%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP028-3 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 7.37s 7.56s
% Output : Proof 7.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP028-3 : TPTP v9.0.0. Released v1.1.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n015.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 15:28:26 EDT 2025
% 0.11/0.33 % CPUTime :
% 7.37/7.56 % SZS status Unsatisfiable
% 7.37/7.56 % SZS output start Proof
% 7.37/7.56 tff(product_type, type, (
% 7.37/7.56 product: ( $i * $i * $i ) > $o)).
% 7.37/7.56 tff(not_identity_type, type, (
% 7.37/7.56 not_identity: $i > $i)).
% 7.37/7.56 tff(left_solution_type, type, (
% 7.37/7.56 left_solution: ( $i * $i ) > $i)).
% 7.37/7.56 tff(elem_0_type, type, (
% 7.37/7.56 elem_0: $i)).
% 7.37/7.56 tff(multiply_type, type, (
% 7.37/7.56 multiply: ( $i * $i ) > $i)).
% 7.37/7.56 tff(right_solution_type, type, (
% 7.37/7.56 right_solution: ( $i * $i ) > $i)).
% 7.37/7.56 tff(1,plain,
% 7.37/7.56 (^[Y: $i, X: $i] : refl(product(left_solution(X, Y), X, Y) <=> product(left_solution(X, Y), X, Y))),
% 7.37/7.56 inference(bind,[status(th)],[])).
% 7.37/7.56 tff(2,plain,
% 7.37/7.56 (![Y: $i, X: $i] : product(left_solution(X, Y), X, Y) <=> ![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 7.37/7.56 inference(quant_intro,[status(thm)],[1])).
% 7.37/7.56 tff(3,plain,
% 7.37/7.56 (![Y: $i, X: $i] : product(left_solution(X, Y), X, Y) <=> ![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 7.37/7.56 inference(rewrite,[status(thm)],[])).
% 7.37/7.56 tff(4,axiom,(![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','left_soln')).
% 7.37/7.56 tff(5,plain,
% 7.37/7.56 (![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 7.37/7.56 inference(modus_ponens,[status(thm)],[4, 3])).
% 7.37/7.56 tff(6,plain,(
% 7.37/7.56 ![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 7.37/7.56 inference(skolemize,[status(sab)],[5])).
% 7.37/7.56 tff(7,plain,
% 7.37/7.56 (![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 7.37/7.56 inference(modus_ponens,[status(thm)],[6, 2])).
% 7.37/7.56 tff(8,plain,
% 7.37/7.56 ((~![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)) | product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))))),
% 7.37/7.56 inference(quant_inst,[status(thm)],[])).
% 7.37/7.56 tff(9,plain,
% 7.37/7.56 (product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))))),
% 7.37/7.56 inference(unit_resolution,[status(thm)],[8, 7])).
% 7.37/7.56 tff(10,plain,
% 7.37/7.56 ((~![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)) | product(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), multiply(elem!0, elem!0), left_solution(elem!0, elem!0))),
% 7.37/7.56 inference(quant_inst,[status(thm)],[])).
% 7.37/7.56 tff(11,plain,
% 7.37/7.56 (product(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), multiply(elem!0, elem!0), left_solution(elem!0, elem!0))),
% 7.37/7.56 inference(unit_resolution,[status(thm)],[10, 7])).
% 7.37/7.56 tff(12,plain,
% 7.37/7.56 ((~![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)) | product(left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))), multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))),
% 7.37/7.56 inference(quant_inst,[status(thm)],[])).
% 7.37/7.56 tff(13,plain,
% 7.37/7.56 (product(left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))), multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))),
% 7.37/7.56 inference(unit_resolution,[status(thm)],[12, 7])).
% 7.37/7.56 tff(14,plain,
% 7.37/7.56 (^[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))))),
% 7.37/7.56 inference(bind,[status(th)],[])).
% 7.37/7.56 tff(15,plain,
% 7.37/7.56 (![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)))),
% 7.37/7.56 inference(quant_intro,[status(thm)],[14])).
% 7.37/7.56 tff(16,plain,
% 7.37/7.56 (![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)))),
% 7.37/7.56 inference(rewrite,[status(thm)],[])).
% 7.37/7.56 tff(17,plain,
% 7.37/7.56 (^[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)))))),
% 7.37/7.56 inference(bind,[status(th)],[])).
% 7.37/7.56 tff(18,plain,
% 7.37/7.56 (![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)))),
% 7.37/7.56 inference(quant_intro,[status(thm)],[17])).
% 7.37/7.56 tff(19,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')).
% 7.37/7.56 tff(20,plain,
% 7.37/7.56 (![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)))),
% 7.37/7.56 inference(modus_ponens,[status(thm)],[19, 18])).
% 7.37/7.56 tff(21,plain,
% 7.37/7.56 (![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)))),
% 7.37/7.56 inference(modus_ponens,[status(thm)],[20, 16])).
% 7.37/7.56 tff(22,plain,(
% 7.37/7.56 ![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)))),
% 7.37/7.56 inference(skolemize,[status(sab)],[21])).
% 7.37/7.56 tff(23,plain,
% 7.37/7.56 (![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)))),
% 7.37/7.56 inference(modus_ponens,[status(thm)],[22, 15])).
% 7.37/7.56 tff(24,plain,
% 7.37/7.56 (((~![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(left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))), multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), multiply(elem!0, elem!0), left_solution(elem!0, elem!0))) | product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))))))) <=> ((~![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(left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))), multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), multiply(elem!0, elem!0), left_solution(elem!0, elem!0))) | product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))))))),
% 7.41/7.56 inference(rewrite,[status(thm)],[])).
% 7.41/7.56 tff(25,plain,
% 7.41/7.56 ((product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))), multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), multiply(elem!0, elem!0), left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))))) <=> ((~product(left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))), multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), multiply(elem!0, elem!0), left_solution(elem!0, elem!0))) | product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))))))),
% 7.41/7.56 inference(rewrite,[status(thm)],[])).
% 7.41/7.56 tff(26,plain,
% 7.41/7.56 (((~![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(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))), multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), multiply(elem!0, elem!0), left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))))))) <=> ((~![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(left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))), multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), multiply(elem!0, elem!0), left_solution(elem!0, elem!0))) | product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))))))),
% 7.41/7.56 inference(monotonicity,[status(thm)],[25])).
% 7.41/7.56 tff(27,plain,
% 7.41/7.56 (((~![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(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))), multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), multiply(elem!0, elem!0), left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))))))) <=> ((~![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(left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))), multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), multiply(elem!0, elem!0), left_solution(elem!0, elem!0))) | product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))))))),
% 7.41/7.56 inference(transitivity,[status(thm)],[26, 24])).
% 7.41/7.56 tff(28,plain,
% 7.41/7.56 ((~![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(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))), multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), multiply(elem!0, elem!0), left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))))))),
% 7.41/7.56 inference(quant_inst,[status(thm)],[])).
% 7.41/7.56 tff(29,plain,
% 7.41/7.56 ((~![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(left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))), multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))) | (~product(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), multiply(elem!0, elem!0), left_solution(elem!0, elem!0))) | product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))))),
% 7.41/7.57 inference(modus_ponens,[status(thm)],[28, 27])).
% 7.41/7.57 tff(30,plain,
% 7.41/7.57 (product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[29, 23, 13, 11, 9])).
% 7.41/7.57 tff(31,plain,
% 7.41/7.57 (^[Y: $i, X: $i] : refl(product(X, right_solution(X, Y), Y) <=> product(X, right_solution(X, Y), Y))),
% 7.41/7.57 inference(bind,[status(th)],[])).
% 7.41/7.57 tff(32,plain,
% 7.41/7.57 (![Y: $i, X: $i] : product(X, right_solution(X, Y), Y) <=> ![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 7.41/7.57 inference(quant_intro,[status(thm)],[31])).
% 7.41/7.57 tff(33,plain,
% 7.41/7.57 (![Y: $i, X: $i] : product(X, right_solution(X, Y), Y) <=> ![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 7.41/7.57 inference(rewrite,[status(thm)],[])).
% 7.41/7.57 tff(34,axiom,(![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','right_soln')).
% 7.41/7.57 tff(35,plain,
% 7.41/7.57 (![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 7.41/7.57 inference(modus_ponens,[status(thm)],[34, 33])).
% 7.41/7.57 tff(36,plain,(
% 7.41/7.57 ![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 7.41/7.57 inference(skolemize,[status(sab)],[35])).
% 7.41/7.57 tff(37,plain,
% 7.41/7.57 (![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 7.41/7.57 inference(modus_ponens,[status(thm)],[36, 32])).
% 7.41/7.57 tff(38,plain,
% 7.41/7.57 ((~![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)) | product(elem!0, right_solution(elem!0, left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0))),
% 7.41/7.57 inference(quant_inst,[status(thm)],[])).
% 7.41/7.57 tff(39,plain,
% 7.41/7.57 (product(elem!0, right_solution(elem!0, left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0))),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[38, 37])).
% 7.41/7.57 tff(40,plain,
% 7.41/7.57 ((~![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)) | product(left_solution(elem!0, elem!0), elem!0, elem!0)),
% 7.41/7.57 inference(quant_inst,[status(thm)],[])).
% 7.41/7.57 tff(41,plain,
% 7.41/7.57 (product(left_solution(elem!0, elem!0), elem!0, elem!0)),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[40, 7])).
% 7.41/7.57 tff(42,plain,
% 7.41/7.57 (((~![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(left_solution(elem!0, elem!0), elem!0, elem!0)) | product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0)) | (~product(elem!0, right_solution(elem!0, left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0))))) <=> ((~![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(left_solution(elem!0, elem!0), elem!0, elem!0)) | product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0)) | (~product(elem!0, right_solution(elem!0, left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0))))),
% 7.41/7.57 inference(rewrite,[status(thm)],[])).
% 7.41/7.57 tff(43,plain,
% 7.41/7.57 ((product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0)) | (~product(elem!0, right_solution(elem!0, left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0))) | (~product(elem!0, right_solution(elem!0, left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), elem!0, elem!0))) <=> ((~product(left_solution(elem!0, elem!0), elem!0, elem!0)) | product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0)) | (~product(elem!0, right_solution(elem!0, left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0))))),
% 7.41/7.57 inference(rewrite,[status(thm)],[])).
% 7.41/7.57 tff(44,plain,
% 7.41/7.57 (((~![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(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0)) | (~product(elem!0, right_solution(elem!0, left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0))) | (~product(elem!0, right_solution(elem!0, left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), elem!0, elem!0)))) <=> ((~![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(left_solution(elem!0, elem!0), elem!0, elem!0)) | product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0)) | (~product(elem!0, right_solution(elem!0, left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0)))))),
% 7.41/7.57 inference(monotonicity,[status(thm)],[43])).
% 7.41/7.57 tff(45,plain,
% 7.41/7.57 (((~![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(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0)) | (~product(elem!0, right_solution(elem!0, left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0))) | (~product(elem!0, right_solution(elem!0, left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), elem!0, elem!0)))) <=> ((~![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(left_solution(elem!0, elem!0), elem!0, elem!0)) | product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0)) | (~product(elem!0, right_solution(elem!0, left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0))))),
% 7.41/7.57 inference(transitivity,[status(thm)],[44, 42])).
% 7.41/7.57 tff(46,plain,
% 7.41/7.57 ((~![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(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0)) | (~product(elem!0, right_solution(elem!0, left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0))) | (~product(elem!0, right_solution(elem!0, left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), elem!0, elem!0)))),
% 7.41/7.57 inference(quant_inst,[status(thm)],[])).
% 7.41/7.57 tff(47,plain,
% 7.41/7.57 ((~![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(left_solution(elem!0, elem!0), elem!0, elem!0)) | product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0)) | (~product(elem!0, right_solution(elem!0, left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0)))),
% 7.41/7.57 inference(modus_ponens,[status(thm)],[46, 45])).
% 7.41/7.57 tff(48,plain,
% 7.41/7.57 (product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0))),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[47, 23, 41, 39])).
% 7.41/7.57 tff(49,plain,
% 7.41/7.57 (^[X: $i] : refl((~product(not_identity(X), X, not_identity(X))) <=> (~product(not_identity(X), X, not_identity(X))))),
% 7.41/7.57 inference(bind,[status(th)],[])).
% 7.41/7.57 tff(50,plain,
% 7.41/7.57 (![X: $i] : (~product(not_identity(X), X, not_identity(X))) <=> ![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 7.41/7.57 inference(quant_intro,[status(thm)],[49])).
% 7.41/7.57 tff(51,plain,
% 7.41/7.57 (![X: $i] : (~product(not_identity(X), X, not_identity(X))) <=> ![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 7.41/7.57 inference(rewrite,[status(thm)],[])).
% 7.41/7.57 tff(52,axiom,(![X: $i] : (~product(not_identity(X), X, not_identity(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_there_is_a_right_identity')).
% 7.41/7.57 tff(53,plain,
% 7.41/7.57 (![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 7.41/7.57 inference(modus_ponens,[status(thm)],[52, 51])).
% 7.41/7.57 tff(54,plain,(
% 7.41/7.57 ![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 7.41/7.57 inference(skolemize,[status(sab)],[53])).
% 7.41/7.57 tff(55,plain,
% 7.41/7.57 (![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 7.41/7.57 inference(modus_ponens,[status(thm)],[54, 50])).
% 7.41/7.57 tff(56,plain,
% 7.41/7.57 ((~![X: $i] : (~product(not_identity(X), X, not_identity(X)))) | (~product(not_identity(left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))))),
% 7.41/7.57 inference(quant_inst,[status(thm)],[])).
% 7.41/7.57 tff(57,plain,
% 7.41/7.57 (~product(not_identity(left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))),
% 7.41/7.57 inference(unit_resolution,[status(thm)],[56, 55])).
% 7.41/7.57 tff(58,plain,
% 7.41/7.57 (^[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))))),
% 7.41/7.57 inference(bind,[status(th)],[])).
% 7.41/7.57 tff(59,plain,
% 7.41/7.57 (![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)))),
% 7.41/7.57 inference(quant_intro,[status(thm)],[58])).
% 7.41/7.57 tff(60,plain,
% 7.41/7.57 (![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)))),
% 7.41/7.57 inference(rewrite,[status(thm)],[])).
% 7.41/7.57 tff(61,plain,
% 7.41/7.57 (^[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)))))),
% 7.41/7.57 inference(bind,[status(th)],[])).
% 7.41/7.57 tff(62,plain,
% 7.41/7.57 (![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)))),
% 7.41/7.57 inference(quant_intro,[status(thm)],[61])).
% 7.41/7.57 tff(63,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')).
% 7.41/7.57 tff(64,plain,
% 7.41/7.57 (![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)))),
% 7.41/7.57 inference(modus_ponens,[status(thm)],[63, 62])).
% 7.41/7.57 tff(65,plain,
% 7.41/7.57 (![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)))),
% 7.41/7.57 inference(modus_ponens,[status(thm)],[64, 60])).
% 7.41/7.57 tff(66,plain,(
% 7.41/7.57 ![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)))),
% 7.41/7.57 inference(skolemize,[status(sab)],[65])).
% 7.41/7.57 tff(67,plain,
% 7.41/7.57 (![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)))),
% 7.41/7.57 inference(modus_ponens,[status(thm)],[66, 59])).
% 7.41/7.57 tff(68,plain,
% 7.41/7.57 (((~![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(left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_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(not_identity(left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))))),
% 7.41/7.57 inference(rewrite,[status(thm)],[])).
% 7.41/7.57 tff(69,plain,
% 7.41/7.57 ((product(not_identity(left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))))) <=> (product(not_identity(left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))))),
% 7.41/7.57 inference(rewrite,[status(thm)],[])).
% 7.41/7.57 tff(70,plain,
% 7.41/7.57 (((~![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(left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_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(not_identity(left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))))))),
% 7.41/7.58 inference(monotonicity,[status(thm)],[69])).
% 7.41/7.58 tff(71,plain,
% 7.41/7.58 (((~![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(left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_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(not_identity(left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))))),
% 7.41/7.58 inference(transitivity,[status(thm)],[70, 68])).
% 7.41/7.58 tff(72,plain,
% 7.41/7.58 ((~![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(left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))))),
% 7.41/7.58 inference(quant_inst,[status(thm)],[])).
% 7.41/7.58 tff(73,plain,
% 7.41/7.58 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | product(not_identity(left_solution(elem!0, elem!0)), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), left_solution(elem!0, elem!0), left_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(multiply(elem!0, elem!0), left_solution(elem!0, elem!0)), left_solution(multiply(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0)))), left_solution(elem!0, elem!0), not_identity(left_solution(elem!0, elem!0))))),
% 7.41/7.58 inference(modus_ponens,[status(thm)],[72, 71])).
% 7.41/7.58 tff(74,plain,
% 7.41/7.58 ($false),
% 7.41/7.58 inference(unit_resolution,[status(thm)],[73, 67, 57, 48, 30])).
% 7.41/7.58 % SZS output end Proof
% 7.41/7.58 % E exiting
%------------------------------------------------------------------------------