%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP592-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 07:24:06 AM UTC 2026
% Result : Unsatisfiable 25.87s 3.66s
% Output : CNFRefutation 25.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of clauses : 41 ( 41 unt; 0 nHn; 3 RR)
% Number of literals : 41 ( 40 equ; 2 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 : 83 ( 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$udivide'(X1,X0)) ).
cnf(prove_these_axioms_4,negated_conjecture,
multiply(a,b) != multiply(b,a) ).
cnf(c0,plain,
'double$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(a,b) != multiply(b,a),
inference(clausification,[status(esa)],[prove_these_axioms_4]) ).
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'(multiply(inverse(X0),'double$udivide'(multiply(inverse(X1),X1),X2)),X2) = X0,
inference(superposition,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
X1 = 'double$udivide'(multiply(inverse(X0),X0),inverse(X1)),
inference(superposition,[status(thm)],[d4,d6]) ).
cnf(d8,plain,
X1 = 'double$udivide'(inverse(multiply(inverse(X0),X0)),inverse(X1)),
inference(superposition,[status(thm)],[d5,d7]) ).
cnf(d9,plain,
'double$udivide'(multiply(inverse(X2),X1),inverse(X1)) = X2,
inference(superposition,[status(thm)],[d4,d6]) ).
cnf(d10,plain,
multiply(inverse(X1),multiply(inverse(X0),X1)) = inverse(X0),
inference(superposition,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
'double$udivide'(inverse(X1),inverse(multiply(inverse(X1),X0))) = X0,
inference(superposition,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
multiply(inverse(multiply(inverse(X0),X0)),X1) = X1,
inference(superposition,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
'double$udivide'(inverse(multiply(inverse(X0),X0)),inverse(X1)) = X1,
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d14,plain,
X1 = multiply(inverse(multiply(inverse(X0),X0)),X1),
inference(superposition,[status(thm)],[d11,d13]) ).
cnf(d15,plain,
'double$udivide'(X1,inverse(X1)) = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[d14,d9]) ).
cnf(d16,plain,
multiply(inverse('double$udivide'(X1,inverse(X1))),X2) = X2,
inference(superposition,[status(thm)],[d15,d12]) ).
cnf(d17,plain,
multiply(multiply(inverse(X0),X0),X1) = X1,
inference(demodulation,[status(thm)],[d16,c1]) ).
cnf(d18,plain,
'double$udivide'('double$udivide'(X0,X1),X1) = X0,
inference(superposition,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
'double$udivide'(X0,inverse(X1)) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[d9,d18]) ).
cnf(d20,plain,
multiply(X1,'double$udivide'(X0,X1)) = inverse(X0),
inference(superposition,[status(thm)],[d17,d3]) ).
cnf(d21,plain,
'double$udivide'(inverse(X1),multiply(inverse(X0),X1)) = X0,
inference(superposition,[status(thm)],[d20,d1]) ).
cnf(d22,plain,
'double$udivide'(inverse(X1),'double$udivide'(X0,inverse(X1))) = X0,
inference(demodulation,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
inverse(X1) = 'double$udivide'(X1,multiply(inverse(X0),X0)),
inference(superposition,[status(thm)],[d20,d17]) ).
cnf(d24,plain,
inverse(X1) = 'double$udivide'(X1,'double$udivide'(X0,inverse(X0))),
inference(demodulation,[status(thm)],[d23,d19]) ).
cnf(d25,plain,
inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[d24,d22]) ).
cnf(d26,plain,
inverse(multiply(X1,X0)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[c1,d25]) ).
cnf(d27,plain,
inverse('double$udivide'(X1,X0)) = multiply(X0,X1),
inference(superposition,[status(thm)],[d26,d25]) ).
cnf(d28,plain,
inverse(X0) = multiply(X1,'double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[d18,d27]) ).
cnf(d29,plain,
'double$udivide'(inverse(inverse(X0)),'double$udivide'(X1,X0)) = X1,
inference(superposition,[status(thm)],[d25,d22]) ).
cnf(d30,plain,
'double$udivide'(X0,'double$udivide'(X1,X0)) = X1,
inference(demodulation,[status(thm)],[d29,d25]) ).
cnf(d31,plain,
'double$udivide'('double$udivide'(X1,X0),X1) = X0,
inference(superposition,[status(thm)],[d30,d30]) ).
cnf(d32,plain,
inverse('double$udivide'(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[d31,d28]) ).
cnf(d33,plain,
multiply(X1,X0) = multiply(X0,X1),
inference(superposition,[status(thm)],[d32,c1]) ).
cnf(d34,plain,
$false,
inference(resolution,[status(thm)],[d33,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP592-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 15:03:51 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.87/3.66 % SZS status Unsatisfiable for theBenchmark.p
% 25.87/3.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------