%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP004_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 : Fri Sep 25 01:47:31 PM UTC 2026
% Result : Theorem 1.98s 1.34s
% Output : CNFRefutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 457 ( 11 equ)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 246 ( 107 ~; 105 |; 17 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 262 ( 262 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 2 con; 0-3 aty)
% Number of variables : 111 ( 0 sgn 107 !; 4 ?; 111 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
bool: del ).
tff(pred_def_1,type,
mem: ( del * $i ) > $o ).
tff(func_def_2,type,
arr: ( del * del ) > del ).
tff(func_def_4,type,
k: ( $i * del ) > $i ).
tff(func_def_5,type,
i: del > $i ).
tff(func_def_6,type,
inj__o: tp__o > $i ).
tff(func_def_7,type,
surj__o: $i > tp__o ).
tff(func_def_9,type,
fo__c_2Emin_2E_3D_3D_3E: ( tp__o * tp__o ) > tp__o ).
tff(func_def_10,type,
c_2Epred__set_2ESUBSET: del > $i ).
tff(func_def_12,type,
fo__c_2Ebool_2E_7E: tp__o > tp__o ).
tff(func_def_14,type,
fo__c_2Ebool_2E_2F_5C: ( tp__o * tp__o ) > tp__o ).
tff(func_def_15,type,
c_2Ebool_2EIN: del > $i ).
tff(func_def_16,type,
c_2Epred__set_2ECHOICE: del > $i ).
tff(func_def_17,type,
c_2Epred__set_2EDELETE: del > $i ).
tff(func_def_18,type,
c_2Epred__set_2EREST: del > $i ).
tff(func_def_19,type,
c_2Emin_2E_3D: del > $i ).
tff(func_def_20,type,
c_2Ebool_2E_21: del > $i ).
tff(func_def_21,type,
sK0: del ).
tff(func_def_23,type,
sK2: ( $i * ( $i * del ) ) > $i ).
tff(func_def_24,type,
sK3: ( $i * ( $i * del ) ) > $i ).
tff(f1,axiom,
! [X0: del,X1: del,X2: $i] :
( mem(X2,arr(X0,X1))
=> ! [X3: $i] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001_2.ax',ap_tp) ).
tff(f20,axiom,
! [X0: del] : mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECHOICE) ).
tff(f22,axiom,
! [X0: del] : mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epred__set_2EREST) ).
tff(f27,axiom,
! [X0: del,X1: $i] :
( mem(X1,arr(X0,bool))
=> ! [X2: $i] :
( mem(X2,arr(X0,bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
<=> ! [X3: $i] :
( mem(X3,X0)
=> ( p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
=> p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Epred__set_2ESUBSET__DEF) ).
tff(f28,axiom,
! [X0: del,X1: $i] :
( mem(X1,arr(X0,bool))
=> ! [X2: $i] :
( mem(X2,X0)
=> ! [X3: $i] :
( mem(X3,X0)
=> ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
<=> ( ( X2 != X3 )
& p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EIN__DELETE) ).
tff(f29,axiom,
! [X0: del,X1: $i] :
( mem(X1,arr(X0,bool))
=> ( ap(c_2Epred__set_2EREST(X0),X1) = ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Epred__set_2EREST__DEF) ).
tff(f30,conjecture,
! [X0: del,X1: $i] :
( mem(X1,arr(X0,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EREST__SUBSET) ).
tff(f31,negated_conjecture,
~ ! [X0: del,X1: $i] :
( mem(X1,arr(X0,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1)) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
tff(f32,plain,
? [X0: del,X1: $i] :
( mem(X1,arr(X0,bool))
& ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1)) ),
inference(ennf_transformation,[],[f31]) ).
tff(f37,plain,
! [X0: del,X1: del,X2: $i] :
( ~ mem(X2,arr(X0,X1))
| ! [X3: $i] :
( ~ mem(X3,X0)
| mem(ap(X2,X3),X1) ) ),
inference(ennf_transformation,[],[f1]) ).
tff(f38,plain,
! [X0: del,X1: $i] :
( ~ mem(X1,arr(X0,bool))
| ! [X2: $i] :
( ~ mem(X2,arr(X0,bool))
| ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
<=> ! [X3: $i] :
( ~ mem(X3,X0)
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
| p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) ) ) ) ),
inference(ennf_transformation,[],[f27]) ).
tff(f39,plain,
! [X0: del,X1: $i] :
( ~ mem(X1,arr(X0,bool))
| ! [X2: $i] :
( ~ mem(X2,arr(X0,bool))
| ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
<=> ! [X3: $i] :
( ~ mem(X3,X0)
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
| p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) ) ) ) ),
inference(flattening,[],[f38]) ).
tff(f40,plain,
! [X0: del,X1: $i] :
( ~ mem(X1,arr(X0,bool))
| ( ap(c_2Epred__set_2EREST(X0),X1) = ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1)) ) ),
inference(ennf_transformation,[],[f29]) ).
tff(f41,plain,
! [X0: del,X1: $i] :
( ~ mem(X1,arr(X0,bool))
| ! [X2: $i] :
( ~ mem(X2,X0)
| ! [X3: $i] :
( ~ mem(X3,X0)
| ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
<=> ( ( X2 != X3 )
& p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) ) ) ) ) ),
inference(ennf_transformation,[],[f28]) ).
tff(f42,plain,
( mem(sK1,arr(sK0,bool))
& ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK0),ap(c_2Epred__set_2EREST(sK0),sK1)),sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f32]) ).
tff(f45,plain,
! [X0: del,X1: $i] :
( ~ mem(X1,arr(X0,bool))
| ! [X2: $i] :
( ~ mem(X2,arr(X0,bool))
| ( ( ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ! [X3: $i] :
( ~ mem(X3,X0)
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
| p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) ) )
& ( ? [X3: $i] :
( mem(X3,X0)
& p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
& ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) )
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) ) ) ),
inference(nnf_transformation,[],[f39]) ).
tff(f46,plain,
! [X0: del,X1: $i] :
( ~ mem(X1,arr(X0,bool))
| ! [X2: $i] :
( ~ mem(X2,arr(X0,bool))
| ( ( ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ! [X4: $i] :
( ~ mem(X4,X0)
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X4),X1))
| p(ap(ap(c_2Ebool_2EIN(X0),X4),X2)) ) )
& ( ? [X3: $i] :
( mem(X3,X0)
& p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
& ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) )
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) ) ) ),
inference(rectify,[],[f45]) ).
tff(f47,plain,
! [X0: del,X1: $i] :
( ~ mem(X1,arr(X0,bool))
| ! [X2: $i] :
( ~ mem(X2,arr(X0,bool))
| ( ( ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ! [X4: $i] :
( ~ mem(X4,X0)
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X4),X1))
| p(ap(ap(c_2Ebool_2EIN(X0),X4),X2)) ) )
& ( ( mem(sK3(X0,X1,X2),X0)
& p(ap(ap(c_2Ebool_2EIN(X0),sK3(X0,X1,X2)),X1))
& ~ p(ap(ap(c_2Ebool_2EIN(X0),sK3(X0,X1,X2)),X2)) )
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f46]) ).
tff(f48,plain,
! [X0: del,X1: $i] :
( ~ mem(X1,arr(X0,bool))
| ! [X2: $i] :
( ~ mem(X2,X0)
| ! [X3: $i] :
( ~ mem(X3,X0)
| ( ( ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| ( ( X2 != X3 )
& p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) ) )
& ( ( X2 = X3 )
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
| p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3))) ) ) ) ) ),
inference(nnf_transformation,[],[f41]) ).
tff(f49,plain,
! [X0: del,X1: $i] :
( ~ mem(X1,arr(X0,bool))
| ! [X2: $i] :
( ~ mem(X2,X0)
| ! [X3: $i] :
( ~ mem(X3,X0)
| ( ( ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| ( ( X2 != X3 )
& p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) ) )
& ( ( X2 = X3 )
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
| p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3))) ) ) ) ) ),
inference(flattening,[],[f48]) ).
tff(f50,plain,
mem(sK1,arr(sK0,bool)),
inference(cnf_transformation,[],[f42]) ).
tff(f51,plain,
~ p(ap(ap(c_2Epred__set_2ESUBSET(sK0),ap(c_2Epred__set_2EREST(sK0),sK1)),sK1)),
inference(cnf_transformation,[],[f42]) ).
tff(f56,plain,
! [X2: $i,X3: $i,X0: del,X1: del] :
( ~ mem(X2,arr(X0,X1))
| ~ mem(X3,X0)
| mem(ap(X2,X3),X1) ),
inference(cnf_transformation,[],[f37]) ).
tff(f58,plain,
! [X2: $i,X0: del,X1: $i] :
( ~ mem(X1,arr(X0,bool))
| ~ mem(X2,arr(X0,bool))
| mem(sK3(X0,X1,X2),X0)
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ),
inference(cnf_transformation,[],[f47]) ).
tff(f59,plain,
! [X2: $i,X0: del,X1: $i] :
( ~ mem(X1,arr(X0,bool))
| ~ mem(X2,arr(X0,bool))
| p(ap(ap(c_2Ebool_2EIN(X0),sK3(X0,X1,X2)),X1))
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ),
inference(cnf_transformation,[],[f47]) ).
tff(f60,plain,
! [X2: $i,X0: del,X1: $i] :
( ~ mem(X1,arr(X0,bool))
| ~ mem(X2,arr(X0,bool))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),sK3(X0,X1,X2)),X2))
| p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ),
inference(cnf_transformation,[],[f47]) ).
tff(f62,plain,
! [X0: del,X1: $i] :
( ~ mem(X1,arr(X0,bool))
| ( ap(c_2Epred__set_2EREST(X0),X1) = ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1)) ) ),
inference(cnf_transformation,[],[f40]) ).
tff(f63,plain,
! [X0: del] : mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool))),
inference(cnf_transformation,[],[f22]) ).
tff(f65,plain,
! [X2: $i,X3: $i,X0: del,X1: $i] :
( ~ mem(X1,arr(X0,bool))
| ~ mem(X2,X0)
| ~ mem(X3,X0)
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) ),
inference(cnf_transformation,[],[f49]) ).
tff(f68,plain,
! [X0: del] : mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_49,negated_conjecture,
~ p(ap(ap(c_2Epred__set_2ESUBSET(sK0),ap(c_2Epred__set_2EREST(sK0),sK1)),sK1)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_50,negated_conjecture,
mem(sK1,arr(sK0,bool)),
inference(cnf_transformation,[],[f50]) ).
tcf(c_55,plain,
! [X0: $i,X0_del: del,X1: $i,X1_del: del] :
( mem(ap(X0,X1),X1_del)
| ~ mem(X1,X0_del)
| ~ mem(X0,arr(X0_del,X1_del)) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_56,plain,
! [X0: $i,X0_del: del,X1: $i] :
( p(ap(ap(c_2Epred__set_2ESUBSET(X0_del),X0),X1))
| ~ mem(X1,arr(X0_del,bool))
| ~ mem(X0,arr(X0_del,bool))
| ~ p(ap(ap(c_2Ebool_2EIN(X0_del),sK3(X0_del,X0,X1)),X1)) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_57,plain,
! [X0: $i,X0_del: del,X1: $i] :
( p(ap(ap(c_2Epred__set_2ESUBSET(X0_del),X0),X1))
| p(ap(ap(c_2Ebool_2EIN(X0_del),sK3(X0_del,X0,X1)),X0))
| ~ mem(X1,arr(X0_del,bool))
| ~ mem(X0,arr(X0_del,bool)) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_58,plain,
! [X0: $i,X0_del: del,X1: $i] :
( mem(sK3(X0_del,X0,X1),X0_del)
| p(ap(ap(c_2Epred__set_2ESUBSET(X0_del),X0),X1))
| ~ mem(X1,arr(X0_del,bool))
| ~ mem(X0,arr(X0_del,bool)) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_61,plain,
! [X0: $i,X0_del: del] :
( ( ap(ap(c_2Epred__set_2EDELETE(X0_del),X0),ap(c_2Epred__set_2ECHOICE(X0_del),X0)) = ap(c_2Epred__set_2EREST(X0_del),X0) )
| ~ mem(X0,arr(X0_del,bool)) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_62,plain,
! [X0_del: del] : mem(c_2Epred__set_2EREST(X0_del),arr(arr(X0_del,bool),arr(X0_del,bool))),
inference(cnf_transformation,[],[f63]) ).
tcf(c_64,plain,
! [X0: $i,X0_del: del,X1: $i,X2: $i] :
( p(ap(ap(c_2Ebool_2EIN(X0_del),X0),X1))
| ~ mem(X2,X0_del)
| ~ mem(X0,X0_del)
| ~ mem(X1,arr(X0_del,bool))
| ~ p(ap(ap(c_2Ebool_2EIN(X0_del),X0),ap(ap(c_2Epred__set_2EDELETE(X0_del),X1),X2))) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_67,plain,
! [X0_del: del] : mem(c_2Epred__set_2ECHOICE(X0_del),arr(arr(X0_del,bool),X0_del)),
inference(cnf_transformation,[],[f68]) ).
tcf(c_546,plain,
ap(ap(c_2Epred__set_2EDELETE(sK0),sK1),ap(c_2Epred__set_2ECHOICE(sK0),sK1)) = ap(c_2Epred__set_2EREST(sK0),sK1),
inference(superposition,[status(thm)],[c_50,c_61]) ).
tcf(c_792,plain,
! [X0: $i,X0_del: del] :
( mem(ap(X0,sK1),X0_del)
| ~ mem(sK1,arr(sK0,bool))
| ~ mem(X0,arr(arr(sK0,bool),X0_del)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_904,plain,
( mem(sK3(sK0,ap(c_2Epred__set_2EREST(sK0),sK1),sK1),sK0)
| ~ mem(sK1,arr(sK0,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK0),sK1),arr(sK0,bool)) ),
inference(superposition,[status(thm)],[c_58,c_49]) ).
tcf(c_905,plain,
( mem(sK3(sK0,ap(c_2Epred__set_2EREST(sK0),sK1),sK1),sK0)
| ~ mem(ap(c_2Epred__set_2EREST(sK0),sK1),arr(sK0,bool)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_904,c_50]) ).
tcf(c_1430,plain,
! [X0: $i] :
( p(ap(ap(c_2Ebool_2EIN(sK0),X0),sK1))
| ~ mem(X0,sK0)
| ~ mem(sK1,arr(sK0,bool))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK0),sK1),sK0)
| ~ p(ap(ap(c_2Ebool_2EIN(sK0),X0),ap(c_2Epred__set_2EREST(sK0),sK1))) ),
inference(superposition,[status(thm)],[c_546,c_64]) ).
tcf(c_1431,plain,
! [X0: $i] :
( p(ap(ap(c_2Ebool_2EIN(sK0),X0),sK1))
| ~ mem(X0,sK0)
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK0),sK1),sK0)
| ~ p(ap(ap(c_2Ebool_2EIN(sK0),X0),ap(c_2Epred__set_2EREST(sK0),sK1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1430,c_50]) ).
tcf(c_1728,plain,
( mem(ap(c_2Epred__set_2EREST(sK0),sK1),arr(sK0,bool))
| ~ mem(sK1,arr(sK0,bool))
| ~ mem(c_2Epred__set_2EREST(sK0),arr(arr(sK0,bool),arr(sK0,bool))) ),
inference(instantiation,[status(thm)],[c_792]) ).
tcf(c_1729,plain,
mem(c_2Epred__set_2EREST(sK0),arr(arr(sK0,bool),arr(sK0,bool))),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_1732,plain,
( mem(ap(c_2Epred__set_2ECHOICE(sK0),sK1),sK0)
| ~ mem(sK1,arr(sK0,bool))
| ~ mem(c_2Epred__set_2ECHOICE(sK0),arr(arr(sK0,bool),sK0)) ),
inference(instantiation,[status(thm)],[c_792]) ).
tcf(c_1733,plain,
mem(c_2Epred__set_2ECHOICE(sK0),arr(arr(sK0,bool),sK0)),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_1736,plain,
! [X0: $i] :
( p(ap(ap(c_2Ebool_2EIN(sK0),X0),sK1))
| ~ mem(X0,sK0)
| ~ p(ap(ap(c_2Ebool_2EIN(sK0),X0),ap(c_2Epred__set_2EREST(sK0),sK1))) ),
inference(global_subsumption_just,[status(thm)],[c_1431,c_50,c_1431,c_1732,c_1733]) ).
tcf(c_1745,plain,
! [X0: $i] :
( p(ap(ap(c_2Epred__set_2ESUBSET(sK0),ap(c_2Epred__set_2EREST(sK0),sK1)),X0))
| p(ap(ap(c_2Ebool_2EIN(sK0),sK3(sK0,ap(c_2Epred__set_2EREST(sK0),sK1),X0)),sK1))
| ~ mem(X0,arr(sK0,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK0),sK1),arr(sK0,bool))
| ~ mem(sK3(sK0,ap(c_2Epred__set_2EREST(sK0),sK1),X0),sK0) ),
inference(superposition,[status(thm)],[c_57,c_1736]) ).
tcf(c_1860,plain,
! [X0: $i] :
( p(ap(ap(c_2Epred__set_2ESUBSET(sK0),ap(c_2Epred__set_2EREST(sK0),sK1)),X0))
| p(ap(ap(c_2Ebool_2EIN(sK0),sK3(sK0,ap(c_2Epred__set_2EREST(sK0),sK1),X0)),sK1))
| ~ mem(X0,arr(sK0,bool))
| ~ mem(sK3(sK0,ap(c_2Epred__set_2EREST(sK0),sK1),X0),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_1745,c_50,c_1728,c_1729,c_1745]) ).
tcf(c_1871,plain,
( p(ap(ap(c_2Epred__set_2ESUBSET(sK0),ap(c_2Epred__set_2EREST(sK0),sK1)),sK1))
| ~ mem(sK1,arr(sK0,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK0),sK1),arr(sK0,bool))
| ~ mem(sK3(sK0,ap(c_2Epred__set_2EREST(sK0),sK1),sK1),sK0) ),
inference(superposition,[status(thm)],[c_1860,c_56]) ).
tcf(c_1873,plain,
( ~ mem(ap(c_2Epred__set_2EREST(sK0),sK1),arr(sK0,bool))
| ~ mem(sK3(sK0,ap(c_2Epred__set_2EREST(sK0),sK1),sK1),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1871,c_49,c_50]) ).
tcf(c_1884,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1873,c_1729,c_1728,c_905,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP004_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n011.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 17:28:27 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 1.98/1.34 % SZS status Started for theBenchmark.p
% 1.98/1.34 % SZS status Theorem for theBenchmark.p
% 1.98/1.34
% 1.98/1.34 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.98/1.34
% 1.98/1.34 % ------ iProver source info
% 1.98/1.34
% 1.98/1.34 % git: date: 2026-07-19 20:42:38 +0200
% 1.98/1.34 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.98/1.34 % git: non_committed_changes: false
% 1.98/1.34
% 1.98/1.34 % ------ Parsing...
% 1.98/1.34 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.98/1.34 %
% 1.98/1.34
% 1.98/1.34 % ------ Preprocessing... sup_sim: 0 pe_s pe_e %
% 1.98/1.34
% 1.98/1.34 % ------ Preprocessing...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.98/1.34 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e % ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.98/1.34 %
% 1.98/1.34
% 1.98/1.34 % ------ Preprocessing...
% 1.98/1.34 % ------ Proving...
% 1.98/1.34 % ------ Problem Properties
% 1.98/1.34
% 1.98/1.34 %
% 1.98/1.34 % clauses 20
% 1.98/1.34 % conjectures 2
% 1.98/1.34 % EPR 2
% 1.98/1.34 % Horn 15
% 1.98/1.34 % unary 7
% 1.98/1.34 % binary 1
% 1.98/1.34 % lits 62
% 1.98/1.34 % lits eq 7
% 1.98/1.34 % fd_pure 0
% 1.98/1.34 % fd_pseudo 0
% 1.98/1.34 % fd_cond 0
% 1.98/1.34 % fd_pseudo_cond 5
% 1.98/1.34 % AC symbols 0
% 1.98/1.34
% 1.98/1.34 % ------ Schedule dynamic 5 is on
% 1.98/1.34
% 1.98/1.34 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.98/1.34
% 1.98/1.34
% 1.98/1.34 % ------
% 1.98/1.34 % Current options:
% 1.98/1.34 % ------
% 1.98/1.34
% 1.98/1.34
% 1.98/1.34 %
% 1.98/1.34
% 1.98/1.34 % ------ Proving...
% 1.98/1.34 %
% 1.98/1.34
% 1.98/1.34 % SZS status Theorem for theBenchmark.p
% 1.98/1.34
% 1.98/1.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.98/1.34
% 1.98/1.34
%------------------------------------------------------------------------------