%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP087-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 07:22:17 AM UTC 2026
% Result : Unsatisfiable 26.40s 3.78s
% Output : CNFRefutation 26.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of clauses : 29 ( 19 unt; 0 nHn; 12 RR)
% Number of literals : 50 ( 49 equ; 32 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X0,multiply(multiply(inverse(multiply(X0,X1)),X2),X1)) = X2 ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ) ).
cnf(c0,plain,
multiply(X0,multiply(multiply(inverse(multiply(X0,X1)),X2),X1)) = X2,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(clausification,[status(esa)],[prove_these_axioms]) ).
cnf(d0,plain,
multiply(X0,multiply(multiply(inverse(X2),X3),multiply(multiply(inverse(multiply(X0,X1)),X2),X1))) = X3,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
multiply(multiply(inverse(X0),X1),X0) = X1,
inference(superposition,[status(thm)],[c0,d0]) ).
cnf(d2,plain,
multiply(X2,X0) = multiply(multiply(inverse(multiply(inverse(X0),X1)),X2),X1),
inference(superposition,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
multiply(X0,multiply(X3,X1)) = multiply(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),X3),X2),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d4,plain,
multiply(X0,multiply(X3,X1)) = multiply(X3,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
multiply(X2,X0) = multiply(multiply(inverse(X1),X2),multiply(multiply(inverse(multiply(inverse(X0),X3)),X1),X3)),
inference(superposition,[status(thm)],[d0,d1]) ).
cnf(d6,plain,
multiply(X3,X0) = multiply(multiply(inverse(X2),X3),multiply(X2,X0)),
inference(demodulation,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
multiply(X1,X2) = multiply(X0,multiply(multiply(inverse(X0),X1),X2)),
inference(demodulation,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
multiply(X1,X0) = multiply(X0,X1),
inference(superposition,[status(thm)],[d1,d7]) ).
cnf(d9,plain,
multiply(multiply(inverse(X0),X1),multiply(multiply(inverse(X1),X2),X0)) = X2,
inference(superposition,[status(thm)],[d1,c0]) ).
cnf(d10,plain,
multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[status(thm)],[d1,d9]) ).
cnf(d11,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(resolution,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)) ),
inference(demodulation,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)) ),
inference(demodulation,[status(thm)],[d12,d4]) ).
cnf(d14,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)) ),
inference(demodulation,[status(thm)],[d13,d8]) ).
cnf(d15,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(a1,inverse(a1)) != multiply(inverse(b1),b1)
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)) ),
inference(demodulation,[status(thm)],[d14,d8]) ).
cnf(d16,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)) ),
inference(demodulation,[status(thm)],[d15,d8]) ).
cnf(d17,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)) ),
inference(demodulation,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
multiply(inverse(X0),multiply(X2,X0)) = X2,
inference(superposition,[status(thm)],[d2,c0]) ).
cnf(d19,plain,
multiply(inverse(X1),X1) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d10,d18]) ).
cnf(d20,plain,
multiply(X0,inverse(X0)) = multiply(inverse(X1),X1),
inference(demodulation,[status(thm)],[d19,d8]) ).
cnf(d21,plain,
multiply(X1,inverse(X1)) = multiply(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d20,d8]) ).
cnf(d22,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)) ),
inference(resolution,[status(thm)],[d21,d17]) ).
cnf(d23,plain,
multiply(a4,b4) != multiply(a4,b4),
inference(equality_resolution,[status(thm)],[d22]) ).
cnf(d24,plain,
$false,
inference(equality_resolution,[status(thm)],[d23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP087-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n001.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % 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 14:27:10 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.40/3.78 % SZS status Unsatisfiable for theBenchmark.p
% 26.40/3.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------