%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP590-1 : 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 : n013.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 10.71s 2.40s
% Output : CNFRefutation 10.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 6 RR)
% Number of literals : 26 ( 25 equ; 5 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 : 54 ( 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$udivide'(X1,X0)) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
cnf(c0,plain,
'double$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(inverse(b2),b2),a2) != a2,
inference(clausification,[status(esa)],[prove_these_axioms_2]) ).
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'(inverse(X0),inverse(multiply(inverse(X1),X1))) = X0,
inference(superposition,[status(thm)],[d5,d9]) ).
cnf(d15,plain,
multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[d14,d6]) ).
cnf(d16,plain,
multiply(multiply(inverse(X0),X0),a2) != a2,
inference(superposition,[status(thm)],[d15,c2]) ).
cnf(d17,plain,
multiply(inverse(multiply(inverse(X0),X0)),a2) != a2,
inference(superposition,[status(thm)],[d5,d16]) ).
cnf(d18,plain,
a2 != a2,
inference(demodulation,[status(thm)],[d17,d13]) ).
cnf(d19,plain,
$false,
inference(equality_resolution,[status(thm)],[d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP590-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 15:00:37 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.71/2.40 % SZS status Unsatisfiable for theBenchmark.p
% 10.71/2.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------