TSTP Solution File: SWV381+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n011.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 : Sat Sep 2 13:04:12 EDT 2023
% Result : Theorem 7.00s 1.41s
% Output : Refutation 7.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 47
% Syntax : Number of formulae : 231 ( 23 unt; 0 def)
% Number of atoms : 603 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 629 ( 257 ~; 295 |; 34 &)
% ( 32 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 23 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 290 (; 272 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12024,plain,
$false,
inference(avatar_smt_refutation,[],[f245,f250,f255,f304,f595,f1092,f1098,f1117,f1123,f1131,f1367,f1428,f7666,f7671,f7949,f8048,f8051,f8095,f8096,f8392,f8472,f10539,f10652,f10747,f10749,f12023]) ).
fof(f12023,plain,
( ~ spl7_3
| spl7_5
| spl7_6 ),
inference(avatar_contradiction_clause,[],[f12022]) ).
fof(f12022,plain,
( $false
| ~ spl7_3
| spl7_5
| spl7_6 ),
inference(subsumption_resolution,[],[f12021,f594]) ).
fof(f594,plain,
( ~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0))
| spl7_6 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f592,plain,
( spl7_6
<=> issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).
fof(f12021,plain,
( issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0))
| ~ spl7_3
| spl7_5 ),
inference(duplicate_literal_removal,[],[f12000]) ).
fof(f12000,plain,
( issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0))
| issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0))
| ~ spl7_3
| spl7_5 ),
inference(resolution,[],[f11999,f202]) ).
fof(f202,plain,
! [X0,X1] :
( ~ less_than(X1,sK6(X0,X1))
| issmallestelement_pq(X0,X1) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0,X1] :
( ( issmallestelement_pq(X0,X1)
| ( ~ less_than(X1,sK6(X0,X1))
& contains_pq(X0,sK6(X0,X1)) ) )
& ( ! [X3] :
( less_than(X1,X3)
| ~ contains_pq(X0,X3) )
| ~ issmallestelement_pq(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f139,f140]) ).
fof(f140,plain,
! [X0,X1] :
( ? [X2] :
( ~ less_than(X1,X2)
& contains_pq(X0,X2) )
=> ( ~ less_than(X1,sK6(X0,X1))
& contains_pq(X0,sK6(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f139,plain,
! [X0,X1] :
( ( issmallestelement_pq(X0,X1)
| ? [X2] :
( ~ less_than(X1,X2)
& contains_pq(X0,X2) ) )
& ( ! [X3] :
( less_than(X1,X3)
| ~ contains_pq(X0,X3) )
| ~ issmallestelement_pq(X0,X1) ) ),
inference(rectify,[],[f138]) ).
fof(f138,plain,
! [X0,X1] :
( ( issmallestelement_pq(X0,X1)
| ? [X2] :
( ~ less_than(X1,X2)
& contains_pq(X0,X2) ) )
& ( ! [X2] :
( less_than(X1,X2)
| ~ contains_pq(X0,X2) )
| ~ issmallestelement_pq(X0,X1) ) ),
inference(nnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
<=> ! [X2] :
( less_than(X1,X2)
| ~ contains_pq(X0,X2) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
<=> ! [X2] :
( contains_pq(X0,X2)
=> less_than(X1,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',ax10) ).
fof(f11999,plain,
( ! [X0] :
( less_than(findmin_pqp_res(sK0),sK6(i(triple(sK0,sK1,sK2)),X0))
| issmallestelement_pq(i(triple(sK0,sK1,sK2)),X0) )
| ~ spl7_3
| spl7_5 ),
inference(resolution,[],[f8108,f319]) ).
fof(f319,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(subsumption_resolution,[],[f199,f180]) ).
fof(f180,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',totality) ).
fof(f199,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0,X1] :
( ( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) )
& ( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
| ~ strictly_less_than(X0,X1) ) ),
inference(flattening,[],[f136]) ).
fof(f136,plain,
! [X0,X1] :
( ( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) )
& ( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
| ~ strictly_less_than(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( strictly_less_than(X0,X1)
<=> ( ~ less_than(X1,X0)
& less_than(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',stricly_smaller_definition) ).
fof(f8108,plain,
( ! [X1] :
( ~ strictly_less_than(sK6(i(triple(sK0,sK1,sK2)),X1),findmin_pqp_res(sK0))
| issmallestelement_pq(i(triple(sK0,sK1,sK2)),X1) )
| ~ spl7_3
| spl7_5 ),
inference(resolution,[],[f8104,f761]) ).
fof(f761,plain,
! [X16,X14,X17,X15] :
( contains_cpq(triple(X14,X15,X16),sK6(i(triple(X14,X15,X16)),X17))
| issmallestelement_pq(i(triple(X14,X15,X16)),X17) ),
inference(resolution,[],[f154,f201]) ).
fof(f201,plain,
! [X0,X1] :
( contains_pq(X0,sK6(X0,X1))
| issmallestelement_pq(X0,X1) ),
inference(cnf_transformation,[],[f141]) ).
fof(f154,plain,
! [X2,X3,X0,X1] :
( ~ contains_pq(i(triple(X0,X1,X2)),X3)
| contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1,X2,X3] :
( ( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_pq(i(triple(X0,X1,X2)),X3) )
& ( contains_pq(i(triple(X0,X1,X2)),X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0,X1,X2,X3] :
( contains_cpq(triple(X0,X1,X2),X3)
<=> contains_pq(i(triple(X0,X1,X2)),X3) ),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',l17_li56) ).
fof(f8104,plain,
( ! [X0] :
( ~ contains_cpq(triple(sK0,sK1,sK2),X0)
| ~ strictly_less_than(X0,findmin_pqp_res(sK0)) )
| ~ spl7_3
| spl7_5 ),
inference(subsumption_resolution,[],[f7610,f589]) ).
fof(f589,plain,
( create_slb != sK1
| spl7_5 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f588,plain,
( spl7_5
<=> create_slb = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).
fof(f7610,plain,
( ! [X0] :
( ~ strictly_less_than(X0,findmin_pqp_res(sK0))
| ~ contains_cpq(triple(sK0,sK1,sK2),X0)
| create_slb = sK1 )
| ~ spl7_3 ),
inference(resolution,[],[f2065,f254]) ).
fof(f254,plain,
( phi(findmin_cpq_eff(triple(sK0,sK1,sK2)))
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f252,plain,
( spl7_3
<=> phi(findmin_cpq_eff(triple(sK0,sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).
fof(f2065,plain,
! [X3,X6,X4,X5] :
( ~ phi(findmin_cpq_eff(triple(X3,X4,X5)))
| ~ strictly_less_than(X6,findmin_pqp_res(X3))
| ~ contains_cpq(triple(X3,X4,X5),X6)
| create_slb = X4 ),
inference(superposition,[],[f152,f217]) ).
fof(f217,plain,
! [X2,X0,X1] :
( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2] :
( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1,X2] :
( create_slb != X1
=> findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
inference(rectify,[],[f51]) ).
fof(f51,axiom,
! [X0,X1,X2,X3] :
( create_slb != X1
=> findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',ax51) ).
fof(f152,plain,
! [X2,X3,X0,X1] :
( ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ! [X3] :
( ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,axiom,
! [X0,X1,X2] :
( ? [X3] :
( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_cpq(triple(X0,X1,X2),X3) )
=> ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',l17_l18) ).
fof(f10749,plain,
( ~ spl7_7
| ~ spl7_15
| spl7_22 ),
inference(avatar_contradiction_clause,[],[f10748]) ).
fof(f10748,plain,
( $false
| ~ spl7_7
| ~ spl7_15
| spl7_22 ),
inference(subsumption_resolution,[],[f10683,f1087]) ).
fof(f1087,plain,
( less_than(sK3(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0))
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f1085]) ).
fof(f1085,plain,
( spl7_7
<=> less_than(sK3(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_7])]) ).
fof(f10683,plain,
( ~ less_than(sK3(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0))
| ~ spl7_15
| spl7_22 ),
inference(resolution,[],[f10650,f8511]) ).
fof(f8511,plain,
( ! [X11] :
( less_than(X11,sK4(triple(sK0,sK1,sK2)))
| ~ less_than(X11,findmin_pqp_res(sK0)) )
| ~ spl7_15 ),
inference(resolution,[],[f1427,f212]) ).
fof(f212,plain,
! [X2,X0,X1] :
( ~ less_than(X1,X2)
| less_than(X0,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(flattening,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2] :
( ( less_than(X1,X2)
& less_than(X0,X1) )
=> less_than(X0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',transitivity) ).
fof(f1427,plain,
( less_than(findmin_pqp_res(sK0),sK4(triple(sK0,sK1,sK2)))
| ~ spl7_15 ),
inference(avatar_component_clause,[],[f1425]) ).
fof(f1425,plain,
( spl7_15
<=> less_than(findmin_pqp_res(sK0),sK4(triple(sK0,sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_15])]) ).
fof(f10650,plain,
( ~ less_than(sK3(triple(sK0,sK1,sK2)),sK4(triple(sK0,sK1,sK2)))
| spl7_22 ),
inference(avatar_component_clause,[],[f10649]) ).
fof(f10649,plain,
( spl7_22
<=> less_than(sK3(triple(sK0,sK1,sK2)),sK4(triple(sK0,sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_22])]) ).
fof(f10747,plain,
( spl7_12
| ~ spl7_15
| spl7_22 ),
inference(avatar_contradiction_clause,[],[f10746]) ).
fof(f10746,plain,
( $false
| spl7_12
| ~ spl7_15
| spl7_22 ),
inference(subsumption_resolution,[],[f10682,f1129]) ).
fof(f1129,plain,
( ~ less_than(findmin_pqp_res(sK0),sK3(triple(sK0,sK1,sK2)))
| spl7_12 ),
inference(avatar_component_clause,[],[f1128]) ).
fof(f1128,plain,
( spl7_12
<=> less_than(findmin_pqp_res(sK0),sK3(triple(sK0,sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_12])]) ).
fof(f10682,plain,
( less_than(findmin_pqp_res(sK0),sK3(triple(sK0,sK1,sK2)))
| ~ spl7_15
| spl7_22 ),
inference(resolution,[],[f10650,f8513]) ).
fof(f8513,plain,
( ! [X14] :
( less_than(X14,sK4(triple(sK0,sK1,sK2)))
| less_than(findmin_pqp_res(sK0),X14) )
| ~ spl7_15 ),
inference(resolution,[],[f1427,f328]) ).
fof(f328,plain,
! [X6,X4,X5] :
( ~ less_than(X4,X6)
| less_than(X4,X5)
| less_than(X5,X6) ),
inference(resolution,[],[f212,f180]) ).
fof(f10652,plain,
( spl7_22
| spl7_21 ),
inference(avatar_split_clause,[],[f10617,f10536,f10649]) ).
fof(f10536,plain,
( spl7_21
<=> less_than(sK4(triple(sK0,sK1,sK2)),sK3(triple(sK0,sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_21])]) ).
fof(f10617,plain,
( less_than(sK3(triple(sK0,sK1,sK2)),sK4(triple(sK0,sK1,sK2)))
| spl7_21 ),
inference(resolution,[],[f10537,f180]) ).
fof(f10537,plain,
( ~ less_than(sK4(triple(sK0,sK1,sK2)),sK3(triple(sK0,sK1,sK2)))
| spl7_21 ),
inference(avatar_component_clause,[],[f10536]) ).
fof(f10539,plain,
( spl7_21
| ~ spl7_12
| ~ spl7_13 ),
inference(avatar_split_clause,[],[f10434,f1360,f1128,f10536]) ).
fof(f1360,plain,
( spl7_13
<=> less_than(sK4(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_13])]) ).
fof(f10434,plain,
( less_than(sK4(triple(sK0,sK1,sK2)),sK3(triple(sK0,sK1,sK2)))
| ~ spl7_12
| ~ spl7_13 ),
inference(resolution,[],[f9526,f159]) ).
fof(f159,plain,
! [X0] : less_than(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : less_than(X0,X0),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',reflexivity) ).
fof(f9526,plain,
( ! [X69] :
( ~ less_than(X69,sK4(triple(sK0,sK1,sK2)))
| less_than(X69,sK3(triple(sK0,sK1,sK2))) )
| ~ spl7_12
| ~ spl7_13 ),
inference(resolution,[],[f8600,f1362]) ).
fof(f1362,plain,
( less_than(sK4(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0))
| ~ spl7_13 ),
inference(avatar_component_clause,[],[f1360]) ).
fof(f8600,plain,
( ! [X24,X23] :
( ~ less_than(X23,findmin_pqp_res(sK0))
| less_than(X24,sK3(triple(sK0,sK1,sK2)))
| ~ less_than(X24,X23) )
| ~ spl7_12 ),
inference(resolution,[],[f8490,f212]) ).
fof(f8490,plain,
( ! [X12] :
( less_than(X12,sK3(triple(sK0,sK1,sK2)))
| ~ less_than(X12,findmin_pqp_res(sK0)) )
| ~ spl7_12 ),
inference(resolution,[],[f1130,f212]) ).
fof(f1130,plain,
( less_than(findmin_pqp_res(sK0),sK3(triple(sK0,sK1,sK2)))
| ~ spl7_12 ),
inference(avatar_component_clause,[],[f1128]) ).
fof(f8472,plain,
( spl7_6
| ~ spl7_18 ),
inference(avatar_contradiction_clause,[],[f8464]) ).
fof(f8464,plain,
( $false
| spl7_6
| ~ spl7_18 ),
inference(resolution,[],[f8090,f594]) ).
fof(f8090,plain,
( ! [X56] : issmallestelement_pq(X56,findmin_pqp_res(sK0))
| ~ spl7_18 ),
inference(resolution,[],[f7945,f202]) ).
fof(f7945,plain,
( ! [X32] : less_than(findmin_pqp_res(sK0),X32)
| ~ spl7_18 ),
inference(avatar_component_clause,[],[f7944]) ).
fof(f7944,plain,
( spl7_18
<=> ! [X32] : less_than(findmin_pqp_res(sK0),X32) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_18])]) ).
fof(f8392,plain,
( spl7_18
| spl7_20
| ~ spl7_3
| spl7_5 ),
inference(avatar_split_clause,[],[f8137,f588,f252,f8390,f7944]) ).
fof(f8390,plain,
( spl7_20
<=> ! [X46] :
( ~ contains_slb(sK1,sK4(X46))
| ~ pi_remove(X46,bottom) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_20])]) ).
fof(f8137,plain,
( ! [X46,X47] :
( ~ contains_slb(sK1,sK4(X46))
| less_than(findmin_pqp_res(sK0),X47)
| ~ pi_remove(X46,bottom) )
| ~ spl7_3
| spl7_5 ),
inference(resolution,[],[f8109,f445]) ).
fof(f445,plain,
! [X6,X7,X5] :
( ~ less_than(X6,sK4(X5))
| less_than(X6,X7)
| ~ pi_remove(X5,bottom) ),
inference(resolution,[],[f442,f212]) ).
fof(f442,plain,
! [X8,X9] :
( less_than(sK4(X8),X9)
| ~ pi_remove(X8,bottom) ),
inference(subsumption_resolution,[],[f441,f372]) ).
fof(f372,plain,
! [X0] :
( ~ pi_remove(X0,bottom)
| pi_removemin(X0) ),
inference(resolution,[],[f367,f271]) ).
fof(f271,plain,
! [X0,X1] :
( contains_pq(i(X0),X1)
| ~ pi_remove(X0,X1) ),
inference(resolution,[],[f187,f192]) ).
fof(f192,plain,
! [X0,X1] :
( ~ pi_sharp_remove(X0,X1)
| contains_pq(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0,X1] :
( ( pi_sharp_remove(X0,X1)
| ~ contains_pq(X0,X1) )
& ( contains_pq(X0,X1)
| ~ pi_sharp_remove(X0,X1) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0,X1] :
( pi_sharp_remove(X0,X1)
<=> contains_pq(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',ax56) ).
fof(f187,plain,
! [X0,X1] :
( pi_sharp_remove(i(X0),X1)
| ~ pi_remove(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1] :
( ( pi_remove(X0,X1)
| ~ pi_sharp_remove(i(X0),X1) )
& ( pi_sharp_remove(i(X0),X1)
| ~ pi_remove(X0,X1) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0,X1] :
( pi_remove(X0,X1)
<=> pi_sharp_remove(i(X0),X1) ),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',ax57) ).
fof(f367,plain,
! [X2] :
( ~ contains_pq(i(X2),bottom)
| pi_removemin(X2) ),
inference(resolution,[],[f314,f294]) ).
fof(f294,plain,
! [X0] : issmallestelement_pq(X0,bottom),
inference(resolution,[],[f202,f160]) ).
fof(f160,plain,
! [X0] : less_than(bottom,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] : less_than(bottom,X0),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',bottom_smallest) ).
fof(f314,plain,
! [X0,X1] :
( ~ issmallestelement_pq(i(X0),X1)
| ~ contains_pq(i(X0),X1)
| pi_removemin(X0) ),
inference(resolution,[],[f196,f168]) ).
fof(f168,plain,
! [X0,X1] :
( ~ pi_sharp_find_min(i(X0),X1)
| pi_removemin(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ( pi_removemin(X0)
| ! [X1] : ~ pi_sharp_find_min(i(X0),X1) )
& ( pi_sharp_find_min(i(X0),sK4(X0))
| ~ pi_removemin(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f123,f124]) ).
fof(f124,plain,
! [X0] :
( ? [X2] : pi_sharp_find_min(i(X0),X2)
=> pi_sharp_find_min(i(X0),sK4(X0)) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
! [X0] :
( ( pi_removemin(X0)
| ! [X1] : ~ pi_sharp_find_min(i(X0),X1) )
& ( ? [X2] : pi_sharp_find_min(i(X0),X2)
| ~ pi_removemin(X0) ) ),
inference(rectify,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ( pi_removemin(X0)
| ! [X1] : ~ pi_sharp_find_min(i(X0),X1) )
& ( ? [X1] : pi_sharp_find_min(i(X0),X1)
| ~ pi_removemin(X0) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0] :
( pi_removemin(X0)
<=> ? [X1] : pi_sharp_find_min(i(X0),X1) ),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',ax61) ).
fof(f196,plain,
! [X0,X1] :
( pi_sharp_find_min(X0,X1)
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0,X1] :
( ( pi_sharp_find_min(X0,X1)
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) )
& ( ( issmallestelement_pq(X0,X1)
& contains_pq(X0,X1) )
| ~ pi_sharp_find_min(X0,X1) ) ),
inference(flattening,[],[f134]) ).
fof(f134,plain,
! [X0,X1] :
( ( pi_sharp_find_min(X0,X1)
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) )
& ( ( issmallestelement_pq(X0,X1)
& contains_pq(X0,X1) )
| ~ pi_sharp_find_min(X0,X1) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0,X1] :
( pi_sharp_find_min(X0,X1)
<=> ( issmallestelement_pq(X0,X1)
& contains_pq(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',ax58) ).
fof(f441,plain,
! [X8,X9] :
( ~ pi_removemin(X8)
| ~ pi_remove(X8,bottom)
| less_than(sK4(X8),X9) ),
inference(resolution,[],[f431,f327]) ).
fof(f327,plain,
! [X2,X3] :
( ~ less_than(X2,bottom)
| less_than(X2,X3) ),
inference(resolution,[],[f212,f160]) ).
fof(f431,plain,
! [X2,X3] :
( less_than(sK4(X2),X3)
| ~ pi_removemin(X2)
| ~ pi_remove(X2,X3) ),
inference(resolution,[],[f323,f271]) ).
fof(f323,plain,
! [X2,X3] :
( ~ contains_pq(i(X2),X3)
| less_than(sK4(X2),X3)
| ~ pi_removemin(X2) ),
inference(resolution,[],[f200,f264]) ).
fof(f264,plain,
! [X2] :
( issmallestelement_pq(i(X2),sK4(X2))
| ~ pi_removemin(X2) ),
inference(resolution,[],[f167,f195]) ).
fof(f195,plain,
! [X0,X1] :
( ~ pi_sharp_find_min(X0,X1)
| issmallestelement_pq(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
fof(f167,plain,
! [X0] :
( pi_sharp_find_min(i(X0),sK4(X0))
| ~ pi_removemin(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f200,plain,
! [X3,X0,X1] :
( ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X3)
| less_than(X1,X3) ),
inference(cnf_transformation,[],[f141]) ).
fof(f8109,plain,
( ! [X0] :
( less_than(findmin_pqp_res(sK0),X0)
| ~ contains_slb(sK1,X0) )
| ~ spl7_3
| spl7_5 ),
inference(resolution,[],[f8105,f319]) ).
fof(f8105,plain,
( ! [X0] :
( ~ strictly_less_than(X0,findmin_pqp_res(sK0))
| ~ contains_slb(sK1,X0) )
| ~ spl7_3
| spl7_5 ),
inference(resolution,[],[f8104,f229]) ).
fof(f229,plain,
! [X2,X3,X0,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0,X1,X2,X3] :
( ( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) )
& ( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1,X2,X3] :
( contains_cpq(triple(X0,X1,X2),X3)
<=> contains_slb(X1,X3) ),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',ax39) ).
fof(f8096,plain,
( spl7_12
| ~ spl7_18 ),
inference(avatar_contradiction_clause,[],[f8055]) ).
fof(f8055,plain,
( $false
| spl7_12
| ~ spl7_18 ),
inference(resolution,[],[f7945,f1129]) ).
fof(f8095,plain,
( spl7_15
| ~ spl7_18 ),
inference(avatar_contradiction_clause,[],[f8056]) ).
fof(f8056,plain,
( $false
| spl7_15
| ~ spl7_18 ),
inference(resolution,[],[f7945,f1426]) ).
fof(f1426,plain,
( ~ less_than(findmin_pqp_res(sK0),sK4(triple(sK0,sK1,sK2)))
| spl7_15 ),
inference(avatar_component_clause,[],[f1425]) ).
fof(f8051,plain,
( ~ spl7_5
| spl7_6 ),
inference(avatar_contradiction_clause,[],[f8050]) ).
fof(f8050,plain,
( $false
| ~ spl7_5
| spl7_6 ),
inference(subsumption_resolution,[],[f8049,f292]) ).
fof(f292,plain,
! [X0] : issmallestelement_pq(create_pq,X0),
inference(resolution,[],[f201,f157]) ).
fof(f157,plain,
! [X0] : ~ contains_pq(create_pq,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] : ~ contains_pq(create_pq,X0),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',ax8) ).
fof(f8049,plain,
( ~ issmallestelement_pq(create_pq,findmin_pqp_res(sK0))
| ~ spl7_5
| spl7_6 ),
inference(forward_demodulation,[],[f7952,f177]) ).
fof(f177,plain,
! [X0,X1] : create_pq = i(triple(X0,create_slb,X1)),
inference(cnf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0,X1] : create_pq = i(triple(X0,create_slb,X1)),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',ax54) ).
fof(f7952,plain,
( ~ issmallestelement_pq(i(triple(sK0,create_slb,sK2)),findmin_pqp_res(sK0))
| ~ spl7_5
| spl7_6 ),
inference(superposition,[],[f594,f590]) ).
fof(f590,plain,
( create_slb = sK1
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f8048,plain,
( spl7_4
| ~ spl7_5 ),
inference(avatar_contradiction_clause,[],[f8047]) ).
fof(f8047,plain,
( $false
| spl7_4
| ~ spl7_5 ),
inference(subsumption_resolution,[],[f8046,f294]) ).
fof(f8046,plain,
( ~ issmallestelement_pq(i(triple(sK0,create_slb,sK2)),bottom)
| spl7_4
| ~ spl7_5 ),
inference(forward_demodulation,[],[f7951,f176]) ).
fof(f176,plain,
! [X0,X1] : bottom = findmin_cpq_res(triple(X0,create_slb,X1)),
inference(cnf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1] : bottom = findmin_cpq_res(triple(X0,create_slb,X1)),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',ax50) ).
fof(f7951,plain,
( ~ issmallestelement_pq(i(triple(sK0,create_slb,sK2)),findmin_cpq_res(triple(sK0,create_slb,sK2)))
| spl7_4
| ~ spl7_5 ),
inference(superposition,[],[f303,f590]) ).
fof(f303,plain,
( ~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))
| spl7_4 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f301,plain,
( spl7_4
<=> issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).
fof(f7949,plain,
( spl7_18
| spl7_19
| ~ spl7_3
| spl7_5 ),
inference(avatar_split_clause,[],[f7639,f588,f252,f7947,f7944]) ).
fof(f7947,plain,
( spl7_19
<=> ! [X31] :
( ~ contains_slb(sK1,sK3(X31))
| ~ pi_remove(X31,bottom) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_19])]) ).
fof(f7639,plain,
( ! [X31,X32] :
( ~ contains_slb(sK1,sK3(X31))
| less_than(findmin_pqp_res(sK0),X32)
| ~ pi_remove(X31,bottom) )
| ~ spl7_3
| spl7_5 ),
inference(resolution,[],[f7621,f413]) ).
fof(f413,plain,
! [X6,X7,X5] :
( ~ less_than(X6,sK3(X5))
| less_than(X6,X7)
| ~ pi_remove(X5,bottom) ),
inference(resolution,[],[f410,f212]) ).
fof(f410,plain,
! [X8,X9] :
( less_than(sK3(X8),X9)
| ~ pi_remove(X8,bottom) ),
inference(subsumption_resolution,[],[f409,f390]) ).
fof(f390,plain,
! [X0] :
( ~ pi_remove(X0,bottom)
| pi_find_min(X0) ),
inference(resolution,[],[f385,f271]) ).
fof(f385,plain,
! [X2] :
( ~ contains_pq(i(X2),bottom)
| pi_find_min(X2) ),
inference(resolution,[],[f315,f294]) ).
fof(f315,plain,
! [X2,X3] :
( ~ issmallestelement_pq(i(X2),X3)
| ~ contains_pq(i(X2),X3)
| pi_find_min(X2) ),
inference(resolution,[],[f196,f166]) ).
fof(f166,plain,
! [X0,X1] :
( ~ pi_sharp_find_min(i(X0),X1)
| pi_find_min(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0] :
( ( pi_find_min(X0)
| ! [X1] : ~ pi_sharp_find_min(i(X0),X1) )
& ( pi_sharp_find_min(i(X0),sK3(X0))
| ~ pi_find_min(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f119,f120]) ).
fof(f120,plain,
! [X0] :
( ? [X2] : pi_sharp_find_min(i(X0),X2)
=> pi_sharp_find_min(i(X0),sK3(X0)) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
! [X0] :
( ( pi_find_min(X0)
| ! [X1] : ~ pi_sharp_find_min(i(X0),X1) )
& ( ? [X2] : pi_sharp_find_min(i(X0),X2)
| ~ pi_find_min(X0) ) ),
inference(rectify,[],[f118]) ).
fof(f118,plain,
! [X0] :
( ( pi_find_min(X0)
| ! [X1] : ~ pi_sharp_find_min(i(X0),X1) )
& ( ? [X1] : pi_sharp_find_min(i(X0),X1)
| ~ pi_find_min(X0) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0] :
( pi_find_min(X0)
<=> ? [X1] : pi_sharp_find_min(i(X0),X1) ),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',ax59) ).
fof(f409,plain,
! [X8,X9] :
( ~ pi_find_min(X8)
| ~ pi_remove(X8,bottom)
| less_than(sK3(X8),X9) ),
inference(resolution,[],[f399,f327]) ).
fof(f399,plain,
! [X2,X3] :
( less_than(sK3(X2),X3)
| ~ pi_find_min(X2)
| ~ pi_remove(X2,X3) ),
inference(resolution,[],[f322,f271]) ).
fof(f322,plain,
! [X0,X1] :
( ~ contains_pq(i(X0),X1)
| less_than(sK3(X0),X1)
| ~ pi_find_min(X0) ),
inference(resolution,[],[f200,f260]) ).
fof(f260,plain,
! [X2] :
( issmallestelement_pq(i(X2),sK3(X2))
| ~ pi_find_min(X2) ),
inference(resolution,[],[f165,f195]) ).
fof(f165,plain,
! [X0] :
( pi_sharp_find_min(i(X0),sK3(X0))
| ~ pi_find_min(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f7621,plain,
( ! [X0] :
( less_than(findmin_pqp_res(sK0),X0)
| ~ contains_slb(sK1,X0) )
| ~ spl7_3
| spl7_5 ),
inference(resolution,[],[f7617,f319]) ).
fof(f7617,plain,
( ! [X0] :
( ~ strictly_less_than(X0,findmin_pqp_res(sK0))
| ~ contains_slb(sK1,X0) )
| ~ spl7_3
| spl7_5 ),
inference(resolution,[],[f7615,f229]) ).
fof(f7615,plain,
( ! [X0] :
( ~ contains_cpq(triple(sK0,sK1,sK2),X0)
| ~ strictly_less_than(X0,findmin_pqp_res(sK0)) )
| ~ spl7_3
| spl7_5 ),
inference(subsumption_resolution,[],[f7610,f589]) ).
fof(f7671,plain,
( ~ spl7_17
| ~ spl7_3
| spl7_5
| spl7_15 ),
inference(avatar_split_clause,[],[f7623,f1425,f588,f252,f7668]) ).
fof(f7668,plain,
( spl7_17
<=> contains_slb(sK1,sK4(triple(sK0,sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_17])]) ).
fof(f7623,plain,
( ~ contains_slb(sK1,sK4(triple(sK0,sK1,sK2)))
| ~ spl7_3
| spl7_5
| spl7_15 ),
inference(resolution,[],[f7621,f1426]) ).
fof(f7666,plain,
( ~ spl7_16
| ~ spl7_3
| spl7_5
| spl7_12 ),
inference(avatar_split_clause,[],[f7622,f1128,f588,f252,f7663]) ).
fof(f7663,plain,
( spl7_16
<=> contains_slb(sK1,sK3(triple(sK0,sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_16])]) ).
fof(f7622,plain,
( ~ contains_slb(sK1,sK3(triple(sK0,sK1,sK2)))
| ~ spl7_3
| spl7_5
| spl7_12 ),
inference(resolution,[],[f7621,f1129]) ).
fof(f1428,plain,
( spl7_15
| spl7_13 ),
inference(avatar_split_clause,[],[f1375,f1360,f1425]) ).
fof(f1375,plain,
( less_than(findmin_pqp_res(sK0),sK4(triple(sK0,sK1,sK2)))
| spl7_13 ),
inference(resolution,[],[f1361,f180]) ).
fof(f1361,plain,
( ~ less_than(sK4(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0))
| spl7_13 ),
inference(avatar_component_clause,[],[f1360]) ).
fof(f1367,plain,
( spl7_13
| ~ spl7_14
| spl7_6 ),
inference(avatar_split_clause,[],[f1352,f592,f1364,f1360]) ).
fof(f1364,plain,
( spl7_14
<=> pi_removemin(triple(sK0,sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_14])]) ).
fof(f1352,plain,
( ~ pi_removemin(triple(sK0,sK1,sK2))
| less_than(sK4(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0))
| spl7_6 ),
inference(resolution,[],[f1347,f594]) ).
fof(f1347,plain,
! [X2,X1] :
( issmallestelement_pq(i(X1),X2)
| ~ pi_removemin(X1)
| less_than(sK4(X1),X2) ),
inference(duplicate_literal_removal,[],[f1342]) ).
fof(f1342,plain,
! [X2,X1] :
( ~ pi_removemin(X1)
| issmallestelement_pq(i(X1),X2)
| less_than(sK4(X1),X2)
| issmallestelement_pq(i(X1),X2) ),
inference(resolution,[],[f432,f330]) ).
fof(f330,plain,
! [X10,X11,X12] :
( ~ less_than(X10,sK6(X12,X11))
| less_than(X10,X11)
| issmallestelement_pq(X12,X11) ),
inference(resolution,[],[f212,f295]) ).
fof(f295,plain,
! [X2,X1] :
( less_than(sK6(X1,X2),X2)
| issmallestelement_pq(X1,X2) ),
inference(resolution,[],[f202,f180]) ).
fof(f432,plain,
! [X4,X5] :
( less_than(sK4(X4),sK6(i(X4),X5))
| ~ pi_removemin(X4)
| issmallestelement_pq(i(X4),X5) ),
inference(resolution,[],[f323,f201]) ).
fof(f1131,plain,
( spl7_12
| spl7_7 ),
inference(avatar_split_clause,[],[f1104,f1085,f1128]) ).
fof(f1104,plain,
( less_than(findmin_pqp_res(sK0),sK3(triple(sK0,sK1,sK2)))
| spl7_7 ),
inference(resolution,[],[f1086,f180]) ).
fof(f1086,plain,
( ~ less_than(sK3(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0))
| spl7_7 ),
inference(avatar_component_clause,[],[f1085]) ).
fof(f1123,plain,
( ~ spl7_11
| spl7_10 ),
inference(avatar_split_clause,[],[f1118,f1114,f1120]) ).
fof(f1120,plain,
( spl7_11
<=> contains_cpq(triple(sK0,sK1,sK2),bottom) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_11])]) ).
fof(f1114,plain,
( spl7_10
<=> pi_remove(triple(sK0,sK1,sK2),bottom) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_10])]) ).
fof(f1118,plain,
( ~ contains_cpq(triple(sK0,sK1,sK2),bottom)
| spl7_10 ),
inference(resolution,[],[f1116,f660]) ).
fof(f660,plain,
! [X10,X11,X8,X9] :
( pi_remove(triple(X8,X9,X10),X11)
| ~ contains_cpq(triple(X8,X9,X10),X11) ),
inference(resolution,[],[f153,f274]) ).
fof(f274,plain,
! [X2,X3] :
( ~ contains_pq(i(X2),X3)
| pi_remove(X2,X3) ),
inference(resolution,[],[f188,f193]) ).
fof(f193,plain,
! [X0,X1] :
( pi_sharp_remove(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f188,plain,
! [X0,X1] :
( ~ pi_sharp_remove(i(X0),X1)
| pi_remove(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f153,plain,
! [X2,X3,X0,X1] :
( contains_pq(i(triple(X0,X1,X2)),X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f117]) ).
fof(f1116,plain,
( ~ pi_remove(triple(sK0,sK1,sK2),bottom)
| spl7_10 ),
inference(avatar_component_clause,[],[f1114]) ).
fof(f1117,plain,
( ~ spl7_10
| spl7_7 ),
inference(avatar_split_clause,[],[f1102,f1085,f1114]) ).
fof(f1102,plain,
( ~ pi_remove(triple(sK0,sK1,sK2),bottom)
| spl7_7 ),
inference(resolution,[],[f1086,f410]) ).
fof(f1098,plain,
( ~ spl7_9
| spl7_8 ),
inference(avatar_split_clause,[],[f1093,f1089,f1095]) ).
fof(f1095,plain,
( spl7_9
<=> contains_slb(sK1,bottom) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_9])]) ).
fof(f1089,plain,
( spl7_8
<=> pi_find_min(triple(sK0,sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_8])]) ).
fof(f1093,plain,
( ~ contains_slb(sK1,bottom)
| spl7_8 ),
inference(resolution,[],[f1091,f675]) ).
fof(f675,plain,
! [X2,X0,X1] :
( pi_find_min(triple(X0,X1,X2))
| ~ contains_slb(X1,bottom) ),
inference(resolution,[],[f661,f229]) ).
fof(f661,plain,
! [X14,X12,X13] :
( ~ contains_cpq(triple(X12,X13,X14),bottom)
| pi_find_min(triple(X12,X13,X14)) ),
inference(resolution,[],[f153,f385]) ).
fof(f1091,plain,
( ~ pi_find_min(triple(sK0,sK1,sK2))
| spl7_8 ),
inference(avatar_component_clause,[],[f1089]) ).
fof(f1092,plain,
( spl7_7
| ~ spl7_8
| spl7_6 ),
inference(avatar_split_clause,[],[f1077,f592,f1089,f1085]) ).
fof(f1077,plain,
( ~ pi_find_min(triple(sK0,sK1,sK2))
| less_than(sK3(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0))
| spl7_6 ),
inference(resolution,[],[f1072,f594]) ).
fof(f1072,plain,
! [X2,X1] :
( issmallestelement_pq(i(X1),X2)
| ~ pi_find_min(X1)
| less_than(sK3(X1),X2) ),
inference(duplicate_literal_removal,[],[f1067]) ).
fof(f1067,plain,
! [X2,X1] :
( ~ pi_find_min(X1)
| issmallestelement_pq(i(X1),X2)
| less_than(sK3(X1),X2)
| issmallestelement_pq(i(X1),X2) ),
inference(resolution,[],[f400,f330]) ).
fof(f400,plain,
! [X4,X5] :
( less_than(sK3(X4),sK6(i(X4),X5))
| ~ pi_find_min(X4)
| issmallestelement_pq(i(X4),X5) ),
inference(resolution,[],[f322,f201]) ).
fof(f595,plain,
( spl7_5
| ~ spl7_6
| spl7_4 ),
inference(avatar_split_clause,[],[f585,f301,f592,f588]) ).
fof(f585,plain,
( ~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_pqp_res(sK0))
| create_slb = sK1
| spl7_4 ),
inference(superposition,[],[f303,f217]) ).
fof(f304,plain,
~ spl7_4,
inference(avatar_split_clause,[],[f151,f301]) ).
fof(f151,plain,
~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
( ~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))
& phi(findmin_cpq_eff(triple(sK0,sK1,sK2))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f75,f115]) ).
fof(f115,plain,
( ? [X0,X1,X2] :
( ~ issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2)))
& phi(findmin_cpq_eff(triple(X0,X1,X2))) )
=> ( ~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))
& phi(findmin_cpq_eff(triple(sK0,sK1,sK2))) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
? [X0,X1,X2] :
( ~ issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2)))
& phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,negated_conjecture,
~ ! [X0,X1,X2] :
( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
inference(negated_conjecture,[],[f65]) ).
fof(f65,conjecture,
! [X0,X1,X2] :
( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',l17_co) ).
fof(f255,plain,
spl7_3,
inference(avatar_split_clause,[],[f150,f252]) ).
fof(f150,plain,
phi(findmin_cpq_eff(triple(sK0,sK1,sK2))),
inference(cnf_transformation,[],[f116]) ).
fof(f250,plain,
~ spl7_2,
inference(avatar_split_clause,[],[f156,f247]) ).
fof(f247,plain,
( spl7_2
<=> isnonempty_slb(create_slb) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
fof(f156,plain,
~ isnonempty_slb(create_slb),
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
~ isnonempty_slb(create_slb),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',ax18) ).
fof(f245,plain,
~ spl7_1,
inference(avatar_split_clause,[],[f155,f242]) ).
fof(f242,plain,
( spl7_1
<=> isnonempty_pq(create_pq) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
fof(f155,plain,
~ isnonempty_pq(create_pq),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
~ isnonempty_pq(create_pq),
file('/export/starexec/sandbox/tmp/tmp.PC9rjAecqk/Vampire---4.8_5089',ax6) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.15 % Problem : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.36 % Computer : n011.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Wed Aug 30 17:34:27 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.18/0.42 % (5199)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.43 % (5201)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.18/0.43 % (5202)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.18/0.43 % (5203)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.18/0.43 % (5204)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.18/0.43 % (5205)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.18/0.43 % (5206)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.18/0.43 % (5200)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.18/0.43 TRYING [1]
% 0.18/0.44 TRYING [2]
% 0.18/0.45 TRYING [3]
% 0.18/0.46 TRYING [1]
% 0.18/0.47 TRYING [2]
% 0.18/0.51 TRYING [4]
% 0.18/0.53 TRYING [3]
% 1.62/0.69 TRYING [4]
% 2.10/0.73 TRYING [5]
% 6.18/1.33 TRYING [5]
% 6.74/1.40 % (5202)First to succeed.
% 7.00/1.41 % (5202)Refutation found. Thanks to Tanya!
% 7.00/1.41 % SZS status Theorem for Vampire---4
% 7.00/1.41 % SZS output start Proof for Vampire---4
% See solution above
% 7.00/1.41 % (5202)------------------------------
% 7.00/1.41 % (5202)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 7.00/1.41 % (5202)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 7.00/1.41 % (5202)Termination reason: Refutation
% 7.00/1.41
% 7.00/1.41 % (5202)Memory used [KB]: 18421
% 7.00/1.41 % (5202)Time elapsed: 0.976 s
% 7.00/1.41 % (5202)------------------------------
% 7.00/1.41 % (5202)------------------------------
% 7.00/1.41 % (5199)Success in time 1.028 s
% 7.00/1.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------