%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP570-1 : 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 : 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 07:24:03 AM UTC 2026
% Result : Unsatisfiable 13.77s 2.74s
% Output : CNFRefutation 13.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 6 RR)
% Number of literals : 60 ( 59 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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 : 94 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(X2,identity))),'double$udivide'(identity,identity)) = X1 ).
cnf(multiply,axiom,
multiply(X0,X1) = 'double$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$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(X2,identity))),'double$udivide'(identity,identity)) = X1,
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,
'double$udivide'('double$udivide'(identity,'double$udivide'(X1,'double$udivide'(identity,identity))),'double$udivide'(identity,identity)) = 'double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(X2,identity))),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d1,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X0,inverse(identity))),'double$udivide'(identity,identity)) = 'double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),'double$udivide'(X2,identity))),
inference(demodulation,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X0,inverse(identity))),inverse(identity)) = 'double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),'double$udivide'(X2,identity))),
inference(demodulation,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)) = 'double$udivide'(X2,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),inverse(X0))),
inference(demodulation,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,X0)),inverse(X0))),'double$udivide'(identity,identity)) = X2,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d5,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),inverse(X2))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
multiply(X1,X0) = inverse('double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d8,plain,
multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c2,d7]) ).
cnf(d9,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)) = 'double$udivide'(X0,'double$udivide'('double$udivide'(X1,identity),inverse(inverse(X0)))),
inference(superposition,[status(thm)],[c3,d3]) ).
cnf(d10,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X0,inverse(identity))),inverse(identity)) = 'double$udivide'(X1,'double$udivide'(inverse(X0),inverse(inverse(X1)))),
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)) = 'double$udivide'(X0,'double$udivide'(inverse(X1),multiply(identity,X0))),
inference(demodulation,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'(inverse(X0),multiply(identity,X1))),inverse(identity)) = X0,
inference(superposition,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
identity = 'double$udivide'(inverse(X0),multiply(identity,X0)),
inference(superposition,[status(thm)],[d8,c3]) ).
cnf(d14,plain,
'double$udivide'('double$udivide'(X0,identity),inverse(identity)) = X0,
inference(superposition,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
'double$udivide'(inverse(X0),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d14,c2]) ).
cnf(d16,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)) = 'double$udivide'(X0,'double$udivide'('double$udivide'(X1,inverse(X0)),inverse(identity))),
inference(superposition,[status(thm)],[c2,d3]) ).
cnf(d17,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X0,inverse(X1)),inverse(identity))),inverse(identity)) = X0,
inference(superposition,[status(thm)],[d16,d6]) ).
cnf(d18,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,X0),inverse(identity)),inverse(identity)) = 'double$udivide'('double$udivide'(identity,'double$udivide'(X0,inverse(identity))),inverse(identity)),
inference(superposition,[status(thm)],[d6,d6]) ).
cnf(d19,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X1,'double$udivide'('double$udivide'(X0,inverse(X1)),inverse(identity)))),inverse(identity)),inverse(identity)) = 'double$udivide'(identity,'double$udivide'(X0,inverse(identity))),
inference(superposition,[status(thm)],[d16,d6]) ).
cnf(d20,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,inverse(X0)),inverse(identity))),inverse(identity))),inverse(identity)) = 'double$udivide'(identity,'double$udivide'(X1,inverse(identity))),
inference(demodulation,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
'double$udivide'('double$udivide'(identity,X1),inverse(identity)) = 'double$udivide'(identity,'double$udivide'(X1,inverse(identity))),
inference(demodulation,[status(thm)],[d20,d17]) ).
cnf(d22,plain,
'double$udivide'('double$udivide'(identity,identity),inverse(identity)) = 'double$udivide'(X0,'double$udivide'('double$udivide'(identity,inverse(X0)),inverse(identity))),
inference(superposition,[status(thm)],[c3,d16]) ).
cnf(d23,plain,
'double$udivide'(identity,'double$udivide'(identity,inverse(identity))) = 'double$udivide'(X0,'double$udivide'('double$udivide'(identity,inverse(X0)),inverse(identity))),
inference(demodulation,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
'double$udivide'(identity,identity) = 'double$udivide'(X0,'double$udivide'('double$udivide'(identity,inverse(X0)),inverse(identity))),
inference(demodulation,[status(thm)],[d23,c3]) ).
cnf(d25,plain,
inverse(identity) = 'double$udivide'(X0,'double$udivide'('double$udivide'(identity,inverse(X0)),inverse(identity))),
inference(demodulation,[status(thm)],[d24,c2]) ).
cnf(d26,plain,
inverse(identity) = 'double$udivide'(X0,'double$udivide'(identity,'double$udivide'(inverse(X0),inverse(identity)))),
inference(demodulation,[status(thm)],[d25,d21]) ).
cnf(d27,plain,
inverse(identity) = 'double$udivide'(X0,'double$udivide'(identity,X0)),
inference(demodulation,[status(thm)],[d26,d15]) ).
cnf(d28,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(X2,identity))),'double$udivide'('double$udivide'(X3,X1),'double$udivide'('double$udivide'(identity,identity),identity))),'double$udivide'(identity,identity)) = X3,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d29,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X1,X0)),inverse(X0))),'double$udivide'('double$udivide'(X3,X2),'double$udivide'('double$udivide'(identity,identity),identity))),'double$udivide'(identity,identity)) = X3,
inference(demodulation,[status(thm)],[d28,c2]) ).
cnf(d30,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)),'double$udivide'('double$udivide'(X3,X1),'double$udivide'('double$udivide'(identity,identity),identity))),'double$udivide'(identity,identity)) = X3,
inference(demodulation,[status(thm)],[d29,d3]) ).
cnf(d31,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X0,inverse(identity))),inverse(identity)),'double$udivide'('double$udivide'(X1,X0),inverse('double$udivide'(identity,identity)))),'double$udivide'(identity,identity)) = X1,
inference(demodulation,[status(thm)],[d30,c2]) ).
cnf(d32,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X0,inverse(identity))),inverse(identity)),'double$udivide'('double$udivide'(X1,X0),multiply(identity,identity))),'double$udivide'(identity,identity)) = X1,
inference(demodulation,[status(thm)],[d31,d7]) ).
cnf(d33,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X0,inverse(identity))),inverse(identity)),'double$udivide'('double$udivide'(X1,X0),multiply(identity,identity))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d32,c2]) ).
cnf(d34,plain,
identity = 'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0)),
inference(superposition,[status(thm)],[d7,c3]) ).
cnf(d35,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(multiply(X1,X0),inverse(identity))),inverse(identity)),'double$udivide'(identity,multiply(identity,identity))),inverse(identity)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d34,d33]) ).
cnf(d36,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(multiply(identity,X0),inverse(identity))),inverse(identity)),'double$udivide'(identity,multiply(identity,identity))),inverse(identity)) = inverse(X0),
inference(superposition,[status(thm)],[d13,d33]) ).
cnf(d37,plain,
'double$udivide'(X0,identity) = inverse(X0),
inference(demodulation,[status(thm)],[d36,d35]) ).
cnf(d38,plain,
inverse(identity) = 'double$udivide'(identity,inverse(identity)),
inference(superposition,[status(thm)],[d37,d27]) ).
cnf(d39,plain,
inverse(identity) = identity,
inference(demodulation,[status(thm)],[d38,c3]) ).
cnf(d40,plain,
'double$udivide'(inverse(X0),identity) = X0,
inference(demodulation,[status(thm)],[d15,d39]) ).
cnf(d41,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d40,c2]) ).
cnf(d42,plain,
'double$udivide'(multiply(X1,X0),inverse(identity)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d7,d15]) ).
cnf(d43,plain,
multiply(identity,inverse(X0)) = inverse(multiply(identity,X0)),
inference(superposition,[status(thm)],[d8,d8]) ).
cnf(d44,plain,
'double$udivide'(multiply(identity,inverse(X0)),inverse(identity)) = multiply(identity,X0),
inference(superposition,[status(thm)],[d43,d15]) ).
cnf(d45,plain,
'double$udivide'(inverse(X0),identity) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d44,d42]) ).
cnf(d46,plain,
inverse(inverse(X0)) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d45,c2]) ).
cnf(d47,plain,
X0 = multiply(identity,X0),
inference(demodulation,[status(thm)],[d46,d41]) ).
cnf(d48,plain,
a2 != a2,
inference(demodulation,[status(thm)],[c4,d47]) ).
cnf(d49,plain,
$false,
inference(equality_resolution,[status(thm)],[d48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP570-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n014.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Fri Sep 25 15:00:33 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.77/2.74 % SZS status Unsatisfiable for theBenchmark.p
% 13.77/2.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------