%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP006_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 : Tue Sep 29 11:27:49 AM UTC 2026
% Result : Theorem 2.09s 1.40s
% Output : Refutation 4.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 11 unt; 0 typ; 5 def)
% Number of atoms : 574 ( 8 equ)
% Maximal formula atoms : 36 ( 13 avg)
% Number of connectives : 429 ( 150 ~; 141 |; 78 &)
% ( 24 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 253 ( 253 fml; 0 var)
% Number of types : 4 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 4 prp; 0-4 aty)
% Number of functors : 34 ( 34 usr; 6 con; 0-4 aty)
% Number of variables : 210 ( 180 !; 30 ?; 210 :)
% 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_2Ebool_2ET: tp__o ).
tff(func_def_10,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP: ( del * del ) > $i ).
tff(func_def_11,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP: ( del * del ) > $i ).
tff(func_def_12,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT: ( del * del ) > $i ).
tff(func_def_13,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT: ( del * del ) > $i ).
tff(func_def_14,type,
c_2EquantHeuristics_2EGUESS__FORALL: ( del * del ) > $i ).
tff(func_def_15,type,
c_2Ebool_2E_3F: del > $i ).
tff(func_def_16,type,
c_2EquantHeuristics_2EGUESS__EXISTS: ( del * del ) > $i ).
tff(func_def_18,type,
fo__c_2Ebool_2EF: tp__o ).
tff(func_def_20,type,
fo__c_2Ebool_2E_5C_2F: ( tp__o * tp__o ) > tp__o ).
tff(func_def_22,type,
fo__c_2Ebool_2E_2F_5C: ( tp__o * tp__o ) > tp__o ).
tff(func_def_23,type,
c_2Emin_2E_3D: del > $i ).
tff(func_def_25,type,
fo__c_2Ebool_2E_7E: tp__o > tp__o ).
tff(func_def_27,type,
fo__c_2Emin_2E_3D_3D_3E: ( tp__o * tp__o ) > tp__o ).
tff(func_def_28,type,
c_2Ebool_2E_21: del > $i ).
tff(func_def_29,type,
sK5: del ).
tff(func_def_30,type,
sK6: del ).
tff(func_def_34,type,
sK10: ( del * $i * $i ) > $i ).
tff(func_def_35,type,
sK11: ( del * $i * $i * del ) > $i ).
tff(func_def_36,type,
sK12: ( del * $i * $i ) > $i ).
tff(func_def_37,type,
sK13: ( del * $i * $i * del ) > $i ).
tff(func_def_38,type,
sK14: ( del * $i * $i ) > $i ).
tff(func_def_39,type,
sK15: ( del * del * $i * $i ) > $i ).
tff(func_def_40,type,
sK16: ( del * $i * $i ) > $i ).
tff(func_def_41,type,
sK17: ( del * del * $i * $i ) > $i ).
tff(func_def_42,type,
sK18: ( del * $i * $i ) > $i ).
tff(func_def_43,type,
sK19: ( del * $i * $i ) > $i ).
tff(pred_def_1,type,
mem: ( $i * del ) > $o ).
tff(pred_def_3,type,
sP0: ( del * del ) > $o ).
tff(pred_def_4,type,
sP1: ( del * del ) > $o ).
tff(pred_def_5,type,
sP2: ( del * $i * $i * del ) > $o ).
tff(pred_def_6,type,
sP3: ( del * $i * $i * del ) > $o ).
tff(pred_def_7,type,
sP4: ( del * del ) > $o ).
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/sandbox/benchmark/theBenchmark.p',ap_tp) ).
tff(f46,axiom,
! [X0: del,X1: del,X2: $i] :
( mem(X2,arr(X0,X1))
=> ! [X3: $i] :
( mem(X3,arr(X1,bool))
=> ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X0,X1),X2),X3))
<=> ! [X4: $i] :
( mem(X4,X1)
=> ( p(ap(X3,X4))
=> ? [X5: $i] :
( mem(X5,X0)
& p(ap(X3,ap(X2,X5))) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X0,X1),X2),X3))
<=> ! [X6: $i] :
( mem(X6,X1)
=> ( ~ p(ap(X3,X6))
=> ? [X7: $i] :
( mem(X7,X0)
& ~ p(ap(X3,ap(X2,X7))) ) ) ) )
& ! [X8: $i] :
( mem(X8,arr(X0,X1))
=> ! [X9: $i] :
( mem(X9,arr(X1,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X8),X9))
<=> ! [X10: $i] :
( mem(X10,X0)
=> p(ap(X9,ap(X8,X10))) ) ) ) )
& ! [X11: $i] :
( mem(X11,arr(X0,X1))
=> ! [X12: $i] :
( mem(X12,arr(X1,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X11),X12))
<=> ! [X13: $i] :
( mem(X13,X0)
=> ~ p(ap(X12,ap(X11,X13))) ) ) ) )
& ! [X14: $i] :
( mem(X14,arr(X0,X1))
=> ! [X15: $i] :
( mem(X15,arr(X1,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X0,X1),X14),X15))
<=> ! [X16: $i] :
( mem(X16,X1)
=> ( p(ap(X15,X16))
=> ? [X17: $i] :
( mem(X17,X0)
& ( X16 = ap(X14,X17) ) ) ) ) ) ) )
& ! [X18: $i] :
( mem(X18,arr(X0,X1))
=> ! [X19: $i] :
( mem(X19,arr(X1,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X0,X1),X18),X19))
<=> ! [X20: $i] :
( mem(X20,X1)
=> ( ~ p(ap(X19,X20))
=> ? [X21: $i] :
( mem(X21,X0)
& ( X20 = ap(X18,X21) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2EquantHeuristics_2EGUESS__REWRITES) ).
tff(f58,conjecture,
! [X0: del,X1: del,X2: $i] :
( mem(X2,arr(X1,X0))
=> ! [X3: $i] :
( mem(X3,arr(X0,bool))
=> ! [X4: $i] :
( mem(X4,arr(X0,bool))
=> ( ! [X5: $i] :
( mem(X5,X0)
=> ( p(ap(X4,X5))
=> p(ap(X3,X5)) ) )
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X3))
=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X4)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT) ).
tff(f59,negated_conjecture,
~ ! [X0: del,X1: del,X2: $i] :
( mem(X2,arr(X1,X0))
=> ! [X3: $i] :
( mem(X3,arr(X0,bool))
=> ! [X4: $i] :
( mem(X4,arr(X0,bool))
=> ( ! [X5: $i] :
( mem(X5,X0)
=> ( p(ap(X4,X5))
=> p(ap(X3,X5)) ) )
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X3))
=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X4)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f58]) ).
tff(f60,plain,
? [X0: del,X1: del,X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X4))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X3))
& ! [X5: $i] :
( p(ap(X3,X5))
| ~ p(ap(X4,X5))
| ~ mem(X5,X0) )
& mem(X4,arr(X0,bool)) )
& mem(X3,arr(X0,bool)) )
& mem(X2,arr(X1,X0)) ),
inference(ennf_transformation,[],[f59]) ).
tff(f61,plain,
? [X0: del,X1: del,X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X4))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X3))
& ! [X5: $i] :
( p(ap(X3,X5))
| ~ p(ap(X4,X5))
| ~ mem(X5,X0) )
& mem(X4,arr(X0,bool)) )
& mem(X3,arr(X0,bool)) )
& mem(X2,arr(X1,X0)) ),
inference(flattening,[],[f60]) ).
tff(f62,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f1]) ).
tff(f63,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X0,X1),X2),X3))
<=> ! [X4: $i] :
( ? [X5: $i] :
( mem(X5,X0)
& p(ap(X3,ap(X2,X5))) )
| ~ p(ap(X3,X4))
| ~ mem(X4,X1) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X0,X1),X2),X3))
<=> ! [X6: $i] :
( ? [X7: $i] :
( mem(X7,X0)
& ~ p(ap(X3,ap(X2,X7))) )
| p(ap(X3,X6))
| ~ mem(X6,X1) ) )
& ! [X8: $i] :
( ! [X9: $i] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X8),X9))
<=> ! [X10: $i] :
( p(ap(X9,ap(X8,X10)))
| ~ mem(X10,X0) ) )
| ~ mem(X9,arr(X1,bool)) )
| ~ mem(X8,arr(X0,X1)) )
& ! [X11: $i] :
( ! [X12: $i] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X11),X12))
<=> ! [X13: $i] :
( ~ p(ap(X12,ap(X11,X13)))
| ~ mem(X13,X0) ) )
| ~ mem(X12,arr(X1,bool)) )
| ~ mem(X11,arr(X0,X1)) )
& ! [X14: $i] :
( ! [X15: $i] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X0,X1),X14),X15))
<=> ! [X16: $i] :
( ? [X17: $i] :
( mem(X17,X0)
& ( X16 = ap(X14,X17) ) )
| ~ p(ap(X15,X16))
| ~ mem(X16,X1) ) )
| ~ mem(X15,arr(X1,bool)) )
| ~ mem(X14,arr(X0,X1)) )
& ! [X18: $i] :
( ! [X19: $i] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X0,X1),X18),X19))
<=> ! [X20: $i] :
( ? [X21: $i] :
( mem(X21,X0)
& ( X20 = ap(X18,X21) ) )
| p(ap(X19,X20))
| ~ mem(X20,X1) ) )
| ~ mem(X19,arr(X1,bool)) )
| ~ mem(X18,arr(X0,X1)) ) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f46]) ).
tff(f64,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X0,X1),X2),X3))
<=> ! [X4: $i] :
( ? [X5: $i] :
( mem(X5,X0)
& p(ap(X3,ap(X2,X5))) )
| ~ p(ap(X3,X4))
| ~ mem(X4,X1) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X0,X1),X2),X3))
<=> ! [X6: $i] :
( ? [X7: $i] :
( mem(X7,X0)
& ~ p(ap(X3,ap(X2,X7))) )
| p(ap(X3,X6))
| ~ mem(X6,X1) ) )
& ! [X8: $i] :
( ! [X9: $i] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X8),X9))
<=> ! [X10: $i] :
( p(ap(X9,ap(X8,X10)))
| ~ mem(X10,X0) ) )
| ~ mem(X9,arr(X1,bool)) )
| ~ mem(X8,arr(X0,X1)) )
& ! [X11: $i] :
( ! [X12: $i] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X11),X12))
<=> ! [X13: $i] :
( ~ p(ap(X12,ap(X11,X13)))
| ~ mem(X13,X0) ) )
| ~ mem(X12,arr(X1,bool)) )
| ~ mem(X11,arr(X0,X1)) )
& ! [X14: $i] :
( ! [X15: $i] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X0,X1),X14),X15))
<=> ! [X16: $i] :
( ? [X17: $i] :
( mem(X17,X0)
& ( X16 = ap(X14,X17) ) )
| ~ p(ap(X15,X16))
| ~ mem(X16,X1) ) )
| ~ mem(X15,arr(X1,bool)) )
| ~ mem(X14,arr(X0,X1)) )
& ! [X18: $i] :
( ! [X19: $i] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X0,X1),X18),X19))
<=> ! [X20: $i] :
( ? [X21: $i] :
( mem(X21,X0)
& ( X20 = ap(X18,X21) ) )
| p(ap(X19,X20))
| ~ mem(X20,X1) ) )
| ~ mem(X19,arr(X1,bool)) )
| ~ mem(X18,arr(X0,X1)) ) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,X1)) ),
inference(flattening,[],[f63]) ).
tff(f65,definition,
! [X0: del,X1: del] :
( ! [X18: $i] :
( ! [X19: $i] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X0,X1),X18),X19))
<=> ! [X20: $i] :
( ? [X21: $i] :
( mem(X21,X0)
& ( X20 = ap(X18,X21) ) )
| p(ap(X19,X20))
| ~ mem(X20,X1) ) )
| ~ mem(X19,arr(X1,bool)) )
| ~ mem(X18,arr(X0,X1)) )
| ~ sP0(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
tff(f66,definition,
! [X0: del,X1: del] :
( ! [X14: $i] :
( ! [X15: $i] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X0,X1),X14),X15))
<=> ! [X16: $i] :
( ? [X17: $i] :
( mem(X17,X0)
& ( X16 = ap(X14,X17) ) )
| ~ p(ap(X15,X16))
| ~ mem(X16,X1) ) )
| ~ mem(X15,arr(X1,bool)) )
| ~ mem(X14,arr(X0,X1)) )
| ~ sP1(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
tff(f67,definition,
! [X0: del,X2: $i,X3: $i,X1: del] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X0,X1),X2),X3))
<=> ! [X6: $i] :
( ? [X7: $i] :
( mem(X7,X0)
& ~ p(ap(X3,ap(X2,X7))) )
| p(ap(X3,X6))
| ~ mem(X6,X1) ) )
| ~ sP2(X0,X2,X3,X1) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
tff(f68,definition,
! [X0: del,X2: $i,X3: $i,X1: del] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X0,X1),X2),X3))
<=> ! [X4: $i] :
( ? [X5: $i] :
( mem(X5,X0)
& p(ap(X3,ap(X2,X5))) )
| ~ p(ap(X3,X4))
| ~ mem(X4,X1) ) )
| ~ sP3(X0,X2,X3,X1) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
tff(f69,definition,
! [X0: del,X1: del] :
( ! [X11: $i] :
( ! [X12: $i] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X11),X12))
<=> ! [X13: $i] :
( ~ p(ap(X12,ap(X11,X13)))
| ~ mem(X13,X0) ) )
| ~ mem(X12,arr(X1,bool)) )
| ~ mem(X11,arr(X0,X1)) )
| ~ sP4(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
tff(f70,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ( sP3(X0,X2,X3,X1)
& sP2(X0,X2,X3,X1)
& ! [X8: $i] :
( ! [X9: $i] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X8),X9))
<=> ! [X10: $i] :
( p(ap(X9,ap(X8,X10)))
| ~ mem(X10,X0) ) )
| ~ mem(X9,arr(X1,bool)) )
| ~ mem(X8,arr(X0,X1)) )
& sP4(X0,X1)
& sP1(X0,X1)
& sP0(X0,X1) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,X1)) ),
inference(definition_folding,[],[f64,f69,f68,f67,f66,f65]) ).
tff(f71,plain,
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK6,sK5),sK7),sK9))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK6,sK5),sK7),sK8))
& ! [X5: $i] :
( p(ap(sK8,X5))
| ~ p(ap(sK9,X5))
| ~ mem(X5,sK5) )
& mem(sK9,arr(sK5,bool))
& mem(sK8,arr(sK5,bool))
& mem(sK7,arr(sK6,sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7),skolemize(X3,sK8),skolemize(X4,sK9)],[f61]) ).
tff(f72,plain,
! [X0: del,X1: del] :
( ! [X11: $i] :
( ! [X12: $i] :
( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X11),X12))
| ? [X13: $i] :
( p(ap(X12,ap(X11,X13)))
& mem(X13,X0) ) )
& ( ! [X13: $i] :
( ~ p(ap(X12,ap(X11,X13)))
| ~ mem(X13,X0) )
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X11),X12)) ) )
| ~ mem(X12,arr(X1,bool)) )
| ~ mem(X11,arr(X0,X1)) )
| ~ sP4(X0,X1) ),
inference(nnf_transformation,[],[f69]) ).
tff(f73,plain,
! [X0: del,X1: del] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3))
| ? [X4: $i] :
( p(ap(X3,ap(X2,X4)))
& mem(X4,X0) ) )
& ( ! [X5: $i] :
( ~ p(ap(X3,ap(X2,X5)))
| ~ mem(X5,X0) )
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3)) ) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,X1)) )
| ~ sP4(X0,X1) ),
inference(rectify,[],[f72]) ).
tff(f74,plain,
! [X0: del,X1: del] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3))
| ( p(ap(X3,ap(X2,sK10(X0,X2,X3))))
& mem(sK10(X0,X2,X3),X0) ) )
& ( ! [X5: $i] :
( ~ p(ap(X3,ap(X2,X5)))
| ~ mem(X5,X0) )
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3)) ) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,X1)) )
| ~ sP4(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X4,sK10(X0,X2,X3))],[f73]) ).
tff(f87,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ( sP3(X0,X2,X3,X1)
& sP2(X0,X2,X3,X1)
& ! [X8: $i] :
( ! [X9: $i] :
( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X8),X9))
| ? [X10: $i] :
( ~ p(ap(X9,ap(X8,X10)))
& mem(X10,X0) ) )
& ( ! [X10: $i] :
( p(ap(X9,ap(X8,X10)))
| ~ mem(X10,X0) )
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X8),X9)) ) )
| ~ mem(X9,arr(X1,bool)) )
| ~ mem(X8,arr(X0,X1)) )
& sP4(X0,X1)
& sP1(X0,X1)
& sP0(X0,X1) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,X1)) ),
inference(nnf_transformation,[],[f70]) ).
tff(f88,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ( sP3(X0,X2,X3,X1)
& sP2(X0,X2,X3,X1)
& ! [X4: $i] :
( ! [X5: $i] :
( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X4),X5))
| ? [X6: $i] :
( ~ p(ap(X5,ap(X4,X6)))
& mem(X6,X0) ) )
& ( ! [X7: $i] :
( p(ap(X5,ap(X4,X7)))
| ~ mem(X7,X0) )
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X4),X5)) ) )
| ~ mem(X5,arr(X1,bool)) )
| ~ mem(X4,arr(X0,X1)) )
& sP4(X0,X1)
& sP1(X0,X1)
& sP0(X0,X1) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,X1)) ),
inference(rectify,[],[f87]) ).
tff(f89,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ( sP3(X0,X2,X3,X1)
& sP2(X0,X2,X3,X1)
& ! [X4: $i] :
( ! [X5: $i] :
( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X4),X5))
| ( ~ p(ap(X5,ap(X4,sK19(X0,X4,X5))))
& mem(sK19(X0,X4,X5),X0) ) )
& ( ! [X7: $i] :
( p(ap(X5,ap(X4,X7)))
| ~ mem(X7,X0) )
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X4),X5)) ) )
| ~ mem(X5,arr(X1,bool)) )
| ~ mem(X4,arr(X0,X1)) )
& sP4(X0,X1)
& sP1(X0,X1)
& sP0(X0,X1) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X6,sK19(X0,X4,X5))],[f88]) ).
tff(f90,plain,
mem(sK7,arr(sK6,sK5)),
inference(cnf_transformation,[],[f71]) ).
tff(f91,plain,
mem(sK8,arr(sK5,bool)),
inference(cnf_transformation,[],[f71]) ).
tff(f92,plain,
mem(sK9,arr(sK5,bool)),
inference(cnf_transformation,[],[f71]) ).
tff(f93,plain,
! [X5: $i] :
( ~ p(ap(sK9,X5))
| p(ap(sK8,X5))
| ~ mem(X5,sK5) ),
inference(cnf_transformation,[],[f71]) ).
tff(f94,plain,
p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK6,sK5),sK7),sK8)),
inference(cnf_transformation,[],[f71]) ).
tff(f95,plain,
~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK6,sK5),sK7),sK9)),
inference(cnf_transformation,[],[f71]) ).
tff(f96,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,[],[f62]) ).
tff(f97,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X5: $i] :
( ~ p(ap(X3,ap(X2,X5)))
| ~ mem(X5,X0)
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
tff(f98,plain,
! [X2: $i,X3: $i,X0: del,X1: del] :
( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3))
| mem(sK10(X0,X2,X3),X0)
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
tff(f99,plain,
! [X2: $i,X3: $i,X0: del,X1: del] :
( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3))
| p(ap(X3,ap(X2,sK10(X0,X2,X3))))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
tff(f122,plain,
! [X2: $i,X3: $i,X0: del,X1: del] :
( ~ mem(X3,arr(X1,bool))
| sP4(X0,X1)
| ~ mem(X2,arr(X0,X1)) ),
inference(cnf_transformation,[],[f89]) ).
tff(f139,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X5: $i] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3))
| ~ mem(X5,X0)
| ~ p(ap(X3,ap(X2,X5)))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f97,f122]) ).
tff(f140,plain,
! [X2: $i,X3: $i,X0: del,X1: del] :
( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3))
| mem(sK10(X0,X2,X3),X0)
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f98,f122]) ).
tff(f141,plain,
! [X2: $i,X3: $i,X0: del,X1: del] :
( p(ap(X3,ap(X2,sK10(X0,X2,X3))))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f99,f122]) ).
tff(f162,plain,
mem(sK10(sK6,sK7,sK9),sK6),
inference(unit_resulting_resolution,[],[f140,f90,f92,f95]) ).
tff(f163,plain,
mem(ap(sK7,sK10(sK6,sK7,sK9)),sK5),
inference(unit_resulting_resolution,[],[f96,f90,f162]) ).
tff(f169,plain,
~ p(ap(sK8,ap(sK7,sK10(sK6,sK7,sK9)))),
inference(unit_resulting_resolution,[],[f139,f162,f90,f91,f94]) ).
tff(f170,plain,
~ p(ap(sK9,ap(sK7,sK10(sK6,sK7,sK9)))),
inference(unit_resulting_resolution,[],[f93,f163,f169]) ).
tff(f172,plain,
p(ap(sK9,ap(sK7,sK10(sK6,sK7,sK9)))),
inference(unit_resulting_resolution,[],[f141,f90,f92,f95]) ).
tff(f173,plain,
$false,
inference(forward_subsumption_resolution,[],[f172,f170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP006_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n013.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 11:51:51 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.09/1.40 % (92177)Detected formulas, will run a generic FOF schedule.
% 2.09/1.40 % (92186)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1159987390:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.09/1.40 % (92186)Refutation not found, incomplete strategy
% 2.09/1.40 % (92186)------------------------------
% 2.09/1.40 % (92186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.09/1.40 % (92186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/1.40 % (92186)CaDiCaL version: 2.1.3
% 2.09/1.40 % (92186)Termination reason: Refutation not found, incomplete strategy
% 2.09/1.40 % (92186)Time elapsed: 0.001 s
% 2.09/1.40 % (92186)Peak memory usage: 88 MB
% 2.09/1.40 % (92182)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=409070422:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.09/1.40 % (92184)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4281125104:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.09/1.40 % (92185)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3831716400:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.09/1.40 % (92183)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=330165077:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.09/1.40 % (92185)Refutation not found, incomplete strategy
% 2.09/1.40 % (92185)------------------------------
% 2.09/1.40 % (92185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.09/1.40 % (92185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/1.40 % (92185)CaDiCaL version: 2.1.3
% 2.09/1.40 % (92185)Termination reason: Refutation not found, incomplete strategy
% 2.09/1.40 % (92185)Time elapsed: 0.001 s
% 2.09/1.40 % (92185)Peak memory usage: 87 MB
% 2.09/1.40 % (92187)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1968760394:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.09/1.40 % (92188)dis-21_1_sil=8000:lcm=predicate:random_seed=1952159660:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.09/1.40 % (92188)Instruction limit reached!
% 2.09/1.40 % (92188)------------------------------
% 2.09/1.40 % (92188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.09/1.40 % (92188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/1.40 % (92188)CaDiCaL version: 2.1.3
% 2.09/1.40 % (92188)Termination reason: Instruction limit
% 2.09/1.40 % (92188)Termination phase: Saturation
% 2.09/1.40 % (92188)Time elapsed: 0.078 s
% 2.09/1.40 % (92188)Peak memory usage: 90 MB
% 2.09/1.40 % (92188)Instructions burned: 131 (million)
% 2.09/1.40 % (92186)------------------------------
% 2.09/1.40 % (92186)------------------------------
% 2.09/1.40 % (92187)Instruction limit reached!
% 2.09/1.40 % (92187)------------------------------
% 2.09/1.40 % (92187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.09/1.40 % (92187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.09/1.40 % (92187)CaDiCaL version: 2.1.3
% 2.09/1.40 % (92187)Termination reason: Instruction limit
% 2.09/1.40 % (92187)Termination phase: Saturation
% 2.09/1.40 % (92187)Time elapsed: 0.094 s
% 2.09/1.40 % (92187)Peak memory usage: 90 MB
% 2.09/1.40 % (92187)Instructions burned: 139 (million)
% 2.09/1.40 % (92197)lrs+10_1_sil=32000:urr=on:br=off:random_seed=320944100:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.09/1.40 % (92197)First to succeed.
% 2.09/1.40 % (92197)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-92177"
% 2.09/1.40 % (92196)lrs+10_1_sil=8000:sp=occurrence:random_seed=3703562956:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.09/1.40 % (92185)------------------------------
% 2.09/1.40 % (92185)------------------------------
% 2.09/1.40 % (92198)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3870415613:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.09/1.40 % (92196)Also succeeded, but the first one will report.
% 2.09/1.40 % (92197)Refutation found. Thanks to Tanya!
% 2.09/1.40 % SZS status Theorem for theBenchmark
% 2.09/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 4.58/1.62 % (92197)------------------------------
% 4.58/1.62 % (92197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.58/1.62 % (92197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.58/1.62 % (92197)CaDiCaL version: 2.1.3
% 4.58/1.62 % (92197)Termination reason: Refutation
% 4.58/1.62 % (92197)Time elapsed: 0.005 s
% 4.58/1.62 % (92197)Peak memory usage: 89 MB
% 4.58/1.62 % (92197)Instructions burned: 14 (million)
% 4.58/1.62 % (92197)------------------------------
% 4.58/1.62 % (92197)------------------------------
% 4.58/1.62 % (92177)Success in time 0.554 s
% 4.58/1.62 % Vampire exiting
%------------------------------------------------------------------------------