TSTP Solution File: SWV406+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SWV406+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n019.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 18:56:44 EDT 2022
% Result : Theorem 0.20s 0.57s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 28
% Syntax : Number of formulae : 132 ( 2 unt; 0 def)
% Number of atoms : 426 ( 27 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 478 ( 184 ~; 191 |; 49 &)
% ( 33 <=>; 20 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 18 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-3 aty)
% Number of variables : 302 ( 250 !; 52 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f482,plain,
$false,
inference(avatar_sat_refutation,[],[f215,f223,f228,f236,f240,f245,f249,f337,f346,f360,f391,f396,f398,f410,f427,f431,f449,f456,f458,f460,f481]) ).
fof(f481,plain,
( spl11_7
| ~ spl11_10 ),
inference(avatar_split_clause,[],[f480,f247,f234]) ).
fof(f234,plain,
( spl11_7
<=> ! [X13,X14] :
( less_than(X13,X14)
| ~ pair_in_list(sK0,X14,X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_7])]) ).
fof(f247,plain,
( spl11_10
<=> ! [X8,X7] :
( ~ pair_in_list(insert_slb(sK0,pair(sK4,sK2)),X7,X8)
| less_than(X8,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_10])]) ).
fof(f480,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| ~ pair_in_list(sK0,X1,X0) )
| ~ spl11_10 ),
inference(resolution,[],[f248,f181]) ).
fof(f181,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(insert_slb(X1,pair(X4,X2)),X3,X0)
| ~ pair_in_list(X1,X3,X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0,X1,X2,X3,X4] :
( ( pair_in_list(insert_slb(X1,pair(X4,X2)),X3,X0)
| ( ( X3 != X4
| X0 != X2 )
& ~ pair_in_list(X1,X3,X0) ) )
& ( ( X3 = X4
& X0 = X2 )
| pair_in_list(X1,X3,X0)
| ~ pair_in_list(insert_slb(X1,pair(X4,X2)),X3,X0) ) ),
inference(rectify,[],[f130]) ).
fof(f130,plain,
! [X2,X4,X0,X1,X3] :
( ( pair_in_list(insert_slb(X4,pair(X3,X0)),X1,X2)
| ( ( X1 != X3
| X0 != X2 )
& ~ pair_in_list(X4,X1,X2) ) )
& ( ( X1 = X3
& X0 = X2 )
| pair_in_list(X4,X1,X2)
| ~ pair_in_list(insert_slb(X4,pair(X3,X0)),X1,X2) ) ),
inference(flattening,[],[f129]) ).
fof(f129,plain,
! [X2,X4,X0,X1,X3] :
( ( pair_in_list(insert_slb(X4,pair(X3,X0)),X1,X2)
| ( ( X1 != X3
| X0 != X2 )
& ~ pair_in_list(X4,X1,X2) ) )
& ( ( X1 = X3
& X0 = X2 )
| pair_in_list(X4,X1,X2)
| ~ pair_in_list(insert_slb(X4,pair(X3,X0)),X1,X2) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X2,X4,X0,X1,X3] :
( pair_in_list(insert_slb(X4,pair(X3,X0)),X1,X2)
<=> ( ( X1 = X3
& X0 = X2 )
| pair_in_list(X4,X1,X2) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X3,X2,X4,X1,X0] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
<=> ( pair_in_list(X0,X2,X4)
| ( X3 = X4
& X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).
fof(f248,plain,
( ! [X8,X7] :
( ~ pair_in_list(insert_slb(sK0,pair(sK4,sK2)),X7,X8)
| less_than(X8,X7) )
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f460,plain,
( spl11_13
| ~ spl11_14
| ~ spl11_1 ),
inference(avatar_split_clause,[],[f440,f208,f334,f330]) ).
fof(f330,plain,
( spl11_13
<=> check_cpq(triple(sK1,sK0,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_13])]) ).
fof(f334,plain,
( spl11_14
<=> less_than(sK2,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_14])]) ).
fof(f208,plain,
( spl11_1
<=> check_cpq(triple(sK1,insert_slb(sK0,pair(sK4,sK2)),sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_1])]) ).
fof(f440,plain,
( ~ less_than(sK2,sK4)
| check_cpq(triple(sK1,sK0,sK3))
| ~ spl11_1 ),
inference(resolution,[],[f209,f173]) ).
fof(f173,plain,
! [X2,X3,X0,X1,X4] :
( ~ check_cpq(triple(X0,insert_slb(X4,pair(X2,X3)),X1))
| ~ less_than(X3,X2)
| check_cpq(triple(X0,X4,X1)) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0,X1,X2,X3,X4] :
( ~ less_than(X3,X2)
| ( ( check_cpq(triple(X0,insert_slb(X4,pair(X2,X3)),X1))
| ~ check_cpq(triple(X0,X4,X1)) )
& ( check_cpq(triple(X0,X4,X1))
| ~ check_cpq(triple(X0,insert_slb(X4,pair(X2,X3)),X1)) ) ) ),
inference(rectify,[],[f125]) ).
fof(f125,plain,
! [X0,X2,X4,X3,X1] :
( ~ less_than(X3,X4)
| ( ( check_cpq(triple(X0,insert_slb(X1,pair(X4,X3)),X2))
| ~ check_cpq(triple(X0,X1,X2)) )
& ( check_cpq(triple(X0,X1,X2))
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X4,X3)),X2)) ) ) ),
inference(nnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X2,X4,X3,X1] :
( ~ less_than(X3,X4)
| ( check_cpq(triple(X0,insert_slb(X1,pair(X4,X3)),X2))
<=> check_cpq(triple(X0,X1,X2)) ) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,plain,
! [X3,X0,X4,X2,X1] :
( less_than(X3,X4)
=> ( check_cpq(triple(X0,insert_slb(X1,pair(X4,X3)),X2))
<=> check_cpq(triple(X0,X1,X2)) ) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X0,X1,X2,X4,X3] :
( less_than(X4,X3)
=> ( check_cpq(triple(X0,X1,X2))
<=> check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f209,plain,
( check_cpq(triple(sK1,insert_slb(sK0,pair(sK4,sK2)),sK3))
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f458,plain,
( spl11_14
| spl11_18 ),
inference(avatar_split_clause,[],[f455,f446,f334]) ).
fof(f446,plain,
( spl11_18
<=> less_than(sK4,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_18])]) ).
fof(f455,plain,
( less_than(sK2,sK4)
| spl11_18 ),
inference(resolution,[],[f448,f178]) ).
fof(f178,plain,
! [X0,X1] :
( less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(rectify,[],[f66]) ).
fof(f66,plain,
! [X1,X0] :
( less_than(X0,X1)
| less_than(X1,X0) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( less_than(X1,X0)
| less_than(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
fof(f448,plain,
( ~ less_than(sK4,sK2)
| spl11_18 ),
inference(avatar_component_clause,[],[f446]) ).
fof(f456,plain,
( spl11_9
| ~ spl11_16
| ~ spl11_17
| spl11_18 ),
inference(avatar_contradiction_clause,[],[f450]) ).
fof(f450,plain,
( $false
| spl11_9
| ~ spl11_16
| ~ spl11_17
| spl11_18 ),
inference(resolution,[],[f448,f422]) ).
fof(f422,plain,
( less_than(sK4,sK2)
| spl11_9
| ~ spl11_16
| ~ spl11_17 ),
inference(backward_demodulation,[],[f414,f390]) ).
fof(f390,plain,
( sK4 = sK5
| ~ spl11_16 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f388,plain,
( spl11_16
<=> sK4 = sK5 ),
introduced(avatar_definition,[new_symbols(naming,[spl11_16])]) ).
fof(f414,plain,
( less_than(sK5,sK2)
| spl11_9
| ~ spl11_17 ),
inference(backward_demodulation,[],[f365,f395]) ).
fof(f395,plain,
( sK6 = sK2
| ~ spl11_17 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f393,plain,
( spl11_17
<=> sK6 = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl11_17])]) ).
fof(f365,plain,
( less_than(sK5,sK6)
| spl11_9 ),
inference(resolution,[],[f244,f178]) ).
fof(f244,plain,
( ~ less_than(sK6,sK5)
| spl11_9 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f242,plain,
( spl11_9
<=> less_than(sK6,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_9])]) ).
fof(f449,plain,
( spl11_14
| ~ spl11_18
| ~ spl11_1 ),
inference(avatar_split_clause,[],[f444,f208,f446,f334]) ).
fof(f444,plain,
( ~ less_than(sK4,sK2)
| less_than(sK2,sK4)
| ~ spl11_1 ),
inference(resolution,[],[f441,f172]) ).
fof(f172,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) ),
inference(flattening,[],[f75]) ).
fof(f75,plain,
! [X1,X0] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,plain,
! [X1,X0] :
( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
=> strictly_less_than(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( strictly_less_than(X0,X1)
<=> ( ~ less_than(X1,X0)
& less_than(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).
fof(f441,plain,
( ~ strictly_less_than(sK4,sK2)
| ~ spl11_1 ),
inference(resolution,[],[f209,f154]) ).
fof(f154,plain,
! [X2,X3,X0,X1,X4] :
( ~ check_cpq(triple(X2,insert_slb(X4,pair(X0,X1)),X3))
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1,X2,X3,X4] :
( ~ strictly_less_than(X0,X1)
| ~ check_cpq(triple(X2,insert_slb(X4,pair(X0,X1)),X3)) ),
inference(rectify,[],[f101]) ).
fof(f101,plain,
! [X2,X0,X1,X4,X3] :
( ~ strictly_less_than(X2,X0)
| ~ check_cpq(triple(X1,insert_slb(X3,pair(X2,X0)),X4)) ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,plain,
! [X1,X3,X2,X0,X4] :
( strictly_less_than(X2,X0)
=> ~ check_cpq(triple(X1,insert_slb(X3,pair(X2,X0)),X4)) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X2,X0)
=> ~ check_cpq(triple(X1,insert_slb(X3,pair(X2,X0)),X4)) ),
inference(true_and_false_elimination,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X2,X0)
=> ( check_cpq(triple(X1,insert_slb(X3,pair(X2,X0)),X4))
<=> $false ) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X4,X0,X3,X1,X2] :
( strictly_less_than(X3,X4)
=> ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
<=> $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f431,plain,
( spl11_4
| ~ spl11_5
| ~ spl11_7 ),
inference(avatar_split_clause,[],[f430,f234,f225,f220]) ).
fof(f220,plain,
( spl11_4
<=> less_than(sK7,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_4])]) ).
fof(f225,plain,
( spl11_5
<=> pair_in_list(sK0,sK8,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_5])]) ).
fof(f430,plain,
( less_than(sK7,sK8)
| ~ spl11_5
| ~ spl11_7 ),
inference(resolution,[],[f235,f227]) ).
fof(f227,plain,
( pair_in_list(sK0,sK8,sK7)
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f235,plain,
( ! [X14,X13] :
( ~ pair_in_list(sK0,X14,X13)
| less_than(X13,X14) )
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f427,plain,
( ~ spl11_14
| spl11_9
| ~ spl11_16
| ~ spl11_17 ),
inference(avatar_split_clause,[],[f420,f393,f388,f242,f334]) ).
fof(f420,plain,
( ~ less_than(sK2,sK4)
| spl11_9
| ~ spl11_16
| ~ spl11_17 ),
inference(backward_demodulation,[],[f412,f390]) ).
fof(f412,plain,
( ~ less_than(sK2,sK5)
| spl11_9
| ~ spl11_17 ),
inference(backward_demodulation,[],[f244,f395]) ).
fof(f410,plain,
( ~ spl11_8
| ~ spl11_13 ),
inference(avatar_contradiction_clause,[],[f409]) ).
fof(f409,plain,
( $false
| ~ spl11_8
| ~ spl11_13 ),
inference(resolution,[],[f408,f239]) ).
fof(f239,plain,
( ! [X9] : ~ sP9(X9)
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f238,plain,
( spl11_8
<=> ! [X9] : ~ sP9(X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_8])]) ).
fof(f408,plain,
( sP9(sK1)
| ~ spl11_13 ),
inference(resolution,[],[f331,f203]) ).
fof(f203,plain,
! [X10,X9] :
( ~ check_cpq(triple(X9,sK0,X10))
| sP9(X9) ),
inference(cnf_transformation,[],[f203_D]) ).
fof(f203_D,plain,
! [X9] :
( ! [X10] : ~ check_cpq(triple(X9,sK0,X10))
<=> ~ sP9(X9) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP9])]) ).
fof(f331,plain,
( check_cpq(triple(sK1,sK0,sK3))
| ~ spl11_13 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f398,plain,
( spl11_9
| ~ spl11_7
| ~ spl11_15 ),
inference(avatar_split_clause,[],[f397,f384,f234,f242]) ).
fof(f384,plain,
( spl11_15
<=> pair_in_list(sK0,sK5,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_15])]) ).
fof(f397,plain,
( less_than(sK6,sK5)
| ~ spl11_7
| ~ spl11_15 ),
inference(resolution,[],[f386,f235]) ).
fof(f386,plain,
( pair_in_list(sK0,sK5,sK6)
| ~ spl11_15 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f396,plain,
( spl11_17
| spl11_15
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f382,f212,f384,f393]) ).
fof(f212,plain,
( spl11_2
<=> pair_in_list(insert_slb(sK0,pair(sK4,sK2)),sK5,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_2])]) ).
fof(f382,plain,
( pair_in_list(sK0,sK5,sK6)
| sK6 = sK2
| ~ spl11_2 ),
inference(resolution,[],[f214,f179]) ).
fof(f179,plain,
! [X2,X3,X0,X1,X4] :
( ~ pair_in_list(insert_slb(X1,pair(X4,X2)),X3,X0)
| pair_in_list(X1,X3,X0)
| X0 = X2 ),
inference(cnf_transformation,[],[f131]) ).
fof(f214,plain,
( pair_in_list(insert_slb(sK0,pair(sK4,sK2)),sK5,sK6)
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f391,plain,
( spl11_15
| spl11_16
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f381,f212,f388,f384]) ).
fof(f381,plain,
( sK4 = sK5
| pair_in_list(sK0,sK5,sK6)
| ~ spl11_2 ),
inference(resolution,[],[f214,f180]) ).
fof(f180,plain,
! [X2,X3,X0,X1,X4] :
( ~ pair_in_list(insert_slb(X1,pair(X4,X2)),X3,X0)
| pair_in_list(X1,X3,X0)
| X3 = X4 ),
inference(cnf_transformation,[],[f131]) ).
fof(f360,plain,
( ~ spl11_3
| spl11_13 ),
inference(avatar_contradiction_clause,[],[f359]) ).
fof(f359,plain,
( $false
| ~ spl11_3
| spl11_13 ),
inference(resolution,[],[f332,f218]) ).
fof(f218,plain,
( ! [X10,X9] : check_cpq(triple(X9,sK0,X10))
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f217,plain,
( spl11_3
<=> ! [X9,X10] : check_cpq(triple(X9,sK0,X10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_3])]) ).
fof(f332,plain,
( ~ check_cpq(triple(sK1,sK0,sK3))
| spl11_13 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f346,plain,
( ~ spl11_10
| spl11_14 ),
inference(avatar_contradiction_clause,[],[f338]) ).
fof(f338,plain,
( $false
| ~ spl11_10
| spl11_14 ),
inference(resolution,[],[f336,f279]) ).
fof(f279,plain,
( less_than(sK2,sK4)
| ~ spl11_10 ),
inference(resolution,[],[f248,f201]) ).
fof(f201,plain,
! [X2,X1,X4] : pair_in_list(insert_slb(X1,pair(X4,X2)),X4,X2),
inference(equality_resolution,[],[f200]) ).
fof(f200,plain,
! [X2,X0,X1,X4] :
( pair_in_list(insert_slb(X1,pair(X4,X2)),X4,X0)
| X0 != X2 ),
inference(equality_resolution,[],[f182]) ).
fof(f182,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(insert_slb(X1,pair(X4,X2)),X3,X0)
| X3 != X4
| X0 != X2 ),
inference(cnf_transformation,[],[f131]) ).
fof(f336,plain,
( ~ less_than(sK2,sK4)
| spl11_14 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f337,plain,
( ~ spl11_13
| ~ spl11_14
| spl11_1 ),
inference(avatar_split_clause,[],[f320,f208,f334,f330]) ).
fof(f320,plain,
( ~ less_than(sK2,sK4)
| ~ check_cpq(triple(sK1,sK0,sK3))
| spl11_1 ),
inference(resolution,[],[f174,f210]) ).
fof(f210,plain,
( ~ check_cpq(triple(sK1,insert_slb(sK0,pair(sK4,sK2)),sK3))
| spl11_1 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f174,plain,
! [X2,X3,X0,X1,X4] :
( check_cpq(triple(X0,insert_slb(X4,pair(X2,X3)),X1))
| ~ less_than(X3,X2)
| ~ check_cpq(triple(X0,X4,X1)) ),
inference(cnf_transformation,[],[f126]) ).
fof(f249,plain,
( spl11_1
| spl11_10 ),
inference(avatar_split_clause,[],[f150,f247,f208]) ).
fof(f150,plain,
! [X8,X7] :
( ~ pair_in_list(insert_slb(sK0,pair(sK4,sK2)),X7,X8)
| less_than(X8,X7)
| check_cpq(triple(sK1,insert_slb(sK0,pair(sK4,sK2)),sK3)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
( ( ~ check_cpq(triple(sK1,insert_slb(sK0,pair(sK4,sK2)),sK3))
| ( pair_in_list(insert_slb(sK0,pair(sK4,sK2)),sK5,sK6)
& ~ less_than(sK6,sK5) ) )
& ( check_cpq(triple(sK1,insert_slb(sK0,pair(sK4,sK2)),sK3))
| ! [X7,X8] :
( ~ pair_in_list(insert_slb(sK0,pair(sK4,sK2)),X7,X8)
| less_than(X8,X7) ) )
& ! [X9,X10] :
( ( check_cpq(triple(X9,sK0,X10))
| ( ~ less_than(sK7,sK8)
& pair_in_list(sK0,sK8,sK7) ) )
& ( ! [X13,X14] :
( less_than(X13,X14)
| ~ pair_in_list(sK0,X14,X13) )
| ~ check_cpq(triple(X9,sK0,X10)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f108,f112,f111,f110,f109]) ).
fof(f109,plain,
( ? [X0] :
( ? [X1,X2,X3,X4] :
( ( ~ check_cpq(triple(X1,insert_slb(X0,pair(X4,X2)),X3))
| ? [X5,X6] :
( pair_in_list(insert_slb(X0,pair(X4,X2)),X5,X6)
& ~ less_than(X6,X5) ) )
& ( check_cpq(triple(X1,insert_slb(X0,pair(X4,X2)),X3))
| ! [X7,X8] :
( ~ pair_in_list(insert_slb(X0,pair(X4,X2)),X7,X8)
| less_than(X8,X7) ) ) )
& ! [X9,X10] :
( ( check_cpq(triple(X9,X0,X10))
| ? [X11,X12] :
( ~ less_than(X11,X12)
& pair_in_list(X0,X12,X11) ) )
& ( ! [X13,X14] :
( less_than(X13,X14)
| ~ pair_in_list(X0,X14,X13) )
| ~ check_cpq(triple(X9,X0,X10)) ) ) )
=> ( ? [X4,X3,X2,X1] :
( ( ~ check_cpq(triple(X1,insert_slb(sK0,pair(X4,X2)),X3))
| ? [X6,X5] :
( pair_in_list(insert_slb(sK0,pair(X4,X2)),X5,X6)
& ~ less_than(X6,X5) ) )
& ( check_cpq(triple(X1,insert_slb(sK0,pair(X4,X2)),X3))
| ! [X8,X7] :
( ~ pair_in_list(insert_slb(sK0,pair(X4,X2)),X7,X8)
| less_than(X8,X7) ) ) )
& ! [X10,X9] :
( ( check_cpq(triple(X9,sK0,X10))
| ? [X12,X11] :
( ~ less_than(X11,X12)
& pair_in_list(sK0,X12,X11) ) )
& ( ! [X14,X13] :
( less_than(X13,X14)
| ~ pair_in_list(sK0,X14,X13) )
| ~ check_cpq(triple(X9,sK0,X10)) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
( ? [X4,X3,X2,X1] :
( ( ~ check_cpq(triple(X1,insert_slb(sK0,pair(X4,X2)),X3))
| ? [X6,X5] :
( pair_in_list(insert_slb(sK0,pair(X4,X2)),X5,X6)
& ~ less_than(X6,X5) ) )
& ( check_cpq(triple(X1,insert_slb(sK0,pair(X4,X2)),X3))
| ! [X8,X7] :
( ~ pair_in_list(insert_slb(sK0,pair(X4,X2)),X7,X8)
| less_than(X8,X7) ) ) )
=> ( ( ~ check_cpq(triple(sK1,insert_slb(sK0,pair(sK4,sK2)),sK3))
| ? [X6,X5] :
( pair_in_list(insert_slb(sK0,pair(sK4,sK2)),X5,X6)
& ~ less_than(X6,X5) ) )
& ( check_cpq(triple(sK1,insert_slb(sK0,pair(sK4,sK2)),sK3))
| ! [X8,X7] :
( ~ pair_in_list(insert_slb(sK0,pair(sK4,sK2)),X7,X8)
| less_than(X8,X7) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
( ? [X6,X5] :
( pair_in_list(insert_slb(sK0,pair(sK4,sK2)),X5,X6)
& ~ less_than(X6,X5) )
=> ( pair_in_list(insert_slb(sK0,pair(sK4,sK2)),sK5,sK6)
& ~ less_than(sK6,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f112,plain,
( ? [X12,X11] :
( ~ less_than(X11,X12)
& pair_in_list(sK0,X12,X11) )
=> ( ~ less_than(sK7,sK8)
& pair_in_list(sK0,sK8,sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f108,plain,
? [X0] :
( ? [X1,X2,X3,X4] :
( ( ~ check_cpq(triple(X1,insert_slb(X0,pair(X4,X2)),X3))
| ? [X5,X6] :
( pair_in_list(insert_slb(X0,pair(X4,X2)),X5,X6)
& ~ less_than(X6,X5) ) )
& ( check_cpq(triple(X1,insert_slb(X0,pair(X4,X2)),X3))
| ! [X7,X8] :
( ~ pair_in_list(insert_slb(X0,pair(X4,X2)),X7,X8)
| less_than(X8,X7) ) ) )
& ! [X9,X10] :
( ( check_cpq(triple(X9,X0,X10))
| ? [X11,X12] :
( ~ less_than(X11,X12)
& pair_in_list(X0,X12,X11) ) )
& ( ! [X13,X14] :
( less_than(X13,X14)
| ~ pair_in_list(X0,X14,X13) )
| ~ check_cpq(triple(X9,X0,X10)) ) ) ),
inference(rectify,[],[f107]) ).
fof(f107,plain,
? [X0] :
( ? [X7,X6,X8,X5] :
( ( ~ check_cpq(triple(X7,insert_slb(X0,pair(X5,X6)),X8))
| ? [X10,X9] :
( pair_in_list(insert_slb(X0,pair(X5,X6)),X10,X9)
& ~ less_than(X9,X10) ) )
& ( check_cpq(triple(X7,insert_slb(X0,pair(X5,X6)),X8))
| ! [X10,X9] :
( ~ pair_in_list(insert_slb(X0,pair(X5,X6)),X10,X9)
| less_than(X9,X10) ) ) )
& ! [X1,X2] :
( ( check_cpq(triple(X1,X0,X2))
| ? [X3,X4] :
( ~ less_than(X3,X4)
& pair_in_list(X0,X4,X3) ) )
& ( ! [X3,X4] :
( less_than(X3,X4)
| ~ pair_in_list(X0,X4,X3) )
| ~ check_cpq(triple(X1,X0,X2)) ) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f102,plain,
? [X0] :
( ? [X7,X6,X8,X5] :
( ! [X10,X9] :
( ~ pair_in_list(insert_slb(X0,pair(X5,X6)),X10,X9)
| less_than(X9,X10) )
<~> check_cpq(triple(X7,insert_slb(X0,pair(X5,X6)),X8)) )
& ! [X1,X2] :
( check_cpq(triple(X1,X0,X2))
<=> ! [X3,X4] :
( less_than(X3,X4)
| ~ pair_in_list(X0,X4,X3) ) ) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,plain,
~ ! [X0] :
( ! [X2,X1] :
( check_cpq(triple(X1,X0,X2))
<=> ! [X3,X4] :
( pair_in_list(X0,X4,X3)
=> less_than(X3,X4) ) )
=> ! [X5,X7,X6,X8] :
( ! [X9,X10] :
( pair_in_list(insert_slb(X0,pair(X5,X6)),X10,X9)
=> less_than(X9,X10) )
<=> check_cpq(triple(X7,insert_slb(X0,pair(X5,X6)),X8)) ) ),
inference(rectify,[],[f43]) ).
fof(f43,negated_conjecture,
~ ! [X0] :
( ! [X1,X2] :
( ! [X4,X3] :
( pair_in_list(X0,X3,X4)
=> less_than(X4,X3) )
<=> check_cpq(triple(X1,X0,X2)) )
=> ! [X7,X8,X5,X6] :
( ! [X10,X9] :
( pair_in_list(insert_slb(X0,pair(X7,X8)),X9,X10)
=> less_than(X10,X9) )
<=> check_cpq(triple(X5,insert_slb(X0,pair(X7,X8)),X6)) ) ),
inference(negated_conjecture,[],[f42]) ).
fof(f42,conjecture,
! [X0] :
( ! [X1,X2] :
( ! [X4,X3] :
( pair_in_list(X0,X3,X4)
=> less_than(X4,X3) )
<=> check_cpq(triple(X1,X0,X2)) )
=> ! [X7,X8,X5,X6] :
( ! [X10,X9] :
( pair_in_list(insert_slb(X0,pair(X7,X8)),X9,X10)
=> less_than(X10,X9) )
<=> check_cpq(triple(X5,insert_slb(X0,pair(X7,X8)),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l42_co) ).
fof(f245,plain,
( ~ spl11_9
| ~ spl11_1 ),
inference(avatar_split_clause,[],[f151,f208,f242]) ).
fof(f151,plain,
( ~ check_cpq(triple(sK1,insert_slb(sK0,pair(sK4,sK2)),sK3))
| ~ less_than(sK6,sK5) ),
inference(cnf_transformation,[],[f113]) ).
fof(f240,plain,
( spl11_6
| spl11_8 ),
inference(avatar_split_clause,[],[f205,f238,f230]) ).
fof(f230,plain,
( spl11_6
<=> sP10 ),
introduced(avatar_definition,[new_symbols(naming,[spl11_6])]) ).
fof(f205,plain,
! [X9] :
( ~ sP9(X9)
| sP10 ),
inference(cnf_transformation,[],[f205_D]) ).
fof(f205_D,plain,
( ! [X9] : ~ sP9(X9)
<=> ~ sP10 ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP10])]) ).
fof(f236,plain,
( ~ spl11_6
| spl11_7 ),
inference(avatar_split_clause,[],[f206,f234,f230]) ).
fof(f206,plain,
! [X14,X13] :
( less_than(X13,X14)
| ~ sP10
| ~ pair_in_list(sK0,X14,X13) ),
inference(general_splitting,[],[f204,f205_D]) ).
fof(f204,plain,
! [X9,X14,X13] :
( less_than(X13,X14)
| ~ pair_in_list(sK0,X14,X13)
| ~ sP9(X9) ),
inference(general_splitting,[],[f147,f203_D]) ).
fof(f147,plain,
! [X10,X9,X14,X13] :
( less_than(X13,X14)
| ~ pair_in_list(sK0,X14,X13)
| ~ check_cpq(triple(X9,sK0,X10)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f228,plain,
( spl11_5
| spl11_3 ),
inference(avatar_split_clause,[],[f148,f217,f225]) ).
fof(f148,plain,
! [X10,X9] :
( check_cpq(triple(X9,sK0,X10))
| pair_in_list(sK0,sK8,sK7) ),
inference(cnf_transformation,[],[f113]) ).
fof(f223,plain,
( spl11_3
| ~ spl11_4 ),
inference(avatar_split_clause,[],[f149,f220,f217]) ).
fof(f149,plain,
! [X10,X9] :
( ~ less_than(sK7,sK8)
| check_cpq(triple(X9,sK0,X10)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f215,plain,
( ~ spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f152,f212,f208]) ).
fof(f152,plain,
( pair_in_list(insert_slb(sK0,pair(sK4,sK2)),sK5,sK6)
| ~ check_cpq(triple(sK1,insert_slb(sK0,pair(sK4,sK2)),sK3)) ),
inference(cnf_transformation,[],[f113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV406+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 19:26:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.51 % (26656)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.52 % (26661)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.52 % (26669)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.53 % (26664)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.53 % (26663)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.53 % (26680)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.20/0.54 % (26673)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.54 % (26659)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.54 % (26671)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.54 % (26659)Instruction limit reached!
% 0.20/0.54 % (26659)------------------------------
% 0.20/0.54 % (26659)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (26659)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (26659)Termination reason: Unknown
% 0.20/0.54 % (26659)Termination phase: Preprocessing 2
% 0.20/0.54
% 0.20/0.54 % (26659)Memory used [KB]: 895
% 0.20/0.54 % (26659)Time elapsed: 0.002 s
% 0.20/0.54 % (26659)Instructions burned: 2 (million)
% 0.20/0.54 % (26659)------------------------------
% 0.20/0.54 % (26659)------------------------------
% 0.20/0.54 % (26651)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.54 % (26653)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.54 % (26654)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54 % (26655)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54 % (26660)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54 % (26658)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.54 % (26657)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54 % (26679)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.54 % (26665)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.54 % (26677)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.54 % (26672)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.54 % (26658)Instruction limit reached!
% 0.20/0.54 % (26658)------------------------------
% 0.20/0.54 % (26658)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (26658)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (26658)Termination reason: Unknown
% 0.20/0.54 % (26658)Termination phase: Saturation
% 0.20/0.54
% 0.20/0.54 % (26658)Memory used [KB]: 5628
% 0.20/0.54 % (26658)Time elapsed: 0.124 s
% 0.20/0.54 % (26658)Instructions burned: 9 (million)
% 0.20/0.54 % (26658)------------------------------
% 0.20/0.54 % (26658)------------------------------
% 0.20/0.54 % (26652)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.54 % (26670)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.55 % (26674)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.55 % (26662)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.55 % (26676)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.56 % (26675)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.56 % (26667)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.56 % (26666)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.56 % (26678)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.20/0.56 % (26668)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.56 % (26661)First to succeed.
% 0.20/0.56 TRYING [1]
% 0.20/0.56 TRYING [2]
% 0.20/0.57 % (26661)Refutation found. Thanks to Tanya!
% 0.20/0.57 % SZS status Theorem for theBenchmark
% 0.20/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.57 % (26661)------------------------------
% 0.20/0.57 % (26661)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.57 % (26661)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.57 % (26661)Termination reason: Refutation
% 0.20/0.57
% 0.20/0.57 % (26661)Memory used [KB]: 5756
% 0.20/0.57 % (26661)Time elapsed: 0.128 s
% 0.20/0.57 % (26661)Instructions burned: 14 (million)
% 0.20/0.57 % (26661)------------------------------
% 0.20/0.57 % (26661)------------------------------
% 0.20/0.57 % (26650)Success in time 0.207 s
%------------------------------------------------------------------------------