%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP513-1 : 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 01:27:25 PM UTC 2026
% Result : Unsatisfiable 5.35s 1.13s
% Output : CNFRefutation 5.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 5 RR)
% Number of literals : 34 ( 33 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 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 : 79 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t0,axiom,
multiply(X1,multiply(multiply(X2,X3),inverse(multiply(X1,X3)))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t1,plain,
multiply(X1,multiply(multiply(X2,X3),inverse(multiply(X1,X3)))) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t2,plain,
X1 = multiply(X2,multiply(X3,inverse(multiply(X2,multiply(multiply(X3,Y3),inverse(multiply(X1,Y3))))))),
inference(cp,[status(thm)],[t1,t1]) ).
cnf(t4,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,multiply(multiply(X2,X3),inverse(multiply(Y3,X3))))))) = Y3,
inference(orient,[status(thm)],[t2]) ).
cnf(t5,plain,
X1 = multiply(X1,multiply(X2,inverse(X2))),
inference(cp,[status(thm)],[t4,t1]) ).
cnf(t12,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t13,plain,
X1 = multiply(X2,multiply(X1,inverse(multiply(X2,multiply(X3,inverse(X3)))))),
inference(cp,[status(thm)],[t1,t12]) ).
cnf(t438,plain,
X1 = multiply(X2,multiply(X1,inverse(X2))),
inference(step,[status(thm)],[t13,t12]) ).
cnf(t18,plain,
multiply(X1,multiply(X2,inverse(X1))) = X2,
inference(orient,[status(thm)],[t438]) ).
cnf(t16,plain,
X1 = multiply(X2,multiply(X3,inverse(multiply(X2,multiply(X3,inverse(multiply(X1,multiply(Y3,inverse(Y3))))))))),
inference(cp,[status(thm)],[t4,t12]) ).
cnf(t439,plain,
X1 = multiply(X2,multiply(X3,inverse(multiply(X2,multiply(X3,inverse(X1)))))),
inference(step,[status(thm)],[t16,t12]) ).
cnf(t51,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,multiply(X2,inverse(X3)))))) = X3,
inference(orient,[status(thm)],[t439]) ).
cnf(t53,plain,
multiply(X1,X2) = multiply(X1,multiply(multiply(X3,X2),inverse(X3))),
inference(cp,[status(thm)],[t51,t1]) ).
cnf(t61,plain,
multiply(X1,multiply(multiply(X2,X3),inverse(X2))) = multiply(X1,X3),
inference(orient,[status(thm)],[t53]) ).
cnf(t21,plain,
X1 = multiply(multiply(X1,X2),multiply(X3,inverse(multiply(X3,X2)))),
inference(cp,[status(thm)],[t4,t18]) ).
cnf(t24,plain,
multiply(multiply(X1,X2),multiply(X3,inverse(multiply(X3,X2)))) = X1,
inference(orient,[status(thm)],[t21]) ).
cnf(t35,plain,
multiply(X1,X2) = multiply(multiply(X3,X2),multiply(X1,inverse(X3))),
inference(cp,[status(thm)],[t4,t24]) ).
cnf(t38,plain,
multiply(multiply(X1,X2),multiply(X3,inverse(X1))) = multiply(X3,X2),
inference(orient,[status(thm)],[t35]) ).
cnf(t62,plain,
multiply(multiply(X1,X2),X3) = multiply(multiply(X1,X3),X2),
inference(cp,[status(thm)],[t61,t38]) ).
cnf(t68,plain,
multiply(multiply(X1,X2),X3) = multiply(multiply(X1,X3),X2),
inference(orient,[status(thm)],[t62]) ).
cnf(t76,plain,
multiply(X1,X2) = multiply(X1,multiply(multiply(X3,inverse(X3)),X2)),
inference(cp,[status(thm)],[t61,t68]) ).
cnf(t91,plain,
multiply(X1,multiply(multiply(X2,inverse(X2)),X3)) = multiply(X1,X3),
inference(orient,[status(thm)],[t76]) ).
cnf(t92,plain,
multiply(X1,inverse(multiply(X1,inverse(X2)))) = X2,
inference(cp,[status(thm)],[t91,t1]) ).
cnf(t108,plain,
multiply(X1,inverse(multiply(X1,inverse(X2)))) = X2,
inference(orient,[status(thm)],[t92]) ).
cnf(t113,plain,
X1 = multiply(multiply(X1,inverse(X2)),X2),
inference(cp,[status(thm)],[t18,t108]) ).
cnf(t440,plain,
X1 = multiply(multiply(X1,X2),inverse(X2)),
inference(step,[status(thm)],[t113,t68]) ).
cnf(t125,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(orient,[status(thm)],[t440]) ).
cnf(t140,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(cp,[status(thm)],[t18,t125]) ).
cnf(t150,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t140]) ).
cnf(goal_0,negated_conjecture,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(b1,inverse(b1)) != multiply(inverse(a1),a1),
inference(rw,[status(thm)],[goal_0,t150]) ).
cnf(g0_1,plain,
multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[g0_0,t150]) ).
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
% 0.00/0.03 % Problem : GRP513-1 : 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 14:57:27 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.35/1.13 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.35/1.13 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------