%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP012-3 : 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 : n014.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 07:22:05 AM UTC 2026
% Result : Unsatisfiable 53.76s 13.23s
% Output : CNFRefutation 53.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 30 ( 20 unt; 0 nHn; 12 RR)
% Number of literals : 48 ( 10 equ; 20 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_inverse_of_product_is_product_of_inverses,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)) ).
cnf(left_identity,axiom,
product(identity,X0,X0) ).
cnf(right_identity,axiom,
product(X0,identity,X0) ).
cnf(left_inverse,axiom,
product(inverse(X0),X0,identity) ).
cnf(right_inverse,axiom,
product(X0,inverse(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,
multiply(inverse(b),inverse(a)) != inverse(multiply(a,b)),
inference(clausification,[status(esa)],[prove_inverse_of_product_is_product_of_inverses]) ).
cnf(c1,plain,
product(identity,X0,X0),
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c2,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c3,plain,
product(inverse(X0),X0,identity),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c4,plain,
product(X0,inverse(X0),identity),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c5,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[total_function1]) ).
cnf(c6,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[total_function2]) ).
cnf(c7,plain,
( product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity1]) ).
cnf(d0,plain,
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[status(thm)],[c6,c5]) ).
cnf(d1,plain,
multiply(identity,X0) = X0,
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
( ~ product(X4,X2,X3)
| ~ product(X0,X1,X4)
| product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(d3,plain,
( product(X0,multiply(X1,X3),multiply(X2,X3))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
product(inverse(X0),multiply(X0,X1),multiply(identity,X1)),
inference(resolution,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
product(inverse(X1),multiply(X1,X0),X0),
inference(demodulation,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
( ~ product(X0,identity,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c6,c2]) ).
cnf(d8,plain,
( ~ product(X3,inverse(X2),X1)
| ~ product(X0,X2,X3)
| product(X0,identity,X1) ),
inference(resolution,[status(thm)],[c7,c4]) ).
cnf(d9,plain,
( product(X0,identity,multiply(X2,inverse(X1)))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d8,c5]) ).
cnf(d10,plain,
product(inverse(X0),identity,multiply(X1,inverse(multiply(X0,X1)))),
inference(resolution,[status(thm)],[d5,d9]) ).
cnf(d11,plain,
inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(resolution,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP012-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.44 % Computer : n014.cluster.edu
% 0.18/5.44 % Model : x86_64 x86_64
% 0.18/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.44 % Memory : 8046.5625MB
% 0.18/5.44 % OS : Linux 6.8.0-71-generic
% 0.18/5.44 % CPULimit : 300
% 0.18/5.44 % WCLimit : 300
% 0.18/5.44 % DateTime : Fri Sep 25 14:16:23 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 53.76/13.23 % SZS status Unsatisfiable for theBenchmark.p
% 53.76/13.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------