%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ITP019+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 07:38:10 AM UTC 2026
% Result : Theorem 22.53s 21.46s
% Output : CNFRefutation 22.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 12 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 2 |; 0 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 20 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Ei__thm,axiom,
! [X0,X1] : s(X0,'app$u2E2'(s('tyop$u2Emin$u2Efun'(X0,X0),'combin$ui$u2E0'),s(X0,X1))) = s(X0,X1) ).
fof(reserved_2Eho_2Ek__thm,axiom,
! [X0,X1,X2,X3] : s(X0,'app$u2E2'(s('tyop$u2Emin$u2Efun'(X1,X0),'app$u2E2'(s('tyop$u2Emin$u2Efun'(X0,'tyop$u2Emin$u2Efun'(X1,X0)),'combin$uk$u2E0'),s(X0,X2))),s(X1,X3))) = s(X0,X2) ).
fof(thm_2Ecomplex_2ECOMPLEX__INV__EQ__0,axiom,
! [X0] :
( s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uinv$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),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) = 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__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(c8,plain,
s(X0,'app$u2E2'(s('tyop$u2Emin$u2Efun'(X0,X0),'combin$ui$u2E0'),s(X0,X1))) = s(X0,X1),
inference(clausification,[status(esa)],[reserved_2Eho_2Ei__thm]) ).
cnf(c9,plain,
s(X0,'app$u2E2'(s('tyop$u2Emin$u2Efun'(X1,X0),'app$u2E2'(s('tyop$u2Emin$u2Efun'(X0,'tyop$u2Emin$u2Efun'(X1,X0)),'combin$uk$u2E0'),s(X0,X2))),s(X1,X3))) = s(X0,X2),
inference(clausification,[status(esa)],[reserved_2Eho_2Ek__thm]) ).
cnf(c63,plain,
( s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$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(clausification,[status(esa)],[thm_2Ecomplex_2ECOMPLEX__INV__EQ__0]) ).
cnf(c65,plain,
s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),sK60) != 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)],[negated_conjecture]) ).
cnf(c66,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$u2Ereal'),sK60))) = s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'app$u2E2'(s('tyop$u2Emin$u2Efun'('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),'tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal')),'combin$ui$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'),'c$u2Ecomplex$u2Ecomplex$u$uinv$u2E1'(s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),sK60))),
inference(superposition,[status(thm)],[c66,c8]) ).
cnf(d1,plain,
s('tyop$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'),sK60))),
inference(demodulation,[status(thm)],[d0,c8]) ).
cnf(d2,plain,
( s('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),sK60) = 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'),'c$u2Ecomplex$u2Ecomplex$u$uof$u$unum$u2E1'(s('tyop$u2Enum$u2Enum','c$u2Enum$u2E0$u2E0'))) ),
inference(superposition,[status(thm)],[d1,c63]) ).
cnf(d3,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(resolution,[status(thm)],[c65,d2]) ).
cnf(d4,plain,
s(X0,'app$u2E2'(s('tyop$u2Emin$u2Efun'('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0),'app$u2E2'(s('tyop$u2Emin$u2Efun'(X0,'tyop$u2Emin$u2Efun'('tyop$u2Epair$u2Eprod'('tyop$u2Erealax$u2Ereal','tyop$u2Erealax$u2Ereal'),X0)),'combin$uk$u2E0'),s(X0,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'))))) = s(X0,X1),
inference(superposition,[status(thm)],[d1,c9]) ).
cnf(d5,plain,
s(X0,X1) = s(X0,X1),
inference(demodulation,[status(thm)],[d4,c9]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.38 % Computer : n003.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Fri Sep 25 17:30:18 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.53/21.46 % SZS status Theorem for theBenchmark.p
% 22.53/21.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------