%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP488-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 07:23:52 AM UTC 2026
% Result : Unsatisfiable 34.26s 6.54s
% Output : CNFRefutation 34.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 5
% Syntax : Number of clauses : 91 ( 91 unt; 0 nHn; 17 RR)
% Number of literals : 91 ( 90 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 147 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'(X0,'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,identity),'double$udivide'(X1,X2))),X1),identity)) = X2 ).
cnf(multiply,axiom,
multiply(X0,X1) = 'double$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'(X0,'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,identity),'double$udivide'(X1,X2))),X1),identity)) = X2,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
'double$udivide'('double$udivide'(X0,X1),identity) = multiply(X1,X0),
inference(clausification,[status(esa)],[multiply]) ).
cnf(c2,plain,
'double$udivide'(X0,identity) = inverse(X0),
inference(clausification,[status(esa)],[inverse]) ).
cnf(c3,plain,
'double$udivide'(X0,inverse(X0)) = identity,
inference(clausification,[status(esa)],[identity]) ).
cnf(c4,plain,
multiply(identity,a2) != a2,
inference(clausification,[status(esa)],[prove_these_axioms_2]) ).
cnf(d0,plain,
inverse('double$udivide'(X0,X1)) = multiply(X1,X0),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
inverse(inverse(X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d2,plain,
inverse(multiply(identity,X0)) = multiply(identity,inverse(X0)),
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
inverse(multiply(X1,X0)) = multiply(identity,'double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[d0,d1]) ).
cnf(d4,plain,
'double$udivide'(X0,inverse('double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,identity),'double$udivide'(X1,X2))),X1))) = X2,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d5,plain,
'double$udivide'(X0,inverse('double$udivide'('double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(X1,X2))),X1))) = X2,
inference(demodulation,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
'double$udivide'(X0,multiply(X1,'double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(X1,X2))))) = X2,
inference(demodulation,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
'double$udivide'(X3,'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X3,identity),X2)),X0),identity)) = 'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,identity),'double$udivide'(X1,X2))),X1),identity),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d8,plain,
'double$udivide'(X0,inverse('double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,identity),X1)),X2))) = 'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X2,identity),'double$udivide'(X3,X1))),X3),identity),
inference(demodulation,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
'double$udivide'(X0,multiply(X2,'double$udivide'(identity,'double$udivide'('double$udivide'(X0,identity),X1)))) = 'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X2,identity),'double$udivide'(X3,X1))),X3),identity),
inference(demodulation,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
'double$udivide'(X0,multiply(X1,'double$udivide'(identity,'double$udivide'(inverse(X0),X2)))) = 'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X1,identity),'double$udivide'(X3,X2))),X3),identity),
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
'double$udivide'(X3,multiply(X0,'double$udivide'(identity,'double$udivide'(inverse(X3),X2)))) = inverse('double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,identity),'double$udivide'(X1,X2))),X1)),
inference(demodulation,[status(thm)],[d10,c2]) ).
cnf(d12,plain,
'double$udivide'(X3,multiply(X0,'double$udivide'(identity,'double$udivide'(inverse(X3),X2)))) = multiply(X1,'double$udivide'(identity,'double$udivide'('double$udivide'(X0,identity),'double$udivide'(X1,X2)))),
inference(demodulation,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
'double$udivide'(X1,multiply(X0,'double$udivide'(identity,'double$udivide'(inverse(X1),X2)))) = multiply(X3,'double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(X3,X2)))),
inference(demodulation,[status(thm)],[d12,c2]) ).
cnf(d14,plain,
'double$udivide'(X0,multiply(X1,'double$udivide'(identity,identity))) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X2,inverse(inverse(X0)))))),
inference(superposition,[status(thm)],[c3,d13]) ).
cnf(d15,plain,
'double$udivide'(X0,multiply(X1,inverse(identity))) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X2,inverse(inverse(X0)))))),
inference(demodulation,[status(thm)],[d14,c2]) ).
cnf(d16,plain,
'double$udivide'(X0,multiply(X1,inverse(identity))) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X2,multiply(identity,X0))))),
inference(demodulation,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
'double$udivide'(X1,'double$udivide'(X2,multiply(X1,inverse(identity)))) = multiply(identity,X2),
inference(superposition,[status(thm)],[d16,d6]) ).
cnf(d18,plain,
'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0)) = identity,
inference(superposition,[status(thm)],[d0,c3]) ).
cnf(d19,plain,
'double$udivide'(X0,identity) = multiply(identity,'double$udivide'(inverse(identity),X0)),
inference(superposition,[status(thm)],[d18,d17]) ).
cnf(d20,plain,
inverse(X0) = multiply(identity,'double$udivide'(inverse(identity),X0)),
inference(demodulation,[status(thm)],[d19,c2]) ).
cnf(d21,plain,
inverse(X0) = inverse(multiply(X0,inverse(identity))),
inference(demodulation,[status(thm)],[d20,d3]) ).
cnf(d22,plain,
inverse(identity) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d23,plain,
inverse(inverse(inverse(identity))) = inverse(inverse(identity)),
inference(superposition,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
multiply(identity,inverse(identity)) = inverse(inverse(identity)),
inference(demodulation,[status(thm)],[d23,d1]) ).
cnf(d25,plain,
multiply(identity,inverse(identity)) = multiply(identity,identity),
inference(demodulation,[status(thm)],[d24,d1]) ).
cnf(d26,plain,
inverse(identity) = inverse(multiply(identity,identity)),
inference(superposition,[status(thm)],[d25,d21]) ).
cnf(d27,plain,
inverse(identity) = multiply(identity,inverse(identity)),
inference(demodulation,[status(thm)],[d26,d2]) ).
cnf(d28,plain,
inverse(identity) = multiply(identity,identity),
inference(demodulation,[status(thm)],[d25,d27]) ).
cnf(d29,plain,
inverse(identity) = multiply(multiply(identity,X0),inverse(X0)),
inference(superposition,[status(thm)],[d1,d22]) ).
cnf(d30,plain,
inverse(identity) = multiply(inverse(identity),inverse(identity)),
inference(superposition,[status(thm)],[d28,d29]) ).
cnf(d31,plain,
'double$udivide'(inverse(identity),'double$udivide'(X0,inverse(identity))) = multiply(identity,X0),
inference(superposition,[status(thm)],[d30,d17]) ).
cnf(d32,plain,
'double$udivide'(identity,multiply(X0,'double$udivide'(identity,multiply(identity,X0)))) = inverse(identity),
inference(superposition,[status(thm)],[d31,d6]) ).
cnf(d33,plain,
'double$udivide'(identity,inverse(multiply(multiply(identity,identity),identity))) = inverse(identity),
inference(superposition,[status(thm)],[d3,d32]) ).
cnf(d34,plain,
'double$udivide'(identity,inverse(multiply(inverse(identity),identity))) = inverse(identity),
inference(demodulation,[status(thm)],[d33,d28]) ).
cnf(d35,plain,
'double$udivide'(identity,inverse(inverse(identity))) = inverse(identity),
inference(demodulation,[status(thm)],[d34,d22]) ).
cnf(d36,plain,
'double$udivide'(identity,multiply(identity,identity)) = inverse(identity),
inference(demodulation,[status(thm)],[d35,d1]) ).
cnf(d37,plain,
'double$udivide'(identity,inverse(identity)) = inverse(identity),
inference(demodulation,[status(thm)],[d36,d28]) ).
cnf(d38,plain,
identity = inverse(identity),
inference(demodulation,[status(thm)],[d37,c3]) ).
cnf(d39,plain,
inverse(X0) = inverse(multiply(X0,identity)),
inference(demodulation,[status(thm)],[d21,d38]) ).
cnf(d40,plain,
'double$udivide'(X0,inverse(multiply('double$udivide'(inverse(X0),'double$udivide'(identity,X1)),identity))) = X1,
inference(superposition,[status(thm)],[d3,d6]) ).
cnf(d41,plain,
'double$udivide'(X0,inverse('double$udivide'(inverse(X0),'double$udivide'(identity,X1)))) = X1,
inference(demodulation,[status(thm)],[d40,d39]) ).
cnf(d42,plain,
'double$udivide'(X0,multiply('double$udivide'(identity,X1),inverse(X0))) = X1,
inference(demodulation,[status(thm)],[d41,d0]) ).
cnf(d43,plain,
'double$udivide'(identity,'double$udivide'(X0,inverse(identity))) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d31,d38]) ).
cnf(d44,plain,
'double$udivide'(identity,'double$udivide'(X0,identity)) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d43,d38]) ).
cnf(d45,plain,
'double$udivide'(identity,inverse(X0)) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d44,c2]) ).
cnf(d46,plain,
'double$udivide'(X2,multiply(X0,'double$udivide'(identity,'double$udivide'(inverse(X2),X1)))) = inverse(multiply('double$udivide'(inverse(X0),'double$udivide'(identity,X1)),identity)),
inference(superposition,[status(thm)],[d3,d13]) ).
cnf(d47,plain,
'double$udivide'(X2,multiply(X0,'double$udivide'(identity,'double$udivide'(inverse(X2),X1)))) = inverse('double$udivide'(inverse(X0),'double$udivide'(identity,X1))),
inference(demodulation,[status(thm)],[d46,d39]) ).
cnf(d48,plain,
'double$udivide'(X2,multiply(X0,'double$udivide'(identity,'double$udivide'(inverse(X2),X1)))) = multiply('double$udivide'(identity,X1),inverse(X0)),
inference(demodulation,[status(thm)],[d47,d0]) ).
cnf(d49,plain,
multiply(X3,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X3,X2)))) = multiply(X4,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X4,X2)))),
inference(superposition,[status(thm)],[d13,d13]) ).
cnf(d50,plain,
'double$udivide'(X4,multiply(X1,'double$udivide'(identity,'double$udivide'(inverse(X4),X2)))) = multiply(X3,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X3,X2)))),
inference(superposition,[status(thm)],[d49,d13]) ).
cnf(d51,plain,
multiply('double$udivide'(identity,X2),inverse(X1)) = multiply(X3,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X3,X2)))),
inference(demodulation,[status(thm)],[d50,d48]) ).
cnf(d52,plain,
'double$udivide'(X1,multiply(X3,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X3,X2))))) = X2,
inference(superposition,[status(thm)],[d49,d6]) ).
cnf(d53,plain,
multiply('double$udivide'(identity,'double$udivide'(X1,X2)),inverse(X1)) = X2,
inference(demodulation,[status(thm)],[d52,d48]) ).
cnf(d54,plain,
multiply('double$udivide'(identity,identity),inverse(X0)) = inverse(X0),
inference(superposition,[status(thm)],[c3,d53]) ).
cnf(d55,plain,
multiply(inverse(identity),inverse(X0)) = inverse(X0),
inference(demodulation,[status(thm)],[d54,c2]) ).
cnf(d56,plain,
multiply(identity,inverse(X0)) = inverse(X0),
inference(demodulation,[status(thm)],[d55,d38]) ).
cnf(d57,plain,
multiply(X0,'double$udivide'(identity,'double$udivide'(inverse(X1),identity))) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X1),'double$udivide'(X2,inverse(X0))))),
inference(superposition,[status(thm)],[c3,d49]) ).
cnf(d58,plain,
multiply(X1,'double$udivide'(identity,inverse(inverse(X0)))) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(X2,inverse(X1))))),
inference(demodulation,[status(thm)],[d57,c2]) ).
cnf(d59,plain,
multiply(X1,multiply(identity,inverse(X0))) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(X2,inverse(X1))))),
inference(demodulation,[status(thm)],[d58,d45]) ).
cnf(d60,plain,
multiply(X1,inverse(X0)) = multiply(X2,'double$udivide'(identity,'double$udivide'(inverse(X0),'double$udivide'(X2,inverse(X1))))),
inference(demodulation,[status(thm)],[d59,d56]) ).
cnf(d61,plain,
multiply(X2,inverse(X1)) = multiply('double$udivide'(identity,inverse(X2)),inverse(X1)),
inference(demodulation,[status(thm)],[d60,d51]) ).
cnf(d62,plain,
multiply(X0,inverse(X1)) = multiply(multiply(identity,X0),inverse(X1)),
inference(demodulation,[status(thm)],[d61,d45]) ).
cnf(d63,plain,
identity = multiply(inverse(X0),X0),
inference(demodulation,[status(thm)],[d22,d38]) ).
cnf(d64,plain,
'double$udivide'('double$udivide'(X0,inverse(X0)),identity) = identity,
inference(superposition,[status(thm)],[d63,d18]) ).
cnf(d65,plain,
inverse('double$udivide'(X0,inverse(X0))) = identity,
inference(demodulation,[status(thm)],[d64,c2]) ).
cnf(d66,plain,
multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[d65,d0]) ).
cnf(d67,plain,
multiply(multiply(identity,X0),inverse(X0)) = identity,
inference(superposition,[status(thm)],[d1,d66]) ).
cnf(d68,plain,
multiply(X0,inverse(X0)) = identity,
inference(demodulation,[status(thm)],[d67,d62]) ).
cnf(d69,plain,
'double$udivide'('double$udivide'(identity,X0),identity) = X0,
inference(superposition,[status(thm)],[d68,d42]) ).
cnf(d70,plain,
inverse('double$udivide'(identity,X0)) = X0,
inference(demodulation,[status(thm)],[d69,c2]) ).
cnf(d71,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[d70,d0]) ).
cnf(d72,plain,
'double$udivide'(identity,multiply('double$udivide'(identity,X0),identity)) = X0,
inference(superposition,[status(thm)],[d38,d42]) ).
cnf(d73,plain,
'double$udivide'(identity,'double$udivide'(identity,X0)) = X0,
inference(demodulation,[status(thm)],[d72,d71]) ).
cnf(d74,plain,
inverse(X0) = multiply('double$udivide'(identity,X0),identity),
inference(superposition,[status(thm)],[d73,d0]) ).
cnf(d75,plain,
inverse(X0) = 'double$udivide'(identity,X0),
inference(demodulation,[status(thm)],[d74,d71]) ).
cnf(d76,plain,
inverse('double$udivide'(identity,X0)) = X0,
inference(demodulation,[status(thm)],[d73,d75]) ).
cnf(d77,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d76,d75]) ).
cnf(d78,plain,
X0 = multiply(identity,X0),
inference(demodulation,[status(thm)],[d1,d77]) ).
cnf(d79,plain,
a2 != a2,
inference(demodulation,[status(thm)],[c4,d78]) ).
cnf(d80,plain,
$false,
inference(equality_resolution,[status(thm)],[d79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP488-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n017.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 14:51:47 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.26/6.54 % SZS status Unsatisfiable for theBenchmark.p
% 34.26/6.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------