%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ITP004+2 : 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 : 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 07:37:54 AM UTC 2026
% Result : Theorem 66.92s 14.94s
% Output : CNFRefutation 66.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 7 unt; 0 def)
% Number of atoms : 145 ( 5 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 192 ( 88 ~; 82 |; 1 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 52 ( 0 sgn 20 !; 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(mem_c_2Epred__set_2EREST,axiom,
! [X0] :
( ne(X0)
=> mem('c$u2Epred$u$uset$u2EREST'(X0),arr(arr(X0,bool),arr(X0,bool))) ) ).
fof(ax_thm_2Epred__set_2ESUBSET__DEF,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,bool))
=> ! [X2] :
( mem(X2,arr(X0,bool))
=> ( p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(X0),X1),X2))
<=> ! [X3] :
( mem(X3,X0)
=> ( p(ap(ap('c$u2Ebool$u2EIN'(X0),X3),X1))
=> p(ap(ap('c$u2Ebool$u2EIN'(X0),X3),X2)) ) ) ) ) ) ) ).
fof(conj_thm_2Epred__set_2EIN__DELETE,axiom,
! [X0] :
( ne(X0)
=> ! [X1] :
( mem(X1,arr(X0,bool))
=> ! [X2] :
( mem(X2,X0)
=> ! [X3] :
( mem(X3,X0)
=> ( p(ap(ap('c$u2Ebool$u2EIN'(X0),X2),ap(ap('c$u2Epred$u$uset$u2EDELETE'(X0),X1),X3)))
<=> ( X2 != X3
& p(ap(ap('c$u2Ebool$u2EIN'(X0),X2),X1)) ) ) ) ) ) ) ).
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(c13,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(c15,plain,
( mem('c$u2Epred$u$uset$u2EREST'(X0),arr(arr(X0,bool),arr(X0,bool)))
| ~ ne(X0) ),
inference(clausification,[status(esa)],[mem_c_2Epred__set_2EREST]) ).
cnf(c24,plain,
( p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(X1),X2),X0))
| mem(sK23(X1,X2,X0),X1)
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1)
| ~ mem(X0,arr(X1,bool)) ),
inference(clausification,[status(esa)],[ax_thm_2Epred__set_2ESUBSET__DEF]) ).
cnf(c25,plain,
( p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(X1),X2),X0))
| ~ p(ap(ap('c$u2Ebool$u2EIN'(X1),sK23(X1,X2,X0)),X0))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1)
| ~ mem(X0,arr(X1,bool)) ),
inference(clausification,[status(esa)],[ax_thm_2Epred__set_2ESUBSET__DEF]) ).
cnf(c26,plain,
( p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(X0),X1),X2))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0)
| ~ mem(X2,arr(X0,bool))
| p(ap(ap('c$u2Ebool$u2EIN'(X0),sK23(X0,X1,X2)),X1)) ),
inference(clausification,[status(esa)],[ax_thm_2Epred__set_2ESUBSET__DEF]) ).
cnf(c27,plain,
( ~ mem(X3,X0)
| ~ mem(X2,X0)
| p(ap(ap('c$u2Ebool$u2EIN'(X0),X2),X1))
| ~ p(ap(ap('c$u2Ebool$u2EIN'(X0),X2),ap(ap('c$u2Epred$u$uset$u2EDELETE'(X0),X1),X3)))
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(clausification,[status(esa)],[conj_thm_2Epred__set_2EIN__DELETE]) ).
cnf(c30,plain,
( ap(ap('c$u2Epred$u$uset$u2EDELETE'(X0),X1),ap('c$u2Epred$u$uset$u2ECHOICE'(X0),X1)) = ap('c$u2Epred$u$uset$u2EREST'(X0),X1)
| ~ mem(X1,arr(X0,bool))
| ~ ne(X0) ),
inference(clausification,[status(esa)],[ax_thm_2Epred__set_2EREST__DEF]) ).
cnf(c34,plain,
( mem(ap(X0,X3),X2)
| ~ mem(X3,X1)
| ~ mem(X0,arr(X1,X2)) ),
inference(clausification,[status(esa)],[ap_tp]) ).
cnf(c43,plain,
ne(sK48),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c44,plain,
mem(sK49,arr(sK48,bool)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c45,plain,
~ p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(sK48),ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49)),sK49)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ ne(X1)
| mem(ap('c$u2Epred$u$uset$u2ECHOICE'(X1),X0),X1)
| ~ mem(X0,arr(X1,bool)) ),
inference(resolution,[status(thm)],[c34,c13]) ).
cnf(d1,plain,
( ~ ne(X1)
| mem(ap('c$u2Epred$u$uset$u2EREST'(X1),X0),arr(X1,bool))
| ~ mem(X0,arr(X1,bool)) ),
inference(resolution,[status(thm)],[c34,c15]) ).
cnf(d2,plain,
( ~ ne(sK48)
| mem(sK23(sK48,ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),sK49),sK48)
| ~ mem(sK49,arr(sK48,bool))
| ~ mem(ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),arr(sK48,bool)) ),
inference(resolution,[status(thm)],[c45,c24]) ).
cnf(d3,plain,
( ~ mem(sK49,arr(sK48,bool))
| mem(sK23(sK48,ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),sK49),sK48)
| ~ mem(ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),arr(sK48,bool)) ),
inference(resolution,[status(thm)],[c43,d2]) ).
cnf(d4,plain,
( mem(sK23(sK48,ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),sK49),sK48)
| ~ mem(ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),arr(sK48,bool)) ),
inference(resolution,[status(thm)],[c44,d3]) ).
cnf(d5,plain,
( ~ ne(sK48)
| ap(ap('c$u2Epred$u$uset$u2EDELETE'(sK48),sK49),ap('c$u2Epred$u$uset$u2ECHOICE'(sK48),sK49)) = ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49) ),
inference(resolution,[status(thm)],[c30,c44]) ).
cnf(d6,plain,
ap(ap('c$u2Epred$u$uset$u2EDELETE'(sK48),sK49),ap('c$u2Epred$u$uset$u2ECHOICE'(sK48),sK49)) = ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),
inference(resolution,[status(thm)],[c43,d5]) ).
cnf(d7,plain,
( ~ ne(X1)
| p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(X1),ap(ap('c$u2Epred$u$uset$u2EDELETE'(X1),X2),X0)),X3))
| ~ mem(X3,arr(X1,bool))
| ~ mem(ap(ap('c$u2Epred$u$uset$u2EDELETE'(X1),X2),X0),arr(X1,bool))
| ~ ne(X1)
| p(ap(ap('c$u2Ebool$u2EIN'(X1),sK23(X1,ap(ap('c$u2Epred$u$uset$u2EDELETE'(X1),X2),X0),X3)),X2))
| ~ mem(sK23(X1,ap(ap('c$u2Epred$u$uset$u2EDELETE'(X1),X2),X0),X3),X1)
| ~ mem(X2,arr(X1,bool))
| ~ mem(X0,X1) ),
inference(resolution,[status(thm)],[c27,c26]) ).
cnf(d8,plain,
( ~ ne(X1)
| p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(X1),ap(ap('c$u2Epred$u$uset$u2EDELETE'(X1),X0),X2)),X0))
| ~ mem(X0,arr(X1,bool))
| ~ mem(ap(ap('c$u2Epred$u$uset$u2EDELETE'(X1),X0),X2),arr(X1,bool))
| ~ ne(X1)
| p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(X1),ap(ap('c$u2Epred$u$uset$u2EDELETE'(X1),X0),X2)),X0))
| ~ mem(sK23(X1,ap(ap('c$u2Epred$u$uset$u2EDELETE'(X1),X0),X2),X0),X1)
| ~ mem(ap(ap('c$u2Epred$u$uset$u2EDELETE'(X1),X0),X2),arr(X1,bool))
| ~ mem(X2,X1)
| ~ mem(X0,arr(X1,bool))
| ~ mem(X0,arr(X1,bool)) ),
inference(resolution,[status(thm)],[d7,c25]) ).
cnf(d9,plain,
( ~ ne(sK48)
| p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(sK48),ap(ap('c$u2Epred$u$uset$u2EDELETE'(sK48),sK49),ap('c$u2Epred$u$uset$u2ECHOICE'(sK48),sK49))),sK49))
| ~ mem(ap(ap('c$u2Epred$u$uset$u2EDELETE'(sK48),sK49),ap('c$u2Epred$u$uset$u2ECHOICE'(sK48),sK49)),arr(sK48,bool))
| ~ mem(sK49,arr(sK48,bool))
| ~ mem(ap('c$u2Epred$u$uset$u2ECHOICE'(sK48),sK49),sK48)
| ~ mem(sK23(sK48,ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),sK49),sK48) ),
inference(superposition,[status(thm)],[d6,d8]) ).
cnf(d10,plain,
( ~ ne(sK48)
| p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(sK48),ap(ap('c$u2Epred$u$uset$u2EDELETE'(sK48),sK49),ap('c$u2Epred$u$uset$u2ECHOICE'(sK48),sK49))),sK49))
| ~ mem(sK49,arr(sK48,bool))
| ~ mem(sK23(sK48,ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),sK49),sK48)
| ~ mem(ap('c$u2Epred$u$uset$u2ECHOICE'(sK48),sK49),sK48)
| ~ mem(ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),arr(sK48,bool)) ),
inference(demodulation,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
( ~ ne(sK48)
| p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(sK48),ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49)),sK49))
| ~ mem(sK49,arr(sK48,bool))
| ~ mem(sK23(sK48,ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),sK49),sK48)
| ~ mem(ap('c$u2Epred$u$uset$u2ECHOICE'(sK48),sK49),sK48)
| ~ mem(ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),arr(sK48,bool)) ),
inference(demodulation,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
( p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(sK48),ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49)),sK49))
| ~ mem(sK49,arr(sK48,bool))
| ~ mem(sK23(sK48,ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),sK49),sK48)
| ~ mem(ap('c$u2Epred$u$uset$u2ECHOICE'(sK48),sK49),sK48)
| ~ mem(ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),arr(sK48,bool)) ),
inference(resolution,[status(thm)],[c43,d11]) ).
cnf(d13,plain,
( p(ap(ap('c$u2Epred$u$uset$u2ESUBSET'(sK48),ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49)),sK49))
| ~ mem(sK23(sK48,ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),sK49),sK48)
| ~ mem(ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),arr(sK48,bool))
| ~ mem(ap('c$u2Epred$u$uset$u2ECHOICE'(sK48),sK49),sK48) ),
inference(resolution,[status(thm)],[c44,d12]) ).
cnf(d14,plain,
( ~ mem(sK23(sK48,ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),sK49),sK48)
| ~ mem(ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),arr(sK48,bool))
| ~ mem(ap('c$u2Epred$u$uset$u2ECHOICE'(sK48),sK49),sK48) ),
inference(resolution,[status(thm)],[c45,d13]) ).
cnf(d15,plain,
( ~ mem(ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),arr(sK48,bool))
| ~ mem(ap('c$u2Epred$u$uset$u2EREST'(sK48),sK49),arr(sK48,bool))
| ~ mem(ap('c$u2Epred$u$uset$u2ECHOICE'(sK48),sK49),sK48) ),
inference(resolution,[status(thm)],[d14,d4]) ).
cnf(d16,plain,
( ~ ne(sK48)
| ~ mem(sK49,arr(sK48,bool))
| ~ mem(ap('c$u2Epred$u$uset$u2ECHOICE'(sK48),sK49),sK48) ),
inference(resolution,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
( ~ mem(sK49,arr(sK48,bool))
| ~ mem(ap('c$u2Epred$u$uset$u2ECHOICE'(sK48),sK49),sK48) ),
inference(resolution,[status(thm)],[c43,d16]) ).
cnf(d18,plain,
~ mem(ap('c$u2Epred$u$uset$u2ECHOICE'(sK48),sK49),sK48),
inference(resolution,[status(thm)],[c44,d17]) ).
cnf(d19,plain,
( ~ ne(sK48)
| ~ mem(sK49,arr(sK48,bool)) ),
inference(resolution,[status(thm)],[d18,d0]) ).
cnf(d20,plain,
~ mem(sK49,arr(sK48,bool)),
inference(resolution,[status(thm)],[c43,d19]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[c44,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP004+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n004.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Fri Sep 25 17:02:41 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 66.92/14.94 % SZS status Theorem for theBenchmark.p
% 66.92/14.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------