%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP485-1 : 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 : n007.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 7.77s 5.17s
% Output : CNFRefutation 7.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 5
% Syntax : Number of clauses : 85 ( 85 unt; 0 nHn; 10 RR)
% Number of literals : 85 ( 84 equ; 2 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 : 148 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'('double$udivide'(X0,X1),X2),'double$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$udivide'(X0,inverse(X0)) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(identity,a2) != a2 ).
cnf(c0,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'('double$udivide'(X0,X1),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(identity,a2) != a2,
inference(clausification,[status(esa)],[prove_these_axioms_2]) ).
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'(X1,X0),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'(X0,X1),X2),inverse(X1))),inverse(identity)) = X2,
inference(demodulation,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(identity,inverse(X1))),inverse(identity)) = inverse('double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[c3,d2]) ).
cnf(d4,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(identity,inverse(X1))),inverse(identity)) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
'double$udivide'('double$udivide'(X0,identity),inverse(identity)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c3,d4]) ).
cnf(d6,plain,
'double$udivide'(inverse(X0),inverse(identity)) = multiply(identity,X0),
inference(demodulation,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c2,d0]) ).
cnf(d8,plain,
identity = 'double$udivide'(inverse(X0),multiply(identity,X0)),
inference(superposition,[status(thm)],[d7,c3]) ).
cnf(d9,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(X2,'double$udivide'('double$udivide'('double$udivide'('double$udivide'(X0,X1),X2),'double$udivide'(X1,identity)),identity))),'double$udivide'(identity,identity)) = 'double$udivide'(identity,identity),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d10,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(X2,inverse('double$udivide'('double$udivide'('double$udivide'(X0,X1),X2),'double$udivide'(X1,identity))))),'double$udivide'(identity,identity)) = 'double$udivide'(identity,identity),
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(X2,multiply('double$udivide'(X1,identity),'double$udivide'('double$udivide'(X0,X1),X2)))),'double$udivide'(identity,identity)) = 'double$udivide'(identity,identity),
inference(demodulation,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'(X2,multiply(inverse(X0),'double$udivide'('double$udivide'(X1,X0),X2)))),'double$udivide'(identity,identity)) = 'double$udivide'(identity,identity),
inference(demodulation,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(X1,multiply(inverse(X2),'double$udivide'('double$udivide'(X0,X2),X1)))),inverse(identity)) = 'double$udivide'(identity,identity),
inference(demodulation,[status(thm)],[d12,c2]) ).
cnf(d14,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(X1,multiply(inverse(X2),'double$udivide'('double$udivide'(X0,X2),X1)))),inverse(identity)) = inverse(identity),
inference(demodulation,[status(thm)],[d13,c2]) ).
cnf(d15,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(X1,multiply(inverse(inverse(X0)),'double$udivide'(identity,X1)))),inverse(identity)) = inverse(identity),
inference(superposition,[status(thm)],[c3,d14]) ).
cnf(d16,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(X1,multiply(multiply(identity,X0),'double$udivide'(identity,X1)))),inverse(identity)) = inverse(identity),
inference(demodulation,[status(thm)],[d15,d7]) ).
cnf(d17,plain,
multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d18,plain,
multiply(multiply(X1,X0),'double$udivide'(X0,X1)) = inverse(identity),
inference(superposition,[status(thm)],[d0,d17]) ).
cnf(d19,plain,
'double$udivide'('double$udivide'(identity,'double$udivide'(identity,inverse(identity))),inverse(identity)) = inverse(identity),
inference(superposition,[status(thm)],[d18,d16]) ).
cnf(d20,plain,
'double$udivide'('double$udivide'(identity,identity),inverse(identity)) = inverse(identity),
inference(demodulation,[status(thm)],[d19,c3]) ).
cnf(d21,plain,
'double$udivide'(inverse(identity),inverse(identity)) = inverse(identity),
inference(demodulation,[status(thm)],[d20,c2]) ).
cnf(d22,plain,
multiply(identity,identity) = inverse(identity),
inference(demodulation,[status(thm)],[d21,d6]) ).
cnf(d23,plain,
identity = 'double$udivide'(inverse(identity),inverse(identity)),
inference(superposition,[status(thm)],[d22,d8]) ).
cnf(d24,plain,
identity = multiply(identity,identity),
inference(demodulation,[status(thm)],[d23,d6]) ).
cnf(d25,plain,
identity = inverse(identity),
inference(demodulation,[status(thm)],[d22,d24]) ).
cnf(d26,plain,
multiply(identity,inverse(X0)) = inverse(multiply(identity,X0)),
inference(superposition,[status(thm)],[d7,d7]) ).
cnf(d27,plain,
'double$udivide'('double$udivide'(X1,'double$udivide'('double$udivide'('double$udivide'(X1,multiply(identity,X0)),X2),multiply(identity,inverse(X0)))),inverse(identity)) = X2,
inference(superposition,[status(thm)],[d26,d2]) ).
cnf(d28,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'('double$udivide'('double$udivide'(X0,multiply(identity,X1)),X2),multiply(identity,inverse(X1)))),identity) = X2,
inference(demodulation,[status(thm)],[d27,d25]) ).
cnf(d29,plain,
inverse('double$udivide'(X0,'double$udivide'('double$udivide'('double$udivide'(X0,multiply(identity,X1)),X2),multiply(identity,inverse(X1))))) = X2,
inference(demodulation,[status(thm)],[d28,c2]) ).
cnf(d30,plain,
multiply('double$udivide'('double$udivide'('double$udivide'(X0,multiply(identity,X1)),X2),multiply(identity,inverse(X1))),X0) = X2,
inference(demodulation,[status(thm)],[d29,d0]) ).
cnf(d31,plain,
'double$udivide'('double$udivide'(X0,X2),'double$udivide'(identity,identity)) = 'double$udivide'('double$udivide'('double$udivide'('double$udivide'(X0,identity),X1),X2),'double$udivide'(X1,identity)),
inference(superposition,[status(thm)],[c0,c0]) ).
cnf(d32,plain,
'double$udivide'('double$udivide'(X0,X1),inverse(identity)) = 'double$udivide'('double$udivide'('double$udivide'('double$udivide'(X0,identity),X2),X1),'double$udivide'(X2,identity)),
inference(demodulation,[status(thm)],[d31,c2]) ).
cnf(d33,plain,
'double$udivide'('double$udivide'(X0,X1),inverse(identity)) = 'double$udivide'('double$udivide'('double$udivide'(inverse(X0),X2),X1),'double$udivide'(X2,identity)),
inference(demodulation,[status(thm)],[d32,c2]) ).
cnf(d34,plain,
'double$udivide'('double$udivide'(X1,X2),inverse(identity)) = 'double$udivide'('double$udivide'('double$udivide'(inverse(X1),X0),X2),inverse(X0)),
inference(demodulation,[status(thm)],[d33,c2]) ).
cnf(d35,plain,
'double$udivide'('double$udivide'(X1,X2),inverse(identity)) = 'double$udivide'('double$udivide'('double$udivide'(inverse(X1),multiply(identity,X0)),X2),multiply(identity,inverse(X0))),
inference(superposition,[status(thm)],[d26,d34]) ).
cnf(d36,plain,
'double$udivide'('double$udivide'(X0,X1),identity) = 'double$udivide'('double$udivide'('double$udivide'(inverse(X0),multiply(identity,X2)),X1),multiply(identity,inverse(X2))),
inference(demodulation,[status(thm)],[d35,d25]) ).
cnf(d37,plain,
inverse('double$udivide'(X0,X1)) = 'double$udivide'('double$udivide'('double$udivide'(inverse(X0),multiply(identity,X2)),X1),multiply(identity,inverse(X2))),
inference(demodulation,[status(thm)],[d36,c2]) ).
cnf(d38,plain,
multiply(X1,X0) = 'double$udivide'('double$udivide'('double$udivide'(inverse(X0),multiply(identity,X2)),X1),multiply(identity,inverse(X2))),
inference(demodulation,[status(thm)],[d37,d0]) ).
cnf(d39,plain,
multiply(multiply(X2,X0),inverse(X0)) = X2,
inference(superposition,[status(thm)],[d38,d30]) ).
cnf(d40,plain,
identity = 'double$udivide'('double$udivide'(X0,X1),multiply(X1,X0)),
inference(superposition,[status(thm)],[d0,c3]) ).
cnf(d41,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(identity,inverse(X1))),inverse(identity)) = multiply(X1,X0),
inference(superposition,[status(thm)],[d40,d2]) ).
cnf(d42,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(identity,inverse(X1))),identity) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d41,d25]) ).
cnf(d43,plain,
inverse('double$udivide'(X0,'double$udivide'(identity,inverse(X1)))) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d42,c2]) ).
cnf(d44,plain,
multiply('double$udivide'(identity,inverse(X1)),X0) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d43,d0]) ).
cnf(d45,plain,
'double$udivide'('double$udivide'(X0,inverse('double$udivide'(inverse(X0),X1))),inverse(identity)) = 'double$udivide'(identity,inverse(X1)),
inference(superposition,[status(thm)],[c3,d34]) ).
cnf(d46,plain,
'double$udivide'('double$udivide'(X0,multiply(X1,inverse(X0))),inverse(identity)) = 'double$udivide'(identity,inverse(X1)),
inference(demodulation,[status(thm)],[d45,d0]) ).
cnf(d47,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(identity,inverse(X1))),inverse(identity)) = multiply(X1,inverse('double$udivide'(X0,identity))),
inference(superposition,[status(thm)],[d46,d2]) ).
cnf(d48,plain,
'double$udivide'('double$udivide'(X0,'double$udivide'(identity,inverse(X1))),identity) = multiply(X1,inverse('double$udivide'(X0,identity))),
inference(demodulation,[status(thm)],[d47,d25]) ).
cnf(d49,plain,
inverse('double$udivide'(X0,'double$udivide'(identity,inverse(X1)))) = multiply(X1,inverse('double$udivide'(X0,identity))),
inference(demodulation,[status(thm)],[d48,c2]) ).
cnf(d50,plain,
multiply('double$udivide'(identity,inverse(X1)),X0) = multiply(X1,inverse('double$udivide'(X0,identity))),
inference(demodulation,[status(thm)],[d49,d0]) ).
cnf(d51,plain,
multiply(X0,X1) = multiply(X0,inverse('double$udivide'(X1,identity))),
inference(demodulation,[status(thm)],[d50,d44]) ).
cnf(d52,plain,
multiply(X1,X0) = multiply(X1,multiply(identity,X0)),
inference(demodulation,[status(thm)],[d51,d0]) ).
cnf(d53,plain,
'double$udivide'('double$udivide'(inverse(X0),multiply(X1,multiply(identity,X0))),inverse(identity)) = 'double$udivide'(identity,inverse(X1)),
inference(superposition,[status(thm)],[d7,d46]) ).
cnf(d54,plain,
'double$udivide'('double$udivide'(inverse(X1),multiply(X0,X1)),inverse(identity)) = 'double$udivide'(identity,inverse(X0)),
inference(demodulation,[status(thm)],[d53,d52]) ).
cnf(d55,plain,
'double$udivide'('double$udivide'(inverse(X0),multiply(X1,X0)),identity) = 'double$udivide'(identity,inverse(X1)),
inference(demodulation,[status(thm)],[d54,d25]) ).
cnf(d56,plain,
inverse('double$udivide'(inverse(X0),multiply(X1,X0))) = 'double$udivide'(identity,inverse(X1)),
inference(demodulation,[status(thm)],[d55,c2]) ).
cnf(d57,plain,
multiply(multiply(X1,X0),inverse(X0)) = 'double$udivide'(identity,inverse(X1)),
inference(demodulation,[status(thm)],[d56,d0]) ).
cnf(d58,plain,
X0 = 'double$udivide'(identity,inverse(X0)),
inference(demodulation,[status(thm)],[d57,d39]) ).
cnf(d59,plain,
multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[d17,d25]) ).
cnf(d60,plain,
identity = 'double$udivide'('double$udivide'(X0,inverse(X0)),identity),
inference(superposition,[status(thm)],[d59,d40]) ).
cnf(d61,plain,
identity = inverse('double$udivide'(X0,inverse(X0))),
inference(demodulation,[status(thm)],[d60,c2]) ).
cnf(d62,plain,
identity = multiply(inverse(X0),X0),
inference(demodulation,[status(thm)],[d61,d0]) ).
cnf(d63,plain,
multiply(identity,inverse(X0)) = inverse(X0),
inference(superposition,[status(thm)],[d62,d39]) ).
cnf(d64,plain,
'double$udivide'('double$udivide'(X0,X1),inverse(identity)) = 'double$udivide'('double$udivide'(identity,X1),inverse(inverse(inverse(X0)))),
inference(superposition,[status(thm)],[c3,d34]) ).
cnf(d65,plain,
'double$udivide'('double$udivide'(X0,X1),inverse(identity)) = 'double$udivide'('double$udivide'(identity,X1),multiply(identity,inverse(X0))),
inference(demodulation,[status(thm)],[d64,d7]) ).
cnf(d66,plain,
'double$udivide'('double$udivide'(X0,identity),inverse(identity)) = 'double$udivide'(inverse(identity),multiply(identity,inverse(X0))),
inference(superposition,[status(thm)],[c2,d65]) ).
cnf(d67,plain,
'double$udivide'(inverse(X0),inverse(identity)) = 'double$udivide'(inverse(identity),multiply(identity,inverse(X0))),
inference(demodulation,[status(thm)],[d66,c2]) ).
cnf(d68,plain,
'double$udivide'(inverse(X0),identity) = 'double$udivide'(inverse(identity),multiply(identity,inverse(X0))),
inference(demodulation,[status(thm)],[d67,d25]) ).
cnf(d69,plain,
inverse(inverse(X0)) = 'double$udivide'(inverse(identity),multiply(identity,inverse(X0))),
inference(demodulation,[status(thm)],[d68,c2]) ).
cnf(d70,plain,
multiply(identity,X0) = 'double$udivide'(inverse(identity),multiply(identity,inverse(X0))),
inference(demodulation,[status(thm)],[d69,d7]) ).
cnf(d71,plain,
multiply(identity,X0) = 'double$udivide'(identity,multiply(identity,inverse(X0))),
inference(demodulation,[status(thm)],[d70,d25]) ).
cnf(d72,plain,
multiply(identity,X0) = 'double$udivide'(identity,inverse(X0)),
inference(demodulation,[status(thm)],[d71,d63]) ).
cnf(d73,plain,
multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[d72,d58]) ).
cnf(d74,plain,
$false,
inference(resolution,[status(thm)],[d73,c4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP485-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.35 % Computer : n007.cluster.edu
% 0.05/0.35 % Model : x86_64 x86_64
% 0.05/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.35 % Memory : 8046.5625MB
% 0.05/0.35 % OS : Linux 6.8.0-71-generic
% 0.05/0.36 % CPULimit : 300
% 0.05/0.36 % WCLimit : 300
% 0.05/0.36 % DateTime : Fri Sep 25 14:54:23 UTC 2026
% 0.05/0.36 % CPUTime :
% 0.05/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.77/5.17 % SZS status Unsatisfiable for theBenchmark.p
% 7.77/5.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------