%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP519-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.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 01:27:26 PM UTC 2026
% Result : Unsatisfiable 5.85s 1.29s
% Output : CNFRefutation 5.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 3 RR)
% Number of literals : 23 ( 22 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t0,axiom,
multiply(X1,multiply(multiply(inverse(multiply(X1,X2)),X3),X2)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t1,plain,
multiply(X1,multiply(multiply(inverse(multiply(X1,X2)),X3),X2)) = X3,
inference(orient,[status(thm)],[t0]) ).
cnf(t2,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),Y3),X3) = multiply(X1,multiply(Y3,X2)),
inference(cp,[status(thm)],[t1,t1]) ).
cnf(t4,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),Y3),X3) = multiply(X1,multiply(Y3,X2)),
inference(orient,[status(thm)],[t2]) ).
cnf(t5,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(inverse(Y3),X2),multiply(multiply(inverse(multiply(inverse(multiply(X1,X3)),Y4)),Y3),Y4)),
inference(cp,[status(thm)],[t4,t1]) ).
cnf(t141,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(inverse(Y3),X2),multiply(X1,multiply(Y3,X3))),
inference(step,[status(thm)],[t5,t4]) ).
cnf(t38,plain,
multiply(multiply(inverse(X1),X2),multiply(X3,multiply(X1,Y3))) = multiply(X3,multiply(X2,Y3)),
inference(orient,[status(thm)],[t141]) ).
cnf(t53,plain,
multiply(multiply(inverse(X1),X2),multiply(X3,multiply(X1,Y3))) = multiply(multiply(inverse(Y4),X3),multiply(Y4,multiply(X2,Y3))),
inference(cp,[status(thm)],[t38,t38]) ).
cnf(t142,plain,
multiply(X3,multiply(X2,Y3)) = multiply(multiply(inverse(Y4),X3),multiply(Y4,multiply(X2,Y3))),
inference(step,[status(thm)],[t53,t38]) ).
cnf(t59,plain,
multiply(multiply(inverse(X1),X2),multiply(X1,multiply(X3,Y3))) = multiply(X2,multiply(X3,Y3)),
inference(orient,[status(thm)],[t142]) ).
cnf(t69,plain,
multiply(X1,multiply(X2,multiply(multiply(inverse(multiply(X2,X3)),Y3),X3))) = multiply(multiply(inverse(Y4),X1),multiply(Y4,Y3)),
inference(cp,[status(thm)],[t59,t1]) ).
cnf(t143,plain,
multiply(X1,Y3) = multiply(multiply(inverse(Y4),X1),multiply(Y4,Y3)),
inference(step,[status(thm)],[t69,t1]) ).
cnf(t82,plain,
multiply(multiply(inverse(X1),X2),multiply(X1,X3)) = multiply(X2,X3),
inference(orient,[status(thm)],[t143]) ).
cnf(t7,plain,
X1 = multiply(inverse(multiply(X2,X3)),multiply(X2,multiply(X1,X3))),
inference(cp,[status(thm)],[t1,t4]) ).
cnf(t10,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X3,X2))) = X3,
inference(orient,[status(thm)],[t7]) ).
cnf(t84,plain,
multiply(multiply(X1,multiply(X2,X3)),Y3) = multiply(X2,multiply(multiply(X1,X3),Y3)),
inference(cp,[status(thm)],[t82,t10]) ).
cnf(t102,plain,
multiply(multiply(X1,multiply(X2,X3)),Y3) = multiply(X2,multiply(multiply(X1,X3),Y3)),
inference(orient,[status(thm)],[t84]) ).
cnf(t105,plain,
multiply(X1,multiply(multiply(inverse(X2),X3),multiply(X2,Y3))) = multiply(multiply(X1,X3),Y3),
inference(cp,[status(thm)],[t102,t82]) ).
cnf(t144,plain,
multiply(X1,multiply(X3,Y3)) = multiply(multiply(X1,X3),Y3),
inference(step,[status(thm)],[t105,t82]) ).
cnf(t128,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t144]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(rw,[status(thm)],[goal_0,t128]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP519-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 14:57:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.85/1.29 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.85/1.29 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------