%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP010-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 : Sun Sep 27 07:22:04 AM UTC 2026
% Result : Unsatisfiable 8.01s 1.73s
% Output : CNFRefutation 8.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 6 RR)
% Number of literals : 17 ( 16 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 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 : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(c_times_b_is_e,hypothesis,
multiply(c,b) = identity ).
cnf(prove_b_times_c_is_e,negated_conjecture,
multiply(b,c) != identity ).
cnf(c0,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(c1,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c2,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c3,plain,
multiply(c,b) = identity,
inference(clausification,[status(esa)],[c_times_b_is_e]) ).
cnf(c4,plain,
multiply(b,c) != identity,
inference(clausification,[status(esa)],[prove_b_times_c_is_e]) ).
cnf(d0,plain,
multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d1,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
multiply(identity,X0) = multiply(c,multiply(b,X0)),
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d3,plain,
X0 = multiply(c,multiply(b,X0)),
inference(demodulation,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
multiply(b,X0) = multiply(inverse(c),X0),
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
multiply(b,c) = identity,
inference(superposition,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c4,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP010-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 14:17:53 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.01/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 8.01/1.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------