%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP481-1 : 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 : n016.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 07:23:51 AM UTC 2026
% Result : Unsatisfiable 9.79s 3.21s
% Output : CNFRefutation 9.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 10 RR)
% Number of literals : 42 ( 41 equ; 4 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 : 69 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'(X1,identity)),'double$udivide'('double$udivide'(X2,'double$udivide'(X3,'double$udivide'(X3,identity))),'double$udivide'(X0,identity))),X1) = X2 ).
cnf(multiply,axiom,
multiply(X0,X1) = 'double$udivide'('double$udivide'(X1,X0),identity) ).
cnf(inverse,axiom,
inverse(X0) = 'double$udivide'(X0,identity) ).
cnf(identity,axiom,
identity = 'double$udivide'(X0,inverse(X0)) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != identity ).
cnf(c0,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,'double$udivide'(X1,identity)),'double$udivide'('double$udivide'(X2,'double$udivide'(X3,'double$udivide'(X3,identity))),'double$udivide'(X0,identity))),X1) = 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(inverse(a1),a1) != identity,
inference(clausification,[status(esa)],[prove_these_axioms_1]) ).
cnf(d0,plain,
multiply(X1,X0) = inverse('double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,inverse(X0)),'double$udivide'('double$udivide'(X2,'double$udivide'(X3,'double$udivide'(X3,identity))),'double$udivide'(X1,identity))),X0) = X2,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d2,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,inverse(X2)),'double$udivide'('double$udivide'(X3,'double$udivide'(X0,inverse(X0))),'double$udivide'(X1,identity))),X2) = X3,
inference(demodulation,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
'double$udivide'('double$udivide'('double$udivide'(X0,inverse(X1)),'double$udivide'('double$udivide'(X2,'double$udivide'(X3,inverse(X3))),inverse(X0))),X1) = X2,
inference(demodulation,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
'double$udivide'('double$udivide'('double$udivide'(X2,inverse(X3)),X0),X3) = 'double$udivide'('double$udivide'(X0,'double$udivide'(X1,inverse(X1))),inverse(inverse(X2))),
inference(superposition,[status(thm)],[d3,d3]) ).
cnf(d5,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,inverse(X2)),X3),X2) = 'double$udivide'('double$udivide'(X3,identity),inverse(inverse(X1))),
inference(demodulation,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,inverse(X2)),X0),X2) = 'double$udivide'(inverse(X0),inverse(inverse(X1))),
inference(demodulation,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
'double$udivide'('double$udivide'('double$udivide'(X1,inverse(X2)),'double$udivide'('double$udivide'(X3,identity),inverse(X1))),X2) = X3,
inference(demodulation,[status(thm)],[d3,c3]) ).
cnf(d8,plain,
'double$udivide'(inverse('double$udivide'('double$udivide'(X2,identity),inverse(X0))),inverse(inverse(X0))) = X2,
inference(demodulation,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
'double$udivide'(multiply(inverse(X1),'double$udivide'(X0,identity)),inverse(inverse(X1))) = X0,
inference(demodulation,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
'double$udivide'(multiply(inverse(X1),inverse(X0)),inverse(inverse(X1))) = X0,
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d12,plain,
inverse('double$udivide'('double$udivide'(X0,inverse(identity)),'double$udivide'('double$udivide'(X1,'double$udivide'(X2,inverse(X2))),inverse(X0)))) = X1,
inference(superposition,[status(thm)],[d3,c2]) ).
cnf(d13,plain,
multiply('double$udivide'('double$udivide'(X1,'double$udivide'(X2,inverse(X2))),inverse(X0)),'double$udivide'(X0,inverse(identity))) = X1,
inference(demodulation,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
multiply('double$udivide'('double$udivide'(X1,identity),inverse(X2)),'double$udivide'(X2,inverse(identity))) = X1,
inference(demodulation,[status(thm)],[d13,c3]) ).
cnf(d15,plain,
multiply('double$udivide'(inverse(X0),inverse(X1)),'double$udivide'(X1,inverse(identity))) = X0,
inference(demodulation,[status(thm)],[d14,c2]) ).
cnf(d16,plain,
multiply(identity,'double$udivide'(inverse(X0),inverse(identity))) = X0,
inference(superposition,[status(thm)],[c3,d15]) ).
cnf(d17,plain,
inverse(inverse('double$udivide'(inverse(X0),inverse(identity)))) = X0,
inference(demodulation,[status(thm)],[d16,d11]) ).
cnf(d18,plain,
inverse(multiply(inverse(identity),inverse(X0))) = X0,
inference(demodulation,[status(thm)],[d17,d0]) ).
cnf(d19,plain,
identity = 'double$udivide'(multiply(inverse(identity),inverse(X0)),X0),
inference(superposition,[status(thm)],[d18,c3]) ).
cnf(d20,plain,
identity = inverse(inverse(identity)),
inference(superposition,[status(thm)],[d19,d10]) ).
cnf(d21,plain,
multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d22,plain,
inverse(multiply(inverse(identity),identity)) = inverse(identity),
inference(superposition,[status(thm)],[d20,d18]) ).
cnf(d23,plain,
inverse(inverse(identity)) = inverse(identity),
inference(demodulation,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
identity = inverse(identity),
inference(demodulation,[status(thm)],[d23,d20]) ).
cnf(d25,plain,
inverse(identity) != identity,
inference(demodulation,[status(thm)],[c4,d21]) ).
cnf(d26,plain,
identity != identity,
inference(demodulation,[status(thm)],[d25,d24]) ).
cnf(d27,plain,
identity = 'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0)),
inference(superposition,[status(thm)],[d0,c3]) ).
cnf(d28,plain,
identity = 'double$udivide'(inverse(X0),multiply(identity,X0)),
inference(superposition,[status(thm)],[c2,d27]) ).
cnf(d29,plain,
identity = 'double$udivide'(inverse(X0),inverse(inverse(X0))),
inference(demodulation,[status(thm)],[d28,d11]) ).
cnf(d30,plain,
identity = identity,
inference(demodulation,[status(thm)],[d29,c3]) ).
cnf(d31,plain,
$false,
inference(resolution,[status(thm)],[d30,d26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP481-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.41 % Computer : n016.cluster.edu
% 0.10/0.41 % Model : x86_64 x86_64
% 0.10/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.41 % Memory : 8046.5625MB
% 0.10/0.41 % OS : Linux 6.8.0-71-generic
% 0.10/0.41 % CPULimit : 300
% 0.10/0.41 % WCLimit : 300
% 0.10/0.41 % DateTime : Fri Sep 25 15:00:59 UTC 2026
% 0.10/0.41 % CPUTime :
% 0.10/0.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.79/3.21 % SZS status Unsatisfiable for theBenchmark.p
% 9.79/3.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------