%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP573-1 : 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 : n006.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 12.79s 7.13s
% Output : CNFRefutation 12.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 14 RR)
% Number of literals : 37 ( 36 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 38 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),'double$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$udivide'(X0,inverse(X0)) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != identity ).
cnf(c0,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),'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(inverse(a1),a1) != identity,
inference(clausification,[status(esa)],[prove_these_axioms_1]) ).
cnf(d0,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'(X2,'double$udivide'(X0,X1)),inverse(X0))),'double$udivide'(identity,identity)) = X2,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d1,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'(X1,'double$udivide'(X2,X0)),inverse(X2))),inverse(identity)) = X1,
inference(demodulation,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(X1,inverse(X0)),inverse(X0))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[c2,d1]) ).
cnf(d3,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(X0))),inverse(identity)) = X0,
inference(superposition,[status(thm)],[c3,d2]) ).
cnf(d4,plain,
'double$udivide'('double$udivide'(identity,identity),inverse(identity)) = identity,
inference(superposition,[status(thm)],[c3,d3]) ).
cnf(d5,plain,
'double$udivide'(inverse(identity),inverse(identity)) = identity,
inference(demodulation,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
'double$udivide'('double$udivide'(inverse(X0),X0),inverse(identity)) = identity,
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d7,plain,
'double$udivide'('double$udivide'(identity,identity),inverse(identity)) = inverse(inverse(identity)),
inference(superposition,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
'double$udivide'(inverse(identity),inverse(identity)) = inverse(inverse(identity)),
inference(demodulation,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
identity = inverse(inverse(identity)),
inference(demodulation,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
'double$udivide'('double$udivide'(inverse(X0),'double$udivide'('double$udivide'(X1,identity),inverse(X0))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[c3,d1]) ).
cnf(d11,plain,
'double$udivide'('double$udivide'(inverse(X1),'double$udivide'(inverse(X0),inverse(X1))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d10,c2]) ).
cnf(d12,plain,
'double$udivide'('double$udivide'(inverse(inverse(X0)),identity),inverse(identity)) = X0,
inference(superposition,[status(thm)],[c3,d11]) ).
cnf(d13,plain,
'double$udivide'(inverse(inverse(inverse(X0))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d12,c2]) ).
cnf(d14,plain,
'double$udivide'(inverse(inverse(identity)),inverse(identity)) = inverse(identity),
inference(superposition,[status(thm)],[d9,d13]) ).
cnf(d15,plain,
'double$udivide'(identity,inverse(identity)) = inverse(identity),
inference(demodulation,[status(thm)],[d14,d9]) ).
cnf(d16,plain,
identity = inverse(identity),
inference(demodulation,[status(thm)],[d15,c3]) ).
cnf(d17,plain,
multiply(X1,X0) = inverse('double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d18,plain,
multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[status(thm)],[c3,d17]) ).
cnf(d19,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm)],[c4,d18]) ).
cnf(d20,plain,
identity != identity,
inference(demodulation,[status(thm)],[d19,d16]) ).
cnf(d21,plain,
multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c2,d17]) ).
cnf(d22,plain,
identity = 'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0)),
inference(superposition,[status(thm)],[d17,c3]) ).
cnf(d23,plain,
identity = 'double$udivide'(inverse(X0),multiply(identity,X0)),
inference(superposition,[status(thm)],[c2,d22]) ).
cnf(d24,plain,
identity = 'double$udivide'(inverse(X0),inverse(inverse(X0))),
inference(demodulation,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
identity = identity,
inference(demodulation,[status(thm)],[d24,c3]) ).
cnf(d26,plain,
$false,
inference(resolution,[status(thm)],[d25,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP573-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.37 % Computer : n006.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.37 % CPULimit : 300
% 0.12/5.37 % WCLimit : 300
% 0.12/5.37 % DateTime : Fri Sep 25 15:00:16 UTC 2026
% 0.12/5.37 % CPUTime :
% 0.12/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.79/7.13 % SZS status Unsatisfiable for theBenchmark.p
% 12.79/7.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------