%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP509-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 01:27:24 PM UTC 2026
% Result : Unsatisfiable 8.03s 6.59s
% Output : CNFRefutation 8.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 2
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 5 RR)
% Number of literals : 37 ( 36 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t0,axiom,
multiply(multiply(multiply(X1,X2),X3),inverse(multiply(X1,X3))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t1,plain,
multiply(multiply(multiply(X1,X2),X3),inverse(multiply(X1,X3))) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t3,plain,
inverse(multiply(X1,X2)) = multiply(multiply(X3,Y3),inverse(multiply(multiply(multiply(X1,X3),X2),Y3))),
inference(cp,[status(thm)],[t1,t1]) ).
cnf(t13,plain,
multiply(multiply(X1,X2),inverse(multiply(multiply(multiply(X3,X1),Y3),X2))) = inverse(multiply(X3,Y3)),
inference(orient,[status(thm)],[t3]) ).
cnf(t17,plain,
inverse(multiply(X1,X2)) = multiply(multiply(X3,inverse(multiply(X1,X2))),inverse(X3)),
inference(cp,[status(thm)],[t13,t1]) ).
cnf(t32,plain,
multiply(multiply(X1,inverse(multiply(X2,X3))),inverse(X1)) = inverse(multiply(X2,X3)),
inference(orient,[status(thm)],[t17]) ).
cnf(t2,plain,
X1 = multiply(X2,inverse(multiply(multiply(X3,X2),inverse(multiply(X3,X1))))),
inference(cp,[status(thm)],[t1,t1]) ).
cnf(t5,plain,
multiply(X1,inverse(multiply(multiply(X2,X1),inverse(multiply(X2,X3))))) = X3,
inference(orient,[status(thm)],[t2]) ).
cnf(t36,plain,
inverse(multiply(X1,inverse(multiply(multiply(X2,X1),inverse(multiply(X2,X3)))))) = multiply(multiply(Y3,inverse(X3)),inverse(Y3)),
inference(cp,[status(thm)],[t32,t5]) ).
cnf(t338,plain,
inverse(X3) = multiply(multiply(Y3,inverse(X3)),inverse(Y3)),
inference(step,[status(thm)],[t36,t5]) ).
cnf(t50,plain,
multiply(multiply(X1,inverse(X2)),inverse(X1)) = inverse(X2),
inference(orient,[status(thm)],[t338]) ).
cnf(t57,plain,
inverse(X1) = multiply(inverse(X2),inverse(multiply(X1,inverse(X2)))),
inference(cp,[status(thm)],[t50,t50]) ).
cnf(t72,plain,
multiply(inverse(X1),inverse(multiply(X2,inverse(X1)))) = inverse(X2),
inference(orient,[status(thm)],[t57]) ).
cnf(t73,plain,
inverse(multiply(X1,inverse(multiply(X1,X2)))) = X2,
inference(cp,[status(thm)],[t72,t5]) ).
cnf(t87,plain,
inverse(multiply(X1,inverse(multiply(X1,X2)))) = X2,
inference(orient,[status(thm)],[t73]) ).
cnf(t96,plain,
inverse(multiply(X1,inverse(multiply(X1,X2)))) = multiply(multiply(X3,X2),inverse(X3)),
inference(cp,[status(thm)],[t50,t87]) ).
cnf(t340,plain,
X2 = multiply(multiply(X3,X2),inverse(X3)),
inference(step,[status(thm)],[t96,t87]) ).
cnf(t117,plain,
multiply(multiply(X1,X2),inverse(X1)) = X2,
inference(orient,[status(thm)],[t340]) ).
cnf(t120,plain,
inverse(multiply(X1,inverse(X2))) = multiply(inverse(X1),inverse(inverse(X2))),
inference(cp,[status(thm)],[t117,t72]) ).
cnf(t88,plain,
inverse(X1) = inverse(inverse(inverse(X1))),
inference(cp,[status(thm)],[t87,t72]) ).
cnf(t105,plain,
inverse(inverse(inverse(X1))) = inverse(X1),
inference(orient,[status(thm)],[t88]) ).
cnf(t106,plain,
inverse(multiply(X1,inverse(multiply(X1,X2)))) = inverse(inverse(X2)),
inference(cp,[status(thm)],[t105,t87]) ).
cnf(t339,plain,
X2 = inverse(inverse(X2)),
inference(step,[status(thm)],[t106,t87]) ).
cnf(t109,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t339]) ).
cnf(t341,plain,
inverse(multiply(X1,inverse(X2))) = multiply(inverse(X1),X2),
inference(step,[status(thm)],[t120,t109]) ).
cnf(t153,plain,
inverse(multiply(X1,inverse(X2))) = multiply(inverse(X1),X2),
inference(orient,[status(thm)],[t341]) ).
cnf(t343,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t87,t153]) ).
cnf(t166,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[t343]) ).
cnf(t169,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t166]) ).
cnf(t176,plain,
multiply(X1,X2) = multiply(X2,inverse(inverse(X1))),
inference(cp,[status(thm)],[t117,t169]) ).
cnf(t346,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(step,[status(thm)],[t176,t109]) ).
cnf(t182,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t346]) ).
cnf(goal_0,negated_conjecture,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(b1,inverse(b1)) != multiply(inverse(a1),a1),
inference(rw,[status(thm)],[goal_0,t182]) ).
cnf(g0_1,plain,
multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[g0_0,t182]) ).
cnf(g0_2,plain,
multiply(b1,inverse(b1)) != multiply(b1,inverse(b1)),
inference(rw,[status(thm)],[g0_1]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP509-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/5.44 % Computer : n015.cluster.edu
% 0.18/5.44 % Model : x86_64 x86_64
% 0.18/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.44 % Memory : 8046.5625MB
% 0.18/5.44 % OS : Linux 6.8.0-71-generic
% 0.18/5.44 % CPULimit : 300
% 0.18/5.44 % WCLimit : 300
% 0.18/5.44 % DateTime : Wed Sep 23 15:00:14 UTC 2026
% 0.18/5.44 % CPUTime :
% 0.18/5.44 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.03/6.59 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.03/6.59 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------