%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP017-1 : 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 : n005.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 07:22:06 AM UTC 2026
% Result : Unsatisfiable 16.30s 2.80s
% Output : CNFRefutation 16.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 14 unt; 0 nHn; 17 RR)
% Number of literals : 35 ( 7 equ; 17 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 31 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_times_b_is_identity,hypothesis,
product(a,b,identity) ).
cnf(c_times_a_is_identity,hypothesis,
product(c,a,identity) ).
cnf(prove_b_equals_c,negated_conjecture,
b != c ).
cnf(left_identity,axiom,
product(identity,X0,X0) ).
cnf(right_identity,axiom,
product(X0,identity,X0) ).
cnf(total_function2,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(associativity1,axiom,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
product(a,b,identity),
inference(clausification,[status(esa)],[a_times_b_is_identity]) ).
cnf(c3,plain,
product(c,a,identity),
inference(clausification,[status(esa)],[c_times_a_is_identity]) ).
cnf(c4,plain,
b != c,
inference(clausification,[status(esa)],[prove_b_equals_c]) ).
cnf(c5,plain,
product(identity,X0,X0),
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c6,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c10,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[total_function2]) ).
cnf(c11,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity1]) ).
cnf(d0,plain,
( ~ product(X0,identity,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c10,c6]) ).
cnf(d1,plain,
( ~ product(X3,X0,identity)
| product(X3,X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c11,c5]) ).
cnf(d2,plain,
( ~ product(X0,a,identity)
| product(X0,identity,b) ),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
product(c,identity,b),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
c = b,
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
b != b,
inference(demodulation,[status(thm)],[c4,d4]) ).
cnf(d6,plain,
$false,
inference(equality_resolution,[status(thm)],[d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP017-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n005.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 14:16:32 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.30/2.80 % SZS status Unsatisfiable for theBenchmark.p
% 16.30/2.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------