%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP499-1 : 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 : n004.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 07:23:53 AM UTC 2026
% Result : Unsatisfiable 10.40s 14.50s
% Output : CNFRefutation 72.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 3
% Syntax : Number of clauses : 72 ( 72 unt; 0 nHn; 5 RR)
% Number of literals : 72 ( 71 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 : 217 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'(inverse(X0),inverse('double$udivide'(inverse('double$udivide'(X0,'double$udivide'(X1,X2))),'double$udivide'(X3,'double$udivide'(X1,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'(inverse(X0),inverse('double$udivide'(inverse('double$udivide'(X0,'double$udivide'(X1,X2))),'double$udivide'(X3,'double$udivide'(X1,X3))))) = X2,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(X0,X1) = inverse('double$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$udivide'(inverse(X0),multiply('double$udivide'(X3,'double$udivide'(X1,X3)),inverse('double$udivide'(X0,'double$udivide'(X1,X2))))) = X2,
inference(demodulation,[status(thm)],[c0,c1]) ).
cnf(d1,plain,
'double$udivide'(inverse(X0),multiply('double$udivide'(X3,'double$udivide'(X1,X3)),multiply('double$udivide'(X1,X2),X0))) = X2,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
'double$udivide'(inverse(X4),multiply('double$udivide'(X5,'double$udivide'(inverse(X0),X5)),multiply(X3,X4))) = multiply('double$udivide'(X1,'double$udivide'(X2,X1)),multiply('double$udivide'(X2,X3),X0)),
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
'double$udivide'(inverse(X3),'double$udivide'(inverse(X4),multiply('double$udivide'(X5,'double$udivide'(inverse(X3),X5)),multiply(X2,X4)))) = X2,
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
multiply('double$udivide'(X4,'double$udivide'(X5,X4)),multiply('double$udivide'(X5,'double$udivide'(inverse(X2),X3)),X2)) = X3,
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d5,plain,
multiply('double$udivide'(X4,'double$udivide'(inverse(X0),X4)),multiply(X3,X1)) = multiply('double$udivide'(X2,'double$udivide'(inverse(X0),X2)),multiply(X3,X1)),
inference(superposition,[status(thm)],[d3,d4]) ).
cnf(d6,plain,
multiply('double$udivide'(X4,'double$udivide'(X0,X4)),multiply('double$udivide'(X3,'double$udivide'(inverse(multiply(X1,X2)),X3)),multiply(X1,X2))) = X0,
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
'double$udivide'(inverse(X1),'double$udivide'(inverse(multiply(X3,X4)),inverse(X1))) = 'double$udivide'(X2,'double$udivide'(inverse(multiply(X3,X4)),X2)),
inference(superposition,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
'double$udivide'(X3,'double$udivide'(inverse(multiply(X1,X2)),X3)) = 'double$udivide'(X4,'double$udivide'(inverse(multiply(X1,X2)),X4)),
inference(superposition,[status(thm)],[d7,d7]) ).
cnf(d9,plain,
multiply('double$udivide'(inverse(multiply(X1,X2)),X0),X0) = inverse('double$udivide'(X3,'double$udivide'(inverse(multiply(X1,X2)),X3))),
inference(superposition,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
multiply('double$udivide'(inverse(multiply(X1,X2)),X3),X3) = multiply('double$udivide'(inverse(multiply(X1,X2)),X0),X0),
inference(demodulation,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
'double$udivide'(inverse(X2),multiply('double$udivide'(X4,'double$udivide'(inverse(multiply(X0,X1)),X4)),multiply('double$udivide'(inverse(multiply(X0,X1)),X3),X3))) = X2,
inference(superposition,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
'double$udivide'(inverse(X6),'double$udivide'(inverse(X4),multiply('double$udivide'(X5,'double$udivide'(inverse(X3),X5)),multiply(X3,X4)))) = X6,
inference(superposition,[status(thm)],[d2,d11]) ).
cnf(d13,plain,
'double$udivide'(inverse(X5),multiply('double$udivide'(X3,'double$udivide'(X4,X3)),multiply('double$udivide'(X4,X2),X2))) = X5,
inference(superposition,[status(thm)],[d2,d12]) ).
cnf(d14,plain,
'double$udivide'(inverse(multiply('double$udivide'(X1,'double$udivide'(inverse(X2),X3)),X2)),multiply('double$udivide'(X4,'double$udivide'(X0,X4)),X3)) = 'double$udivide'(X1,X0),
inference(superposition,[status(thm)],[d4,d1]) ).
cnf(d15,plain,
'double$udivide'(X0,X2) = multiply('double$udivide'(X0,'double$udivide'(inverse(X1),multiply('double$udivide'(X2,X3),X3))),X1),
inference(superposition,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
multiply('double$udivide'(X2,'double$udivide'(X3,X2)),multiply('double$udivide'(X3,'double$udivide'(multiply(X1,X0),X4)),'double$udivide'(X0,X1))) = X4,
inference(superposition,[status(thm)],[c1,d4]) ).
cnf(d17,plain,
multiply('double$udivide'(X0,'double$udivide'(inverse(X1),multiply('double$udivide'(X2,X3),X3))),X1) = 'double$udivide'(X0,X2),
inference(superposition,[status(thm)],[d13,d14]) ).
cnf(d18,plain,
multiply('double$udivide'(X4,'double$udivide'(X5,X4)),'double$udivide'(multiply('double$udivide'(X0,X1),X1),X0)) = X5,
inference(superposition,[status(thm)],[d17,d6]) ).
cnf(d19,plain,
multiply('double$udivide'(X3,'double$udivide'(X0,X3)),multiply(X1,multiply('double$udivide'(X1,X2),X2))) = X0,
inference(superposition,[status(thm)],[d18,d16]) ).
cnf(d20,plain,
'double$udivide'(inverse(X3),'double$udivide'(inverse(multiply('double$udivide'(X1,X2),X2)),inverse(X1))) = X3,
inference(superposition,[status(thm)],[d19,d12]) ).
cnf(d21,plain,
'double$udivide'(inverse(multiply('double$udivide'('double$udivide'(X1,X2),X3),X3)),X1) = X2,
inference(superposition,[status(thm)],[d19,d1]) ).
cnf(d22,plain,
multiply('double$udivide'(X4,'double$udivide'(X0,X4)),'double$udivide'(X0,X2)) = multiply('double$udivide'(X2,X3),X3),
inference(superposition,[status(thm)],[d17,d4]) ).
cnf(d23,plain,
'double$udivide'(inverse(multiply('double$udivide'(X3,'double$udivide'(X4,X3)),'double$udivide'(X4,'double$udivide'(X0,X1)))),X0) = X1,
inference(superposition,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
X3 = multiply('double$udivide'(X4,'double$udivide'(X5,X4)),multiply('double$udivide'(X5,'double$udivide'(inverse(X2),X3)),X2)),
inference(superposition,[status(thm)],[d1,d2]) ).
cnf(d25,plain,
multiply('double$udivide'(X2,X3),X3) = multiply('double$udivide'(X4,'double$udivide'(X0,X4)),'double$udivide'(X0,X2)),
inference(superposition,[status(thm)],[d17,d24]) ).
cnf(d26,plain,
multiply('double$udivide'(X2,X4),X4) = multiply('double$udivide'(X2,X3),X3),
inference(superposition,[status(thm)],[d25,d25]) ).
cnf(d27,plain,
'double$udivide'(X2,'double$udivide'(inverse(multiply('double$udivide'(X0,X1),X1)),X2)) = X0,
inference(superposition,[status(thm)],[d20,d8]) ).
cnf(d28,plain,
multiply('double$udivide'(inverse(multiply('double$udivide'(X1,X2),X2)),X0),X0) = inverse(X1),
inference(superposition,[status(thm)],[d27,c1]) ).
cnf(d29,plain,
inverse(X0) = multiply('double$udivide'(inverse(multiply('double$udivide'(X0,X1),X1)),X3),X3),
inference(superposition,[status(thm)],[d28,d26]) ).
cnf(d30,plain,
inverse('double$udivide'(X0,X1)) = multiply(X1,X0),
inference(superposition,[status(thm)],[d21,d29]) ).
cnf(d31,plain,
'double$udivide'(X3,'double$udivide'(inverse(inverse(X0)),X3)) = inverse(multiply('double$udivide'(X0,X1),X1)),
inference(superposition,[status(thm)],[d28,d27]) ).
cnf(d32,plain,
'double$udivide'('double$udivide'(X3,'double$udivide'(inverse(inverse('double$udivide'(X0,X1))),X3)),X0) = X1,
inference(superposition,[status(thm)],[d31,d21]) ).
cnf(d33,plain,
'double$udivide'('double$udivide'(X2,'double$udivide'(inverse(multiply(X1,X0)),X2)),X0) = X1,
inference(demodulation,[status(thm)],[d32,c1]) ).
cnf(d34,plain,
inverse(X1) = multiply(X2,'double$udivide'(X0,'double$udivide'(inverse(multiply(X1,X2)),X0))),
inference(superposition,[status(thm)],[d33,d30]) ).
cnf(d35,plain,
'double$udivide'(inverse(inverse(X2)),inverse(multiply(X2,'double$udivide'(X0,'double$udivide'(X1,X0))))) = X1,
inference(superposition,[status(thm)],[d34,d23]) ).
cnf(d36,plain,
'double$udivide'(inverse(inverse(X3)),inverse(multiply(X3,X1))) = inverse(multiply('double$udivide'(X1,X2),X2)),
inference(superposition,[status(thm)],[d27,d35]) ).
cnf(d37,plain,
inverse(multiply('double$udivide'('double$udivide'(X1,'double$udivide'(X2,X1)),X3),X3)) = X2,
inference(superposition,[status(thm)],[d36,d35]) ).
cnf(d38,plain,
'double$udivide'(inverse(X3),'double$udivide'(X1,inverse('double$udivide'(X0,'double$udivide'(X1,X0))))) = X3,
inference(superposition,[status(thm)],[d37,d20]) ).
cnf(d39,plain,
'double$udivide'(inverse(X2),'double$udivide'(X1,multiply('double$udivide'(X1,X0),X0))) = X2,
inference(demodulation,[status(thm)],[d38,c1]) ).
cnf(d40,plain,
'double$udivide'(inverse(X0),inverse(X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[d39,d15]) ).
cnf(d41,plain,
'double$udivide'(inverse(X2),multiply(X1,X0)) = multiply(X2,'double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[d30,d40]) ).
cnf(d42,plain,
X0 = 'double$udivide'(X2,'double$udivide'(inverse(multiply('double$udivide'(X0,X1),X1)),X2)),
inference(superposition,[status(thm)],[d20,d8]) ).
cnf(d43,plain,
X0 = 'double$udivide'(inverse(X2),multiply(multiply('double$udivide'(X0,X1),X1),X2)),
inference(superposition,[status(thm)],[d40,d42]) ).
cnf(d44,plain,
X1 = multiply(X0,'double$udivide'(X0,multiply('double$udivide'(X1,X2),X2))),
inference(demodulation,[status(thm)],[d43,d41]) ).
cnf(d45,plain,
'double$udivide'(inverse(X2),multiply(multiply('double$udivide'(X0,X1),X1),X0)) = X2,
inference(demodulation,[status(thm)],[d20,d40]) ).
cnf(d46,plain,
multiply(X0,'double$udivide'(X1,multiply('double$udivide'(X1,X2),X2))) = X0,
inference(demodulation,[status(thm)],[d45,d41]) ).
cnf(d47,plain,
multiply(X2,multiply(X0,'double$udivide'(X1,'double$udivide'(inverse(X0),X1)))) = X2,
inference(superposition,[status(thm)],[d41,d46]) ).
cnf(d48,plain,
multiply(X0,X1) = 'double$udivide'(inverse(X0),inverse(X1)),
inference(superposition,[status(thm)],[d39,d17]) ).
cnf(d49,plain,
multiply(X2,multiply(X0,'double$udivide'(inverse(X1),multiply(X0,X1)))) = X2,
inference(superposition,[status(thm)],[d48,d47]) ).
cnf(d50,plain,
multiply(X2,multiply(X1,multiply(X0,'double$udivide'(X0,X1)))) = X2,
inference(demodulation,[status(thm)],[d49,d41]) ).
cnf(d51,plain,
multiply(X1,'double$udivide'(inverse(X0),X0)) = X1,
inference(superposition,[status(thm)],[d47,d50]) ).
cnf(d52,plain,
X0 = inverse(multiply('double$udivide'(X0,X1),X1)),
inference(superposition,[status(thm)],[d51,d44]) ).
cnf(d53,plain,
multiply('double$udivide'(X0,X2),X2) = inverse(X0),
inference(demodulation,[status(thm)],[d28,d52]) ).
cnf(d54,plain,
X0 = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[d52,d53]) ).
cnf(d55,plain,
'double$udivide'(X0,inverse(X1)) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d54,d40]) ).
cnf(d56,plain,
'double$udivide'(a1,inverse(a1)) != multiply(inverse(b1),b1),
inference(demodulation,[status(thm)],[c2,d55]) ).
cnf(d57,plain,
'double$udivide'(a1,inverse(a1)) != 'double$udivide'(b1,inverse(b1)),
inference(demodulation,[status(thm)],[d56,d55]) ).
cnf(d58,plain,
X0 = 'double$udivide'(X2,'double$udivide'(X0,X2)),
inference(demodulation,[status(thm)],[d42,d52]) ).
cnf(d59,plain,
X1 = multiply(inverse(X0),multiply(X0,'double$udivide'(X2,'double$udivide'(X1,X2)))),
inference(superposition,[status(thm)],[d41,d44]) ).
cnf(d60,plain,
X1 = multiply(inverse(X2),multiply(X2,X1)),
inference(demodulation,[status(thm)],[d59,d58]) ).
cnf(d61,plain,
multiply(X1,multiply(inverse(X0),X0)) = X1,
inference(superposition,[status(thm)],[d48,d51]) ).
cnf(d62,plain,
multiply(inverse(X1),X1) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d61,d60]) ).
cnf(d63,plain,
'double$udivide'(X0,inverse(X0)) = multiply(inverse(X1),X1),
inference(demodulation,[status(thm)],[d62,d55]) ).
cnf(d64,plain,
'double$udivide'(X1,inverse(X1)) = 'double$udivide'(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d63,d55]) ).
cnf(d65,plain,
$false,
inference(resolution,[status(thm)],[d64,d57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP499-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n004.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Fri Sep 25 14:57:12 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.40/14.50 % SZS status Unsatisfiable for theBenchmark.p
% 10.40/14.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------