%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP580-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 07:24:05 AM UTC 2026
% Result : Unsatisfiable 19.13s 2.82s
% Output : CNFRefutation 19.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 5
% Syntax : Number of clauses : 64 ( 64 unt; 0 nHn; 13 RR)
% Number of literals : 64 ( 63 equ; 2 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'('double$udivide'(X1,X0),X2),'double$udivide'(X1,identity))),'double$udivide'(identity,identity)) = X2 ).
cnf(multiply,axiom,
multiply(X0,X1) = 'double$udivide'('double$udivide'(X1,X0),identity) ).
cnf(inverse,axiom,
inverse(X0) = 'double$udivide'(X0,identity) ).
cnf(identity,axiom,
identity = 'double$udivide'(X0,inverse(X0)) ).
cnf(prove_these_axioms_4,negated_conjecture,
multiply(a,b) != multiply(b,a) ).
cnf(c0,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'('double$udivide'(X1,X0),X2),'double$udivide'(X1,identity))),'double$udivide'(identity,identity)) = 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(a,b) != multiply(b,a),
inference(clausification,[status(esa)],[prove_these_axioms_4]) ).
cnf(d0,plain,
multiply(X1,X0) = inverse('double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'('double$udivide'(X0,X1),X2),inverse(X0))),'double$udivide'(identity,identity)) = X2,
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d2,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'('double$udivide'(X1,X0),X2),inverse(X1))),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'(identity,inverse(X0))),inverse(identity)) = inverse('double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[c3,d2]) ).
cnf(d4,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'(identity,inverse(X0))),inverse(identity)) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
'double$udivide'('double$udivide'(X0,identity),inverse(identity)) = multiply(X0,identity),
inference(superposition,[status(thm)],[c3,d4]) ).
cnf(d6,plain,
'double$udivide'(inverse(X0),inverse(identity)) = multiply(X0,identity),
inference(demodulation,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
'double$udivide'('double$udivide'(inverse(X0),'double$udivide'('double$udivide'(identity,X1),inverse(X0))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[c3,d2]) ).
cnf(d8,plain,
'double$udivide'('double$udivide'(inverse('double$udivide'(identity,X0)),identity),inverse(identity)) = X0,
inference(superposition,[status(thm)],[c3,d7]) ).
cnf(d9,plain,
'double$udivide'(inverse(inverse('double$udivide'(identity,X0))),inverse(identity)) = X0,
inference(demodulation,[status(thm)],[d8,c2]) ).
cnf(d10,plain,
multiply(inverse('double$udivide'(identity,X0)),identity) = X0,
inference(demodulation,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
multiply(multiply(X0,identity),identity) = X0,
inference(demodulation,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d13,plain,
identity = 'double$udivide'(inverse(X0),multiply(identity,X0)),
inference(superposition,[status(thm)],[d12,c3]) ).
cnf(d14,plain,
multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d15,plain,
multiply(multiply(X1,X0),'double$udivide'(X0,X1)) = inverse(identity),
inference(superposition,[status(thm)],[d0,d14]) ).
cnf(d16,plain,
multiply(X0,'double$udivide'(identity,multiply(X0,identity))) = inverse(identity),
inference(superposition,[status(thm)],[d11,d15]) ).
cnf(d17,plain,
identity = 'double$udivide'(inverse('double$udivide'(identity,multiply(identity,identity))),inverse(identity)),
inference(superposition,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
identity = multiply('double$udivide'(identity,multiply(identity,identity)),identity),
inference(demodulation,[status(thm)],[d17,d6]) ).
cnf(d19,plain,
multiply(identity,identity) = 'double$udivide'(identity,multiply(identity,identity)),
inference(superposition,[status(thm)],[d18,d11]) ).
cnf(d20,plain,
'double$udivide'('double$udivide'('double$udivide'('double$udivide'('double$udivide'(X1,X0),X2),inverse(X1)),'double$udivide'(X2,inverse(X0))),inverse(identity)) = inverse(identity),
inference(superposition,[status(thm)],[d2,d2]) ).
cnf(d21,plain,
'double$udivide'('double$udivide'('double$udivide'(inverse('double$udivide'(X0,X1)),inverse(X0)),'double$udivide'(identity,inverse(X1))),inverse(identity)) = inverse(identity),
inference(superposition,[status(thm)],[c2,d20]) ).
cnf(d22,plain,
multiply('double$udivide'(inverse('double$udivide'(X0,X1)),inverse(X0)),X1) = inverse(identity),
inference(demodulation,[status(thm)],[d21,d4]) ).
cnf(d23,plain,
multiply('double$udivide'(multiply(X1,X0),inverse(X0)),X1) = inverse(identity),
inference(demodulation,[status(thm)],[d22,d0]) ).
cnf(d24,plain,
multiply(identity,inverse(X0)) = inverse(multiply(identity,X0)),
inference(superposition,[status(thm)],[d12,d12]) ).
cnf(d25,plain,
identity = 'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0)),
inference(superposition,[status(thm)],[d0,c3]) ).
cnf(d26,plain,
identity = 'double$udivide'('double$udivide'(identity,multiply(X0,identity)),X0),
inference(superposition,[status(thm)],[d11,d25]) ).
cnf(d27,plain,
identity = 'double$udivide'(multiply(identity,identity),identity),
inference(superposition,[status(thm)],[d19,d26]) ).
cnf(d28,plain,
identity = inverse(multiply(identity,identity)),
inference(demodulation,[status(thm)],[d27,c2]) ).
cnf(d29,plain,
identity = multiply(identity,inverse(identity)),
inference(demodulation,[status(thm)],[d28,d24]) ).
cnf(d30,plain,
multiply('double$udivide'(identity,inverse(inverse(identity))),identity) = inverse(identity),
inference(superposition,[status(thm)],[d29,d23]) ).
cnf(d31,plain,
multiply('double$udivide'(identity,multiply(identity,identity)),identity) = inverse(identity),
inference(demodulation,[status(thm)],[d30,d12]) ).
cnf(d32,plain,
multiply(multiply(identity,identity),identity) = inverse(identity),
inference(demodulation,[status(thm)],[d31,d19]) ).
cnf(d33,plain,
identity = inverse(identity),
inference(demodulation,[status(thm)],[d32,d11]) ).
cnf(d34,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'(identity,inverse(X0))),inverse(identity)) = multiply(X1,X0),
inference(superposition,[status(thm)],[d25,d2]) ).
cnf(d35,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(identity,inverse(X1))),identity) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d34,d33]) ).
cnf(d36,plain,
inverse('double$udivide'(X0,'double$udivide'(identity,inverse(X1)))) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d35,c2]) ).
cnf(d37,plain,
multiply('double$udivide'(identity,inverse(X1)),X0) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d36,d0]) ).
cnf(d38,plain,
multiply(identity,X0) = multiply(X0,identity),
inference(superposition,[status(thm)],[c3,d37]) ).
cnf(d39,plain,
multiply(identity,multiply(X0,identity)) = X0,
inference(demodulation,[status(thm)],[d11,d38]) ).
cnf(d40,plain,
multiply(identity,multiply(identity,X0)) = X0,
inference(superposition,[status(thm)],[d38,d39]) ).
cnf(d41,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'('double$udivide'(inverse(X0),X1),inverse(X0))),inverse(identity)) = X1,
inference(superposition,[status(thm)],[c2,d2]) ).
cnf(d42,plain,
'double$udivide'('double$udivide'(identity,X1),inverse(identity)) = 'double$udivide'('double$udivide'('double$udivide'(X0,inverse(identity)),X1),inverse(X0)),
inference(superposition,[status(thm)],[d2,d41]) ).
cnf(d43,plain,
'double$udivide'('double$udivide'(identity,X0),identity) = 'double$udivide'('double$udivide'('double$udivide'(X1,inverse(identity)),X0),inverse(X1)),
inference(demodulation,[status(thm)],[d42,d33]) ).
cnf(d44,plain,
inverse('double$udivide'(identity,X0)) = 'double$udivide'('double$udivide'('double$udivide'(X1,inverse(identity)),X0),inverse(X1)),
inference(demodulation,[status(thm)],[d43,c2]) ).
cnf(d45,plain,
multiply(X0,identity) = 'double$udivide'('double$udivide'('double$udivide'(X1,inverse(identity)),X0),inverse(X1)),
inference(demodulation,[status(thm)],[d44,d0]) ).
cnf(d46,plain,
multiply(X0,identity) = 'double$udivide'('double$udivide'('double$udivide'(X1,identity),X0),inverse(X1)),
inference(demodulation,[status(thm)],[d45,d33]) ).
cnf(d47,plain,
multiply(X1,identity) = 'double$udivide'('double$udivide'(inverse(X0),X1),inverse(X0)),
inference(demodulation,[status(thm)],[d46,c2]) ).
cnf(d48,plain,
'double$udivide'('double$udivide'(inverse(identity),multiply(identity,X0)),inverse(identity)) = 'double$udivide'(identity,inverse(X0)),
inference(superposition,[status(thm)],[d4,d7]) ).
cnf(d49,plain,
multiply(multiply(identity,X0),identity) = 'double$udivide'(identity,inverse(X0)),
inference(demodulation,[status(thm)],[d48,d47]) ).
cnf(d50,plain,
multiply(identity,multiply(identity,X0)) = 'double$udivide'(identity,inverse(X0)),
inference(demodulation,[status(thm)],[d49,d38]) ).
cnf(d51,plain,
X0 = 'double$udivide'(identity,inverse(X0)),
inference(demodulation,[status(thm)],[d50,d40]) ).
cnf(d52,plain,
multiply(X0,X1) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d37,d51]) ).
cnf(d53,plain,
$false,
inference(resolution,[status(thm)],[d52,c4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP580-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 15:01:33 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.13/2.82 % SZS status Unsatisfiable for theBenchmark.p
% 19.13/2.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------