%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP593-1 : 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 : n018.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 07:24:07 AM UTC 2026
% Result : Unsatisfiable 27.05s 9.34s
% Output : CNFRefutation 27.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 3 RR)
% Number of literals : 39 ( 38 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 : 103 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse('double$udivide'('double$udivide'(X0,X1),inverse('double$udivide'(X0,inverse('double$udivide'(X2,X1)))))) = X2 ).
cnf(multiply,axiom,
multiply(X0,X1) = inverse('double$udivide'(X1,X0)) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
cnf(c0,plain,
inverse('double$udivide'('double$udivide'(X0,X1),inverse('double$udivide'(X0,inverse('double$udivide'(X2,X1)))))) = X2,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
inverse('double$udivide'(X0,X1)) = multiply(X1,X0),
inference(clausification,[status(esa)],[multiply]) ).
cnf(c2,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(clausification,[status(esa)],[prove_these_axioms_1]) ).
cnf(d0,plain,
multiply(inverse('double$udivide'(X0,inverse('double$udivide'(X2,X1)))),'double$udivide'(X0,X1)) = X2,
inference(demodulation,[status(thm)],[c0,c1]) ).
cnf(d1,plain,
multiply(multiply(inverse('double$udivide'(X1,X2)),X0),'double$udivide'(X0,X2)) = X1,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
multiply(multiply(multiply(X1,X0),X2),'double$udivide'(X2,X1)) = X0,
inference(demodulation,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
multiply(X1,'double$udivide'('double$udivide'(X2,X0),multiply(X0,X1))) = X2,
inference(superposition,[status(thm)],[d2,d2]) ).
cnf(d4,plain,
multiply(multiply(X1,X3),'double$udivide'(X3,multiply(multiply(X0,X1),X2))) = 'double$udivide'(X2,X0),
inference(superposition,[status(thm)],[d2,d2]) ).
cnf(d5,plain,
'double$udivide'(multiply(X0,'double$udivide'(X1,multiply(X2,X0))),X2) = X1,
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
'double$udivide'(multiply(X3,X1),X2) = multiply(X0,'double$udivide'(X1,multiply(multiply(X2,X3),X0))),
inference(superposition,[status(thm)],[d5,d5]) ).
cnf(d7,plain,
multiply(multiply(X3,multiply(X0,'double$udivide'(X1,multiply(multiply(multiply(X2,X3),X4),X0)))),X1) = 'double$udivide'(X4,X2),
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d8,plain,
multiply(multiply(X3,'double$udivide'(multiply(X4,X1),multiply(X2,X3))),X1) = 'double$udivide'(X4,X2),
inference(demodulation,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
X1 = 'double$udivide'(multiply(X0,'double$udivide'(X1,multiply(X2,X0))),X2),
inference(superposition,[status(thm)],[d3,d4]) ).
cnf(d10,plain,
X1 = 'double$udivide'('double$udivide'(multiply(X0,X1),X2),multiply(X2,X0)),
inference(superposition,[status(thm)],[d4,d9]) ).
cnf(d11,plain,
multiply(multiply(X1,X3),'double$udivide'(X3,X0)) = 'double$udivide'('double$udivide'(X1,X2),multiply(X2,X0)),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d12,plain,
X1 = multiply(multiply(multiply(X0,X1),X3),'double$udivide'(X3,X0)),
inference(superposition,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
'double$udivide'('double$udivide'(multiply(X0,X1),X2),multiply(X2,X0)) = X1,
inference(superposition,[status(thm)],[d4,d5]) ).
cnf(d14,plain,
inverse(X1) = multiply(multiply(X2,X0),'double$udivide'(multiply(X0,X1),X2)),
inference(superposition,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
X1 = multiply(inverse(X2),'double$udivide'('double$udivide'(multiply(X1,X2),X0),X0)),
inference(superposition,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
'double$udivide'(multiply(X1,X0),multiply(X2,inverse(X0))) = 'double$udivide'(X1,X2),
inference(superposition,[status(thm)],[d15,d9]) ).
cnf(d17,plain,
multiply(multiply(inverse(X1),'double$udivide'(X0,X2)),X1) = 'double$udivide'(X0,X2),
inference(superposition,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
multiply(inverse(X2),'double$udivide'('double$udivide'(multiply(X1,X2),X0),X0)) = X1,
inference(superposition,[status(thm)],[d14,d2]) ).
cnf(d19,plain,
multiply(X1,X0) = 'double$udivide'('double$udivide'(multiply(X1,X0),X2),X2),
inference(superposition,[status(thm)],[d18,d17]) ).
cnf(d20,plain,
X0 = multiply(inverse(X1),multiply(X0,X1)),
inference(demodulation,[status(thm)],[d15,d19]) ).
cnf(d21,plain,
inverse(X0) = multiply(inverse(multiply(X1,X0)),X1),
inference(superposition,[status(thm)],[d20,d20]) ).
cnf(d22,plain,
multiply(inverse(X1),multiply(X0,X1)) = X0,
inference(demodulation,[status(thm)],[d18,d19]) ).
cnf(d23,plain,
multiply(inverse(multiply(X1,X0)),X1) = inverse(X0),
inference(superposition,[status(thm)],[d22,d22]) ).
cnf(d24,plain,
inverse(multiply(X0,X1)) = multiply(inverse(X0),inverse(X1)),
inference(superposition,[status(thm)],[d23,d20]) ).
cnf(d25,plain,
inverse(multiply(multiply(inverse(X0),X1),X0)) = inverse(X1),
inference(superposition,[status(thm)],[d24,d23]) ).
cnf(d26,plain,
X2 = multiply(X1,'double$udivide'('double$udivide'(X2,X0),multiply(X0,X1))),
inference(superposition,[status(thm)],[d12,d12]) ).
cnf(d27,plain,
X0 = multiply(X2,multiply(multiply(X0,X3),'double$udivide'(X3,X2))),
inference(superposition,[status(thm)],[d11,d26]) ).
cnf(d28,plain,
X0 = multiply(multiply(X2,multiply(X0,'double$udivide'(X1,X2))),X1),
inference(superposition,[status(thm)],[d3,d27]) ).
cnf(d29,plain,
inverse(X1) = inverse(multiply(X1,'double$udivide'(X0,inverse(X0)))),
inference(superposition,[status(thm)],[d28,d25]) ).
cnf(d30,plain,
inverse('double$udivide'(X1,inverse(X1))) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d29,d21]) ).
cnf(d31,plain,
multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(demodulation,[status(thm)],[d30,c1]) ).
cnf(d32,plain,
$false,
inference(resolution,[status(thm)],[d31,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP593-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n018.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Fri Sep 25 15:03:56 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.05/9.34 % SZS status Unsatisfiable for theBenchmark.p
% 27.05/9.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------