TSTP Solution File: GRP028-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP028-2 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 22:25:32 EDT 2022
% Result : Unsatisfiable 1.04s 0.89s
% Output : Proof 1.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP028-2 : TPTP v8.1.0. Released v1.1.0.
% 0.00/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 14:09:57 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.04/0.89 % SZS status Unsatisfiable
% 1.04/0.89 % SZS output start Proof
% 1.04/0.89 tff(product_type, type, (
% 1.04/0.89 product: ( $i * $i * $i ) > $o)).
% 1.04/0.89 tff(right_solution_type, type, (
% 1.04/0.89 right_solution: ( $i * $i ) > $i)).
% 1.04/0.89 tff(multiply_type, type, (
% 1.04/0.89 multiply: ( $i * $i ) > $i)).
% 1.04/0.89 tff(elem_0_type, type, (
% 1.04/0.89 elem_0: $i)).
% 1.04/0.89 tff(left_solution_type, type, (
% 1.04/0.89 left_solution: ( $i * $i ) > $i)).
% 1.04/0.89 tff(not_identity_type, type, (
% 1.04/0.89 not_identity: $i > $i)).
% 1.04/0.89 tff(1,plain,
% 1.04/0.89 (^[Y: $i, X: $i] : refl(product(left_solution(X, Y), X, Y) <=> product(left_solution(X, Y), X, Y))),
% 1.04/0.89 inference(bind,[status(th)],[])).
% 1.04/0.89 tff(2,plain,
% 1.04/0.89 (![Y: $i, X: $i] : product(left_solution(X, Y), X, Y) <=> ![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 1.04/0.89 inference(quant_intro,[status(thm)],[1])).
% 1.04/0.89 tff(3,plain,
% 1.04/0.89 (![Y: $i, X: $i] : product(left_solution(X, Y), X, Y) <=> ![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 1.04/0.89 inference(rewrite,[status(thm)],[])).
% 1.04/0.89 tff(4,axiom,(![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','left_soln')).
% 1.04/0.89 tff(5,plain,
% 1.04/0.89 (![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 1.04/0.89 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.04/0.89 tff(6,plain,(
% 1.04/0.89 ![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 1.04/0.89 inference(skolemize,[status(sab)],[5])).
% 1.04/0.89 tff(7,plain,
% 1.04/0.89 (![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)),
% 1.04/0.89 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.04/0.89 tff(8,plain,
% 1.04/0.89 ((~![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)) | product(left_solution(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))),
% 1.04/0.89 inference(quant_inst,[status(thm)],[])).
% 1.04/0.89 tff(9,plain,
% 1.04/0.89 (product(left_solution(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))),
% 1.04/0.89 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.04/0.89 tff(10,plain,
% 1.04/0.89 (^[Y: $i, X: $i] : refl(product(X, right_solution(X, Y), Y) <=> product(X, right_solution(X, Y), Y))),
% 1.04/0.89 inference(bind,[status(th)],[])).
% 1.04/0.89 tff(11,plain,
% 1.04/0.89 (![Y: $i, X: $i] : product(X, right_solution(X, Y), Y) <=> ![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 1.04/0.89 inference(quant_intro,[status(thm)],[10])).
% 1.04/0.89 tff(12,plain,
% 1.04/0.89 (![Y: $i, X: $i] : product(X, right_solution(X, Y), Y) <=> ![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 1.04/0.89 inference(rewrite,[status(thm)],[])).
% 1.04/0.89 tff(13,axiom,(![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','right_soln')).
% 1.04/0.89 tff(14,plain,
% 1.04/0.89 (![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 1.04/0.89 inference(modus_ponens,[status(thm)],[13, 12])).
% 1.04/0.89 tff(15,plain,(
% 1.04/0.89 ![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 1.04/0.89 inference(skolemize,[status(sab)],[14])).
% 1.04/0.89 tff(16,plain,
% 1.04/0.89 (![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)),
% 1.04/0.89 inference(modus_ponens,[status(thm)],[15, 11])).
% 1.04/0.89 tff(17,plain,
% 1.04/0.89 ((~![Y: $i, X: $i] : product(X, right_solution(X, Y), Y)) | product(elem!0, right_solution(elem!0, elem!0), elem!0)),
% 1.04/0.89 inference(quant_inst,[status(thm)],[])).
% 1.04/0.89 tff(18,plain,
% 1.04/0.89 (product(elem!0, right_solution(elem!0, elem!0), elem!0)),
% 1.04/0.89 inference(unit_resolution,[status(thm)],[17, 16])).
% 1.04/0.89 tff(19,plain,
% 1.04/0.89 (^[Y: $i, X: $i] : refl(product(X, Y, multiply(X, Y)) <=> product(X, Y, multiply(X, Y)))),
% 1.04/0.89 inference(bind,[status(th)],[])).
% 1.04/0.89 tff(20,plain,
% 1.04/0.89 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y)) <=> ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 1.04/0.89 inference(quant_intro,[status(thm)],[19])).
% 1.04/0.89 tff(21,plain,
% 1.04/0.89 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y)) <=> ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 1.04/0.89 inference(rewrite,[status(thm)],[])).
% 1.04/0.89 tff(22,axiom,(![Y: $i, X: $i] : product(X, Y, multiply(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP002-0.ax','total_function1')).
% 1.04/0.90 tff(23,plain,
% 1.04/0.90 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[22, 21])).
% 1.04/0.90 tff(24,plain,(
% 1.04/0.90 ![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 1.04/0.90 inference(skolemize,[status(sab)],[23])).
% 1.04/0.90 tff(25,plain,
% 1.04/0.90 (![Y: $i, X: $i] : product(X, Y, multiply(X, Y))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[24, 20])).
% 1.04/0.90 tff(26,plain,
% 1.04/0.90 ((~![Y: $i, X: $i] : product(X, Y, multiply(X, Y))) | product(elem!0, elem!0, multiply(elem!0, elem!0))),
% 1.04/0.90 inference(quant_inst,[status(thm)],[])).
% 1.04/0.90 tff(27,plain,
% 1.04/0.90 (product(elem!0, elem!0, multiply(elem!0, elem!0))),
% 1.04/0.90 inference(unit_resolution,[status(thm)],[26, 25])).
% 1.04/0.90 tff(28,plain,
% 1.04/0.90 (^[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))))),
% 1.04/0.90 inference(bind,[status(th)],[])).
% 1.04/0.90 tff(29,plain,
% 1.04/0.90 (![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)))),
% 1.04/0.90 inference(quant_intro,[status(thm)],[28])).
% 1.04/0.90 tff(30,plain,
% 1.04/0.90 (![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)))),
% 1.04/0.90 inference(rewrite,[status(thm)],[])).
% 1.04/0.90 tff(31,plain,
% 1.04/0.90 (^[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(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)))))),
% 1.04/0.90 inference(bind,[status(th)],[])).
% 1.04/0.90 tff(32,plain,
% 1.04/0.90 (![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(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))),
% 1.04/0.90 inference(quant_intro,[status(thm)],[31])).
% 1.04/0.90 tff(33,axiom,(![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : ((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(X, V, W))) | product(U, Z, W))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP002-0.ax','associativity2')).
% 1.04/0.90 tff(34,plain,
% 1.04/0.90 (![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)))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[33, 32])).
% 1.04/0.90 tff(35,plain,
% 1.04/0.90 (![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)))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[34, 30])).
% 1.04/0.90 tff(36,plain,(
% 1.04/0.90 ![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)))),
% 1.04/0.90 inference(skolemize,[status(sab)],[35])).
% 1.04/0.90 tff(37,plain,
% 1.04/0.90 (![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)))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[36, 29])).
% 1.04/0.90 tff(38,plain,
% 1.04/0.90 (((~![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(elem!0, right_solution(elem!0, elem!0), elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(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(elem!0, right_solution(elem!0, elem!0), elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(elem!0, elem!0)))),
% 1.04/0.90 inference(rewrite,[status(thm)],[])).
% 1.04/0.90 tff(39,plain,
% 1.04/0.90 ((product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(elem!0, elem!0)) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | (~product(elem!0, elem!0, multiply(elem!0, elem!0)))) <=> ((~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(elem!0, elem!0)))),
% 1.04/0.90 inference(rewrite,[status(thm)],[])).
% 1.04/0.90 tff(40,plain,
% 1.04/0.90 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(elem!0, elem!0)) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | (~product(elem!0, elem!0, multiply(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(elem!0, right_solution(elem!0, elem!0), elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(elem!0, elem!0))))),
% 1.04/0.90 inference(monotonicity,[status(thm)],[39])).
% 1.04/0.90 tff(41,plain,
% 1.04/0.90 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(elem!0, elem!0)) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | (~product(elem!0, elem!0, multiply(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(elem!0, right_solution(elem!0, elem!0), elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(elem!0, elem!0)))),
% 1.04/0.90 inference(transitivity,[status(thm)],[40, 38])).
% 1.04/0.90 tff(42,plain,
% 1.04/0.90 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(elem!0, elem!0)) | (~product(elem!0, right_solution(elem!0, elem!0), elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))))),
% 1.04/0.90 inference(quant_inst,[status(thm)],[])).
% 1.04/0.90 tff(43,plain,
% 1.04/0.90 ((~![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(elem!0, right_solution(elem!0, elem!0), elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(elem!0, elem!0))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.04/0.90 tff(44,plain,
% 1.04/0.90 (product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(elem!0, elem!0))),
% 1.04/0.90 inference(unit_resolution,[status(thm)],[43, 37, 27, 18])).
% 1.04/0.90 tff(45,plain,
% 1.04/0.90 ((~![Y: $i, X: $i] : product(X, Y, multiply(X, Y))) | product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 1.04/0.90 inference(quant_inst,[status(thm)],[])).
% 1.04/0.90 tff(46,plain,
% 1.04/0.90 (product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 1.04/0.90 inference(unit_resolution,[status(thm)],[45, 25])).
% 1.04/0.90 tff(47,plain,
% 1.04/0.90 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))))),
% 1.04/0.90 inference(bind,[status(th)],[])).
% 1.04/0.90 tff(48,plain,
% 1.04/0.90 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 1.04/0.90 inference(quant_intro,[status(thm)],[47])).
% 1.04/0.90 tff(49,plain,
% 1.04/0.90 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 1.04/0.90 inference(rewrite,[status(thm)],[])).
% 1.04/0.90 tff(50,plain,
% 1.04/0.90 (^[W: $i, Z: $i, Y: $i, X: $i] : rewrite((((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W)) <=> ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z))))),
% 1.04/0.90 inference(bind,[status(th)],[])).
% 1.04/0.90 tff(51,plain,
% 1.04/0.90 (![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W)) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 1.04/0.90 inference(quant_intro,[status(thm)],[50])).
% 1.04/0.90 tff(52,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : (((~product(X, Y, Z)) | (~product(X, Y, W))) | (Z = W))), file('/export/starexec/sandbox2/benchmark/Axioms/GRP002-0.ax','total_function2')).
% 1.04/0.90 tff(53,plain,
% 1.04/0.90 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.04/0.90 tff(54,plain,
% 1.04/0.90 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[53, 49])).
% 1.04/0.90 tff(55,plain,(
% 1.04/0.90 ![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 1.04/0.90 inference(skolemize,[status(sab)],[54])).
% 1.04/0.90 tff(56,plain,
% 1.04/0.90 (![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[55, 48])).
% 1.04/0.90 tff(57,plain,
% 1.04/0.90 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((multiply(elem!0, elem!0) = multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(elem!0, elem!0))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (multiply(elem!0, elem!0) = multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(elem!0, elem!0))))),
% 1.04/0.90 inference(rewrite,[status(thm)],[])).
% 1.04/0.90 tff(58,plain,
% 1.04/0.90 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | ((multiply(elem!0, elem!0) = multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(elem!0, elem!0))))),
% 1.04/0.90 inference(quant_inst,[status(thm)],[])).
% 1.04/0.90 tff(59,plain,
% 1.04/0.90 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((Z = W) | (~product(X, Y, W)) | (~product(X, Y, Z)))) | (multiply(elem!0, elem!0) = multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0))) | (~product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(elem!0, elem!0)))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[58, 57])).
% 1.04/0.90 tff(60,plain,
% 1.04/0.90 (multiply(elem!0, elem!0) = multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0))),
% 1.04/0.90 inference(unit_resolution,[status(thm)],[59, 56, 46, 44])).
% 1.04/0.90 tff(61,plain,
% 1.04/0.90 (multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)) = multiply(elem!0, elem!0)),
% 1.04/0.90 inference(symmetry,[status(thm)],[60])).
% 1.04/0.90 tff(62,plain,
% 1.04/0.90 (product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0))) <=> product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 1.04/0.90 inference(monotonicity,[status(thm)],[61])).
% 1.04/0.90 tff(63,plain,
% 1.04/0.90 (product(multiply(elem!0, elem!0), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0))) <=> product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 1.04/0.90 inference(symmetry,[status(thm)],[62])).
% 1.04/0.90 tff(64,plain,
% 1.04/0.90 (product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[46, 63])).
% 1.04/0.90 tff(65,plain,
% 1.04/0.90 (product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0))) <=> product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(elem!0, elem!0))),
% 1.04/0.90 inference(monotonicity,[status(thm)],[61])).
% 1.04/0.90 tff(66,plain,
% 1.04/0.90 (product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(elem!0, elem!0)) <=> product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 1.04/0.90 inference(symmetry,[status(thm)],[65])).
% 1.04/0.90 tff(67,plain,
% 1.04/0.90 ((~![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)) | product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(elem!0, elem!0))),
% 1.04/0.90 inference(quant_inst,[status(thm)],[])).
% 1.04/0.90 tff(68,plain,
% 1.04/0.90 (product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(elem!0, elem!0))),
% 1.04/0.90 inference(unit_resolution,[status(thm)],[67, 7])).
% 1.04/0.90 tff(69,plain,
% 1.04/0.90 (product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[68, 66])).
% 1.04/0.90 tff(70,plain,
% 1.04/0.90 (product(left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0))) <=> product(left_solution(elem!0, elem!0), multiply(elem!0, elem!0), multiply(elem!0, elem!0))),
% 1.04/0.90 inference(monotonicity,[status(thm)],[61, 61])).
% 1.04/0.90 tff(71,plain,
% 1.04/0.90 (product(left_solution(elem!0, elem!0), multiply(elem!0, elem!0), multiply(elem!0, elem!0)) <=> product(left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 1.04/0.90 inference(symmetry,[status(thm)],[70])).
% 1.04/0.90 tff(72,plain,
% 1.04/0.90 ((~![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)) | product(left_solution(elem!0, elem!0), elem!0, elem!0)),
% 1.04/0.90 inference(quant_inst,[status(thm)],[])).
% 1.04/0.90 tff(73,plain,
% 1.04/0.90 (product(left_solution(elem!0, elem!0), elem!0, elem!0)),
% 1.04/0.90 inference(unit_resolution,[status(thm)],[72, 7])).
% 1.04/0.90 tff(74,plain,
% 1.04/0.90 (^[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))))),
% 1.04/0.90 inference(bind,[status(th)],[])).
% 1.04/0.90 tff(75,plain,
% 1.04/0.90 (![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)))),
% 1.04/0.90 inference(quant_intro,[status(thm)],[74])).
% 1.04/0.90 tff(76,plain,
% 1.04/0.90 (![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)))),
% 1.04/0.90 inference(rewrite,[status(thm)],[])).
% 1.04/0.90 tff(77,plain,
% 1.04/0.90 (^[W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite((((~product(X, Y, U)) | (~product(Y, Z, V))) | (~product(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)))))),
% 1.04/0.90 inference(bind,[status(th)],[])).
% 1.04/0.90 tff(78,plain,
% 1.04/0.90 (![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)))),
% 1.04/0.90 inference(quant_intro,[status(thm)],[77])).
% 1.04/0.90 tff(79,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/sandbox2/benchmark/Axioms/GRP002-0.ax','associativity1')).
% 1.04/0.90 tff(80,plain,
% 1.04/0.90 (![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)))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.04/0.90 tff(81,plain,
% 1.04/0.90 (![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)))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[80, 76])).
% 1.04/0.90 tff(82,plain,(
% 1.04/0.90 ![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)))),
% 1.04/0.90 inference(skolemize,[status(sab)],[81])).
% 1.04/0.90 tff(83,plain,
% 1.04/0.90 (![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)))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[82, 75])).
% 1.04/0.90 tff(84,plain,
% 1.04/0.90 (((~![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), multiply(elem!0, elem!0), multiply(elem!0, elem!0)) | (~product(elem!0, elem!0, multiply(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), multiply(elem!0, elem!0), multiply(elem!0, elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), elem!0, elem!0)))),
% 1.04/0.90 inference(rewrite,[status(thm)],[])).
% 1.04/0.90 tff(85,plain,
% 1.04/0.90 ((product(left_solution(elem!0, elem!0), multiply(elem!0, elem!0), multiply(elem!0, elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), elem!0, elem!0))) <=> (product(left_solution(elem!0, elem!0), multiply(elem!0, elem!0), multiply(elem!0, elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), elem!0, elem!0)))),
% 1.04/0.90 inference(rewrite,[status(thm)],[])).
% 1.04/0.90 tff(86,plain,
% 1.04/0.90 (((~![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), multiply(elem!0, elem!0), multiply(elem!0, elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | (~product(elem!0, elem!0, multiply(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), multiply(elem!0, elem!0), multiply(elem!0, elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), elem!0, elem!0))))),
% 1.04/0.90 inference(monotonicity,[status(thm)],[85])).
% 1.04/0.90 tff(87,plain,
% 1.04/0.90 (((~![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), multiply(elem!0, elem!0), multiply(elem!0, elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | (~product(elem!0, elem!0, multiply(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), multiply(elem!0, elem!0), multiply(elem!0, elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), elem!0, elem!0)))),
% 1.04/0.90 inference(transitivity,[status(thm)],[86, 84])).
% 1.04/0.90 tff(88,plain,
% 1.04/0.90 ((~![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), multiply(elem!0, elem!0), multiply(elem!0, elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), elem!0, elem!0)))),
% 1.04/0.90 inference(quant_inst,[status(thm)],[])).
% 1.04/0.90 tff(89,plain,
% 1.04/0.90 ((~![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), multiply(elem!0, elem!0), multiply(elem!0, elem!0)) | (~product(elem!0, elem!0, multiply(elem!0, elem!0))) | (~product(left_solution(elem!0, elem!0), elem!0, elem!0))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[88, 87])).
% 1.04/0.90 tff(90,plain,
% 1.04/0.90 (product(left_solution(elem!0, elem!0), multiply(elem!0, elem!0), multiply(elem!0, elem!0))),
% 1.04/0.90 inference(unit_resolution,[status(thm)],[89, 83, 27, 73])).
% 1.04/0.90 tff(91,plain,
% 1.04/0.90 (product(left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))),
% 1.04/0.90 inference(modus_ponens,[status(thm)],[90, 71])).
% 1.04/0.90 tff(92,plain,
% 1.04/0.90 (product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) <=> product(multiply(elem!0, elem!0), multiply(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))),
% 1.04/0.90 inference(monotonicity,[status(thm)],[61, 61])).
% 1.04/0.90 tff(93,plain,
% 1.04/0.90 (product(multiply(elem!0, elem!0), multiply(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) <=> product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))),
% 1.04/0.90 inference(symmetry,[status(thm)],[92])).
% 1.04/0.90 tff(94,plain,
% 1.04/0.90 ((~![Y: $i, X: $i] : product(X, Y, multiply(X, Y))) | product(multiply(elem!0, elem!0), multiply(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))),
% 1.04/0.90 inference(quant_inst,[status(thm)],[])).
% 1.04/0.90 tff(95,plain,
% 1.04/0.90 (product(multiply(elem!0, elem!0), multiply(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[94, 25])).
% 1.04/0.91 tff(96,plain,
% 1.04/0.91 (product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[95, 93])).
% 1.04/0.91 tff(97,plain,
% 1.04/0.91 (((~![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), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_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), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(98,plain,
% 1.04/0.91 ((product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0))))) <=> ((~product(left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(99,plain,
% 1.04/0.91 (((~![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(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_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), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0))))))),
% 1.04/0.91 inference(monotonicity,[status(thm)],[98])).
% 1.04/0.91 tff(100,plain,
% 1.04/0.91 (((~![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(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_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), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))))),
% 1.04/0.91 inference(transitivity,[status(thm)],[99, 97])).
% 1.04/0.91 tff(101,plain,
% 1.04/0.91 ((~![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(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))))),
% 1.04/0.91 inference(quant_inst,[status(thm)],[])).
% 1.04/0.91 tff(102,plain,
% 1.04/0.91 ((~![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), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0))))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[101, 100])).
% 1.04/0.91 tff(103,plain,
% 1.04/0.91 ((~product(left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), left_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0))))),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[102, 83])).
% 1.04/0.91 tff(104,plain,
% 1.04/0.91 (product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[103, 96, 91, 69])).
% 1.04/0.91 tff(105,plain,
% 1.04/0.91 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(106,plain,
% 1.04/0.91 ((product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))))) <=> (product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(107,plain,
% 1.04/0.91 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))))))),
% 1.04/0.91 inference(monotonicity,[status(thm)],[106])).
% 1.04/0.91 tff(108,plain,
% 1.04/0.91 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))))),
% 1.04/0.91 inference(transitivity,[status(thm)],[107, 105])).
% 1.04/0.91 tff(109,plain,
% 1.04/0.91 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))))),
% 1.04/0.91 inference(quant_inst,[status(thm)],[])).
% 1.04/0.91 tff(110,plain,
% 1.04/0.91 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)))) | (~product(left_solution(left_solution(elem!0, elem!0), multiply(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))))),
% 1.04/0.91 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.04/0.91 tff(111,plain,
% 1.04/0.91 (product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), right_solution(elem!0, elem!0))))),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[110, 37, 104])).
% 1.04/0.91 tff(112,plain,
% 1.04/0.91 (product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))),
% 1.04/0.91 inference(unit_resolution,[status(thm)],[111, 64])).
% 1.04/0.91 tff(113,plain,
% 1.04/0.91 (((~![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(left_solution(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(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(left_solution(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(114,plain,
% 1.04/0.91 ((product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))))) <=> ((~product(left_solution(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))))),
% 1.04/0.91 inference(rewrite,[status(thm)],[])).
% 1.04/0.91 tff(115,plain,
% 1.04/0.91 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(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(left_solution(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))))))),
% 1.04/0.92 inference(monotonicity,[status(thm)],[114])).
% 1.04/0.92 tff(116,plain,
% 1.04/0.92 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(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(left_solution(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))))),
% 1.04/0.92 inference(transitivity,[status(thm)],[115, 113])).
% 1.04/0.92 tff(117,plain,
% 1.04/0.92 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))))),
% 1.04/0.92 inference(quant_inst,[status(thm)],[])).
% 1.04/0.92 tff(118,plain,
% 1.04/0.92 ((~![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(left_solution(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))) | (~product(multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), multiply(multiply(elem!0, elem!0), multiply(elem!0, elem!0))))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.04/0.92 tff(119,plain,
% 1.04/0.92 (product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[118, 37, 112, 9])).
% 1.04/0.92 tff(120,plain,
% 1.04/0.92 ((~![Y: $i, X: $i] : product(left_solution(X, Y), X, Y)) | product(left_solution(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))),
% 1.04/0.92 inference(quant_inst,[status(thm)],[])).
% 1.04/0.92 tff(121,plain,
% 1.04/0.92 (product(left_solution(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[120, 7])).
% 1.04/0.92 tff(122,plain,
% 1.04/0.92 (^[X: $i] : refl((~product(not_identity(X), X, not_identity(X))) <=> (~product(not_identity(X), X, not_identity(X))))),
% 1.04/0.92 inference(bind,[status(th)],[])).
% 1.04/0.92 tff(123,plain,
% 1.04/0.92 (![X: $i] : (~product(not_identity(X), X, not_identity(X))) <=> ![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 1.04/0.92 inference(quant_intro,[status(thm)],[122])).
% 1.04/0.92 tff(124,plain,
% 1.04/0.92 (![X: $i] : (~product(not_identity(X), X, not_identity(X))) <=> ![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(125,axiom,(![X: $i] : (~product(not_identity(X), X, not_identity(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_there_is_a_right_identity')).
% 1.04/0.92 tff(126,plain,
% 1.04/0.92 (![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.04/0.92 tff(127,plain,(
% 1.04/0.92 ![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 1.04/0.92 inference(skolemize,[status(sab)],[126])).
% 1.04/0.92 tff(128,plain,
% 1.04/0.92 (![X: $i] : (~product(not_identity(X), X, not_identity(X)))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[127, 123])).
% 1.04/0.92 tff(129,plain,
% 1.04/0.92 ((~![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))))),
% 1.04/0.92 inference(quant_inst,[status(thm)],[])).
% 1.04/0.92 tff(130,plain,
% 1.04/0.92 (~product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0)))),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[129, 128])).
% 1.04/0.92 tff(131,plain,
% 1.04/0.92 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(left_solution(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(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(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(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(132,plain,
% 1.04/0.92 ((product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(multiply(elem!0, elem!0), multiply(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(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))))),
% 1.04/0.92 inference(rewrite,[status(thm)],[])).
% 1.04/0.92 tff(133,plain,
% 1.04/0.92 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(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(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))))))),
% 1.04/0.92 inference(monotonicity,[status(thm)],[132])).
% 1.04/0.92 tff(134,plain,
% 1.04/0.92 (((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))))) <=> ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | product(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(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))))),
% 1.04/0.92 inference(transitivity,[status(thm)],[133, 131])).
% 1.04/0.92 tff(135,plain,
% 1.04/0.92 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | (product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)))) | (~product(left_solution(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(left_solution(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))))),
% 1.04/0.92 inference(quant_inst,[status(thm)],[])).
% 1.04/0.92 tff(136,plain,
% 1.04/0.92 ((~![W: $i, V: $i, Z: $i, Y: $i, U: $i, X: $i] : (product(U, Z, W) | (~product(Y, Z, V)) | (~product(X, Y, U)) | (~product(X, V, W)))) | product(not_identity(right_solution(elem!0, elem!0)), right_solution(elem!0, elem!0), not_identity(right_solution(elem!0, elem!0))) | (~product(left_solution(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0))), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), not_identity(right_solution(elem!0, elem!0)))) | (~product(right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0)), right_solution(elem!0, elem!0), right_solution(multiply(elem!0, elem!0), multiply(elem!0, elem!0))))),
% 1.04/0.92 inference(modus_ponens,[status(thm)],[135, 134])).
% 1.04/0.92 tff(137,plain,
% 1.04/0.92 ($false),
% 1.04/0.92 inference(unit_resolution,[status(thm)],[136, 37, 130, 121, 119])).
% 1.04/0.92 % SZS output end Proof
%------------------------------------------------------------------------------