%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP605-1 : 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 : n014.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 07:24:08 AM UTC 2026
% Result : Unsatisfiable 43.54s 8.84s
% Output : CNFRefutation 43.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 7 RR)
% Number of literals : 60 ( 59 equ; 6 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 : 123 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'(inverse('double$udivide'(X0,inverse('double$udivide'(inverse(X1),'double$udivide'(X0,X2))))),X2) = X1 ).
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('double$udivide'(X0,inverse('double$udivide'(inverse(X1),'double$udivide'(X0,X2))))),X2) = X1,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(X0,X1) = inverse('double$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$udivide'(multiply(inverse('double$udivide'(inverse(X1),'double$udivide'(X0,X2))),X0),X2) = X1,
inference(demodulation,[status(thm)],[c0,c1]) ).
cnf(d1,plain,
'double$udivide'(multiply(multiply('double$udivide'(X1,X2),inverse(X0)),X1),X2) = X0,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
multiply(X1,multiply(multiply('double$udivide'(X0,X1),inverse(X2)),X0)) = inverse(X2),
inference(superposition,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
'double$udivide'(multiply(multiply(X2,inverse(X3)),multiply(multiply('double$udivide'(X0,X1),inverse(X2)),X0)),X1) = X3,
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d4,plain,
'double$udivide'(inverse(X0),multiply(X0,inverse(X1))) = X1,
inference(superposition,[status(thm)],[d2,d3]) ).
cnf(d5,plain,
multiply(multiply(X0,inverse(X1)),inverse(X0)) = inverse(X1),
inference(superposition,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
'double$udivide'(inverse(multiply(X0,inverse(X1))),inverse(X1)) = X0,
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
multiply(multiply(X2,multiply(X1,X0)),inverse(X2)) = inverse('double$udivide'(X0,X1)),
inference(superposition,[status(thm)],[c1,d5]) ).
cnf(d8,plain,
multiply(multiply(X2,multiply(X1,X0)),inverse(X2)) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
'double$udivide'(inverse(multiply(X1,X2)),inverse(X0)) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
multiply(X1,multiply(X0,inverse(X1))) = X0,
inference(demodulation,[status(thm)],[d6,d9]) ).
cnf(d11,plain,
multiply('double$udivide'(inverse(X0),X0),inverse(X1)) = inverse(X1),
inference(superposition,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
'double$udivide'(multiply(inverse(X1),inverse(X0)),X0) = X1,
inference(superposition,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
'double$udivide'(multiply(multiply(X0,inverse(X2)),inverse(multiply(X0,inverse(X1)))),inverse(X1)) = X2,
inference(superposition,[status(thm)],[d6,d1]) ).
cnf(d14,plain,
multiply(X1,inverse(X1)) = 'double$udivide'(inverse(X0),X0),
inference(superposition,[status(thm)],[d11,d10]) ).
cnf(d15,plain,
multiply(X0,'double$udivide'(inverse(X1),X1)) = X0,
inference(superposition,[status(thm)],[d14,d10]) ).
cnf(d16,plain,
multiply(X2,multiply(X1,inverse(X1))) = X2,
inference(superposition,[status(thm)],[d14,d15]) ).
cnf(d17,plain,
multiply(inverse(X1),inverse(multiply(X0,inverse(X1)))) = inverse(X0),
inference(superposition,[status(thm)],[d5,d5]) ).
cnf(d18,plain,
multiply(inverse(X1),inverse(inverse(X0))) = inverse(multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[d17,d5]) ).
cnf(d19,plain,
multiply(X1,inverse(multiply(X0,inverse(X0)))) = X1,
inference(superposition,[status(thm)],[d18,d16]) ).
cnf(d20,plain,
'double$udivide'(multiply(X0,inverse(X1)),inverse(X0)) = X1,
inference(superposition,[status(thm)],[d19,d13]) ).
cnf(d21,plain,
inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[d20,d12]) ).
cnf(d22,plain,
'double$udivide'(inverse(inverse(X1)),inverse(X0)) = multiply(X0,inverse(X1)),
inference(superposition,[status(thm)],[d5,d6]) ).
cnf(d23,plain,
'double$udivide'(X0,inverse(X1)) = multiply(X1,inverse(X0)),
inference(demodulation,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
'double$udivide'(multiply(multiply('double$udivide'(X2,X3),multiply(X1,X0)),X2),X3) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[c1,d1]) ).
cnf(d25,plain,
'double$udivide'(multiply(multiply('double$udivide'(X3,X4),inverse(X2)),X3),X4) = 'double$udivide'(multiply(multiply('double$udivide'(X1,X0),inverse(X2)),X1),X0),
inference(superposition,[status(thm)],[d2,d24]) ).
cnf(d26,plain,
X2 = 'double$udivide'(multiply(multiply('double$udivide'(X3,X4),inverse(X2)),X3),X4),
inference(demodulation,[status(thm)],[d25,d1]) ).
cnf(d27,plain,
multiply(multiply(X1,inverse(X1)),X0) = X0,
inference(superposition,[status(thm)],[d19,d10]) ).
cnf(d28,plain,
multiply('double$udivide'(inverse(X1),X1),X2) = X2,
inference(superposition,[status(thm)],[d14,d27]) ).
cnf(d29,plain,
X1 = 'double$udivide'(multiply(inverse(X1),inverse(X0)),X0),
inference(superposition,[status(thm)],[d28,d26]) ).
cnf(d30,plain,
X0 = 'double$udivide'(inverse(multiply(X0,inverse(X1))),inverse(X1)),
inference(superposition,[status(thm)],[d18,d29]) ).
cnf(d31,plain,
X0 = multiply(X1,multiply(X0,inverse(X1))),
inference(demodulation,[status(thm)],[d30,d9]) ).
cnf(d32,plain,
multiply(multiply('double$udivide'(X0,X1),inverse(X2)),multiply(X1,X0)) = inverse(X2),
inference(superposition,[status(thm)],[c1,d5]) ).
cnf(d33,plain,
inverse('double$udivide'(X0,X1)) = multiply(X1,X0),
inference(superposition,[status(thm)],[d32,d27]) ).
cnf(d34,plain,
inverse(multiply(X1,X0)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d33,d21]) ).
cnf(d35,plain,
multiply(X0,inverse(multiply(X0,inverse(X1)))) = X1,
inference(superposition,[status(thm)],[d20,d13]) ).
cnf(d36,plain,
multiply(X0,'double$udivide'(inverse(X1),X0)) = X1,
inference(demodulation,[status(thm)],[d35,d34]) ).
cnf(d37,plain,
multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(superposition,[status(thm)],[d4,d36]) ).
cnf(d38,plain,
multiply(multiply(X1,X0),inverse(X0)) = X1,
inference(superposition,[status(thm)],[d21,d37]) ).
cnf(d39,plain,
multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[status(thm)],[d38,d31]) ).
cnf(d40,plain,
multiply(a1,inverse(a1)) != multiply(inverse(b1),b1),
inference(demodulation,[status(thm)],[c2,d39]) ).
cnf(d41,plain,
multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)),
inference(demodulation,[status(thm)],[d40,d39]) ).
cnf(d42,plain,
'double$udivide'(a1,inverse(a1)) != multiply(b1,inverse(b1)),
inference(demodulation,[status(thm)],[d41,d23]) ).
cnf(d43,plain,
'double$udivide'(a1,inverse(a1)) != 'double$udivide'(b1,inverse(b1)),
inference(demodulation,[status(thm)],[d42,d23]) ).
cnf(d44,plain,
'double$udivide'(X0,inverse(multiply(X0,X1))) = X1,
inference(superposition,[status(thm)],[d38,d20]) ).
cnf(d45,plain,
'double$udivide'(X0,'double$udivide'(X1,X0)) = X1,
inference(demodulation,[status(thm)],[d44,d34]) ).
cnf(d46,plain,
X0 = 'double$udivide'(inverse(X1),multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[d17,d29]) ).
cnf(d47,plain,
X1 = 'double$udivide'(inverse(multiply(X0,X1)),X0),
inference(superposition,[status(thm)],[d38,d46]) ).
cnf(d48,plain,
X1 = 'double$udivide'('double$udivide'(X1,X0),X0),
inference(demodulation,[status(thm)],[d47,d34]) ).
cnf(d49,plain,
'double$udivide'(X1,X0) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[d48,d45]) ).
cnf(d50,plain,
'double$udivide'(inverse(X1),X1) = 'double$udivide'(inverse(X2),X2),
inference(superposition,[status(thm)],[d14,d14]) ).
cnf(d51,plain,
'double$udivide'(X0,inverse(X0)) = 'double$udivide'(inverse(X1),X1),
inference(superposition,[status(thm)],[d21,d50]) ).
cnf(d52,plain,
'double$udivide'(X1,inverse(X1)) = 'double$udivide'(X0,inverse(X0)),
inference(demodulation,[status(thm)],[d51,d49]) ).
cnf(d53,plain,
$false,
inference(resolution,[status(thm)],[d52,d43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP605-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n014.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 15:01:47 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.54/8.84 % SZS status Unsatisfiable for theBenchmark.p
% 43.54/8.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------