) | (~product(elem!0, right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.51 tff(45,plain,
% 0.19/0.51 (elem!0 = multiply(elem!0, right_solution(elem!0, elem!0))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[44, 38, 28, 19])).
% 0.19/0.51 tff(46,plain,
% 0.19/0.51 (multiply(elem!0, right_solution(elem!0, elem!0)) = elem!0),
% 0.19/0.51 inference(symmetry,[status(thm)],[45])).
% 0.19/0.51 tff(47,plain,
% 0.19/0.51 (product(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0))) <=> product(elem!0, right_solution(elem!0, elem!0), elem!0)),
% 0.19/0.51 inference(monotonicity,[status(thm)],[46, 46])).
% 0.19/0.51 tff(48,plain,
% 0.19/0.51 (product(elem!0, right_solution(elem!0, elem!0), elem!0) <=> product(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))),
% 0.19/0.51 inference(symmetry,[status(thm)],[47])).
% 0.19/0.51 tff(49,plain,
% 0.19/0.51 (product(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[28, 48])).
% 0.19/0.51 tff(50,plain,
% 0.19/0.51 (^[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))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(51,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.51 tff(52,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(53,plain,
% 0.19/0.51 (^[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)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(54,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.51 tff(55,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/GRP002-0.ax','associativity2')).
% 0.19/0.51 tff(56,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.51 tff(57,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.51 tff(58,plain,(
% 0.19/0.51 ![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)))),
% 0.19/0.51 inference(skolemize,[status(sab)],[57])).
% 0.19/0.51 tff(59,plain,
% 0.19/0.51 (![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)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.19/0.51 tff(60,plain,
% 0.19/0.51 (((~![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(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)), multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0))) | product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) <=> ((~![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(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)), multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0))) | product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(61,plain,
% 0.19/0.51 ((product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)) | (~product(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)), multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0))) | (~product(left_solution(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)), multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)))) <=> ((~product(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)), multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0))) | product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 0.35/0.52 inference(rewrite,[status(thm)],[])).
% 0.35/0.52 tff(62,plain,
% 0.35/0.52 (((~![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(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)) | (~product(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)), multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0))) | (~product(left_solution(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)), multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0))))) <=> ((~![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(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)), multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0))) | product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))),
% 0.35/0.52 inference(monotonicity,[status(thm)],[61])).
% 0.35/0.52 tff(63,plain,
% 0.35/0.52 (((~![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(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)) | (~product(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)), multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0))) | (~product(left_solution(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)), multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0))))) <=> ((~![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(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)), multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0))) | product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 0.35/0.52 inference(transitivity,[status(thm)],[62, 60])).
% 0.35/0.52 tff(64,plain,
% 0.35/0.52 ((~![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(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)) | (~product(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)), multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0))) | (~product(left_solution(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)), multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0))))),
% 0.35/0.52 inference(quant_inst,[status(thm)],[])).
% 0.35/0.52 tff(65,plain,
% 0.35/0.52 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(elem!0, right_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0)), multiply(elem!0, right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0))) | product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))),
% 0.35/0.52 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.35/0.52 tff(66,plain,
% 0.35/0.52 ($false),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[65, 59, 49, 10, 1])).
% 0.35/0.52 tff(67,plain,(product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.35/0.52 tff(68,plain,
% 0.35/0.52 ((~![Y: $i, X: $i] : product(X, Y, multiply(X, Y))) | product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 0.35/0.52 inference(quant_inst,[status(thm)],[])).
% 0.35/0.52 tff(69,plain,
% 0.35/0.52 (product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 0.35/0.52 inference(unit_resolution,[status(thm)],[68, 17])).
% 0.35/0.52 tff(70,plain,
% 0.35/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)) = right_solution(elem!0, elem!0)))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)) = right_solution(elem!0, elem!0)))),
% 0.35/0.52 inference(rewrite,[status(thm)],[])).
% 0.35/0.52 tff(71,plain,
% 0.35/0.52 (((multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)) = right_solution(elem!0, elem!0)) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))) <=> ((~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)) = right_solution(elem!0, elem!0)))),
% 0.35/0.52 inference(rewrite,[status(thm)],[])).
% 0.35/0.52 tff(72,plain,
% 0.35/0.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)) = right_solution(elem!0, elem!0)) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)) = right_solution(elem!0, elem!0))))),
% 0.35/0.53 inference(monotonicity,[status(thm)],[71])).
% 0.35/0.53 tff(73,plain,
% 0.35/0.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)) = right_solution(elem!0, elem!0)) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)) = right_solution(elem!0, elem!0)))),
% 0.35/0.53 inference(transitivity,[status(thm)],[72, 70])).
% 0.35/0.53 tff(74,plain,
% 0.35/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)) = right_solution(elem!0, elem!0)) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(75,plain,
% 0.35/0.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)) = right_solution(elem!0, elem!0))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.35/0.53 tff(76,plain,
% 0.35/0.53 (multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)) = right_solution(elem!0, elem!0)),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[75, 38, 69, 67])).
% 0.35/0.53 tff(77,plain,
% 0.35/0.53 (right_solution(elem!0, elem!0) = multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))),
% 0.35/0.53 inference(symmetry,[status(thm)],[76])).
% 0.35/0.53 tff(78,plain,
% 0.35/0.53 (product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) <=> product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))),
% 0.35/0.53 inference(monotonicity,[status(thm)],[77])).
% 0.35/0.53 tff(79,plain,
% 0.35/0.53 (product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))) <=> product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))),
% 0.35/0.53 inference(symmetry,[status(thm)],[78])).
% 0.35/0.53 tff(80,plain,
% 0.35/0.53 ((~![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)) | product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(81,plain,
% 0.35/0.53 (product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[80, 8])).
% 0.35/0.53 tff(82,plain,
% 0.35/0.53 (product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[81, 79])).
% 0.35/0.53 tff(83,plain,
% 0.35/0.53 (^[X: $i] : refl((~product(not_identity(X), X, not_identity(X))) <=> (~product(not_identity(X), X, not_identity(X))))),
% 0.35/0.53 inference(bind,[status(th)],[])).
% 0.35/0.53 tff(84,plain,
% 0.35/0.53 (![X: $i] : (~product(not_identity(X), X, not_identity(X))) <=> ![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 0.35/0.53 inference(quant_intro,[status(thm)],[83])).
% 0.35/0.53 tff(85,plain,
% 0.35/0.53 (![X: $i] : (~product(not_identity(X), X, not_identity(X))) <=> ![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(86,axiom,(![X: $i] : (~product(not_identity(X), X, not_identity(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_there_is_a_right_identity')).
% 0.35/0.53 tff(87,plain,
% 0.35/0.53 (![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.35/0.53 tff(88,plain,(
% 0.35/0.53 ![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 0.35/0.53 inference(skolemize,[status(sab)],[87])).
% 0.35/0.53 tff(89,plain,
% 0.35/0.53 (![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 0.35/0.53 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.35/0.53 tff(90,plain,
% 0.35/0.53 ((~![X: $i] : (~product(not_identity(X), X, not_identity(X)))) | (~product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))))),
% 0.35/0.53 inference(quant_inst,[status(thm)],[])).
% 0.35/0.53 tff(91,plain,
% 0.35/0.53 (~product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))),
% 0.35/0.53 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.35/0.53 tff(92,plain,
% 0.35/0.53 (((~![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(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))))) <=> ((~![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(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(93,plain,
% 0.35/0.53 ((product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))))) <=> ((~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))))),
% 0.35/0.53 inference(rewrite,[status(thm)],[])).
% 0.35/0.53 tff(94,plain,
% 0.35/0.53 (((~![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(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))))) <=> ((~![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(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))))))),
% 0.35/0.53 inference(monotonicity,[status(thm)],[93])).
% 0.35/0.53 tff(95,plain,
% 0.35/0.53 (((~![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(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))))) <=> ((~![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(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))))),
% 0.35/0.53 inference(transitivity,[status(thm)],[94, 92])).
% 0.35/0.53 tff(96,plain,
% 0.35/0.53 ((~![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(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))))),
% 0.37/0.54 inference(quant_inst,[status(thm)],[])).
% 0.37/0.54 tff(97,plain,
% 0.37/0.54 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (~product(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))))),
% 0.37/0.54 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.37/0.54 tff(98,plain,
% 0.37/0.54 (~product(left_solution(multiply(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[97, 59, 91, 67])).
% 0.37/0.54 tff(99,plain,
% 0.37/0.54 ($false),
% 0.37/0.54 inference(unit_resolution,[status(thm)],[98, 82])).
% 0.37/0.54 % SZS output end Proof
% 0.37/0.54 % E exiting
%------------------------------------------------------------------------------