%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP497-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 07:23:53 AM UTC 2026
% Result : Unsatisfiable 19.99s 7.85s
% Output : CNFRefutation 19.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of clauses : 61 ( 61 unt; 0 nHn; 5 RR)
% Number of literals : 61 ( 60 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 131 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'('double$udivide'(identity,'double$udivide'(X0,'double$udivide'(X1,identity))),'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),identity)) = X2 ).
cnf(multiply,axiom,
multiply(X0,X1) = 'double$udivide'('double$udivide'(X1,X0),identity) ).
cnf(inverse,axiom,
inverse(X0) = 'double$udivide'(X0,identity) ).
cnf(identity,axiom,
identity = 'double$udivide'(X0,inverse(X0)) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(identity,a2) != a2 ).
cnf(c0,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X0,'double$udivide'(X1,identity))),'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),identity)) = X2,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(X0,X1) = 'double$udivide'('double$udivide'(X1,X0),identity),
inference(clausification,[status(esa)],[multiply]) ).
cnf(c2,plain,
inverse(X0) = 'double$udivide'(X0,identity),
inference(clausification,[status(esa)],[inverse]) ).
cnf(c3,plain,
identity = 'double$udivide'(X0,inverse(X0)),
inference(clausification,[status(esa)],[identity]) ).
cnf(c4,plain,
multiply(identity,a2) != a2,
inference(clausification,[status(esa)],[prove_these_axioms_2]) ).
cnf(d0,plain,
multiply(X1,X0) = inverse('double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d2,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(X0))),'double$udivide'('double$udivide'(X0,'double$udivide'(X2,X1)),identity)) = X2,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d3,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X2,inverse(X0))),inverse('double$udivide'(X0,'double$udivide'(X1,X2)))) = X1,
inference(demodulation,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X2,inverse(X0))),multiply('double$udivide'(X1,X2),X0)) = X1,
inference(demodulation,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
identity = 'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0)),
inference(superposition,[status(thm)],[d0,c3]) ).
cnf(d6,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d8,plain,
multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[d6,d8]) ).
cnf(d10,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(X0,'double$udivide'(X1,identity))),identity))),'double$udivide'(X2,identity)) = 'double$udivide'(X1,'double$udivide'(X2,X0)),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d11,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse('double$udivide'(identity,'double$udivide'(X0,'double$udivide'(X1,identity)))))),'double$udivide'(X2,identity)) = 'double$udivide'(X1,'double$udivide'(X2,X0)),
inference(demodulation,[status(thm)],[d10,c2]) ).
cnf(d12,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,multiply('double$udivide'(X0,'double$udivide'(X1,identity)),identity))),'double$udivide'(X2,identity)) = 'double$udivide'(X1,'double$udivide'(X2,X0)),
inference(demodulation,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,multiply('double$udivide'(X1,inverse(X0)),identity))),'double$udivide'(X2,identity)) = 'double$udivide'(X0,'double$udivide'(X2,X1)),
inference(demodulation,[status(thm)],[d12,c2]) ).
cnf(d14,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,multiply('double$udivide'(X1,inverse(X2)),identity))),inverse(X0)) = 'double$udivide'(X2,'double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[d13,c2]) ).
cnf(d15,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,multiply(identity,identity))),inverse(X1)) = 'double$udivide'(X0,'double$udivide'(X1,X0)),
inference(superposition,[status(thm)],[c3,d14]) ).
cnf(d16,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,identity)),inverse(X0)) = 'double$udivide'(X1,'double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[d15,d9]) ).
cnf(d17,plain,
'double$udivide'('double$udivide'(identity,inverse(identity)),inverse(X0)) = 'double$udivide'(X1,'double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[d16,c2]) ).
cnf(d18,plain,
'double$udivide'(identity,inverse(X0)) = 'double$udivide'(X1,'double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[d17,c3]) ).
cnf(d19,plain,
'double$udivide'(identity,inverse(X0)) = 'double$udivide'(inverse(X0),identity),
inference(superposition,[status(thm)],[c3,d18]) ).
cnf(d20,plain,
'double$udivide'(identity,inverse(X0)) = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d19,c2]) ).
cnf(d21,plain,
'double$udivide'(identity,inverse(X0)) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d20,d1]) ).
cnf(d22,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),identity),'double$udivide'(X3,identity))),'double$udivide'('double$udivide'(X3,X2),identity)) = 'double$udivide'(identity,'double$udivide'(X0,'double$udivide'(X1,identity))),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d23,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(inverse('double$udivide'(X0,'double$udivide'(X1,X2))),'double$udivide'(X3,identity))),'double$udivide'('double$udivide'(X3,X1),identity)) = 'double$udivide'(identity,'double$udivide'(X2,'double$udivide'(X0,identity))),
inference(demodulation,[status(thm)],[d22,c2]) ).
cnf(d24,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(multiply('double$udivide'(X1,X2),X0),'double$udivide'(X3,identity))),'double$udivide'('double$udivide'(X3,X1),identity)) = 'double$udivide'(identity,'double$udivide'(X2,'double$udivide'(X0,identity))),
inference(demodulation,[status(thm)],[d23,d0]) ).
cnf(d25,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(multiply('double$udivide'(X1,X2),X3),inverse(X0))),'double$udivide'('double$udivide'(X0,X1),identity)) = 'double$udivide'(identity,'double$udivide'(X2,'double$udivide'(X3,identity))),
inference(demodulation,[status(thm)],[d24,c2]) ).
cnf(d26,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(multiply('double$udivide'(X1,X2),X3),inverse(X0))),inverse('double$udivide'(X0,X1))) = 'double$udivide'(identity,'double$udivide'(X2,'double$udivide'(X3,identity))),
inference(demodulation,[status(thm)],[d25,c2]) ).
cnf(d27,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(multiply('double$udivide'(X1,X2),X3),inverse(X0))),multiply(X1,X0)) = 'double$udivide'(identity,'double$udivide'(X2,'double$udivide'(X3,identity))),
inference(demodulation,[status(thm)],[d26,d0]) ).
cnf(d28,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(multiply('double$udivide'(X1,X2),X0),inverse(X3))),multiply(X1,X3)) = 'double$udivide'(identity,'double$udivide'(X2,inverse(X0))),
inference(demodulation,[status(thm)],[d27,c2]) ).
cnf(d29,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(multiply(identity,X1),inverse(X2))),multiply(X0,X2)) = 'double$udivide'(identity,'double$udivide'(inverse(X0),inverse(X1))),
inference(superposition,[status(thm)],[c3,d28]) ).
cnf(d30,plain,
identity = 'double$udivide'(inverse(X0),multiply(identity,X0)),
inference(superposition,[status(thm)],[d1,c3]) ).
cnf(d31,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(multiply(identity,X0),inverse(X1))),multiply(identity,X1)) = inverse(X0),
inference(superposition,[status(thm)],[d30,d4]) ).
cnf(d32,plain,
'double$udivide'(identity,'double$udivide'(inverse(identity),inverse(X0))) = inverse(X0),
inference(demodulation,[status(thm)],[d31,d29]) ).
cnf(d33,plain,
'double$udivide'(identity,'double$udivide'(identity,inverse(X0))) = inverse(X0),
inference(demodulation,[status(thm)],[d32,d6]) ).
cnf(d34,plain,
'double$udivide'(identity,multiply(identity,X0)) = inverse(X0),
inference(demodulation,[status(thm)],[d33,d21]) ).
cnf(d35,plain,
'double$udivide'('double$udivide'(identity,X2),'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),'double$udivide'(X3,'double$udivide'(identity,'double$udivide'(X0,'double$udivide'(X1,identity))))),identity)) = X3,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d36,plain,
'double$udivide'('double$udivide'(identity,X1),inverse('double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),'double$udivide'(X3,'double$udivide'(identity,'double$udivide'(X2,'double$udivide'(X0,identity))))))) = X3,
inference(demodulation,[status(thm)],[d35,c2]) ).
cnf(d37,plain,
'double$udivide'('double$udivide'(identity,X1),multiply('double$udivide'(X3,'double$udivide'(identity,'double$udivide'(X2,'double$udivide'(X0,identity)))),'double$udivide'(X0,'double$udivide'(X1,X2)))) = X3,
inference(demodulation,[status(thm)],[d36,d0]) ).
cnf(d38,plain,
'double$udivide'('double$udivide'(identity,X1),multiply('double$udivide'(X2,'double$udivide'(identity,'double$udivide'(X3,inverse(X0)))),'double$udivide'(X0,'double$udivide'(X1,X3)))) = X2,
inference(demodulation,[status(thm)],[d37,c2]) ).
cnf(d39,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(multiply('double$udivide'(X1,'double$udivide'(identity,'double$udivide'(X2,inverse(X3)))),'double$udivide'(X3,'double$udivide'(X0,X2))),inverse(X4))),multiply(X1,X4)) = 'double$udivide'(identity,X0),
inference(superposition,[status(thm)],[d38,d4]) ).
cnf(d40,plain,
'double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(X2))),inverse('double$udivide'(X2,'double$udivide'(X3,X1))))) = 'double$udivide'(identity,X3),
inference(demodulation,[status(thm)],[d39,d28]) ).
cnf(d41,plain,
'double$udivide'(identity,'double$udivide'('double$udivide'(identity,'double$udivide'(X2,inverse(X0))),multiply('double$udivide'(X1,X2),X0))) = 'double$udivide'(identity,X1),
inference(demodulation,[status(thm)],[d40,d0]) ).
cnf(d42,plain,
'double$udivide'(identity,X2) = 'double$udivide'(identity,X2),
inference(demodulation,[status(thm)],[d41,d4]) ).
cnf(d43,plain,
'double$udivide'('double$udivide'(identity,identity),multiply('double$udivide'(X1,X0),X0)) = X1,
inference(superposition,[status(thm)],[c3,d4]) ).
cnf(d44,plain,
'double$udivide'(inverse(identity),multiply('double$udivide'(X0,X1),X1)) = X0,
inference(demodulation,[status(thm)],[d43,c2]) ).
cnf(d45,plain,
'double$udivide'(identity,multiply('double$udivide'(X0,X1),X1)) = X0,
inference(demodulation,[status(thm)],[d44,d6]) ).
cnf(d46,plain,
'double$udivide'(identity,multiply(identity,inverse(X0))) = X0,
inference(superposition,[status(thm)],[c3,d45]) ).
cnf(d47,plain,
X0 = 'double$udivide'(identity,multiply(identity,inverse(X0))),
inference(superposition,[status(thm)],[d46,d42]) ).
cnf(d48,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d47,d34]) ).
cnf(d49,plain,
multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[d1,d48]) ).
cnf(d50,plain,
$false,
inference(resolution,[status(thm)],[d49,c4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP497-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n018.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 14:59:42 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.99/7.85 % SZS status Unsatisfiable for theBenchmark.p
% 19.99/7.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------