%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP045-2 : 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 : n009.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 07:22:12 AM UTC 2026
% Result : Unsatisfiable 14.17s 2.25s
% Output : CNFRefutation 14.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 38 ( 19 unt; 0 nHn; 26 RR)
% Number of literals : 70 ( 0 equ; 35 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_equals_b,hypothesis,
equalish(a,b) ).
cnf(product_with_a,hypothesis,
product(c,a,result) ).
cnf(prove_product_with_b,negated_conjecture,
~ product(c,b,result) ).
cnf(left_identity,axiom,
product(identity,X0,X0) ).
cnf(left_inverse,axiom,
product(inverse(X0),X0,identity) ).
cnf(total_function1,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(total_function2,axiom,
( equalish(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(product_substitution3,axiom,
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ) ).
cnf(c0,plain,
equalish(a,b),
inference(clausification,[status(esa)],[a_equals_b]) ).
cnf(c1,plain,
product(c,a,result),
inference(clausification,[status(esa)],[product_with_a]) ).
cnf(c2,plain,
~ product(c,b,result),
inference(clausification,[status(esa)],[prove_product_with_b]) ).
cnf(c3,plain,
product(identity,X0,X0),
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c4,plain,
product(inverse(X0),X0,identity),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c5,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[total_function1]) ).
cnf(c6,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[total_function2]) ).
cnf(c7,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity1]) ).
cnf(c9,plain,
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[product_substitution3]) ).
cnf(d0,plain,
( ~ product(X2,X0,c)
| product(X2,X1,result)
| ~ product(X0,a,X1) ),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d1,plain,
( product(identity,X0,X1)
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[c9,c3]) ).
cnf(d2,plain,
( ~ product(X1,identity,c)
| product(X1,X0,result)
| ~ equalish(a,X0) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ product(X3,X0,identity)
| product(X3,X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c7,c3]) ).
cnf(d4,plain,
( ~ product(X0,inverse(X1),identity)
| product(X0,identity,X1) ),
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
( product(X0,X1,X2)
| ~ equalish(multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[c9,c5]) ).
cnf(d6,plain,
( ~ product(identity,X0,X2)
| equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[d1,c6]) ).
cnf(d7,plain,
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[d6,c3]) ).
cnf(d8,plain,
product(inverse(inverse(X0)),identity,X0),
inference(resolution,[status(thm)],[d4,c4]) ).
cnf(d9,plain,
( ~ product(inverse(X1),X1,X0)
| equalish(identity,X0) ),
inference(resolution,[status(thm)],[c6,c4]) ).
cnf(d10,plain,
( ~ product(X3,X0,X4)
| product(X3,X2,multiply(X4,X1))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(d11,plain,
( ~ product(X0,identity,X2)
| product(X0,X1,multiply(X2,X1)) ),
inference(resolution,[status(thm)],[d10,c3]) ).
cnf(d12,plain,
( equalish(identity,multiply(X1,X0))
| ~ product(inverse(X0),identity,X1) ),
inference(resolution,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
equalish(identity,multiply(X0,inverse(X0))),
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
equalish(multiply(X0,inverse(X0)),identity),
inference(resolution,[status(thm)],[d13,d7]) ).
cnf(d15,plain,
product(X0,inverse(X0),identity),
inference(resolution,[status(thm)],[d14,d5]) ).
cnf(d16,plain,
product(X0,identity,X0),
inference(resolution,[status(thm)],[d15,d4]) ).
cnf(d17,plain,
( product(c,X0,result)
| ~ equalish(a,X0) ),
inference(resolution,[status(thm)],[d16,d2]) ).
cnf(d18,plain,
~ equalish(a,b),
inference(resolution,[status(thm)],[d17,c2]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[c0,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP045-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:19:29 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.17/2.25 % SZS status Unsatisfiable for theBenchmark.p
% 14.17/2.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------