%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP502-1 : 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 : n013.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 07:23:54 AM UTC 2026
% Result : Unsatisfiable 140.09s 30.70s
% Output : CNFRefutation 140.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 3
% Syntax : Number of clauses : 71 ( 71 unt; 0 nHn; 3 RR)
% Number of literals : 71 ( 70 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 266 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'('double$udivide'(X0,inverse('double$udivide'(X1,X2))),'double$udivide'(inverse(X1),inverse('double$udivide'(X3,'double$udivide'(X0,X3))))) = X2 ).
cnf(multiply,axiom,
multiply(X0,X1) = inverse('double$udivide'(X1,X0)) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
cnf(c0,plain,
'double$udivide'('double$udivide'(X0,inverse('double$udivide'(X1,X2))),'double$udivide'(inverse(X1),inverse('double$udivide'(X3,'double$udivide'(X0,X3))))) = X2,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(X0,X1) = inverse('double$udivide'(X1,X0)),
inference(clausification,[status(esa)],[multiply]) ).
cnf(c2,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(clausification,[status(esa)],[prove_these_axioms_1]) ).
cnf(d0,plain,
'double$udivide'('double$udivide'(X2,multiply(X1,X0)),'double$udivide'(inverse(X0),inverse('double$udivide'(X3,'double$udivide'(X2,X3))))) = X1,
inference(demodulation,[status(thm)],[c0,c1]) ).
cnf(d1,plain,
'double$udivide'('double$udivide'(X1,multiply(X2,X3)),'double$udivide'(inverse(X3),multiply('double$udivide'(X1,X0),X0))) = X2,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
multiply('double$udivide'(inverse(X2),multiply('double$udivide'(X0,X3),X3)),'double$udivide'(X0,multiply(X1,X2))) = inverse(X1),
inference(superposition,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
'double$udivide'('double$udivide'(X2,multiply(X3,'double$udivide'(X0,X1))),'double$udivide'(multiply(X1,X0),multiply('double$udivide'(X2,X4),X4))) = X3,
inference(superposition,[status(thm)],[c1,d1]) ).
cnf(d4,plain,
'double$udivide'('double$udivide'(X4,inverse(X3)),'double$udivide'(multiply(multiply(X3,X0),X1),multiply('double$udivide'(X4,X5),X5))) = 'double$udivide'(inverse(X0),multiply('double$udivide'(X1,X2),X2)),
inference(superposition,[status(thm)],[d2,d3]) ).
cnf(d5,plain,
'double$udivide'(inverse(X2),multiply('double$udivide'(X3,X5),X5)) = 'double$udivide'(inverse(X2),multiply('double$udivide'(X3,X6),X6)),
inference(superposition,[status(thm)],[d4,d4]) ).
cnf(d6,plain,
multiply('double$udivide'(inverse(X2),multiply('double$udivide'(inverse(X0),X4),X4)),'double$udivide'(inverse(X0),multiply('double$udivide'(X1,X3),X3))) = inverse('double$udivide'(X1,X2)),
inference(superposition,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
multiply('double$udivide'(inverse(X1),multiply('double$udivide'(inverse(X2),X3),X3)),'double$udivide'(inverse(X2),multiply('double$udivide'(X0,X4),X4))) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
inverse('double$udivide'(X3,X0)) = multiply(X0,X3),
inference(superposition,[status(thm)],[d2,d7]) ).
cnf(d9,plain,
'double$udivide'(multiply(X1,X0),multiply('double$udivide'(X2,X3),X3)) = 'double$udivide'(inverse('double$udivide'(X0,X1)),multiply('double$udivide'(X2,X4),X4)),
inference(superposition,[status(thm)],[c1,d5]) ).
cnf(d10,plain,
'double$udivide'(multiply(X1,X0),multiply('double$udivide'(X2,X3),X3)) = 'double$udivide'(multiply(X1,X0),multiply('double$udivide'(X2,X4),X4)),
inference(demodulation,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
'double$udivide'('double$udivide'(inverse(X0),multiply('double$udivide'(X1,X4),X4)),'double$udivide'(multiply(X3,X2),multiply('double$udivide'(inverse(X0),X5),X5))) = 'double$udivide'(X1,'double$udivide'(X2,X3)),
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d12,plain,
multiply(multiply('double$udivide'(X1,X2),X2),inverse(X0)) = inverse('double$udivide'(inverse(X0),multiply('double$udivide'(X1,X3),X3))),
inference(superposition,[status(thm)],[d5,c1]) ).
cnf(d13,plain,
multiply(multiply('double$udivide'(X1,X3),X3),inverse(X0)) = multiply(multiply('double$udivide'(X1,X2),X2),inverse(X0)),
inference(demodulation,[status(thm)],[d12,c1]) ).
cnf(d14,plain,
'double$udivide'('double$udivide'(X4,multiply(multiply('double$udivide'(X0,X3),X3),inverse(X2))),'double$udivide'(inverse(inverse(X2)),multiply('double$udivide'(X4,X5),X5))) = multiply('double$udivide'(X0,X1),X1),
inference(superposition,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
multiply('double$udivide'(X1,X2),X2) = multiply('double$udivide'(X1,X5),X5),
inference(demodulation,[status(thm)],[d14,d1]) ).
cnf(d16,plain,
'double$udivide'('double$udivide'(X3,multiply(X4,'double$udivide'(X1,'double$udivide'(X0,X1)))),'double$udivide'(multiply('double$udivide'(X0,X2),X2),multiply('double$udivide'(X3,X5),X5))) = X4,
inference(superposition,[status(thm)],[d15,d3]) ).
cnf(d17,plain,
'double$udivide'(X1,'double$udivide'(X2,'double$udivide'(X3,X2))) = 'double$udivide'(X1,'double$udivide'(X4,'double$udivide'(X3,X4))),
inference(superposition,[status(thm)],[d16,d11]) ).
cnf(d18,plain,
inverse('double$udivide'(X0,'double$udivide'(X3,'double$udivide'(X2,X3)))) = multiply('double$udivide'(X1,'double$udivide'(X2,X1)),X0),
inference(superposition,[status(thm)],[d17,d8]) ).
cnf(d19,plain,
multiply('double$udivide'(X1,'double$udivide'(X2,X1)),X0) = multiply('double$udivide'(X3,'double$udivide'(X2,X3)),X0),
inference(demodulation,[status(thm)],[d18,c1]) ).
cnf(d20,plain,
'double$udivide'('double$udivide'(X0,multiply(X3,X4)),'double$udivide'(inverse(X4),multiply('double$udivide'(X2,'double$udivide'(X1,X2)),'double$udivide'(X1,X0)))) = X3,
inference(superposition,[status(thm)],[d19,d1]) ).
cnf(d21,plain,
'double$udivide'('double$udivide'(X2,multiply(X1,X0)),'double$udivide'(multiply(multiply('double$udivide'(X0,X1),X3),X4),multiply('double$udivide'(X2,X5),X5))) = 'double$udivide'(inverse(X3),multiply('double$udivide'(X4,X6),X6)),
inference(superposition,[status(thm)],[c1,d4]) ).
cnf(d22,plain,
'double$udivide'(inverse(X3),multiply('double$udivide'(X4,X6),X6)) = 'double$udivide'(X1,'double$udivide'(X4,multiply('double$udivide'(X2,'double$udivide'(X1,X2)),X3))),
inference(superposition,[status(thm)],[d21,d11]) ).
cnf(d23,plain,
'double$udivide'(inverse('double$udivide'('double$udivide'(X0,multiply(X1,X2)),X0)),multiply('double$udivide'(inverse(X2),X4),X4)) = X1,
inference(superposition,[status(thm)],[d22,d20]) ).
cnf(d24,plain,
'double$udivide'(multiply(X0,'double$udivide'(X0,multiply(X1,X2))),multiply('double$udivide'(inverse(X2),X3),X3)) = X1,
inference(demodulation,[status(thm)],[d23,c1]) ).
cnf(d25,plain,
X1 = 'double$udivide'(multiply(X0,'double$udivide'(X0,multiply(X1,X2))),multiply('double$udivide'(inverse(X2),X4),X4)),
inference(superposition,[status(thm)],[d24,d10]) ).
cnf(d26,plain,
inverse(X1) = multiply('double$udivide'(multiply(X3,X2),multiply('double$udivide'(X0,X4),X4)),'double$udivide'(X0,multiply(X1,'double$udivide'(X2,X3)))),
inference(superposition,[status(thm)],[d3,d8]) ).
cnf(d27,plain,
inverse(X4) = multiply(X1,'double$udivide'(inverse(X2),multiply(X4,'double$udivide'('double$udivide'(X0,multiply(X1,X2)),X0)))),
inference(superposition,[status(thm)],[d24,d26]) ).
cnf(d28,plain,
X1 = 'double$udivide'(inverse(X1),multiply('double$udivide'(inverse('double$udivide'('double$udivide'(X2,multiply(inverse(X0),X0)),X2)),X3),X3)),
inference(superposition,[status(thm)],[d27,d25]) ).
cnf(d29,plain,
X2 = 'double$udivide'(inverse(X2),multiply('double$udivide'(multiply(X0,'double$udivide'(X0,multiply(inverse(X1),X1))),X3),X3)),
inference(demodulation,[status(thm)],[d28,c1]) ).
cnf(d30,plain,
'double$udivide'(inverse(X0),multiply('double$udivide'(multiply(X1,'double$udivide'(X1,multiply(inverse(X2),X2))),X4),X4)) = X0,
inference(superposition,[status(thm)],[d29,d5]) ).
cnf(d31,plain,
'double$udivide'(inverse(X3),multiply(inverse(X1),multiply('double$udivide'(inverse(X1),X2),X2))) = X3,
inference(superposition,[status(thm)],[d24,d30]) ).
cnf(d32,plain,
'double$udivide'(inverse(X2),multiply(multiply(X1,X0),multiply('double$udivide'(inverse('double$udivide'(X0,X1)),X3),X3))) = X2,
inference(superposition,[status(thm)],[c1,d31]) ).
cnf(d33,plain,
'double$udivide'(inverse(X2),multiply(multiply(X1,X0),multiply('double$udivide'(multiply(X1,X0),X3),X3))) = X2,
inference(demodulation,[status(thm)],[d32,c1]) ).
cnf(d34,plain,
X3 = 'double$udivide'(inverse(X3),multiply(inverse(X1),multiply('double$udivide'(inverse(X1),X2),X2))),
inference(superposition,[status(thm)],[d24,d29]) ).
cnf(d35,plain,
inverse(X0) = multiply(multiply(inverse(X1),multiply('double$udivide'(inverse(X1),X2),X2)),inverse(X0)),
inference(superposition,[status(thm)],[d34,d8]) ).
cnf(d36,plain,
inverse('double$udivide'(X0,X1)) = multiply(multiply(inverse(X2),multiply('double$udivide'(inverse(X2),X3),X3)),multiply(X1,X0)),
inference(superposition,[status(thm)],[c1,d35]) ).
cnf(d37,plain,
multiply(X1,X0) = multiply(multiply(inverse(X2),multiply('double$udivide'(inverse(X2),X3),X3)),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d36,c1]) ).
cnf(d38,plain,
'double$udivide'(inverse(X3),multiply('double$udivide'(multiply(inverse(X0),multiply('double$udivide'(inverse(X0),X1),X1)),X2),X2)) = X3,
inference(superposition,[status(thm)],[d37,d33]) ).
cnf(d39,plain,
'double$udivide'('double$udivide'(multiply(inverse(X1),multiply('double$udivide'(inverse(X1),X2),X2)),multiply(X4,X0)),X0) = X4,
inference(superposition,[status(thm)],[d38,d1]) ).
cnf(d40,plain,
'double$udivide'(X0,X1) = 'double$udivide'(multiply(X1,X0),multiply(inverse(X2),multiply('double$udivide'(inverse(X2),X3),X3))),
inference(superposition,[status(thm)],[c1,d34]) ).
cnf(d41,plain,
'double$udivide'('double$udivide'(multiply('double$udivide'(inverse(X0),X1),X1),inverse(X0)),multiply('double$udivide'(inverse(X2),X3),X3)) = inverse(X2),
inference(superposition,[status(thm)],[d40,d39]) ).
cnf(d42,plain,
'double$udivide'('double$udivide'(inverse(X2),multiply(X4,'double$udivide'('double$udivide'(X0,multiply(X1,X2)),X0))),X1) = X4,
inference(superposition,[status(thm)],[d24,d3]) ).
cnf(d43,plain,
'double$udivide'('double$udivide'(multiply(X1,X0),multiply(X2,'double$udivide'('double$udivide'(X3,multiply(X4,'double$udivide'(X0,X1))),X3))),X4) = X2,
inference(superposition,[status(thm)],[c1,d42]) ).
cnf(d44,plain,
'double$udivide'('double$udivide'(inverse('double$udivide'('double$udivide'(X2,multiply(inverse(X0),X0)),X2)),multiply(X3,X1)),X1) = X3,
inference(superposition,[status(thm)],[d42,d42]) ).
cnf(d45,plain,
'double$udivide'('double$udivide'(multiply(X0,'double$udivide'(X0,multiply(inverse(X1),X1))),multiply(X2,X3)),X3) = X2,
inference(demodulation,[status(thm)],[d44,c1]) ).
cnf(d46,plain,
multiply(X3,'double$udivide'(multiply(X0,'double$udivide'(X0,multiply(inverse(X1),X1))),multiply(X2,X3))) = inverse(X2),
inference(superposition,[status(thm)],[d45,c1]) ).
cnf(d47,plain,
multiply(multiply('double$udivide'(inverse(X2),X3),X3),'double$udivide'('double$udivide'(X0,multiply(inverse(X1),X1)),X0)) = inverse(inverse(X2)),
inference(superposition,[status(thm)],[d40,d46]) ).
cnf(d48,plain,
'double$udivide'('double$udivide'(multiply(X4,X3),inverse(inverse(X0))),inverse('double$udivide'(X3,X4))) = multiply('double$udivide'(inverse(X0),X1),X1),
inference(superposition,[status(thm)],[d47,d43]) ).
cnf(d49,plain,
'double$udivide'('double$udivide'(multiply(X1,X0),inverse(inverse(X2))),multiply(X1,X0)) = multiply('double$udivide'(inverse(X2),X3),X3),
inference(demodulation,[status(thm)],[d48,c1]) ).
cnf(d50,plain,
multiply('double$udivide'(inverse(X0),X2),X2) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d49,d41]) ).
cnf(d51,plain,
'double$udivide'('double$udivide'(inverse(multiply(X0,'double$udivide'(X0,multiply(inverse(X1),X1)))),multiply(X3,X2)),X2) = X3,
inference(superposition,[status(thm)],[d45,d42]) ).
cnf(d52,plain,
'double$udivide'(multiply(X0,'double$udivide'(X0,multiply(inverse(X1),X1))),multiply('double$udivide'(inverse(X2),X3),X3)) = inverse(X2),
inference(superposition,[status(thm)],[d34,d51]) ).
cnf(d53,plain,
'double$udivide'('double$udivide'(inverse(X2),multiply(X4,'double$udivide'('double$udivide'(X0,multiply(inverse(X1),X1)),X0))),inverse(X2)) = X4,
inference(superposition,[status(thm)],[d52,d3]) ).
cnf(d54,plain,
'double$udivide'('double$udivide'(inverse(X4),inverse(inverse(X0))),inverse(X4)) = multiply('double$udivide'(inverse(X0),X1),X1),
inference(superposition,[status(thm)],[d47,d53]) ).
cnf(d55,plain,
'double$udivide'('double$udivide'(inverse(X2),inverse(inverse(X0))),inverse(X2)) = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d54,d50]) ).
cnf(d56,plain,
multiply(X0,'double$udivide'(multiply(inverse(X1),multiply('double$udivide'(inverse(X1),X2),X2)),multiply(X4,X0))) = inverse(X4),
inference(superposition,[status(thm)],[d38,d2]) ).
cnf(d57,plain,
X2 = 'double$udivide'(inverse(X2),multiply('double$udivide'(inverse(multiply(inverse(X0),multiply('double$udivide'(inverse(X0),X1),X1))),X3),X3)),
inference(superposition,[status(thm)],[d56,d25]) ).
cnf(d58,plain,
X3 = 'double$udivide'(inverse(X3),inverse(inverse(multiply(inverse(X0),multiply('double$udivide'(inverse(X0),X1),X1))))),
inference(demodulation,[status(thm)],[d57,d50]) ).
cnf(d59,plain,
X2 = 'double$udivide'(inverse(X2),inverse(inverse(multiply(inverse(X0),inverse(inverse(X0)))))),
inference(demodulation,[status(thm)],[d58,d50]) ).
cnf(d60,plain,
'double$udivide'(X0,inverse(X0)) = inverse(inverse(multiply(inverse(X1),inverse(inverse(X1))))),
inference(superposition,[status(thm)],[d59,d55]) ).
cnf(d61,plain,
'double$udivide'(X2,inverse(X2)) = 'double$udivide'(X1,inverse(X1)),
inference(superposition,[status(thm)],[d60,d60]) ).
cnf(d62,plain,
inverse('double$udivide'(X1,inverse(X1))) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d61,d8]) ).
cnf(d63,plain,
multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(demodulation,[status(thm)],[d62,c1]) ).
cnf(d64,plain,
$false,
inference(resolution,[status(thm)],[d63,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP502-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n013.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Fri Sep 25 14:56:51 UTC 2026
% 0.09/10.37 % CPUTime :
% 0.09/10.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 140.09/30.70 % SZS status Unsatisfiable for theBenchmark.p
% 140.09/30.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------