%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP010-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 01:24:55 PM UTC 2026
% Result : Unsatisfiable 3.13s 0.82s
% Output : CNFRefutation 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 10 RR)
% Number of literals : 19 ( 18 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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 : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t3,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t5,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t3]) ).
cnf(t2,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t8,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t2]) ).
cnf(t9,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t5,t8]) ).
cnf(t1,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t4,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t22,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t9,t4]) ).
cnf(t11,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t22]) ).
cnf(t0,axiom,
multiply(c,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t6,plain,
multiply(c,b) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t13,plain,
b = multiply(inverse(c),identity),
inference(cp,[status(thm)],[t11,t6]) ).
cnf(t18,plain,
multiply(inverse(c),identity) = b,
inference(orient,[status(thm)],[t13]) ).
cnf(goal_0,negated_conjecture,
multiply(b,c) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(b,c) != multiply(multiply(inverse(c),identity),c),
inference(rw,[status(thm)],[goal_0,t18]) ).
cnf(g0_1,plain,
multiply(b,c) != multiply(inverse(c),multiply(identity,c)),
inference(rw,[status(thm)],[g0_0,t5]) ).
cnf(g0_2,plain,
multiply(b,c) != multiply(inverse(c),c),
inference(rw,[status(thm)],[g0_1,t4]) ).
cnf(g0_3,plain,
multiply(b,c) != identity,
inference(rw,[status(thm)],[g0_2,t8]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP010-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n013.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 13:12:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.13/0.82 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.13/0.82 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------