%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ITP004+5 : 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 : n010.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 07:37:55 AM UTC 2026
% Result : Theorem 250.79s 42.73s
% Output : CNFRefutation 250.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 7 unt; 0 def)
% Number of atoms : 53 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 53 ( 23 ~; 18 |; 0 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mem_c_2Epred__set_2ECHOICE,axiom,
! [X0] :
( ne(X0)
=> mem('c$u2Epred$u$uset$u2ECHOICE'(X0),arr(arr(X0,bool),X0)) ) ).
fof(conj_thm_2Epred__set_2EDELETE__SUBSET,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,X0)
=> ! [X2] :
( mem(X2,arr(X0,bool))
=> p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(X0),ap(ap('c$u2Epred$u$uset$u2EDELETE'(X0),X2),X1)),X2)) ) ) ) ).
fof(ax_thm_2Epred__set_2EREST__DEF,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,bool))
=> ap('c$u2Epred$u$uset$u2EREST'(X0),X1) = ap(ap('c$u2Epred$u$uset$u2EDELETE'(X0),X1),ap('c$u2Epred$u$uset$u2ECHOICE'(X0),X1)) ) ) ).
fof(ap_tp,axiom,
! [X0,X1,X2] :
( mem(X2,arr(X0,X1))
=> ! [X3] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ) ).
fof(conj_thm_2Epred__set_2EREST__SUBSET,conjecture,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,bool))
=> p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(X0),ap('c$u2Epred$u$uset$u2EREST'(X0),X1)),X1)) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,bool))
=> p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(X0),ap('c$u2Epred$u$uset$u2EREST'(X0),X1)),X1)) ) ),
inference(negate_conjecture,[status(cth)],[conj_thm_2Epred__set_2EREST__SUBSET]) ).
cnf(c0,plain,
( mem('c$u2Epred$u$uset$u2ECHOICE'(X0),arr(arr(X0,bool),X0))
| ~ ne(X0) ),
inference(clausification,[status(esa)],[mem_c_2Epred__set_2ECHOICE]) ).
cnf(c313,plain,
( p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(X0),ap(ap('c$u2Epred$u$uset$u2EDELETE'(X0),X2),X1)),X2))
| ~ mem(X2,arr(X0,bool))
| ~ mem(X1,X0)
| ~ ne(X0) ),
inference(clausification,[status(esa)],[conj_thm_2Epred__set_2EDELETE__SUBSET]) ).
cnf(c338,plain,
( ap('c$u2Epred$u$uset$u2EREST'(X0),X1) = ap(ap('c$u2Epred$u$uset$u2EDELETE'(X0),X1),ap('c$u2Epred$u$uset$u2ECHOICE'(X0),X1))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(clausification,[status(esa)],[ax_thm_2Epred__set_2EREST__DEF]) ).
cnf(c349,plain,
( mem(ap(X0,X3),X2)
| ~ mem(X3,X1)
| ~ mem(X0,arr(X1,X2)) ),
inference(clausification,[status(esa)],[ap_tp]) ).
cnf(c2217,plain,
ne(sK2294),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c2218,plain,
mem(sK2295,arr(sK2294,bool)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c2219,plain,
~ p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(sK2294),ap('c$u2Epred$u$uset$u2EREST'(sK2294),sK2295)),sK2295)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ ne(sK2294)
| ap('c$u2Epred$u$uset$u2EREST'(sK2294),sK2295) = ap(ap('c$u2Epred$u$uset$u2EDELETE'(sK2294),sK2295),ap('c$u2Epred$u$uset$u2ECHOICE'(sK2294),sK2295)) ),
inference(resolution,[status(thm)],[c338,c2218]) ).
cnf(d1,plain,
ap('c$u2Epred$u$uset$u2EREST'(sK2294),sK2295) = ap(ap('c$u2Epred$u$uset$u2EDELETE'(sK2294),sK2295),ap('c$u2Epred$u$uset$u2ECHOICE'(sK2294),sK2295)),
inference(resolution,[status(thm)],[c2217,d0]) ).
cnf(d2,plain,
( ~ mem(ap('c$u2Epred$u$uset$u2ECHOICE'(sK2294),sK2295),sK2294)
| ~ mem(sK2295,arr(sK2294,bool))
| ~ ne(sK2294)
| p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(sK2294),ap('c$u2Epred$u$uset$u2EREST'(sK2294),sK2295)),sK2295)) ),
inference(superposition,[status(thm)],[d1,c313]) ).
cnf(d3,plain,
( p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(sK2294),ap('c$u2Epred$u$uset$u2EREST'(sK2294),sK2295)),sK2295))
| ~ mem(sK2295,arr(sK2294,bool))
| ~ mem(ap('c$u2Epred$u$uset$u2ECHOICE'(sK2294),sK2295),sK2294) ),
inference(resolution,[status(thm)],[c2217,d2]) ).
cnf(d4,plain,
( p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(sK2294),ap('c$u2Epred$u$uset$u2EREST'(sK2294),sK2295)),sK2295))
| ~ mem(ap('c$u2Epred$u$uset$u2ECHOICE'(sK2294),sK2295),sK2294) ),
inference(resolution,[status(thm)],[c2218,d3]) ).
cnf(d5,plain,
~ mem(ap('c$u2Epred$u$uset$u2ECHOICE'(sK2294),sK2295),sK2294),
inference(resolution,[status(thm)],[c2219,d4]) ).
cnf(d6,plain,
( ~ ne(X1)
| mem(ap('c$u2Epred$u$uset$u2ECHOICE'(X1),X0),X1)
| ~ mem(X0,arr(X1,bool)) ),
inference(resolution,[status(thm)],[c349,c0]) ).
cnf(d7,plain,
( ~ mem(sK2295,arr(sK2294,bool))
| ~ ne(sK2294) ),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
~ mem(sK2295,arr(sK2294,bool)),
inference(resolution,[status(thm)],[c2217,d7]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c2218,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP004+5 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/6.64 % Computer : n010.cluster.edu
% 0.10/6.64 % Model : x86_64 x86_64
% 0.10/6.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/6.64 % Memory : 8046.5625MB
% 0.10/6.64 % OS : Linux 6.8.0-71-generic
% 0.10/6.64 % CPULimit : 300
% 0.10/6.64 % WCLimit : 300
% 0.10/6.64 % DateTime : Fri Sep 25 17:03:26 UTC 2026
% 0.10/6.64 % CPUTime :
% 0.10/6.64 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 250.79/42.73 % SZS status Theorem for theBenchmark.p
% 250.79/42.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------