%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP591-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 07:24:06 AM UTC 2026
% Result : Unsatisfiable 73.21s 16.99s
% Output : CNFRefutation 73.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 3
% Syntax : Number of clauses : 69 ( 69 unt; 0 nHn; 4 RR)
% Number of literals : 69 ( 68 equ; 3 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 165 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'(inverse('double$udivide'('double$udivide'(X0,X1),inverse('double$udivide'(X0,inverse(X2))))),X1) = X2 ).
cnf(multiply,axiom,
multiply(X0,X1) = inverse('double$udivide'(X1,X0)) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ).
cnf(c0,plain,
'double$udivide'(inverse('double$udivide'('double$udivide'(X0,X1),inverse('double$udivide'(X0,inverse(X2))))),X1) = X2,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(X0,X1) = inverse('double$udivide'(X1,X0)),
inference(clausification,[status(esa)],[multiply]) ).
cnf(c2,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausification,[status(esa)],[prove_these_axioms_3]) ).
cnf(d0,plain,
'double$udivide'(multiply(inverse('double$udivide'(X0,inverse(X2))),'double$udivide'(X0,X1)),X1) = X2,
inference(demodulation,[status(thm)],[c0,c1]) ).
cnf(d1,plain,
'double$udivide'(multiply(multiply(inverse(X1),X0),'double$udivide'(X0,X2)),X2) = X1,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
'double$udivide'(multiply(multiply(inverse(X3),multiply(multiply(inverse(X0),X1),'double$udivide'(X1,X2))),X0),X2) = X3,
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
multiply(X2,multiply(multiply(inverse(X0),X1),'double$udivide'(X1,X2))) = inverse(X0),
inference(superposition,[status(thm)],[d1,c1]) ).
cnf(d4,plain,
'double$udivide'(multiply(inverse(X1),X1),inverse(X0)) = X0,
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
multiply(inverse(X1),multiply(inverse(X0),X0)) = inverse(X1),
inference(superposition,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
'double$udivide'(inverse(multiply(inverse(X0),X0)),inverse(X1)) = X1,
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
'double$udivide'(multiply(inverse(X1),'double$udivide'(multiply(multiply(inverse(X1),X2),'double$udivide'(X2,inverse(X0))),X3)),X3) = X0,
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d8,plain,
'double$udivide'(multiply(multiply(X1,X0),'double$udivide'(X0,X1)),inverse(X2)) = X2,
inference(superposition,[status(thm)],[c1,d4]) ).
cnf(d9,plain,
'double$udivide'(multiply(inverse(X0),X2),inverse(X2)) = X0,
inference(superposition,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
multiply(X3,multiply(inverse(X1),'double$udivide'(multiply(multiply(inverse(X1),X2),'double$udivide'(X2,inverse(X0))),X3))) = inverse(X0),
inference(superposition,[status(thm)],[d3,d3]) ).
cnf(d11,plain,
multiply(inverse(X2),multiply(inverse(X0),X2)) = inverse(X0),
inference(superposition,[status(thm)],[d8,d10]) ).
cnf(d12,plain,
'double$udivide'(inverse(X1),inverse(multiply(inverse(X1),X0))) = X0,
inference(superposition,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
X1 = multiply(inverse(multiply(inverse(X0),X0)),X1),
inference(superposition,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
'double$udivide'(X1,inverse(X1)) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
X2 = multiply(inverse('double$udivide'(X1,inverse(X1))),X2),
inference(superposition,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
X1 = multiply(multiply(inverse(X0),X0),X1),
inference(demodulation,[status(thm)],[d15,c1]) ).
cnf(d17,plain,
'double$udivide'('double$udivide'(X0,X1),X1) = X0,
inference(superposition,[status(thm)],[d16,d1]) ).
cnf(d18,plain,
'double$udivide'(X0,inverse(X1)) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d9,d17]) ).
cnf(d19,plain,
multiply(X1,'double$udivide'(X0,X1)) = inverse(X0),
inference(superposition,[status(thm)],[d16,d3]) ).
cnf(d20,plain,
'double$udivide'(inverse(X1),multiply(inverse(X0),X1)) = X0,
inference(superposition,[status(thm)],[d19,d1]) ).
cnf(d21,plain,
'double$udivide'(inverse(X1),'double$udivide'(X0,inverse(X1))) = X0,
inference(demodulation,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
'double$udivide'(X1,multiply(inverse(X0),X0)) = inverse(X1),
inference(superposition,[status(thm)],[d19,d16]) ).
cnf(d23,plain,
'double$udivide'(X1,'double$udivide'(X0,inverse(X0))) = inverse(X1),
inference(demodulation,[status(thm)],[d22,d18]) ).
cnf(d24,plain,
inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
inverse(multiply(X1,X0)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[c1,d24]) ).
cnf(d26,plain,
inverse('double$udivide'(X1,X0)) = multiply(X0,X1),
inference(superposition,[status(thm)],[d25,d24]) ).
cnf(d27,plain,
inverse(X0) = multiply(X1,'double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[d17,d26]) ).
cnf(d28,plain,
'double$udivide'(X0,'double$udivide'(X1,inverse(inverse(X0)))) = X1,
inference(superposition,[status(thm)],[d24,d21]) ).
cnf(d29,plain,
'double$udivide'(X0,'double$udivide'(X1,X0)) = X1,
inference(demodulation,[status(thm)],[d28,d24]) ).
cnf(d30,plain,
'double$udivide'('double$udivide'(X1,X0),X1) = X0,
inference(superposition,[status(thm)],[d29,d29]) ).
cnf(d31,plain,
inverse('double$udivide'(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[d30,d27]) ).
cnf(d32,plain,
multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[status(thm)],[d31,d26]) ).
cnf(d33,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(demodulation,[status(thm)],[c2,d32]) ).
cnf(d34,plain,
'double$udivide'('double$udivide'(X0,X1),inverse(X2)) = multiply(multiply(X1,X0),X2),
inference(superposition,[status(thm)],[c1,d18]) ).
cnf(d35,plain,
'double$udivide'('double$udivide'(X0,X1),inverse(X2)) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[d31,d18]) ).
cnf(d36,plain,
multiply(multiply(X0,X1),X2) = multiply(multiply(X1,X0),X2),
inference(superposition,[status(thm)],[d35,d34]) ).
cnf(d37,plain,
multiply(multiply(X1,X0),X2) = multiply(X2,multiply(X0,X1)),
inference(superposition,[status(thm)],[d36,d32]) ).
cnf(d38,plain,
inverse(X1) = multiply(X0,'double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[d30,d26]) ).
cnf(d39,plain,
'double$udivide'(inverse(X0),inverse(X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[d24,d18]) ).
cnf(d40,plain,
'double$udivide'('double$udivide'(X1,inverse(X1)),inverse(X2)) = X2,
inference(superposition,[status(thm)],[d14,d4]) ).
cnf(d41,plain,
'double$udivide'('double$udivide'(X1,inverse(X1)),X0) = inverse(X0),
inference(superposition,[status(thm)],[d24,d40]) ).
cnf(d42,plain,
'double$udivide'(X1,X0) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d17,d29]) ).
cnf(d43,plain,
'double$udivide'(multiply(multiply(inverse(X2),multiply(inverse(X0),'double$udivide'(multiply(inverse(X1),X1),X3))),X0),X3) = X2,
inference(superposition,[status(thm)],[d5,d2]) ).
cnf(d44,plain,
'double$udivide'(X3,multiply(multiply(inverse(X0),multiply(inverse(X1),'double$udivide'(multiply(inverse(X2),X2),X3))),X1)) = X0,
inference(demodulation,[status(thm)],[d43,d42]) ).
cnf(d45,plain,
'double$udivide'(X3,multiply(X1,multiply(inverse(X0),multiply(inverse(X1),'double$udivide'(multiply(inverse(X2),X2),X3))))) = X0,
inference(demodulation,[status(thm)],[d44,d32]) ).
cnf(d46,plain,
'double$udivide'(X3,multiply(X1,'double$udivide'(X0,inverse(multiply(inverse(X1),'double$udivide'(multiply(inverse(X2),X2),X3)))))) = X0,
inference(demodulation,[status(thm)],[d45,d18]) ).
cnf(d47,plain,
'double$udivide'(X2,multiply(X0,'double$udivide'(X3,'double$udivide'('double$udivide'(multiply(inverse(X1),X1),X2),inverse(X0))))) = X3,
inference(demodulation,[status(thm)],[d46,d25]) ).
cnf(d48,plain,
'double$udivide'(X1,multiply(X2,'double$udivide'(X3,'double$udivide'('double$udivide'('double$udivide'(X0,inverse(X0)),X1),inverse(X2))))) = X3,
inference(demodulation,[status(thm)],[d47,d18]) ).
cnf(d49,plain,
'double$udivide'(X1,multiply(X2,'double$udivide'(X3,'double$udivide'(inverse(X1),inverse(X2))))) = X3,
inference(demodulation,[status(thm)],[d48,d41]) ).
cnf(d50,plain,
'double$udivide'(X0,multiply(X1,'double$udivide'(X2,multiply(X0,X1)))) = X2,
inference(demodulation,[status(thm)],[d49,d39]) ).
cnf(d51,plain,
'double$udivide'(X1,multiply(X2,'double$udivide'(multiply(X1,X2),X0))) = X0,
inference(superposition,[status(thm)],[d42,d50]) ).
cnf(d52,plain,
inverse(inverse(X1)) = 'double$udivide'('double$udivide'(X1,X0),X0),
inference(superposition,[status(thm)],[d19,d25]) ).
cnf(d53,plain,
X0 = 'double$udivide'('double$udivide'(X0,X1),X1),
inference(demodulation,[status(thm)],[d52,d24]) ).
cnf(d54,plain,
X0 = 'double$udivide'(X1,'double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[d53,d42]) ).
cnf(d55,plain,
X0 = 'double$udivide'('double$udivide'(X1,X0),X1),
inference(superposition,[status(thm)],[d54,d54]) ).
cnf(d56,plain,
X1 = 'double$udivide'(X0,'double$udivide'(X0,X1)),
inference(demodulation,[status(thm)],[d55,d42]) ).
cnf(d57,plain,
multiply(X1,'double$udivide'(X2,multiply(X0,X1))) = 'double$udivide'(X0,X2),
inference(superposition,[status(thm)],[d50,d56]) ).
cnf(d58,plain,
'double$udivide'(X1,'double$udivide'(X2,multiply(X1,X0))) = multiply(X2,X0),
inference(superposition,[status(thm)],[d57,d51]) ).
cnf(d59,plain,
inverse('double$udivide'(X1,multiply(X0,X2))) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[d58,d38]) ).
cnf(d60,plain,
multiply(multiply(X1,X2),X0) = multiply(X1,multiply(X0,X2)),
inference(demodulation,[status(thm)],[d59,c1]) ).
cnf(d61,plain,
multiply(X0,multiply(X2,X1)) = multiply(X2,multiply(X1,X0)),
inference(superposition,[status(thm)],[d60,d37]) ).
cnf(d62,plain,
$false,
inference(resolution,[status(thm)],[d61,d33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP591-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.58 % Computer : n009.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Fri Sep 25 15:01:45 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 73.21/16.99 % SZS status Unsatisfiable for theBenchmark.p
% 73.21/16.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------