TSTP Solution File: GRP028-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP028-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Fri Sep 16 22:25:31 EDT 2022
% Result : Unsatisfiable 1.06s 0.90s
% Output : Proof 1.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP028-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 14:22:00 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.06/0.90 % SZS status Unsatisfiable
% 1.06/0.90 % SZS output start Proof
% 1.06/0.90 tff(product_type, type, (
% 1.06/0.90 product: ( $i * $i * $i ) > $o)).
% 1.06/0.90 tff(left_solution_type, type, (
% 1.06/0.90 left_solution: ( $i * $i ) > $i)).
% 1.06/0.90 tff(right_solution_type, type, (
% 1.06/0.90 right_solution: ( $i * $i ) > $i)).
% 1.06/0.90 tff(elem_0_type, type, (
% 1.06/0.90 elem_0: $i)).
% 1.06/0.90 tff(not_identity_type, type, (
% 1.06/0.90 not_identity: $i > $i)).
% 1.06/0.90 tff(1,plain,
% 1.06/0.90 (^[Y: $i, X: $i] : refl(product(left_solution(X, Y), X, Y) <=> product(left_solution(X, Y), X, Y))),
% 1.06/0.90 inference(bind,[status(th)],[])).
% 1.06/0.90 tff(2,plain,
% 1.06/0.90 (![Y: $i, X: $i] : product(left_solution(X, Y), X, Y) <=> ![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 1.06/0.90 inference(quant_intro,[status(thm)],[1])).
% 1.06/0.90 tff(3,plain,
% 1.06/0.90 (![Y: $i, X: $i] : product(left_solution(X, Y), X, Y) <=> ![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 1.06/0.90 inference(rewrite,[status(thm)],[])).
% 1.06/0.90 tff(4,axiom,(![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','left_soln')).
% 1.06/0.90 tff(5,plain,
% 1.06/0.90 (![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 1.06/0.90 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.06/0.90 tff(6,plain,(
% 1.06/0.90 ![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 1.06/0.90 inference(skolemize,[status(sab)],[5])).
% 1.06/0.90 tff(7,plain,
% 1.06/0.90 (![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 1.06/0.90 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.06/0.90 tff(8,plain,
% 1.06/0.90 ((~![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)) | product(left_solution(elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))), elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))),
% 1.06/0.90 inference(quant_inst,[status(thm)],[])).
% 1.06/0.90 tff(9,plain,
% 1.06/0.90 (product(left_solution(elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))), elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))),
% 1.06/0.90 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.06/0.90 tff(10,plain,
% 1.06/0.90 (^[Y: $i, X: $i] : refl(product(X, right_solution(X, Y), Y) <=> product(X, right_solution(X, Y), Y))),
% 1.06/0.90 inference(bind,[status(th)],[])).
% 1.06/0.90 tff(11,plain,
% 1.06/0.90 (![Y: $i, X: $i] : product(X, right_solution(X, Y), Y) <=> ![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 1.06/0.90 inference(quant_intro,[status(thm)],[10])).
% 1.06/0.90 tff(12,plain,
% 1.06/0.90 (![Y: $i, X: $i] : product(X, right_solution(X, Y), Y) <=> ![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 1.06/0.90 inference(rewrite,[status(thm)],[])).
% 1.06/0.90 tff(13,axiom,(![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','right_soln')).
% 1.06/0.90 tff(14,plain,
% 1.06/0.90 (![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 1.06/0.90 inference(modus_ponens,[status(thm)],[13, 12])).
% 1.06/0.90 tff(15,plain,(
% 1.06/0.90 ![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 1.06/0.90 inference(skolemize,[status(sab)],[14])).
% 1.06/0.90 tff(16,plain,
% 1.06/0.90 (![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 1.06/0.90 inference(modus_ponens,[status(thm)],[15, 11])).
% 1.06/0.90 tff(17,plain,
% 1.06/0.90 ((~![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)) | product(elem!0, right_solution(elem!0, elem!0), elem!0)),
% 1.06/0.90 inference(quant_inst,[status(thm)],[])).
% 1.06/0.90 tff(18,plain,
% 1.06/0.90 (product(elem!0, right_solution(elem!0, elem!0), elem!0)),
% 1.06/0.90 inference(unit_resolution,[status(thm)],[17, 16])).
% 1.06/0.90 tff(19,plain,
% 1.06/0.90 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : refl((product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) <=> (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))))),
% 1.06/0.90 inference(bind,[status(th)],[])).
% 1.06/0.90 tff(20,plain,
% 1.06/0.90 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 1.06/0.90 inference(quant_intro,[status(thm)],[19])).
% 1.06/0.90 tff(21,plain,
% 1.06/0.90 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) <=> ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 1.06/0.90 inference(rewrite,[status(thm)],[])).
% 1.06/0.90 tff(22,plain,
% 1.06/0.90 (^[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(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W)) <=> (((~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) | product(U, Z, W)))), rewrite((((~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U))) | product(U, Z, W)) <=> (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))), (((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W)) <=> (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))))),
% 1.06/0.90 inference(bind,[status(th)],[])).
% 1.06/0.90 tff(23,plain,
% 1.06/0.90 (![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(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 1.06/0.90 inference(quant_intro,[status(thm)],[22])).
% 1.06/0.90 tff(24,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','associativity')).
% 1.06/0.90 tff(25,plain,
% 1.06/0.90 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 1.06/0.90 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.06/0.90 tff(26,plain,
% 1.06/0.90 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 1.06/0.90 inference(modus_ponens,[status(thm)],[25, 21])).
% 1.06/0.90 tff(27,plain,(
% 1.06/0.90 ![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 1.06/0.90 inference(skolemize,[status(sab)],[26])).
% 1.06/0.90 tff(28,plain,
% 1.06/0.90 (![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))),
% 1.06/0.90 inference(modus_ponens,[status(thm)],[27, 20])).
% 1.06/0.90 tff(29,plain,
% 1.06/0.90 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | ((~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))), elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(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(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))), elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))))),
% 1.06/0.90 inference(rewrite,[status(thm)],[])).
% 1.06/0.90 tff(30,plain,
% 1.06/0.90 ((product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))), elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | (~product(left_solution(elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))), elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))))) <=> ((~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))), elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))))),
% 1.06/0.90 inference(rewrite,[status(thm)],[])).
% 1.06/0.90 tff(31,plain,
% 1.06/0.90 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))), elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | (~product(left_solution(elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))), elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(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(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | ((~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))), elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))))))),
% 1.06/0.90 inference(monotonicity,[status(thm)],[30])).
% 1.06/0.90 tff(32,plain,
% 1.06/0.90 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))), elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | (~product(left_solution(elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))), elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(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(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))), elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))))),
% 1.06/0.90 inference(transitivity,[status(thm)],[31, 29])).
% 1.06/0.90 tff(33,plain,
% 1.06/0.90 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))), elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | (~product(left_solution(elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))), elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))))),
% 1.06/0.90 inference(quant_inst,[status(thm)],[])).
% 1.06/0.90 tff(34,plain,
% 1.06/0.90 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))), elem!0, right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))))),
% 1.06/0.90 inference(modus_ponens,[status(thm)],[33, 32])).
% 1.06/0.90 tff(35,plain,
% 1.06/0.90 (product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))),
% 1.06/0.90 inference(unit_resolution,[status(thm)],[34, 28, 18, 9])).
% 1.06/0.90 tff(36,plain,
% 1.06/0.90 ((~![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)) | product(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 1.06/0.90 inference(quant_inst,[status(thm)],[])).
% 1.06/0.90 tff(37,plain,
% 1.06/0.90 (product(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 1.06/0.90 inference(unit_resolution,[status(thm)],[36, 16])).
% 1.06/0.90 tff(38,plain,
% 1.06/0.90 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(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(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))))),
% 1.06/0.91 inference(rewrite,[status(thm)],[])).
% 1.06/0.91 tff(39,plain,
% 1.06/0.91 ((product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))) | (~product(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))) <=> (product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))))),
% 1.06/0.91 inference(rewrite,[status(thm)],[])).
% 1.06/0.91 tff(40,plain,
% 1.06/0.91 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))) | (~product(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(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(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))))))),
% 1.06/0.91 inference(monotonicity,[status(thm)],[39])).
% 1.06/0.91 tff(41,plain,
% 1.06/0.91 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))) | (~product(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(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(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))))),
% 1.06/0.91 inference(transitivity,[status(thm)],[40, 38])).
% 1.06/0.91 tff(42,plain,
% 1.06/0.91 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))) | (~product(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))))),
% 1.06/0.91 inference(quant_inst,[status(thm)],[])).
% 1.06/0.91 tff(43,plain,
% 1.06/0.91 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), right_solution(elem!0, elem!0), right_solution(right_solution(not_identity(right_solution(elem!0, elem!0)), left_solution(left_solution(elem!0, elem!0), right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))))),
% 1.06/0.91 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.06/0.91 tff(44,plain,
% 1.06/0.91 (product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 1.06/0.91 inference(unit_resolution,[status(thm)],[43, 28, 37, 35])).
% 1.06/0.91 tff(45,plain,
% 1.06/0.91 ((~![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)) | product(left_solution(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))),
% 1.06/0.91 inference(quant_inst,[status(thm)],[])).
% 1.06/0.91 tff(46,plain,
% 1.06/0.91 (product(left_solution(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))),
% 1.06/0.91 inference(unit_resolution,[status(thm)],[45, 7])).
% 1.06/0.91 tff(47,plain,
% 1.06/0.91 (^[X: $i] : refl((~product(not_identity(X), X, not_identity(X))) <=> (~product(not_identity(X), X, not_identity(X))))),
% 1.06/0.91 inference(bind,[status(th)],[])).
% 1.06/0.91 tff(48,plain,
% 1.06/0.91 (![X: $i] : (~product(not_identity(X), X, not_identity(X))) <=> ![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 1.06/0.91 inference(quant_intro,[status(thm)],[47])).
% 1.06/0.91 tff(49,plain,
% 1.06/0.91 (![X: $i] : (~product(not_identity(X), X, not_identity(X))) <=> ![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 1.06/0.91 inference(rewrite,[status(thm)],[])).
% 1.06/0.91 tff(50,axiom,(![X: $i] : (~product(not_identity(X), X, not_identity(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_there_is_a_right_identity')).
% 1.06/0.91 tff(51,plain,
% 1.06/0.91 (![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 1.06/0.91 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.06/0.91 tff(52,plain,(
% 1.06/0.91 ![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 1.06/0.91 inference(skolemize,[status(sab)],[51])).
% 1.06/0.91 tff(53,plain,
% 1.06/0.91 (![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 1.06/0.91 inference(modus_ponens,[status(thm)],[52, 48])).
% 1.06/0.91 tff(54,plain,
% 1.06/0.91 ((~![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))))),
% 1.06/0.91 inference(quant_inst,[status(thm)],[])).
% 1.06/0.91 tff(55,plain,
% 1.06/0.91 (~product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))),
% 1.06/0.91 inference(unit_resolution,[status(thm)],[54, 53])).
% 1.06/0.91 tff(56,plain,
% 1.06/0.91 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (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(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(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(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | 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(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))))),
% 1.06/0.91 inference(rewrite,[status(thm)],[])).
% 1.06/0.91 tff(57,plain,
% 1.06/0.91 ((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(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(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(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))))),
% 1.06/0.91 inference(rewrite,[status(thm)],[])).
% 1.06/0.91 tff(58,plain,
% 1.06/0.91 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (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(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), left_solution(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(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (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(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))))),
% 1.06/0.91 inference(monotonicity,[status(thm)],[57])).
% 1.06/0.91 tff(59,plain,
% 1.06/0.91 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (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(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), left_solution(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(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | 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(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))))),
% 1.06/0.91 inference(transitivity,[status(thm)],[58, 56])).
% 1.06/0.91 tff(60,plain,
% 1.06/0.91 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | (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(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))))),
% 1.06/0.91 inference(quant_inst,[status(thm)],[])).
% 1.06/0.91 tff(61,plain,
% 1.06/0.91 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(X, V, W)) | (~product(Y, Z, V)) | (~product(X, Y, U)))) | product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(left_solution(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), left_solution(right_solution(elem!0, elem!0), right_solution(elem!0, elem!0))))),
% 1.06/0.92 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.06/0.92 tff(62,plain,
% 1.06/0.92 ($false),
% 1.06/0.92 inference(unit_resolution,[status(thm)],[61, 28, 55, 46, 44])).
% 1.06/0.92 % SZS output end Proof
%------------------------------------------------------------------------------