%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP541-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 01:27:29 PM UTC 2026
% Result : Unsatisfiable 2.96s 0.74s
% Output : CNFRefutation 2.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 4 RR)
% Number of literals : 15 ( 14 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
divide(X1,divide(identity,X2)) = multiply(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t10,plain,
divide(X1,divide(identity,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t2]) ).
cnf(t1,axiom,
divide(identity,X1) = inverse(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t18,plain,
divide(identity,X1) = inverse(X1),
inference(orient,[status(thm)],[t1]) ).
cnf(t35,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(step,[status(thm)],[t10,t18]) ).
cnf(t20,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[t35]) ).
cnf(t23,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t20]) ).
cnf(t0,axiom,
divide(X1,X1) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t7,plain,
divide(X1,X1) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t24,plain,
multiply(inverse(X1),X1) = identity,
inference(cp,[status(thm)],[t23,t7]) ).
cnf(t33,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t24]) ).
cnf(goal_0,negated_conjecture,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
identity != multiply(inverse(a1),a1),
inference(rw,[status(thm)],[goal_0,t33]) ).
cnf(g0_1,plain,
identity != identity,
inference(rw,[status(thm)],[g0_0,t33]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP541-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Wed Sep 23 15:01:21 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.96/0.74 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.96/0.74 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------