%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP181-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 01:25:35 PM UTC 2026
% Result : Unsatisfiable 33.56s 4.74s
% Output : CNFRefutation 33.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of clauses : 49 ( 49 unt; 0 nHn; 15 RR)
% Number of literals : 49 ( 48 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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 : 68 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t17,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t28,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t17]) ).
cnf(t5,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t43,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t5]) ).
cnf(t53,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t28,t43]) ).
cnf(t4,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t22,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t119847,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t53,t22]) ).
cnf(t239,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t119847]) ).
cnf(t21,axiom,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t38,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t21]) ).
cnf(t46,plain,
multiply(least_upper_bound(X1,inverse(X2)),X2) = least_upper_bound(multiply(X1,X2),identity),
inference(cp,[status(thm)],[t38,t43]) ).
cnf(t9,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t89,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t9]) ).
cnf(t119863,plain,
multiply(least_upper_bound(X1,inverse(X2)),X2) = least_upper_bound(identity,multiply(X1,X2)),
inference(step,[status(thm)],[t46,t89]) ).
cnf(t1187,plain,
multiply(least_upper_bound(X1,inverse(X2)),X2) = least_upper_bound(identity,multiply(X1,X2)),
inference(orient,[status(thm)],[t119863]) ).
cnf(t1207,plain,
X1 = multiply(inverse(least_upper_bound(X2,inverse(X1))),least_upper_bound(identity,multiply(X2,X1))),
inference(cp,[status(thm)],[t239,t1187]) ).
cnf(t12,axiom,
greatest_lower_bound(inverse(X1),inverse(X2)) = inverse(least_upper_bound(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t81,plain,
greatest_lower_bound(inverse(X1),inverse(X2)) = inverse(least_upper_bound(X1,X2)),
inference(orient,[status(thm)],[t12]) ).
cnf(t2,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t27,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t84,plain,
inverse(least_upper_bound(X1,inverse(X2))) = greatest_lower_bound(inverse(X1),X2),
inference(cp,[status(thm)],[t81,t27]) ).
cnf(t322,plain,
inverse(least_upper_bound(X1,inverse(X2))) = greatest_lower_bound(inverse(X1),X2),
inference(orient,[status(thm)],[t84]) ).
cnf(t120428,plain,
X1 = multiply(greatest_lower_bound(inverse(X2),X1),least_upper_bound(identity,multiply(X2,X1))),
inference(step,[status(thm)],[t1207,t322]) ).
cnf(t69306,plain,
multiply(greatest_lower_bound(inverse(X1),X2),least_upper_bound(identity,multiply(X1,X2))) = X2,
inference(orient,[status(thm)],[t120428]) ).
cnf(t20,axiom,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t31,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t20]) ).
cnf(t49,plain,
multiply(inverse(X1),least_upper_bound(X1,X2)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(cp,[status(thm)],[t31,t43]) ).
cnf(t11626,plain,
multiply(inverse(X1),least_upper_bound(X1,X2)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(orient,[status(thm)],[t49]) ).
cnf(t69474,plain,
X1 = multiply(greatest_lower_bound(inverse(inverse(X2)),X1),multiply(inverse(X2),least_upper_bound(X2,X1))),
inference(cp,[status(thm)],[t69306,t11626]) ).
cnf(t120663,plain,
X1 = multiply(greatest_lower_bound(X2,X1),multiply(inverse(X2),least_upper_bound(X2,X1))),
inference(step,[status(thm)],[t69474,t27]) ).
cnf(t119042,plain,
multiply(greatest_lower_bound(X1,X2),multiply(inverse(X1),least_upper_bound(X1,X2))) = X2,
inference(orient,[status(thm)],[t120663]) ).
cnf(t8,axiom,
greatest_lower_bound(b,c) = greatest_lower_bound(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t6,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t67,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t119831,plain,
greatest_lower_bound(c,b) = greatest_lower_bound(a,c),
inference(step,[status(thm)],[t8,t67]) ).
cnf(t119832,plain,
greatest_lower_bound(c,b) = greatest_lower_bound(c,a),
inference(step,[status(thm)],[t119831,t67]) ).
cnf(t87,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(c,b),
inference(orient,[status(thm)],[t119832]) ).
cnf(t119335,plain,
a = multiply(greatest_lower_bound(c,b),multiply(inverse(c),least_upper_bound(c,a))),
inference(cp,[status(thm)],[t119042,t87]) ).
cnf(t11,axiom,
least_upper_bound(b,c) = least_upper_bound(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t119833,plain,
least_upper_bound(c,b) = least_upper_bound(a,c),
inference(step,[status(thm)],[t11,t89]) ).
cnf(t119834,plain,
least_upper_bound(c,b) = least_upper_bound(c,a),
inference(step,[status(thm)],[t119833,t89]) ).
cnf(t108,plain,
least_upper_bound(c,a) = least_upper_bound(c,b),
inference(orient,[status(thm)],[t119834]) ).
cnf(t120664,plain,
a = multiply(greatest_lower_bound(c,b),multiply(inverse(c),least_upper_bound(c,b))),
inference(step,[status(thm)],[t119335,t108]) ).
cnf(t120665,plain,
a = b,
inference(step,[status(thm)],[t120664,t119042]) ).
cnf(t119810,plain,
a = b,
inference(orient,[status(thm)],[t120665]) ).
cnf(goal_0,negated_conjecture,
b != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
b != b,
inference(rw,[status(thm)],[goal_0,t119810]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP181-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 14:01:18 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 33.56/4.74 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.56/4.74 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------