%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP598-1 : 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 : n011.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 20.17s 5.51s
% Output : CNFRefutation 20.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 8 RR)
% Number of literals : 40 ( 39 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 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 : 94 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
'double$udivide'('double$udivide'(X0,X1),inverse('double$udivide'(X0,inverse('double$udivide'(inverse(X2),X1))))) = X2 ).
cnf(multiply,axiom,
multiply(X0,X1) = inverse('double$udivide'(X1,X0)) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
cnf(c0,plain,
'double$udivide'('double$udivide'(X0,X1),inverse('double$udivide'(X0,inverse('double$udivide'(inverse(X2),X1))))) = X2,
inference(clausification,[status(esa)],[single_axiom]) ).
cnf(c1,plain,
multiply(X0,X1) = inverse('double$udivide'(X1,X0)),
inference(clausification,[status(esa)],[multiply]) ).
cnf(c2,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausification,[status(esa)],[prove_these_axioms_2]) ).
cnf(d0,plain,
'double$udivide'('double$udivide'(X0,X2),multiply(inverse('double$udivide'(inverse(X1),X2)),X0)) = X1,
inference(demodulation,[status(thm)],[c0,c1]) ).
cnf(d1,plain,
'double$udivide'('double$udivide'(X2,X1),multiply(multiply(X1,inverse(X0)),X2)) = X0,
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
'double$udivide'(X2,multiply(multiply(multiply(multiply(X1,inverse(X2)),X0),inverse(X3)),'double$udivide'(X0,X1))) = X3,
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
'double$udivide'(X3,multiply(multiply(multiply(multiply(multiply(multiply(X1,inverse(X0)),X2),inverse(X3)),'double$udivide'(X2,X1)),inverse(X4)),X0)) = X4,
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
multiply(multiply(multiply(multiply(multiply(X1,inverse(X0)),X2),inverse(X3)),'double$udivide'(X2,X1)),X0) = inverse(X3),
inference(superposition,[status(thm)],[d2,c1]) ).
cnf(d5,plain,
'double$udivide'(X3,multiply(inverse(X3),inverse(X1))) = X1,
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
multiply(multiply(inverse(X0),inverse(X1)),X0) = inverse(X1),
inference(superposition,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
'double$udivide'('double$udivide'(X0,inverse(X0)),inverse(X1)) = X1,
inference(superposition,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
'double$udivide'('double$udivide'(X2,inverse(X2)),multiply(X1,X0)) = 'double$udivide'(X0,X1),
inference(superposition,[status(thm)],[c1,d7]) ).
cnf(d9,plain,
'double$udivide'('double$udivide'(X0,X1),multiply(multiply(X1,X0),inverse(X2))) = X2,
inference(superposition,[status(thm)],[c1,d5]) ).
cnf(d10,plain,
X1 = 'double$udivide'(inverse(X1),multiply(inverse(X0),X0)),
inference(superposition,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
'double$udivide'(X1,multiply(multiply(multiply(inverse(X3),'double$udivide'('double$udivide'(X2,X0),multiply(multiply(X0,inverse(inverse(X1))),X2))),inverse(X4)),X3)) = X4,
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d12,plain,
'double$udivide'(X2,multiply(multiply(multiply(inverse(X3),inverse(X2)),inverse(X4)),X3)) = X4,
inference(demodulation,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
'double$udivide'(inverse(X1),multiply(inverse(X0),X0)) = X1,
inference(superposition,[status(thm)],[d8,d9]) ).
cnf(d14,plain,
multiply(multiply(inverse(X1),X1),inverse(X0)) = inverse(X0),
inference(superposition,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
'double$udivide'(X0,multiply(inverse(X1),inverse(X0))) = X1,
inference(superposition,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
X0 = inverse(inverse(X0)),
inference(superposition,[status(thm)],[d15,d10]) ).
cnf(d17,plain,
'double$udivide'('double$udivide'(inverse(X1),inverse(inverse(X0))),inverse(X1)) = X0,
inference(superposition,[status(thm)],[d6,d9]) ).
cnf(d18,plain,
'double$udivide'('double$udivide'(inverse(X1),X0),inverse(X1)) = X0,
inference(demodulation,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
'double$udivide'(X0,inverse(X0)) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[d13,d18]) ).
cnf(d20,plain,
multiply('double$udivide'(X0,inverse(X0)),a2) != a2,
inference(superposition,[status(thm)],[d19,c2]) ).
cnf(d21,plain,
multiply(multiply(inverse(X1),X1),a2) != a2,
inference(superposition,[status(thm)],[d19,d20]) ).
cnf(d22,plain,
inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[d15,d13]) ).
cnf(d23,plain,
multiply(multiply(X0,inverse(X0)),a2) != a2,
inference(superposition,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
inverse(inverse(a2)) != a2,
inference(superposition,[status(thm)],[d6,d23]) ).
cnf(d25,plain,
a2 != a2,
inference(demodulation,[status(thm)],[d24,d16]) ).
cnf(d26,plain,
'double$udivide'(X0,multiply(multiply(multiply(inverse(X1),X2),inverse(X3)),'double$udivide'(X2,multiply(inverse(inverse(X0)),inverse(X1))))) = X3,
inference(superposition,[status(thm)],[d6,d2]) ).
cnf(d27,plain,
'double$udivide'(X0,multiply(multiply(multiply(inverse(X1),X2),inverse(X3)),'double$udivide'(X2,multiply(X0,inverse(X1))))) = X3,
inference(demodulation,[status(thm)],[d26,d16]) ).
cnf(d28,plain,
'double$udivide'(X0,X1) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[c1,d16]) ).
cnf(d29,plain,
'double$udivide'('double$udivide'(X0,X1),multiply(multiply(multiply(multiply(X2,multiply(X1,X0)),X3),inverse(X4)),'double$udivide'(X3,X2))) = X4,
inference(superposition,[status(thm)],[c1,d2]) ).
cnf(d30,plain,
'double$udivide'('double$udivide'(X1,X0),multiply(multiply(multiply(inverse(X2),X3),inverse(X4)),'double$udivide'(X3,multiply(inverse(multiply(X0,X1)),inverse(X2))))) = X4,
inference(superposition,[status(thm)],[d6,d29]) ).
cnf(d31,plain,
'double$udivide'('double$udivide'(X1,X0),multiply(multiply(multiply(inverse(X2),X3),inverse(X4)),'double$udivide'(X3,multiply('double$udivide'(X1,X0),inverse(X2))))) = X4,
inference(demodulation,[status(thm)],[d30,d28]) ).
cnf(d32,plain,
X4 = X4,
inference(demodulation,[status(thm)],[d31,d27]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[d32,d25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP598-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n011.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 15:01:28 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.17/5.51 % SZS status Unsatisfiable for theBenchmark.p
% 20.17/5.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------