%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP434-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 01:26:51 PM UTC 2026
% Result : Unsatisfiable 5.59s 1.14s
% Output : CNFRefutation 5.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 2
% Syntax : Number of clauses : 52 ( 52 unt; 0 nHn; 3 RR)
% Number of literals : 52 ( 51 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 3 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 : 130 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t0,axiom,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X1,X2),X3)),X1),X2),multiply(X4,inverse(X4)))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t1,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X1,X2),X3)),X1),X2),multiply(X4,inverse(X4)))) = X3,
inference(orient,[status(thm)],[t0]) ).
cnf(t2,plain,
multiply(X1,inverse(X1)) = inverse(multiply(multiply(multiply(X2,multiply(inverse(multiply(multiply(X3,X4),X2)),X3)),X4),multiply(Y4,inverse(Y4)))),
inference(cp,[status(thm)],[t1,t1]) ).
cnf(t4,plain,
multiply(X1,inverse(X1)) = inverse(multiply(multiply(multiply(X2,multiply(inverse(multiply(multiply(X3,X4),X2)),X3)),X4),multiply(Y4,inverse(Y4)))),
inference(orient,[status(thm)],[t2]) ).
cnf(t20,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(cp,[status(thm)],[t4,t4]) ).
cnf(t21,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(orient,[status(thm)],[t20]) ).
cnf(t25,plain,
inverse(multiply(X1,X2)) = inverse(multiply(multiply(multiply(inverse(multiply(X3,inverse(X3))),X1),X2),multiply(X4,inverse(X4)))),
inference(cp,[status(thm)],[t1,t21]) ).
cnf(t31,plain,
inverse(multiply(multiply(multiply(inverse(multiply(X1,inverse(X1))),X2),X3),multiply(X4,inverse(X4)))) = inverse(multiply(X2,X3)),
inference(orient,[status(thm)],[t25]) ).
cnf(t32,plain,
inverse(multiply(multiply(inverse(multiply(multiply(X1,X2),inverse(multiply(X3,inverse(X3))))),X1),X2)) = multiply(X4,inverse(X4)),
inference(cp,[status(thm)],[t31,t4]) ).
cnf(t80,plain,
inverse(multiply(multiply(inverse(multiply(multiply(X1,X2),inverse(multiply(X3,inverse(X3))))),X1),X2)) = multiply(X4,inverse(X4)),
inference(orient,[status(thm)],[t32]) ).
cnf(t81,plain,
multiply(X1,inverse(X1)) = inverse(multiply(multiply(inverse(multiply(X2,inverse(X2))),X3),inverse(X3))),
inference(cp,[status(thm)],[t80,t21]) ).
cnf(t129,plain,
multiply(X1,inverse(X1)) = inverse(multiply(multiply(inverse(multiply(X2,inverse(X2))),X3),inverse(X3))),
inference(orient,[status(thm)],[t81]) ).
cnf(t185,plain,
inverse(X1) = inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,inverse(X3)))),X1),multiply(X4,inverse(X4)))),
inference(cp,[status(thm)],[t1,t129]) ).
cnf(t268,plain,
inverse(multiply(multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2)))),X3),multiply(X4,inverse(X4)))) = inverse(X3),
inference(orient,[status(thm)],[t185]) ).
cnf(t277,plain,
inverse(X1) = inverse(multiply(multiply(multiply(X2,inverse(X2)),X1),multiply(X3,inverse(X3)))),
inference(cp,[status(thm)],[t268,t21]) ).
cnf(t333,plain,
inverse(multiply(multiply(multiply(X1,inverse(X1)),X2),multiply(X3,inverse(X3)))) = inverse(X2),
inference(orient,[status(thm)],[t277]) ).
cnf(t26,plain,
X1 = inverse(multiply(multiply(multiply(inverse(multiply(multiply(X2,inverse(X2)),X1)),X3),inverse(X3)),multiply(X4,inverse(X4)))),
inference(cp,[status(thm)],[t1,t21]) ).
cnf(t51,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(X1,inverse(X1)),X2)),X3),inverse(X3)),multiply(X4,inverse(X4)))) = X2,
inference(orient,[status(thm)],[t26]) ).
cnf(t334,plain,
inverse(inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),X2))))) = X2,
inference(cp,[status(thm)],[t333,t51]) ).
cnf(t436,plain,
inverse(inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),X2))))) = X2,
inference(orient,[status(thm)],[t334]) ).
cnf(t438,plain,
multiply(X1,inverse(X1)) = inverse(inverse(inverse(inverse(inverse(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,inverse(X3))))))))),
inference(cp,[status(thm)],[t436,t268]) ).
cnf(t908,plain,
multiply(X1,inverse(X1)) = inverse(inverse(multiply(X3,inverse(X3)))),
inference(step,[status(thm)],[t438,t436]) ).
cnf(t485,plain,
multiply(X1,inverse(X1)) = inverse(inverse(multiply(X2,inverse(X2)))),
inference(orient,[status(thm)],[t908]) ).
cnf(t553,plain,
inverse(X1) = inverse(multiply(multiply(multiply(inverse(multiply(X2,inverse(X2))),multiply(X3,inverse(X3))),X1),multiply(X4,inverse(X4)))),
inference(cp,[status(thm)],[t333,t485]) ).
cnf(t909,plain,
inverse(X1) = inverse(multiply(multiply(X3,inverse(X3)),X1)),
inference(step,[status(thm)],[t553,t31]) ).
cnf(t569,plain,
inverse(multiply(multiply(X1,inverse(X1)),X2)) = inverse(X2),
inference(orient,[status(thm)],[t909]) ).
cnf(t910,plain,
inverse(inverse(inverse(inverse(X2)))) = X2,
inference(step,[status(thm)],[t436,t569]) ).
cnf(t618,plain,
inverse(inverse(inverse(inverse(X2)))) = X2,
inference(rw,[status(thm)],[t910]) ).
cnf(t620,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(orient,[status(thm)],[t618]) ).
cnf(t622,plain,
multiply(multiply(X1,inverse(X1)),X2) = inverse(inverse(inverse(inverse(X2)))),
inference(cp,[status(thm)],[t620,t569]) ).
cnf(t912,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(step,[status(thm)],[t622,t620]) ).
cnf(t650,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(orient,[status(thm)],[t912]) ).
cnf(t913,plain,
inverse(multiply(X2,multiply(X3,inverse(X3)))) = inverse(X2),
inference(step,[status(thm)],[t333,t650]) ).
cnf(t685,plain,
inverse(multiply(X2,multiply(X3,inverse(X3)))) = inverse(X2),
inference(rw,[status(thm)],[t913]) ).
cnf(t714,plain,
inverse(multiply(X1,multiply(X2,inverse(X2)))) = inverse(X1),
inference(orient,[status(thm)],[t685]) ).
cnf(t918,plain,
inverse(multiply(multiply(inverse(multiply(multiply(X1,X2),X3)),X1),X2)) = X3,
inference(step,[status(thm)],[t1,t714]) ).
cnf(t734,plain,
inverse(multiply(multiply(inverse(multiply(multiply(X1,X2),X3)),X1),X2)) = X3,
inference(rw,[status(thm)],[t918]) ).
cnf(t844,plain,
inverse(multiply(multiply(inverse(multiply(multiply(X1,X2),X3)),X1),X2)) = X3,
inference(orient,[status(thm)],[t734]) ).
cnf(t725,plain,
multiply(X1,multiply(X2,inverse(X2))) = inverse(inverse(inverse(inverse(X1)))),
inference(cp,[status(thm)],[t620,t714]) ).
cnf(t919,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(step,[status(thm)],[t725,t620]) ).
cnf(t735,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(orient,[status(thm)],[t919]) ).
cnf(t845,plain,
X1 = inverse(multiply(inverse(multiply(multiply(X2,multiply(X3,inverse(X3))),X1)),X2)),
inference(cp,[status(thm)],[t844,t735]) ).
cnf(t921,plain,
X1 = inverse(multiply(inverse(multiply(X2,X1)),X2)),
inference(step,[status(thm)],[t845,t735]) ).
cnf(t867,plain,
inverse(multiply(inverse(multiply(X1,X2)),X1)) = X2,
inference(orient,[status(thm)],[t921]) ).
cnf(t868,plain,
X1 = inverse(inverse(multiply(multiply(X2,inverse(X2)),X1))),
inference(cp,[status(thm)],[t867,t735]) ).
cnf(t922,plain,
X1 = inverse(inverse(X1)),
inference(step,[status(thm)],[t868,t569]) ).
cnf(t885,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t922]) ).
cnf(t889,plain,
X1 = multiply(multiply(inverse(X2),X2),X1),
inference(cp,[status(thm)],[t650,t885]) ).
cnf(t895,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(orient,[status(thm)],[t889]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
a2 != a2,
inference(rw,[status(thm)],[goal_0,t895]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP434-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n010.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 14:45:49 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.59/1.14 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.59/1.14 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------