%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ITP019+4 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 07:38:11 AM UTC 2026
% Result : Theorem 200.09s 29.03s
% Output : CNFRefutation 200.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 16 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 4 |; 0 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm_2Ecomplex_2ECOMPLEX__ADD__RID,axiom,
! [X0] : s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uadd$u2E2'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0),s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))))) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0) ).
fof(thm_2Ecomplex_2ECOMPLEX__ADD__RID__UNIQ,axiom,
! [X0,X1] :
( s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uadd$u2E2'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0),s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X1))) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0)
<=> s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X1) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))) ) ).
fof(thm_2Ecomplex_2ECOMPLEX__INV__0,axiom,
s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uinv$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))))) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))) ).
fof(thm_2Ecomplex_2ECOMPLEX__INV__INV,axiom,
! [X0] : s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uinv$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uinv$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0))))) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0) ).
fof(thm_2Ecomplex_2ECOMPLEX__INV__NZ,conjecture,
! [X0] :
( s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0) != s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0')))
=> s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uinv$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0))) != s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0) != s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0')))
=> s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uinv$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0))) != s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))) ),
inference(negate_conjecture,[status(cth)],[thm_2Ecomplex_2ECOMPLEX__INV__NZ]) ).
cnf(c1,plain,
s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uadd$u2E2'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0),s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))))),
inference(clausification,[status(esa)],[thm_2Ecomplex_2ECOMPLEX__ADD__RID]) ).
cnf(c8,plain,
( s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))) != s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X1)
| s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uadd$u2E2'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0),s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X1))) ),
inference(clausification,[status(esa)],[thm_2Ecomplex_2ECOMPLEX__ADD__RID__UNIQ]) ).
cnf(c31,plain,
s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uinv$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))))) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))),
inference(clausification,[status(esa)],[thm_2Ecomplex_2ECOMPLEX__INV__0]) ).
cnf(c33,plain,
s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uinv$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uinv$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0))))),
inference(clausification,[status(esa)],[thm_2Ecomplex_2ECOMPLEX__INV__INV]) ).
cnf(c48,plain,
s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))) != s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),sK61),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c49,plain,
s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uinv$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),sK61))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),sK61) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uinv$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))))),
inference(superposition,[status(thm)],[c49,c33]) ).
cnf(d1,plain,
s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),sK61) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))),
inference(demodulation,[status(thm)],[c31,d0]) ).
cnf(d2,plain,
s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),sK61) != s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),sK61),
inference(demodulation,[status(thm)],[c48,d1]) ).
cnf(d3,plain,
( s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uadd$u2E2'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0),s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uinv$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),sK61)))))
| s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))) != s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))) ),
inference(superposition,[status(thm)],[c49,c8]) ).
cnf(d4,plain,
( s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))) != s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0')))
| s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uadd$u2E2'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0),s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))))) ),
inference(demodulation,[status(thm)],[d3,c49]) ).
cnf(d5,plain,
( s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))) != s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0')))
| s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0) ),
inference(demodulation,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uinv$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),sK61))) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uadd$u2E2'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))),s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))))),
inference(superposition,[status(thm)],[c49,c1]) ).
cnf(d7,plain,
s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uadd$u2E2'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))),s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))))),
inference(demodulation,[status(thm)],[d6,c49]) ).
cnf(d8,plain,
s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))),
inference(demodulation,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP019+4 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n004.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 17:28:37 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 200.09/29.03 % SZS status Theorem for theBenchmark.p
% 200.09/29.03 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------