%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP181-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:25:34 PM UTC 2026
% Result : Unsatisfiable 16.16s 2.67s
% Output : CNFRefutation 16.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 11
% Syntax : Number of clauses : 83 ( 83 unt; 0 nHn; 22 RR)
% Number of literals : 83 ( 82 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 114 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t14,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t24,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t14]) ).
cnf(t3,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t39,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t3]) ).
cnf(t48,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t24,t39]) ).
cnf(t2,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t19,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t3995,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t48,t19]) ).
cnf(t94,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t3995]) ).
cnf(t95,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t94,t39]) ).
cnf(t113,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t95]) ).
cnf(t98,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t94,t94]) ).
cnf(t141,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t98]) ).
cnf(t3996,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t113,t141]) ).
cnf(t150,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t3996]) ).
cnf(t151,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t150]) ).
cnf(t152,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(cp,[status(thm)],[t151,t141]) ).
cnf(t3997,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t152,t151]) ).
cnf(t164,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t3997]) ).
cnf(t142,plain,
multiply(X1,inverse(X1)) = identity,
inference(cp,[status(thm)],[t141,t39]) ).
cnf(t171,plain,
multiply(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t142]) ).
cnf(t172,plain,
identity = multiply(X1,multiply(X2,inverse(multiply(X1,X2)))),
inference(cp,[status(thm)],[t171,t24]) ).
cnf(t3776,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(orient,[status(thm)],[t172]) ).
cnf(t3833,plain,
multiply(X1,inverse(multiply(X2,X1))) = multiply(inverse(X2),identity),
inference(cp,[status(thm)],[t94,t3776]) ).
cnf(t4049,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(step,[status(thm)],[t3833,t151]) ).
cnf(t3854,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(orient,[status(thm)],[t4049]) ).
cnf(t18,axiom,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t34,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t18]) ).
cnf(t40,plain,
multiply(least_upper_bound(inverse(X1),X2),X1) = least_upper_bound(identity,multiply(X2,X1)),
inference(cp,[status(thm)],[t34,t39]) ).
cnf(t332,plain,
multiply(least_upper_bound(inverse(X1),X2),X1) = least_upper_bound(identity,multiply(X2,X1)),
inference(orient,[status(thm)],[t40]) ).
cnf(t11,axiom,
least_upper_bound(inverse(X1),inverse(X2)) = inverse(greatest_lower_bound(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t77,plain,
least_upper_bound(inverse(X1),inverse(X2)) = inverse(greatest_lower_bound(X1,X2)),
inference(orient,[status(thm)],[t11]) ).
cnf(t333,plain,
least_upper_bound(identity,multiply(inverse(X1),X2)) = multiply(inverse(greatest_lower_bound(X2,X1)),X2),
inference(cp,[status(thm)],[t332,t77]) ).
cnf(t911,plain,
least_upper_bound(identity,multiply(inverse(X1),X2)) = multiply(inverse(greatest_lower_bound(X2,X1)),X2),
inference(orient,[status(thm)],[t333]) ).
cnf(t17,axiom,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t27,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t17]) ).
cnf(t45,plain,
multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(multiply(inverse(X1),X2),identity),
inference(cp,[status(thm)],[t27,t39]) ).
cnf(t7,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t66,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t4006,plain,
multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(step,[status(thm)],[t45,t66]) ).
cnf(t523,plain,
multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(orient,[status(thm)],[t4006]) ).
cnf(t912,plain,
multiply(inverse(greatest_lower_bound(X1,X2)),X1) = multiply(inverse(X2),least_upper_bound(X1,X2)),
inference(cp,[status(thm)],[t911,t523]) ).
cnf(t1602,plain,
multiply(inverse(greatest_lower_bound(X1,X2)),X1) = multiply(inverse(X2),least_upper_bound(X1,X2)),
inference(orient,[status(thm)],[t912]) ).
cnf(t1652,plain,
multiply(inverse(greatest_lower_bound(inverse(X1),inverse(X2))),inverse(X1)) = multiply(inverse(inverse(X2)),inverse(greatest_lower_bound(X1,X2))),
inference(cp,[status(thm)],[t1602,t77]) ).
cnf(t166,plain,
inverse(greatest_lower_bound(inverse(X1),X2)) = least_upper_bound(X1,inverse(X2)),
inference(cp,[status(thm)],[t77,t164]) ).
cnf(t255,plain,
inverse(greatest_lower_bound(inverse(X1),X2)) = least_upper_bound(X1,inverse(X2)),
inference(orient,[status(thm)],[t166]) ).
cnf(t4032,plain,
multiply(least_upper_bound(X1,inverse(inverse(X2))),inverse(X1)) = multiply(inverse(inverse(X2)),inverse(greatest_lower_bound(X1,X2))),
inference(step,[status(thm)],[t1652,t255]) ).
cnf(t4033,plain,
multiply(least_upper_bound(X1,X2),inverse(X1)) = multiply(inverse(inverse(X2)),inverse(greatest_lower_bound(X1,X2))),
inference(step,[status(thm)],[t4032,t164]) ).
cnf(t4034,plain,
multiply(least_upper_bound(X1,X2),inverse(X1)) = multiply(X2,inverse(greatest_lower_bound(X1,X2))),
inference(step,[status(thm)],[t4033,t141]) ).
cnf(t2634,plain,
multiply(least_upper_bound(X1,X2),inverse(X1)) = multiply(X2,inverse(greatest_lower_bound(X1,X2))),
inference(orient,[status(thm)],[t4034]) ).
cnf(t9,axiom,
least_upper_bound(b,c) = least_upper_bound(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t3991,plain,
least_upper_bound(c,b) = least_upper_bound(a,c),
inference(step,[status(thm)],[t9,t66]) ).
cnf(t3992,plain,
least_upper_bound(c,b) = least_upper_bound(c,a),
inference(step,[status(thm)],[t3991,t66]) ).
cnf(t79,plain,
least_upper_bound(c,a) = least_upper_bound(c,b),
inference(orient,[status(thm)],[t3992]) ).
cnf(t2635,plain,
multiply(a,inverse(greatest_lower_bound(c,a))) = multiply(least_upper_bound(c,b),inverse(c)),
inference(cp,[status(thm)],[t2634,t79]) ).
cnf(t6,axiom,
greatest_lower_bound(b,c) = greatest_lower_bound(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t4,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t49,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t3989,plain,
greatest_lower_bound(c,b) = greatest_lower_bound(a,c),
inference(step,[status(thm)],[t6,t49]) ).
cnf(t3990,plain,
greatest_lower_bound(c,b) = greatest_lower_bound(c,a),
inference(step,[status(thm)],[t3989,t49]) ).
cnf(t64,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(c,b),
inference(orient,[status(thm)],[t3990]) ).
cnf(t4044,plain,
multiply(a,inverse(greatest_lower_bound(c,b))) = multiply(least_upper_bound(c,b),inverse(c)),
inference(step,[status(thm)],[t2635,t64]) ).
cnf(t44,plain,
multiply(inverse(X1),least_upper_bound(X1,X2)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(cp,[status(thm)],[t27,t39]) ).
cnf(t500,plain,
multiply(inverse(X1),least_upper_bound(X1,X2)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(orient,[status(thm)],[t44]) ).
cnf(t913,plain,
multiply(inverse(greatest_lower_bound(X1,X2)),X1) = multiply(inverse(X2),least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t911,t500]) ).
cnf(t1660,plain,
multiply(inverse(greatest_lower_bound(X1,X2)),X1) = multiply(inverse(X2),least_upper_bound(X2,X1)),
inference(orient,[status(thm)],[t913]) ).
cnf(t1697,plain,
multiply(inverse(greatest_lower_bound(inverse(X1),inverse(X2))),inverse(X1)) = multiply(inverse(inverse(X2)),inverse(greatest_lower_bound(X2,X1))),
inference(cp,[status(thm)],[t1660,t77]) ).
cnf(t4035,plain,
multiply(least_upper_bound(X1,inverse(inverse(X2))),inverse(X1)) = multiply(inverse(inverse(X2)),inverse(greatest_lower_bound(X2,X1))),
inference(step,[status(thm)],[t1697,t255]) ).
cnf(t4036,plain,
multiply(least_upper_bound(X1,X2),inverse(X1)) = multiply(inverse(inverse(X2)),inverse(greatest_lower_bound(X2,X1))),
inference(step,[status(thm)],[t4035,t164]) ).
cnf(t4037,plain,
multiply(least_upper_bound(X1,X2),inverse(X1)) = multiply(X2,inverse(greatest_lower_bound(X2,X1))),
inference(step,[status(thm)],[t4036,t141]) ).
cnf(t2695,plain,
multiply(least_upper_bound(X1,X2),inverse(X1)) = multiply(X2,inverse(greatest_lower_bound(X2,X1))),
inference(orient,[status(thm)],[t4037]) ).
cnf(t4045,plain,
multiply(a,inverse(greatest_lower_bound(c,b))) = multiply(b,inverse(greatest_lower_bound(b,c))),
inference(step,[status(thm)],[t4044,t2695]) ).
cnf(t4046,plain,
multiply(a,inverse(greatest_lower_bound(c,b))) = multiply(b,inverse(greatest_lower_bound(c,b))),
inference(step,[status(thm)],[t4045,t49]) ).
cnf(t3126,plain,
multiply(a,inverse(greatest_lower_bound(c,b))) = multiply(b,inverse(greatest_lower_bound(c,b))),
inference(orient,[status(thm)],[t4046]) ).
cnf(t3860,plain,
inverse(a) = multiply(inverse(greatest_lower_bound(c,b)),inverse(multiply(b,inverse(greatest_lower_bound(c,b))))),
inference(cp,[status(thm)],[t3854,t3126]) ).
cnf(t4050,plain,
inverse(a) = inverse(b),
inference(step,[status(thm)],[t3860,t3854]) ).
cnf(t3932,plain,
inverse(a) = inverse(b),
inference(orient,[status(thm)],[t4050]) ).
cnf(t3938,plain,
a = inverse(inverse(b)),
inference(cp,[status(thm)],[t164,t3932]) ).
cnf(t4051,plain,
a = b,
inference(step,[status(thm)],[t3938,t164]) ).
cnf(t3988,plain,
a = b,
inference(orient,[status(thm)],[t4051]) ).
cnf(goal_0,negated_conjecture,
b != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
b != b,
inference(rw,[status(thm)],[goal_0,t3988]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP181-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n008.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 14:01:54 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 16.16/2.67 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.16/2.67 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------