%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ITP006+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 : n018.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 07:37:57 AM UTC 2026
% Result : Theorem 126.76s 21.63s
% Output : CNFRefutation 126.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 9 unt; 0 def)
% Number of atoms : 37 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 11 ~; 9 |; 0 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 33 ( 1 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Etruth,axiom,
p(s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2ET$u2E0')) ).
fof(reserved_2Eho_2Enotfalse,axiom,
~ p(s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2EF$u2E0')) ).
fof(reserved_2Eho_2Ebool__cases__ax,axiom,
! [X0] :
( s('tyop$u2Emin$u2Ebool',X0) = s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2EF$u2E0')
| s('tyop$u2Emin$u2Ebool',X0) = s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2ET$u2E0') ) ).
fof(thm_2EquantHeuristics_2EGUESS__FORALL__POINT__def,axiom,
! [X0,X1,X2,X3] :
( p(s('tyop$u2Emin$u2Ebool','c$u2EquantHeuristics$u2EGUESS$u$uFORALL$u$uPOINT$u2E2'(s('tyop$u2Emin$u2Efun'(X0,X1),X2),s('tyop$u2Emin$u2Efun'(X1,'tyop$u2Emin$u2Ebool'),X3))))
<=> ! [X4] : ~ p(s('tyop$u2Emin$u2Ebool','app$u2E2'(s('tyop$u2Emin$u2Efun'(X1,'tyop$u2Emin$u2Ebool'),X3),s(X1,'app$u2E2'(s('tyop$u2Emin$u2Efun'(X0,X1),X2),s(X0,X4)))))) ) ).
fof(thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT,conjecture,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( p(s('tyop$u2Emin$u2Ebool','app$u2E2'(s('tyop$u2Emin$u2Efun'(X0,'tyop$u2Emin$u2Ebool'),X4),s(X0,X5))))
=> p(s('tyop$u2Emin$u2Ebool','app$u2E2'(s('tyop$u2Emin$u2Efun'(X0,'tyop$u2Emin$u2Ebool'),X3),s(X0,X5)))) )
=> ( p(s('tyop$u2Emin$u2Ebool','c$u2EquantHeuristics$u2EGUESS$u$uFORALL$u$uPOINT$u2E2'(s('tyop$u2Emin$u2Efun'(X1,X0),X2),s('tyop$u2Emin$u2Efun'(X0,'tyop$u2Emin$u2Ebool'),X3))))
=> p(s('tyop$u2Emin$u2Ebool','c$u2EquantHeuristics$u2EGUESS$u$uFORALL$u$uPOINT$u2E2'(s('tyop$u2Emin$u2Efun'(X1,X0),X2),s('tyop$u2Emin$u2Efun'(X0,'tyop$u2Emin$u2Ebool'),X4)))) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ! [X5] :
( p(s('tyop$u2Emin$u2Ebool','app$u2E2'(s('tyop$u2Emin$u2Efun'(X0,'tyop$u2Emin$u2Ebool'),X4),s(X0,X5))))
=> p(s('tyop$u2Emin$u2Ebool','app$u2E2'(s('tyop$u2Emin$u2Efun'(X0,'tyop$u2Emin$u2Ebool'),X3),s(X0,X5)))) )
=> ( p(s('tyop$u2Emin$u2Ebool','c$u2EquantHeuristics$u2EGUESS$u$uFORALL$u$uPOINT$u2E2'(s('tyop$u2Emin$u2Efun'(X1,X0),X2),s('tyop$u2Emin$u2Efun'(X0,'tyop$u2Emin$u2Ebool'),X3))))
=> p(s('tyop$u2Emin$u2Ebool','c$u2EquantHeuristics$u2EGUESS$u$uFORALL$u$uPOINT$u2E2'(s('tyop$u2Emin$u2Efun'(X1,X0),X2),s('tyop$u2Emin$u2Efun'(X0,'tyop$u2Emin$u2Ebool'),X4)))) ) ),
inference(negate_conjecture,[status(cth)],[thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT]) ).
cnf(c5,plain,
p(s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2ET$u2E0')),
inference(clausification,[status(esa)],[reserved_2Eho_2Etruth]) ).
cnf(c6,plain,
~ p(s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2EF$u2E0')),
inference(clausification,[status(esa)],[reserved_2Eho_2Enotfalse]) ).
cnf(c7,plain,
( s('tyop$u2Emin$u2Ebool',X0) = s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2EF$u2E0')
| s('tyop$u2Emin$u2Ebool',X0) = s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2ET$u2E0') ),
inference(clausification,[status(esa)],[reserved_2Eho_2Ebool__cases__ax]) ).
cnf(c26,plain,
( ~ p(s('tyop$u2Emin$u2Ebool','app$u2E2'(s('tyop$u2Emin$u2Efun'(X1,'tyop$u2Emin$u2Ebool'),X3),s(X1,'app$u2E2'(s('tyop$u2Emin$u2Efun'(X0,X1),X2),s(X0,X4))))))
| ~ p(s('tyop$u2Emin$u2Ebool','c$u2EquantHeuristics$u2EGUESS$u$uFORALL$u$uPOINT$u2E2'(s('tyop$u2Emin$u2Efun'(X0,X1),X2),s('tyop$u2Emin$u2Efun'(X1,'tyop$u2Emin$u2Ebool'),X3)))) ),
inference(clausification,[status(esa)],[thm_2EquantHeuristics_2EGUESS__FORALL__POINT__def]) ).
cnf(c27,plain,
( p(s('tyop$u2Emin$u2Ebool','app$u2E2'(s('tyop$u2Emin$u2Efun'(X1,'tyop$u2Emin$u2Ebool'),X3),s(X1,'app$u2E2'(s('tyop$u2Emin$u2Efun'(X0,X1),X2),s(X0,sK48(X0,X1,X2,X3)))))))
| p(s('tyop$u2Emin$u2Ebool','c$u2EquantHeuristics$u2EGUESS$u$uFORALL$u$uPOINT$u2E2'(s('tyop$u2Emin$u2Efun'(X0,X1),X2),s('tyop$u2Emin$u2Efun'(X1,'tyop$u2Emin$u2Ebool'),X3)))) ),
inference(clausification,[status(esa)],[thm_2EquantHeuristics_2EGUESS__FORALL__POINT__def]) ).
cnf(c2162,plain,
( p(s('tyop$u2Emin$u2Ebool','app$u2E2'(s('tyop$u2Emin$u2Efun'(sK2801,'tyop$u2Emin$u2Ebool'),sK2804),s(sK2801,X0))))
| ~ p(s('tyop$u2Emin$u2Ebool','app$u2E2'(s('tyop$u2Emin$u2Efun'(sK2801,'tyop$u2Emin$u2Ebool'),sK2805),s(sK2801,X0)))) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c2163,plain,
p(s('tyop$u2Emin$u2Ebool','c$u2EquantHeuristics$u2EGUESS$u$uFORALL$u$uPOINT$u2E2'(s('tyop$u2Emin$u2Efun'(sK2802,sK2801),sK2803),s('tyop$u2Emin$u2Efun'(sK2801,'tyop$u2Emin$u2Ebool'),sK2804)))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c2164,plain,
~ p(s('tyop$u2Emin$u2Ebool','c$u2EquantHeuristics$u2EGUESS$u$uFORALL$u$uPOINT$u2E2'(s('tyop$u2Emin$u2Efun'(sK2802,sK2801),sK2803),s('tyop$u2Emin$u2Efun'(sK2801,'tyop$u2Emin$u2Ebool'),sK2805)))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( p(s('tyop$u2Emin$u2Ebool','app$u2E2'(s('tyop$u2Emin$u2Efun'(sK2801,'tyop$u2Emin$u2Ebool'),sK2804),s(sK2801,'app$u2E2'(s('tyop$u2Emin$u2Efun'(X0,sK2801),X1),s(X0,sK48(X0,sK2801,X1,sK2805)))))))
| p(s('tyop$u2Emin$u2Ebool','c$u2EquantHeuristics$u2EGUESS$u$uFORALL$u$uPOINT$u2E2'(s('tyop$u2Emin$u2Efun'(X0,sK2801),X1),s('tyop$u2Emin$u2Efun'(sK2801,'tyop$u2Emin$u2Ebool'),sK2805)))) ),
inference(resolution,[status(thm)],[c27,c2162]) ).
cnf(d1,plain,
( ~ p(s('tyop$u2Emin$u2Ebool','c$u2EquantHeuristics$u2EGUESS$u$uFORALL$u$uPOINT$u2E2'(s('tyop$u2Emin$u2Efun'(X0,sK2801),X1),s('tyop$u2Emin$u2Efun'(sK2801,'tyop$u2Emin$u2Ebool'),sK2804))))
| p(s('tyop$u2Emin$u2Ebool','c$u2EquantHeuristics$u2EGUESS$u$uFORALL$u$uPOINT$u2E2'(s('tyop$u2Emin$u2Efun'(X0,sK2801),X1),s('tyop$u2Emin$u2Efun'(sK2801,'tyop$u2Emin$u2Ebool'),sK2805)))) ),
inference(resolution,[status(thm)],[d0,c26]) ).
cnf(d2,plain,
( s('tyop$u2Emin$u2Ebool','c$u2EquantHeuristics$u2EGUESS$u$uFORALL$u$uPOINT$u2E2'(s('tyop$u2Emin$u2Efun'(sK2802,sK2801),sK2803),s('tyop$u2Emin$u2Efun'(sK2801,'tyop$u2Emin$u2Ebool'),sK2804))) = s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2ET$u2E0')
| p(s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2EF$u2E0')) ),
inference(superposition,[status(thm)],[c7,c2163]) ).
cnf(d3,plain,
s('tyop$u2Emin$u2Ebool','c$u2EquantHeuristics$u2EGUESS$u$uFORALL$u$uPOINT$u2E2'(s('tyop$u2Emin$u2Efun'(sK2802,sK2801),sK2803),s('tyop$u2Emin$u2Efun'(sK2801,'tyop$u2Emin$u2Ebool'),sK2804))) = s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2ET$u2E0'),
inference(resolution,[status(thm)],[c6,d2]) ).
cnf(d4,plain,
( p(s('tyop$u2Emin$u2Ebool','c$u2EquantHeuristics$u2EGUESS$u$uFORALL$u$uPOINT$u2E2'(s('tyop$u2Emin$u2Efun'(sK2802,sK2801),sK2803),s('tyop$u2Emin$u2Efun'(sK2801,'tyop$u2Emin$u2Ebool'),sK2805))))
| ~ p(s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2ET$u2E0')) ),
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
~ p(s('tyop$u2Emin$u2Ebool','c$u2Ebool$u2ET$u2E0')),
inference(resolution,[status(thm)],[c2164,d4]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c5,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP006+4 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 17:07:51 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 126.76/21.63 % SZS status Theorem for theBenchmark.p
% 126.76/21.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------