%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP566-1 : 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 : 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 07:24:02 AM UTC 2026
% Result : Unsatisfiable 12.59s 3.42s
% Output : CNFRefutation 12.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 7 RR)
% Number of literals : 36 ( 35 equ; 2 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 : 54 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),'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$udivide'(identity,X2))),'double$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'(identity,X2))),
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$udivide'(identity,X2))),
inference(demodulation,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(X0,inverse(identity))),inverse(identity)) = 'double$udivide'(X1,'double$udivide'('double$udivide'(X0,'double$udivide'(X1,X2)),'double$udivide'(identity,X2))),
inference(demodulation,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d4,plain,
'double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
multiply(X1,X0) = inverse('double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d6,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X0,X2)),'double$udivide'(identity,X2))),'double$udivide'('double$udivide'(X3,X1),'double$udivide'(identity,'double$udivide'(identity,identity)))),'double$udivide'(identity,identity)) = X3,
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d7,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'(identity,'double$udivide'(identity,identity)))),'double$udivide'(identity,identity)) = X3,
inference(demodulation,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X0,inverse(identity))),inverse(identity)),'double$udivide'('double$udivide'(X1,X0),'double$udivide'(identity,inverse(identity)))),'double$udivide'(identity,identity)) = X1,
inference(demodulation,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X0,inverse(identity))),inverse(identity)),'double$udivide'('double$udivide'(X1,X0),identity)),'double$udivide'(identity,identity)) = X1,
inference(demodulation,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)),inverse('double$udivide'(X0,X1))),'double$udivide'(identity,identity)) = X0,
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X1,inverse(identity))),inverse(identity)),multiply(X1,X0)),'double$udivide'(identity,identity)) = X0,
inference(demodulation,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(X0,inverse(identity))),inverse(identity)),multiply(X0,X1)),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[status(thm)],[c3,d5]) ).
cnf(d14,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'(identity,'double$udivide'(inverse(X0),inverse(identity))),inverse(identity)),inverse(identity)),inverse(identity)) = X0,
inference(superposition,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
'double$udivide'(inverse(X0),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d14,d4]) ).
cnf(d16,plain,
identity = 'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0)),
inference(superposition,[status(thm)],[d5,c3]) ).
cnf(d17,plain,
'double$udivide'(identity,inverse(identity)) = 'double$udivide'(identity,'double$udivide'(inverse(identity),inverse(identity))),
inference(superposition,[status(thm)],[d16,d12]) ).
cnf(d18,plain,
identity = 'double$udivide'(identity,'double$udivide'(inverse(identity),inverse(identity))),
inference(demodulation,[status(thm)],[d17,c3]) ).
cnf(d19,plain,
identity = 'double$udivide'(identity,identity),
inference(demodulation,[status(thm)],[d18,d15]) ).
cnf(d20,plain,
identity = inverse(identity),
inference(demodulation,[status(thm)],[d19,c2]) ).
cnf(d21,plain,
'double$udivide'(inverse(X0),identity) = X0,
inference(demodulation,[status(thm)],[d15,d20]) ).
cnf(d22,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d21,c2]) ).
cnf(d23,plain,
multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c2,d5]) ).
cnf(d24,plain,
multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
$false,
inference(resolution,[status(thm)],[d24,c4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP566-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 15:06:10 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.59/3.42 % SZS status Unsatisfiable for theBenchmark.p
% 12.59/3.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------