%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP029-1 : 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 : n011.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 07:22:08 AM UTC 2026
% Result : Unsatisfiable 15.74s 2.70s
% Output : CNFRefutation 15.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 37 ( 23 unt; 0 nHn; 15 RR)
% Number of literals : 60 ( 13 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X0,X0) ).
cnf(left_inverse,axiom,
product(inverse(X0),X0,identity) ).
cnf(prove_there_is_a_right_identity,negated_conjecture,
~ product('not$uright$uidentity'(X0),X0,'not$uright$uidentity'(X0)) ).
cnf(total_function1,axiom,
product(X0,X1,multiply(X0,X1)) ).
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(identity,X0,X0),
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c1,plain,
product(inverse(X0),X0,identity),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c2,plain,
~ product('not$uright$uidentity'(X0),X0,'not$uright$uidentity'(X0)),
inference(clausification,[status(esa)],[prove_there_is_a_right_identity]) ).
cnf(c3,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[total_function1]) ).
cnf(c4,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[total_function2]) ).
cnf(c5,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(identity,X1,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d1,plain,
multiply(identity,X0) = X0,
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( ~ product(X1,X2,X0)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[c4,c3]) ).
cnf(d3,plain,
( ~ product(X3,X1,X2)
| ~ product(X0,identity,X3)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(d4,plain,
( product(X0,X1,X2)
| ~ product(multiply(X0,identity),X1,X2) ),
inference(resolution,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
product(X0,X1,multiply(multiply(X0,identity),X1)),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
multiply(multiply(X0,identity),X1) = multiply(X0,X1),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( ~ product(X3,X2,X1)
| ~ product(X0,inverse(X2),X3)
| product(X0,identity,X1) ),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(d8,plain,
( product(X0,identity,X2)
| ~ product(multiply(X0,inverse(X1)),X1,X2) ),
inference(resolution,[status(thm)],[d7,c3]) ).
cnf(d9,plain,
product(X0,identity,multiply(multiply(multiply(X0,inverse(X1)),identity),X1)),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
product(X0,identity,multiply(multiply(X0,inverse(X1)),X1)),
inference(demodulation,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
( ~ product(inverse(X1),X1,X0)
| X0 = identity ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(d12,plain,
multiply(multiply(inverse(X0),identity),X0) = identity,
inference(resolution,[status(thm)],[d5,d11]) ).
cnf(d13,plain,
product(multiply(inverse(X0),identity),X0,identity),
inference(superposition,[status(thm)],[d12,c3]) ).
cnf(d14,plain,
( ~ product(X4,X2,X3)
| ~ product(X0,X1,X4)
| product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(d15,plain,
( product(inverse(X2),multiply(X2,X0),X1)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[d14,c1]) ).
cnf(d16,plain,
( X1 = multiply(inverse(X2),multiply(X2,X0))
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[d15,d2]) ).
cnf(d17,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(resolution,[status(thm)],[d16,c0]) ).
cnf(d18,plain,
identity = multiply(inverse(X0),X0),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d19,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d18,d17]) ).
cnf(d20,plain,
product(X0,inverse(X0),identity),
inference(superposition,[status(thm)],[d19,d13]) ).
cnf(d21,plain,
identity = multiply(X0,inverse(X0)),
inference(resolution,[status(thm)],[d20,d2]) ).
cnf(d22,plain,
product(X0,identity,multiply(identity,X0)),
inference(superposition,[status(thm)],[d21,d10]) ).
cnf(d23,plain,
product(X0,identity,X0),
inference(demodulation,[status(thm)],[d22,d1]) ).
cnf(d24,plain,
$false,
inference(resolution,[status(thm)],[d23,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP029-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.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 : Fri Sep 25 14:18:43 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.74/2.70 % SZS status Unsatisfiable for theBenchmark.p
% 15.74/2.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------