%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP031-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 07:22:09 AM UTC 2026
% Result : Unsatisfiable 11.88s 3.15s
% Output : CNFRefutation 11.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 27 ( 16 unt; 0 nHn; 12 RR)
% Number of literals : 46 ( 9 equ; 21 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,hypothesis,
product(identity,X0,X0) ).
cnf(left_inverse,hypothesis,
product(inverse(X0),X0,identity) ).
cnf(prove_a_has_an_inverse,negated_conjecture,
~ product(a,X0,identity) ).
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(a,X0,identity),
inference(clausification,[status(esa)],[prove_a_has_an_inverse]) ).
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(inverse(X1),X1,X0)
| X0 = identity ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(d1,plain,
( ~ product(X3,X1,X2)
| ~ product(X0,identity,X3)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(d2,plain,
( product(X0,X1,X2)
| ~ product(multiply(X0,identity),X1,X2) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
product(X0,X1,multiply(multiply(X0,identity),X1)),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
multiply(multiply(inverse(X0),identity),X0) = identity,
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
product(multiply(inverse(X0),identity),X0,identity),
inference(superposition,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
( ~ product(X1,X2,X0)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[c4,c3]) ).
cnf(d7,plain,
( ~ product(X4,X2,X3)
| ~ product(X0,X1,X4)
| product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(d8,plain,
( product(inverse(X2),multiply(X2,X0),X1)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
( X1 = multiply(inverse(X2),multiply(X2,X0))
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(resolution,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
identity = multiply(inverse(X0),X0),
inference(resolution,[status(thm)],[d6,c1]) ).
cnf(d12,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
product(X0,inverse(X0),identity),
inference(superposition,[status(thm)],[d12,d5]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP031-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n016.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 14:23:13 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.88/3.15 % SZS status Unsatisfiable for theBenchmark.p
% 11.88/3.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------