TSTP Solution File: SWV406+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---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_uns --cores 0 -t %d %s
% Computer : n003.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 18:45:28 EDT 2022
% Result : Theorem 0.16s 0.51s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 103 ( 2 unt; 0 def)
% Number of atoms : 364 ( 23 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 422 ( 161 ~; 167 |; 49 &)
% ( 24 <=>; 20 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 10 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-3 aty)
% Number of variables : 295 ( 243 !; 52 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f365,plain,
$false,
inference(avatar_sat_refutation,[],[f124,f132,f136,f141,f146,f153,f185,f198,f199,f271,f358]) ).
fof(f358,plain,
( ~ spl9_1
| ~ spl9_2
| spl9_7
| ~ spl9_8 ),
inference(avatar_contradiction_clause,[],[f357]) ).
fof(f357,plain,
( $false
| ~ spl9_1
| ~ spl9_2
| spl9_7
| ~ spl9_8 ),
inference(subsumption_resolution,[],[f340,f245]) ).
fof(f245,plain,
( ~ strictly_less_than(sK5,sK6)
| ~ spl9_2 ),
inference(unit_resulting_resolution,[],[f122,f98]) ).
fof(f98,plain,
! [X2,X3,X0,X1,X4] :
( ~ check_cpq(triple(X3,insert_slb(X1,pair(X0,X4)),X2))
| ~ strictly_less_than(X0,X4) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2,X3,X4] :
( ~ strictly_less_than(X0,X4)
| ~ check_cpq(triple(X3,insert_slb(X1,pair(X0,X4)),X2)) ),
inference(rectify,[],[f57]) ).
fof(f57,plain,
! [X4,X3,X2,X0,X1] :
( ~ strictly_less_than(X4,X1)
| ~ check_cpq(triple(X0,insert_slb(X3,pair(X4,X1)),X2)) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,plain,
! [X1,X0,X2,X3,X4] :
( strictly_less_than(X4,X1)
=> ~ check_cpq(triple(X0,insert_slb(X3,pair(X4,X1)),X2)) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X4,X1)
=> ~ check_cpq(triple(X0,insert_slb(X3,pair(X4,X1)),X2)) ),
inference(true_and_false_elimination,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X4,X1)
=> ( check_cpq(triple(X0,insert_slb(X3,pair(X4,X1)),X2))
<=> $false ) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X0,X4,X2,X1,X3] :
( strictly_less_than(X3,X4)
=> ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f122,plain,
( check_cpq(triple(sK3,insert_slb(sK0,pair(sK5,sK6)),sK4))
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f121,plain,
( spl9_2
<=> check_cpq(triple(sK3,insert_slb(sK0,pair(sK5,sK6)),sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
fof(f340,plain,
( strictly_less_than(sK5,sK6)
| ~ spl9_1
| spl9_7
| ~ spl9_8 ),
inference(backward_demodulation,[],[f318,f308]) ).
fof(f308,plain,
( sK6 = sK7
| ~ spl9_1
| spl9_7
| ~ spl9_8 ),
inference(unit_resulting_resolution,[],[f119,f303,f111]) ).
fof(f111,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(X1,X2,X4)
| ~ pair_in_list(insert_slb(X1,pair(X3,X0)),X2,X4)
| X0 = X4 ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2,X3,X4] :
( ( ( X0 = X4
& X2 = X3 )
| pair_in_list(X1,X2,X4)
| ~ pair_in_list(insert_slb(X1,pair(X3,X0)),X2,X4) )
& ( pair_in_list(insert_slb(X1,pair(X3,X0)),X2,X4)
| ( ( X0 != X4
| X2 != X3 )
& ~ pair_in_list(X1,X2,X4) ) ) ),
inference(rectify,[],[f85]) ).
fof(f85,plain,
! [X1,X0,X3,X2,X4] :
( ( ( X1 = X4
& X2 = X3 )
| pair_in_list(X0,X3,X4)
| ~ pair_in_list(insert_slb(X0,pair(X2,X1)),X3,X4) )
& ( pair_in_list(insert_slb(X0,pair(X2,X1)),X3,X4)
| ( ( X1 != X4
| X2 != X3 )
& ~ pair_in_list(X0,X3,X4) ) ) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
! [X1,X0,X3,X2,X4] :
( ( ( X1 = X4
& X2 = X3 )
| pair_in_list(X0,X3,X4)
| ~ pair_in_list(insert_slb(X0,pair(X2,X1)),X3,X4) )
& ( pair_in_list(insert_slb(X0,pair(X2,X1)),X3,X4)
| ( ( X1 != X4
| X2 != X3 )
& ~ pair_in_list(X0,X3,X4) ) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X1,X0,X3,X2,X4] :
( ( ( X1 = X4
& X2 = X3 )
| pair_in_list(X0,X3,X4) )
<=> pair_in_list(insert_slb(X0,pair(X2,X1)),X3,X4) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X0,X3,X1,X2,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
<=> ( pair_in_list(X0,X2,X4)
| ( X1 = X2
& X3 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
fof(f303,plain,
( ~ pair_in_list(sK0,sK8,sK7)
| spl9_7
| ~ spl9_8 ),
inference(unit_resulting_resolution,[],[f145,f149]) ).
fof(f149,plain,
( ! [X3,X4] :
( ~ pair_in_list(sK0,X4,X3)
| less_than(X3,X4) )
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f148,plain,
( spl9_8
<=> ! [X4,X3] :
( less_than(X3,X4)
| ~ pair_in_list(sK0,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).
fof(f145,plain,
( ~ less_than(sK7,sK8)
| spl9_7 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f143,plain,
( spl9_7
<=> less_than(sK7,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).
fof(f119,plain,
( pair_in_list(insert_slb(sK0,pair(sK5,sK6)),sK8,sK7)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f117,plain,
( spl9_1
<=> pair_in_list(insert_slb(sK0,pair(sK5,sK6)),sK8,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
fof(f318,plain,
( strictly_less_than(sK5,sK7)
| ~ spl9_1
| spl9_7
| ~ spl9_8 ),
inference(backward_demodulation,[],[f208,f310]) ).
fof(f310,plain,
( sK8 = sK5
| ~ spl9_1
| spl9_7
| ~ spl9_8 ),
inference(unit_resulting_resolution,[],[f119,f303,f110]) ).
fof(f110,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(X1,X2,X4)
| X2 = X3
| ~ pair_in_list(insert_slb(X1,pair(X3,X0)),X2,X4) ),
inference(cnf_transformation,[],[f86]) ).
fof(f208,plain,
( strictly_less_than(sK8,sK7)
| spl9_7 ),
inference(subsumption_resolution,[],[f206,f201]) ).
fof(f201,plain,
( less_than(sK8,sK7)
| spl9_7 ),
inference(unit_resulting_resolution,[],[f145,f95]) ).
fof(f95,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( less_than(X0,X1)
| less_than(X1,X0) ),
inference(rectify,[],[f46]) ).
fof(f46,plain,
! [X1,X0] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( less_than(X1,X0)
| less_than(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
fof(f206,plain,
( ~ less_than(sK8,sK7)
| strictly_less_than(sK8,sK7)
| spl9_7 ),
inference(resolution,[],[f145,f99]) ).
fof(f99,plain,
! [X0,X1] :
( ~ less_than(X1,X0)
| less_than(X0,X1)
| strictly_less_than(X1,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( strictly_less_than(X1,X0)
| less_than(X0,X1)
| ~ less_than(X1,X0) ),
inference(rectify,[],[f64]) ).
fof(f64,plain,
! [X1,X0] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
=> strictly_less_than(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
<=> strictly_less_than(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
fof(f271,plain,
( ~ spl9_2
| ~ spl9_9 ),
inference(avatar_contradiction_clause,[],[f270]) ).
fof(f270,plain,
( $false
| ~ spl9_2
| ~ spl9_9 ),
inference(subsumption_resolution,[],[f260,f264]) ).
fof(f264,plain,
( less_than(sK5,sK6)
| ~ spl9_2
| ~ spl9_9 ),
inference(resolution,[],[f246,f95]) ).
fof(f246,plain,
( ~ less_than(sK6,sK5)
| ~ spl9_2
| ~ spl9_9 ),
inference(unit_resulting_resolution,[],[f152,f122,f96]) ).
fof(f96,plain,
! [X2,X3,X0,X1,X4] :
( check_cpq(triple(X3,X4,X1))
| ~ less_than(X0,X2)
| ~ check_cpq(triple(X3,insert_slb(X4,pair(X2,X0)),X1)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2,X3,X4] :
( ( ( check_cpq(triple(X3,insert_slb(X4,pair(X2,X0)),X1))
| ~ check_cpq(triple(X3,X4,X1)) )
& ( check_cpq(triple(X3,X4,X1))
| ~ check_cpq(triple(X3,insert_slb(X4,pair(X2,X0)),X1)) ) )
| ~ less_than(X0,X2) ),
inference(rectify,[],[f72]) ).
fof(f72,plain,
! [X3,X1,X0,X4,X2] :
( ( ( check_cpq(triple(X4,insert_slb(X2,pair(X0,X3)),X1))
| ~ check_cpq(triple(X4,X2,X1)) )
& ( check_cpq(triple(X4,X2,X1))
| ~ check_cpq(triple(X4,insert_slb(X2,pair(X0,X3)),X1)) ) )
| ~ less_than(X3,X0) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X3,X1,X0,X4,X2] :
( ( check_cpq(triple(X4,insert_slb(X2,pair(X0,X3)),X1))
<=> check_cpq(triple(X4,X2,X1)) )
| ~ less_than(X3,X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,plain,
! [X4,X2,X0,X1,X3] :
( less_than(X3,X0)
=> ( check_cpq(triple(X4,insert_slb(X2,pair(X0,X3)),X1))
<=> check_cpq(triple(X4,X2,X1)) ) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X3,X2,X1,X4,X0] :
( less_than(X4,X3)
=> ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
<=> check_cpq(triple(X0,X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
fof(f152,plain,
( ! [X2,X1] : ~ check_cpq(triple(X2,sK0,X1))
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f151,plain,
( spl9_9
<=> ! [X2,X1] : ~ check_cpq(triple(X2,sK0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_9])]) ).
fof(f260,plain,
( ~ less_than(sK5,sK6)
| ~ spl9_2
| ~ spl9_9 ),
inference(unit_resulting_resolution,[],[f245,f246,f99]) ).
fof(f199,plain,
( spl9_8
| ~ spl9_5 ),
inference(avatar_split_clause,[],[f178,f134,f148]) ).
fof(f134,plain,
( spl9_5
<=> ! [X13,X14] :
( less_than(X13,X14)
| ~ pair_in_list(insert_slb(sK0,pair(sK5,sK6)),X14,X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).
fof(f178,plain,
( ! [X8,X9] :
( less_than(X8,X9)
| ~ pair_in_list(sK0,X9,X8) )
| ~ spl9_5 ),
inference(resolution,[],[f135,f108]) ).
fof(f108,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(insert_slb(X1,pair(X3,X0)),X2,X4)
| ~ pair_in_list(X1,X2,X4) ),
inference(cnf_transformation,[],[f86]) ).
fof(f135,plain,
( ! [X14,X13] :
( ~ pair_in_list(insert_slb(sK0,pair(sK5,sK6)),X14,X13)
| less_than(X13,X14) )
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f198,plain,
( spl9_4
| ~ spl9_6
| ~ spl9_8 ),
inference(avatar_contradiction_clause,[],[f197]) ).
fof(f197,plain,
( $false
| spl9_4
| ~ spl9_6
| ~ spl9_8 ),
inference(subsumption_resolution,[],[f187,f140]) ).
fof(f140,plain,
( pair_in_list(sK0,sK2,sK1)
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f138,plain,
( spl9_6
<=> pair_in_list(sK0,sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
fof(f187,plain,
( ~ pair_in_list(sK0,sK2,sK1)
| spl9_4
| ~ spl9_8 ),
inference(unit_resulting_resolution,[],[f131,f149]) ).
fof(f131,plain,
( ~ less_than(sK1,sK2)
| spl9_4 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f129,plain,
( spl9_4
<=> less_than(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
fof(f185,plain,
( spl9_2
| ~ spl9_3
| ~ spl9_5 ),
inference(avatar_contradiction_clause,[],[f184]) ).
fof(f184,plain,
( $false
| spl9_2
| ~ spl9_3
| ~ spl9_5 ),
inference(subsumption_resolution,[],[f173,f158]) ).
fof(f158,plain,
( ~ less_than(sK6,sK5)
| spl9_2
| ~ spl9_3 ),
inference(unit_resulting_resolution,[],[f127,f123,f97]) ).
fof(f97,plain,
! [X2,X3,X0,X1,X4] :
( ~ less_than(X0,X2)
| check_cpq(triple(X3,insert_slb(X4,pair(X2,X0)),X1))
| ~ check_cpq(triple(X3,X4,X1)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f123,plain,
( ~ check_cpq(triple(sK3,insert_slb(sK0,pair(sK5,sK6)),sK4))
| spl9_2 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f127,plain,
( ! [X2,X1] : check_cpq(triple(X2,sK0,X1))
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f126,plain,
( spl9_3
<=> ! [X2,X1] : check_cpq(triple(X2,sK0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
fof(f173,plain,
( less_than(sK6,sK5)
| ~ spl9_5 ),
inference(unit_resulting_resolution,[],[f115,f135]) ).
fof(f115,plain,
! [X3,X1,X4] : pair_in_list(insert_slb(X1,pair(X3,X4)),X3,X4),
inference(equality_resolution,[],[f114]) ).
fof(f114,plain,
! [X2,X3,X1,X4] :
( pair_in_list(insert_slb(X1,pair(X3,X4)),X2,X4)
| X2 != X3 ),
inference(equality_resolution,[],[f109]) ).
fof(f109,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(insert_slb(X1,pair(X3,X0)),X2,X4)
| X0 != X4
| X2 != X3 ),
inference(cnf_transformation,[],[f86]) ).
fof(f153,plain,
( spl9_8
| spl9_9 ),
inference(avatar_split_clause,[],[f107,f151,f148]) ).
fof(f107,plain,
! [X2,X3,X1,X4] :
( ~ check_cpq(triple(X2,sK0,X1))
| less_than(X3,X4)
| ~ pair_in_list(sK0,X4,X3) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
( ! [X1,X2] :
( ( ! [X3,X4] :
( less_than(X3,X4)
| ~ pair_in_list(sK0,X4,X3) )
| ~ check_cpq(triple(X2,sK0,X1)) )
& ( check_cpq(triple(X2,sK0,X1))
| ( ~ less_than(sK1,sK2)
& pair_in_list(sK0,sK2,sK1) ) ) )
& ( ( pair_in_list(insert_slb(sK0,pair(sK5,sK6)),sK8,sK7)
& ~ less_than(sK7,sK8) )
| ~ check_cpq(triple(sK3,insert_slb(sK0,pair(sK5,sK6)),sK4)) )
& ( ! [X13,X14] :
( ~ pair_in_list(insert_slb(sK0,pair(sK5,sK6)),X14,X13)
| less_than(X13,X14) )
| check_cpq(triple(sK3,insert_slb(sK0,pair(sK5,sK6)),sK4)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f78,f82,f81,f80,f79]) ).
fof(f79,plain,
( ? [X0] :
( ! [X1,X2] :
( ( ! [X3,X4] :
( less_than(X3,X4)
| ~ pair_in_list(X0,X4,X3) )
| ~ check_cpq(triple(X2,X0,X1)) )
& ( check_cpq(triple(X2,X0,X1))
| ? [X5,X6] :
( ~ less_than(X5,X6)
& pair_in_list(X0,X6,X5) ) ) )
& ? [X7,X8,X9,X10] :
( ( ? [X11,X12] :
( pair_in_list(insert_slb(X0,pair(X9,X10)),X12,X11)
& ~ less_than(X11,X12) )
| ~ check_cpq(triple(X7,insert_slb(X0,pair(X9,X10)),X8)) )
& ( ! [X13,X14] :
( ~ pair_in_list(insert_slb(X0,pair(X9,X10)),X14,X13)
| less_than(X13,X14) )
| check_cpq(triple(X7,insert_slb(X0,pair(X9,X10)),X8)) ) ) )
=> ( ! [X2,X1] :
( ( ! [X4,X3] :
( less_than(X3,X4)
| ~ pair_in_list(sK0,X4,X3) )
| ~ check_cpq(triple(X2,sK0,X1)) )
& ( check_cpq(triple(X2,sK0,X1))
| ? [X6,X5] :
( ~ less_than(X5,X6)
& pair_in_list(sK0,X6,X5) ) ) )
& ? [X10,X9,X8,X7] :
( ( ? [X12,X11] :
( pair_in_list(insert_slb(sK0,pair(X9,X10)),X12,X11)
& ~ less_than(X11,X12) )
| ~ check_cpq(triple(X7,insert_slb(sK0,pair(X9,X10)),X8)) )
& ( ! [X14,X13] :
( ~ pair_in_list(insert_slb(sK0,pair(X9,X10)),X14,X13)
| less_than(X13,X14) )
| check_cpq(triple(X7,insert_slb(sK0,pair(X9,X10)),X8)) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
( ? [X6,X5] :
( ~ less_than(X5,X6)
& pair_in_list(sK0,X6,X5) )
=> ( ~ less_than(sK1,sK2)
& pair_in_list(sK0,sK2,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
( ? [X10,X9,X8,X7] :
( ( ? [X12,X11] :
( pair_in_list(insert_slb(sK0,pair(X9,X10)),X12,X11)
& ~ less_than(X11,X12) )
| ~ check_cpq(triple(X7,insert_slb(sK0,pair(X9,X10)),X8)) )
& ( ! [X14,X13] :
( ~ pair_in_list(insert_slb(sK0,pair(X9,X10)),X14,X13)
| less_than(X13,X14) )
| check_cpq(triple(X7,insert_slb(sK0,pair(X9,X10)),X8)) ) )
=> ( ( ? [X12,X11] :
( pair_in_list(insert_slb(sK0,pair(sK5,sK6)),X12,X11)
& ~ less_than(X11,X12) )
| ~ check_cpq(triple(sK3,insert_slb(sK0,pair(sK5,sK6)),sK4)) )
& ( ! [X14,X13] :
( ~ pair_in_list(insert_slb(sK0,pair(sK5,sK6)),X14,X13)
| less_than(X13,X14) )
| check_cpq(triple(sK3,insert_slb(sK0,pair(sK5,sK6)),sK4)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
( ? [X12,X11] :
( pair_in_list(insert_slb(sK0,pair(sK5,sK6)),X12,X11)
& ~ less_than(X11,X12) )
=> ( pair_in_list(insert_slb(sK0,pair(sK5,sK6)),sK8,sK7)
& ~ less_than(sK7,sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
? [X0] :
( ! [X1,X2] :
( ( ! [X3,X4] :
( less_than(X3,X4)
| ~ pair_in_list(X0,X4,X3) )
| ~ check_cpq(triple(X2,X0,X1)) )
& ( check_cpq(triple(X2,X0,X1))
| ? [X5,X6] :
( ~ less_than(X5,X6)
& pair_in_list(X0,X6,X5) ) ) )
& ? [X7,X8,X9,X10] :
( ( ? [X11,X12] :
( pair_in_list(insert_slb(X0,pair(X9,X10)),X12,X11)
& ~ less_than(X11,X12) )
| ~ check_cpq(triple(X7,insert_slb(X0,pair(X9,X10)),X8)) )
& ( ! [X13,X14] :
( ~ pair_in_list(insert_slb(X0,pair(X9,X10)),X14,X13)
| less_than(X13,X14) )
| check_cpq(triple(X7,insert_slb(X0,pair(X9,X10)),X8)) ) ) ),
inference(rectify,[],[f77]) ).
fof(f77,plain,
? [X0] :
( ! [X2,X1] :
( ( ! [X4,X3] :
( less_than(X4,X3)
| ~ pair_in_list(X0,X3,X4) )
| ~ check_cpq(triple(X1,X0,X2)) )
& ( check_cpq(triple(X1,X0,X2))
| ? [X4,X3] :
( ~ less_than(X4,X3)
& pair_in_list(X0,X3,X4) ) ) )
& ? [X5,X7,X6,X8] :
( ( ? [X10,X9] :
( pair_in_list(insert_slb(X0,pair(X6,X8)),X9,X10)
& ~ less_than(X10,X9) )
| ~ check_cpq(triple(X5,insert_slb(X0,pair(X6,X8)),X7)) )
& ( ! [X10,X9] :
( ~ pair_in_list(insert_slb(X0,pair(X6,X8)),X9,X10)
| less_than(X10,X9) )
| check_cpq(triple(X5,insert_slb(X0,pair(X6,X8)),X7)) ) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f61,plain,
? [X0] :
( ! [X2,X1] :
( ! [X4,X3] :
( less_than(X4,X3)
| ~ pair_in_list(X0,X3,X4) )
<=> check_cpq(triple(X1,X0,X2)) )
& ? [X5,X7,X6,X8] :
( check_cpq(triple(X5,insert_slb(X0,pair(X6,X8)),X7))
<~> ! [X10,X9] :
( ~ pair_in_list(insert_slb(X0,pair(X6,X8)),X9,X10)
| less_than(X10,X9) ) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,plain,
~ ! [X0] :
( ! [X1,X2] :
( ! [X3,X4] :
( pair_in_list(X0,X3,X4)
=> less_than(X4,X3) )
<=> check_cpq(triple(X1,X0,X2)) )
=> ! [X8,X7,X5,X6] :
( ! [X10,X9] :
( pair_in_list(insert_slb(X0,pair(X6,X8)),X9,X10)
=> less_than(X10,X9) )
<=> check_cpq(triple(X5,insert_slb(X0,pair(X6,X8)),X7)) ) ),
inference(rectify,[],[f43]) ).
fof(f43,negated_conjecture,
~ ! [X0] :
( ! [X1,X2] :
( ! [X3,X4] :
( pair_in_list(X0,X3,X4)
=> less_than(X4,X3) )
<=> check_cpq(triple(X1,X0,X2)) )
=> ! [X5,X7,X6,X8] :
( check_cpq(triple(X5,insert_slb(X0,pair(X7,X8)),X6))
<=> ! [X9,X10] :
( pair_in_list(insert_slb(X0,pair(X7,X8)),X9,X10)
=> less_than(X10,X9) ) ) ),
inference(negated_conjecture,[],[f42]) ).
fof(f42,conjecture,
! [X0] :
( ! [X1,X2] :
( ! [X3,X4] :
( pair_in_list(X0,X3,X4)
=> less_than(X4,X3) )
<=> check_cpq(triple(X1,X0,X2)) )
=> ! [X5,X7,X6,X8] :
( check_cpq(triple(X5,insert_slb(X0,pair(X7,X8)),X6))
<=> ! [X9,X10] :
( pair_in_list(insert_slb(X0,pair(X7,X8)),X9,X10)
=> less_than(X10,X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l42_co) ).
fof(f146,plain,
( ~ spl9_7
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f103,f121,f143]) ).
fof(f103,plain,
( ~ check_cpq(triple(sK3,insert_slb(sK0,pair(sK5,sK6)),sK4))
| ~ less_than(sK7,sK8) ),
inference(cnf_transformation,[],[f83]) ).
fof(f141,plain,
( spl9_6
| spl9_3 ),
inference(avatar_split_clause,[],[f105,f126,f138]) ).
fof(f105,plain,
! [X2,X1] :
( check_cpq(triple(X2,sK0,X1))
| pair_in_list(sK0,sK2,sK1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f136,plain,
( spl9_2
| spl9_5 ),
inference(avatar_split_clause,[],[f102,f134,f121]) ).
fof(f102,plain,
! [X14,X13] :
( less_than(X13,X14)
| ~ pair_in_list(insert_slb(sK0,pair(sK5,sK6)),X14,X13)
| check_cpq(triple(sK3,insert_slb(sK0,pair(sK5,sK6)),sK4)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f132,plain,
( spl9_3
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f106,f129,f126]) ).
fof(f106,plain,
! [X2,X1] :
( ~ less_than(sK1,sK2)
| check_cpq(triple(X2,sK0,X1)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f124,plain,
( spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f104,f121,f117]) ).
fof(f104,plain,
( ~ check_cpq(triple(sK3,insert_slb(sK0,pair(sK5,sK6)),sK4))
| pair_in_list(insert_slb(sK0,pair(sK5,sK6)),sK8,sK7) ),
inference(cnf_transformation,[],[f83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SWV406+1 : TPTP v8.1.0. Released v3.3.0.
% 0.05/0.11 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.10/0.31 % Computer : n003.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Aug 30 19:23:22 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.16/0.47 % (14981)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.16/0.47 % (14983)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.16/0.47 % (14982)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.16/0.48 % (14975)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.16/0.48 % (14982)Instruction limit reached!
% 0.16/0.48 % (14982)------------------------------
% 0.16/0.48 % (14982)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.48 % (14989)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.16/0.48 % (14991)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.16/0.48 % (14990)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.16/0.49 % (14981)Instruction limit reached!
% 0.16/0.49 % (14981)------------------------------
% 0.16/0.49 % (14981)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.49 % (14981)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.49 % (14981)Termination reason: Unknown
% 0.16/0.49 % (14981)Termination phase: Saturation
% 0.16/0.49
% 0.16/0.49 % (14981)Memory used [KB]: 1535
% 0.16/0.49 % (14981)Time elapsed: 0.004 s
% 0.16/0.49 % (14981)Instructions burned: 4 (million)
% 0.16/0.49 % (14981)------------------------------
% 0.16/0.49 % (14981)------------------------------
% 0.16/0.49 % (14974)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.16/0.49 % (14973)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.16/0.49 % (14974)First to succeed.
% 0.16/0.49 % (14982)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.49 % (14982)Termination reason: Unknown
% 0.16/0.49 % (14982)Termination phase: Saturation
% 0.16/0.49
% 0.16/0.49 % (14982)Memory used [KB]: 6140
% 0.16/0.49 % (14982)Time elapsed: 0.102 s
% 0.16/0.49 % (14982)Instructions burned: 7 (million)
% 0.16/0.49 % (14982)------------------------------
% 0.16/0.49 % (14982)------------------------------
% 0.16/0.51 % (14974)Refutation found. Thanks to Tanya!
% 0.16/0.51 % SZS status Theorem for theBenchmark
% 0.16/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.51 % (14974)------------------------------
% 0.16/0.51 % (14974)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.51 % (14974)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.51 % (14974)Termination reason: Refutation
% 0.16/0.51
% 0.16/0.51 % (14974)Memory used [KB]: 6140
% 0.16/0.51 % (14974)Time elapsed: 0.122 s
% 0.16/0.51 % (14974)Instructions burned: 13 (million)
% 0.16/0.51 % (14974)------------------------------
% 0.16/0.51 % (14974)------------------------------
% 0.16/0.51 % (14966)Success in time 0.185 s
%------------------------------------------------------------------------------