TSTP Solution File: ITP004_2 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : ITP004_2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 17:15:39 EDT 2022
% Result : Theorem 0.14s 0.54s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 33
% Syntax : Number of formulae : 78 ( 12 unt; 24 typ; 0 def)
% Number of atoms : 486 ( 12 equ)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 255 ( 107 ~; 94 |; 24 &)
% ( 7 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 284 ( 284 fml; 0 var)
% Number of types : 4 ( 2 usr)
% Number of type conns : 29 ( 19 >; 10 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 3 con; 0-3 aty)
% Number of variables : 113 ( 106 !; 7 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
del: $tType ).
tff(type_def_6,type,
tp__o: $tType ).
tff(func_def_0,type,
bool: del ).
tff(func_def_1,type,
ind: del ).
tff(func_def_2,type,
arr: ( del * del ) > del ).
tff(func_def_4,type,
k: ( del * $i ) > $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_22,type,
sK1: del ).
tff(func_def_23,type,
sK2: ( $i * del * $i ) > $i ).
tff(func_def_24,type,
sK3: ( del * $i ) > $i ).
tff(func_def_25,type,
sK4: ( $i * del * $i ) > $i ).
tff(pred_def_1,type,
mem: ( $i * del ) > $o ).
tff(f189,plain,
$false,
inference(subsumption_resolution,[],[f188,f104]) ).
tff(f104,plain,
mem(sK0,arr(sK1,bool)),
inference(cnf_transformation,[],[f74]) ).
tff(f74,plain,
( mem(sK0,arr(sK1,bool))
& ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK1),ap(c_2Epred__set_2EREST(sK1),sK0)),sK0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f59,f73]) ).
tff(f73,plain,
( ? [X0,X1: del] :
( mem(X0,arr(X1,bool))
& ~ p(ap(ap(c_2Epred__set_2ESUBSET(X1),ap(c_2Epred__set_2EREST(X1),X0)),X0)) )
=> ( mem(sK0,arr(sK1,bool))
& ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK1),ap(c_2Epred__set_2EREST(sK1),sK0)),sK0)) ) ),
introduced(choice_axiom,[]) ).
tff(f59,plain,
? [X0,X1: del] :
( mem(X0,arr(X1,bool))
& ~ p(ap(ap(c_2Epred__set_2ESUBSET(X1),ap(c_2Epred__set_2EREST(X1),X0)),X0)) ),
inference(ennf_transformation,[],[f46]) ).
tff(f46,plain,
~ ! [X0,X1: del] :
( mem(X0,arr(X1,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X1),ap(c_2Epred__set_2EREST(X1),X0)),X0)) ),
inference(rectify,[],[f31]) ).
tff(f31,negated_conjecture,
~ ! [X11,X10: del] :
( mem(X11,arr(X10,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X10),ap(c_2Epred__set_2EREST(X10),X11)),X11)) ),
inference(negated_conjecture,[],[f30]) ).
tff(f30,conjecture,
! [X11,X10: del] :
( mem(X11,arr(X10,bool))
=> p(ap(ap(c_2Epred__set_2ESUBSET(X10),ap(c_2Epred__set_2EREST(X10),X11)),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EREST__SUBSET) ).
tff(f188,plain,
~ mem(sK0,arr(sK1,bool)),
inference(resolution,[],[f183,f112]) ).
tff(f112,plain,
! [X0: del] : mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool))),
inference(cnf_transformation,[],[f50]) ).
tff(f50,plain,
! [X0: del] : mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool))),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X10: del] : mem(c_2Epred__set_2EREST(X10),arr(arr(X10,bool),arr(X10,bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epred__set_2EREST) ).
tff(f183,plain,
! [X0: del] :
( ~ mem(c_2Epred__set_2EREST(sK1),arr(X0,arr(sK1,bool)))
| ~ mem(sK0,X0) ),
inference(resolution,[],[f182,f136]) ).
tff(f136,plain,
! [X2: del,X3: $i,X0: $i,X1: del] :
( mem(ap(X0,X3),X1)
| ~ mem(X3,X2)
| ~ mem(X0,arr(X2,X1)) ),
inference(cnf_transformation,[],[f95]) ).
tff(f95,plain,
! [X0,X1: del,X2: del] :
( ! [X3] :
( mem(ap(X0,X3),X1)
| ~ mem(X3,X2) )
| ~ mem(X0,arr(X2,X1)) ),
inference(rectify,[],[f64]) ).
tff(f64,plain,
! [X2,X1: del,X0: del] :
( ! [X3] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: del,X2,X1: del] :
( mem(X2,arr(X0,X1))
=> ! [X3] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_tp) ).
tff(f182,plain,
~ mem(ap(c_2Epred__set_2EREST(sK1),sK0),arr(sK1,bool)),
inference(subsumption_resolution,[],[f181,f104]) ).
tff(f181,plain,
( ~ mem(ap(c_2Epred__set_2EREST(sK1),sK0),arr(sK1,bool))
| ~ mem(sK0,arr(sK1,bool)) ),
inference(resolution,[],[f180,f105]) ).
tff(f105,plain,
! [X0: del] : mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0)),
inference(cnf_transformation,[],[f41]) ).
tff(f41,plain,
! [X0: del] : mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0)),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X10: del] : mem(c_2Epred__set_2ECHOICE(X10),arr(arr(X10,bool),X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECHOICE) ).
tff(f180,plain,
! [X0: del] :
( ~ mem(c_2Epred__set_2ECHOICE(sK1),arr(X0,sK1))
| ~ mem(ap(c_2Epred__set_2EREST(sK1),sK0),arr(sK1,bool))
| ~ mem(sK0,X0) ),
inference(resolution,[],[f179,f136]) ).
tff(f179,plain,
( ~ mem(ap(c_2Epred__set_2ECHOICE(sK1),sK0),sK1)
| ~ mem(ap(c_2Epred__set_2EREST(sK1),sK0),arr(sK1,bool)) ),
inference(subsumption_resolution,[],[f178,f103]) ).
tff(f103,plain,
~ p(ap(ap(c_2Epred__set_2ESUBSET(sK1),ap(c_2Epred__set_2EREST(sK1),sK0)),sK0)),
inference(cnf_transformation,[],[f74]) ).
tff(f178,plain,
( ~ mem(ap(c_2Epred__set_2EREST(sK1),sK0),arr(sK1,bool))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK1),sK0),sK1)
| p(ap(ap(c_2Epred__set_2ESUBSET(sK1),ap(c_2Epred__set_2EREST(sK1),sK0)),sK0)) ),
inference(subsumption_resolution,[],[f177,f104]) ).
tff(f177,plain,
( ~ mem(sK0,arr(sK1,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK1),sK0),arr(sK1,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(sK1),ap(c_2Epred__set_2EREST(sK1),sK0)),sK0))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK1),sK0),sK1) ),
inference(duplicate_literal_removal,[],[f176]) ).
tff(f176,plain,
( ~ mem(sK0,arr(sK1,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK1),sK0),arr(sK1,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(sK1),ap(c_2Epred__set_2EREST(sK1),sK0)),sK0))
| ~ mem(ap(c_2Epred__set_2EREST(sK1),sK0),arr(sK1,bool))
| ~ mem(sK0,arr(sK1,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(sK1),ap(c_2Epred__set_2EREST(sK1),sK0)),sK0))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK1),sK0),sK1) ),
inference(resolution,[],[f161,f114]) ).
tff(f114,plain,
! [X2: $i,X0: $i,X1: del] :
( ~ p(ap(ap(c_2Ebool_2EIN(X1),sK2(X0,X1,X2)),X2))
| ~ mem(X2,arr(X1,bool))
| ~ mem(X0,arr(X1,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(X1),X0),X2)) ),
inference(cnf_transformation,[],[f80]) ).
tff(f80,plain,
! [X0,X1: del] :
( ~ mem(X0,arr(X1,bool))
| ! [X2] :
( ~ mem(X2,arr(X1,bool))
| ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X1),X0),X2))
| ( mem(sK2(X0,X1,X2),X1)
& p(ap(ap(c_2Ebool_2EIN(X1),sK2(X0,X1,X2)),X0))
& ~ p(ap(ap(c_2Ebool_2EIN(X1),sK2(X0,X1,X2)),X2)) ) )
& ( ! [X4] :
( ~ mem(X4,X1)
| ~ p(ap(ap(c_2Ebool_2EIN(X1),X4),X0))
| p(ap(ap(c_2Ebool_2EIN(X1),X4),X2)) )
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X1),X0),X2)) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f78,f79]) ).
tff(f79,plain,
! [X0,X1: del,X2] :
( ? [X3] :
( mem(X3,X1)
& p(ap(ap(c_2Ebool_2EIN(X1),X3),X0))
& ~ p(ap(ap(c_2Ebool_2EIN(X1),X3),X2)) )
=> ( mem(sK2(X0,X1,X2),X1)
& p(ap(ap(c_2Ebool_2EIN(X1),sK2(X0,X1,X2)),X0))
& ~ p(ap(ap(c_2Ebool_2EIN(X1),sK2(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f78,plain,
! [X0,X1: del] :
( ~ mem(X0,arr(X1,bool))
| ! [X2] :
( ~ mem(X2,arr(X1,bool))
| ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X1),X0),X2))
| ? [X3] :
( mem(X3,X1)
& p(ap(ap(c_2Ebool_2EIN(X1),X3),X0))
& ~ p(ap(ap(c_2Ebool_2EIN(X1),X3),X2)) ) )
& ( ! [X4] :
( ~ mem(X4,X1)
| ~ p(ap(ap(c_2Ebool_2EIN(X1),X4),X0))
| p(ap(ap(c_2Ebool_2EIN(X1),X4),X2)) )
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(X1),X0),X2)) ) ) ) ),
inference(rectify,[],[f77]) ).
tff(f77,plain,
! [X1,X0: del] :
( ~ mem(X1,arr(X0,bool))
| ! [X2] :
( ~ mem(X2,arr(X0,bool))
| ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
| ? [X3] :
( mem(X3,X0)
& p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
& ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) ) )
& ( ! [X3] :
( ~ 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,[],[f58]) ).
tff(f58,plain,
! [X1,X0: del] :
( ~ mem(X1,arr(X0,bool))
| ! [X2] :
( ~ mem(X2,arr(X0,bool))
| ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
<=> ! [X3] :
( ~ mem(X3,X0)
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
| p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) ) ) ) ),
inference(flattening,[],[f57]) ).
tff(f57,plain,
! [X1,X0: del] :
( ! [X2] :
( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
<=> ! [X3] :
( p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
| ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
| ~ mem(X3,X0) ) )
| ~ mem(X2,arr(X0,bool)) )
| ~ mem(X1,arr(X0,bool)) ),
inference(ennf_transformation,[],[f48]) ).
tff(f48,plain,
! [X1,X0: del] :
( mem(X1,arr(X0,bool))
=> ! [X2] :
( mem(X2,arr(X0,bool))
=> ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
<=> ! [X3] :
( mem(X3,X0)
=> ( p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
=> p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) ) ) ) ) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X10: del,X11] :
( mem(X11,arr(X10,bool))
=> ! [X12] :
( mem(X12,arr(X10,bool))
=> ( ! [X13] :
( mem(X13,X10)
=> ( p(ap(ap(c_2Ebool_2EIN(X10),X13),X11))
=> p(ap(ap(c_2Ebool_2EIN(X10),X13),X12)) ) )
<=> p(ap(ap(c_2Epred__set_2ESUBSET(X10),X11),X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Epred__set_2ESUBSET__DEF) ).
tff(f161,plain,
! [X0: $i] :
( p(ap(ap(c_2Ebool_2EIN(sK1),sK2(ap(c_2Epred__set_2EREST(sK1),sK0),sK1,X0)),sK0))
| ~ mem(ap(c_2Epred__set_2EREST(sK1),sK0),arr(sK1,bool))
| ~ mem(X0,arr(sK1,bool))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK1),sK0),sK1)
| p(ap(ap(c_2Epred__set_2ESUBSET(sK1),ap(c_2Epred__set_2EREST(sK1),sK0)),X0)) ),
inference(subsumption_resolution,[],[f160,f116]) ).
tff(f116,plain,
! [X2: $i,X0: $i,X1: del] :
( p(ap(ap(c_2Epred__set_2ESUBSET(X1),X0),X2))
| ~ mem(X0,arr(X1,bool))
| mem(sK2(X0,X1,X2),X1)
| ~ mem(X2,arr(X1,bool)) ),
inference(cnf_transformation,[],[f80]) ).
tff(f160,plain,
! [X0: $i] :
( p(ap(ap(c_2Epred__set_2ESUBSET(sK1),ap(c_2Epred__set_2EREST(sK1),sK0)),X0))
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK1),sK0),sK1)
| ~ mem(X0,arr(sK1,bool))
| ~ mem(ap(c_2Epred__set_2EREST(sK1),sK0),arr(sK1,bool))
| p(ap(ap(c_2Ebool_2EIN(sK1),sK2(ap(c_2Epred__set_2EREST(sK1),sK0),sK1,X0)),sK0))
| ~ mem(sK2(ap(c_2Epred__set_2EREST(sK1),sK0),sK1,X0),sK1) ),
inference(resolution,[],[f156,f115]) ).
tff(f115,plain,
! [X2: $i,X0: $i,X1: del] :
( p(ap(ap(c_2Ebool_2EIN(X1),sK2(X0,X1,X2)),X0))
| ~ mem(X2,arr(X1,bool))
| ~ mem(X0,arr(X1,bool))
| p(ap(ap(c_2Epred__set_2ESUBSET(X1),X0),X2)) ),
inference(cnf_transformation,[],[f80]) ).
tff(f156,plain,
! [X1: $i] :
( ~ p(ap(ap(c_2Ebool_2EIN(sK1),X1),ap(c_2Epred__set_2EREST(sK1),sK0)))
| ~ mem(X1,sK1)
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK1),sK0),sK1)
| p(ap(ap(c_2Ebool_2EIN(sK1),X1),sK0)) ),
inference(subsumption_resolution,[],[f154,f104]) ).
tff(f154,plain,
! [X1: $i] :
( ~ p(ap(ap(c_2Ebool_2EIN(sK1),X1),ap(c_2Epred__set_2EREST(sK1),sK0)))
| p(ap(ap(c_2Ebool_2EIN(sK1),X1),sK0))
| ~ mem(sK0,arr(sK1,bool))
| ~ mem(X1,sK1)
| ~ mem(ap(c_2Epred__set_2ECHOICE(sK1),sK0),sK1) ),
inference(superposition,[],[f123,f145]) ).
tff(f145,plain,
ap(c_2Epred__set_2EREST(sK1),sK0) = ap(ap(c_2Epred__set_2EDELETE(sK1),sK0),ap(c_2Epred__set_2ECHOICE(sK1),sK0)),
inference(resolution,[],[f104,f98]) ).
tff(f98,plain,
! [X0: $i,X1: del] :
( ~ mem(X0,arr(X1,bool))
| ( ap(c_2Epred__set_2EREST(X1),X0) = ap(ap(c_2Epred__set_2EDELETE(X1),X0),ap(c_2Epred__set_2ECHOICE(X1),X0)) ) ),
inference(cnf_transformation,[],[f66]) ).
tff(f66,plain,
! [X0,X1: del] :
( ( ap(c_2Epred__set_2EREST(X1),X0) = ap(ap(c_2Epred__set_2EDELETE(X1),X0),ap(c_2Epred__set_2ECHOICE(X1),X0)) )
| ~ mem(X0,arr(X1,bool)) ),
inference(ennf_transformation,[],[f42]) ).
tff(f42,plain,
! [X1: del,X0] :
( mem(X0,arr(X1,bool))
=> ( ap(c_2Epred__set_2EREST(X1),X0) = ap(ap(c_2Epred__set_2EDELETE(X1),X0),ap(c_2Epred__set_2ECHOICE(X1),X0)) ) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X11,X10: del] :
( mem(X11,arr(X10,bool))
=> ( ap(c_2Epred__set_2EREST(X10),X11) = ap(ap(c_2Epred__set_2EDELETE(X10),X11),ap(c_2Epred__set_2ECHOICE(X10),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Epred__set_2EREST__DEF) ).
tff(f123,plain,
! [X2: $i,X3: $i,X0: del,X1: $i] :
( ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
| ~ mem(X3,X0)
| p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
| ~ mem(X1,arr(X0,bool))
| ~ mem(X2,X0) ),
inference(cnf_transformation,[],[f85]) ).
tff(f85,plain,
! [X0: del,X1] :
( ~ mem(X1,arr(X0,bool))
| ! [X2] :
( ~ mem(X2,X0)
| ! [X3] :
( ( ( 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))) ) )
| ~ mem(X3,X0) ) ) ),
inference(flattening,[],[f84]) ).
tff(f84,plain,
! [X0: del,X1] :
( ~ mem(X1,arr(X0,bool))
| ! [X2] :
( ~ mem(X2,X0)
| ! [X3] :
( ( ( 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))) ) )
| ~ mem(X3,X0) ) ) ),
inference(nnf_transformation,[],[f60]) ).
tff(f60,plain,
! [X0: del,X1] :
( ~ mem(X1,arr(X0,bool))
| ! [X2] :
( ~ mem(X2,X0)
| ! [X3] :
( ( 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)) ) )
| ~ mem(X3,X0) ) ) ),
inference(ennf_transformation,[],[f43]) ).
tff(f43,plain,
! [X0: del,X1] :
( mem(X1,arr(X0,bool))
=> ! [X2] :
( mem(X2,X0)
=> ! [X3] :
( 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(rectify,[],[f28]) ).
tff(f28,axiom,
! [X10: del,X11] :
( mem(X11,arr(X10,bool))
=> ! [X14] :
( mem(X14,X10)
=> ! [X15] :
( mem(X15,X10)
=> ( p(ap(ap(c_2Ebool_2EIN(X10),X14),ap(ap(c_2Epred__set_2EDELETE(X10),X11),X15)))
<=> ( ( X14 != X15 )
& p(ap(ap(c_2Ebool_2EIN(X10),X14),X11)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EIN__DELETE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : ITP004_2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.05/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.09/0.30 % Computer : n022.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Aug 29 23:28:11 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.14/0.45 % (27689)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.14/0.46 % (27699)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.14/0.46 % (27697)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.47 % (27691)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.14/0.47 % (27705)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.14/0.47 % (27697)Instruction limit reached!
% 0.14/0.47 % (27697)------------------------------
% 0.14/0.47 % (27697)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.48 % (27697)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.48 % (27697)Termination reason: Unknown
% 0.14/0.48 % (27697)Termination phase: Saturation
% 0.14/0.48
% 0.14/0.48 % (27697)Memory used [KB]: 6012
% 0.14/0.48 % (27697)Time elapsed: 0.005 s
% 0.14/0.48 % (27697)Instructions burned: 4 (million)
% 0.14/0.48 % (27697)------------------------------
% 0.14/0.48 % (27697)------------------------------
% 0.14/0.48 % (27707)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.14/0.49 % (27687)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.14/0.49 % (27693)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.14/0.49 % (27685)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.49 % (27685)Instruction limit reached!
% 0.14/0.49 % (27685)------------------------------
% 0.14/0.49 % (27685)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.49 % (27685)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.49 % (27685)Termination reason: Unknown
% 0.14/0.49 % (27685)Termination phase: Saturation
% 0.14/0.49
% 0.14/0.49 % (27685)Memory used [KB]: 1535
% 0.14/0.49 % (27685)Time elapsed: 0.005 s
% 0.14/0.49 % (27685)Instructions burned: 4 (million)
% 0.14/0.49 % (27685)------------------------------
% 0.14/0.49 % (27685)------------------------------
% 0.14/0.50 % (27690)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.14/0.50 % (27683)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.14/0.51 % (27686)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.14/0.51 % (27712)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.14/0.51 % (27688)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.14/0.51 % (27688)First to succeed.
% 0.14/0.51 % (27700)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.51 % (27706)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.14/0.51 % (27710)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.14/0.51 % (27700)Instruction limit reached!
% 0.14/0.51 % (27700)------------------------------
% 0.14/0.51 % (27700)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.51 % (27700)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.51 % (27700)Termination reason: Unknown
% 0.14/0.51 % (27700)Termination phase: Property scanning
% 0.14/0.51
% 0.14/0.51 % (27700)Memory used [KB]: 1535
% 0.14/0.51 % (27700)Time elapsed: 0.003 s
% 0.14/0.51 % (27700)Instructions burned: 3 (million)
% 0.14/0.51 % (27700)------------------------------
% 0.14/0.51 % (27700)------------------------------
% 0.14/0.51 % (27695)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.51 % (27704)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.14/0.52 % (27695)Refutation not found, incomplete strategy% (27695)------------------------------
% 0.14/0.52 % (27695)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.52 % (27695)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.52 % (27695)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.52
% 0.14/0.52 % (27695)Memory used [KB]: 1663
% 0.14/0.52 % (27695)Time elapsed: 0.152 s
% 0.14/0.52 % (27695)Instructions burned: 6 (million)
% 0.14/0.52 % (27695)------------------------------
% 0.14/0.52 % (27695)------------------------------
% 0.14/0.52 % (27702)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.14/0.52 % (27696)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.14/0.52 % (27687)Instruction limit reached!
% 0.14/0.52 % (27687)------------------------------
% 0.14/0.52 % (27687)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.52 % (27687)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.52 % (27687)Termination reason: Unknown
% 0.14/0.52 % (27687)Termination phase: Saturation
% 0.14/0.52
% 0.14/0.52 % (27687)Memory used [KB]: 6140
% 0.14/0.52 % (27687)Time elapsed: 0.162 s
% 0.14/0.52 % (27687)Instructions burned: 14 (million)
% 0.14/0.52 % (27687)------------------------------
% 0.14/0.52 % (27687)------------------------------
% 0.14/0.52 % (27708)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.14/0.52 % (27703)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.14/0.52 % (27701)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.52 % (27689)Instruction limit reached!
% 0.14/0.52 % (27689)------------------------------
% 0.14/0.52 % (27689)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.52 % (27701)Instruction limit reached!
% 0.14/0.52 % (27701)------------------------------
% 0.14/0.52 % (27701)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.52 % (27701)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.52 % (27701)Termination reason: Unknown
% 0.14/0.52 % (27701)Termination phase: Preprocessing 3
% 0.14/0.52
% 0.14/0.52 % (27701)Memory used [KB]: 1407
% 0.14/0.52 % (27701)Time elapsed: 0.004 s
% 0.14/0.52 % (27701)Instructions burned: 2 (million)
% 0.14/0.52 % (27701)------------------------------
% 0.14/0.52 % (27701)------------------------------
% 0.14/0.52 % (27689)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.52 % (27689)Termination reason: Unknown
% 0.14/0.52 % (27689)Termination phase: Saturation
% 0.14/0.52
% 0.14/0.52 % (27689)Memory used [KB]: 6396
% 0.14/0.52 % (27689)Time elapsed: 0.141 s
% 0.14/0.52 % (27689)Instructions burned: 39 (million)
% 0.14/0.52 % (27689)------------------------------
% 0.14/0.52 % (27689)------------------------------
% 0.14/0.53 % (27694)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.53 % (27709)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.14/0.53 % (27692)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.14/0.53 % (27711)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.14/0.54 % (27688)Refutation found. Thanks to Tanya!
% 0.14/0.54 % SZS status Theorem for theBenchmark
% 0.14/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.54 % (27688)------------------------------
% 0.14/0.54 % (27688)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.54 % (27688)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.54 % (27688)Termination reason: Refutation
% 0.14/0.54
% 0.14/0.54 % (27688)Memory used [KB]: 1663
% 0.14/0.54 % (27688)Time elapsed: 0.147 s
% 0.14/0.54 % (27688)Instructions burned: 8 (million)
% 0.14/0.54 % (27688)------------------------------
% 0.14/0.54 % (27688)------------------------------
% 0.14/0.54 % (27682)Success in time 0.228 s
%------------------------------------------------------------------------------