TSTP Solution File: SEU615_8 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU615_8 : TPTP v8.2.0. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n012.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 : Tue May 21 04:06:06 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 24
% Syntax : Number of formulae : 81 ( 19 unt; 1 typ; 0 def)
% Number of atoms : 366 ( 53 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 282 ( 113 ~; 86 |; 29 &)
% ( 18 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 201 ( 123 fml; 78 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 1 >; 3 *; 0 +; 0 <<)
% Number of predicates : 27 ( 24 usr; 23 prp; 0-4 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 136 ( 127 !; 9 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_3,type,
sP0: ( $o * $i * $i * $i ) > $o ).
tff(f167,plain,
$false,
inference(avatar_sat_refutation,[],[f35,f40,f45,f50,f55,f59,f63,f71,f75,f79,f84,f89,f96,f101,f145,f158,f162,f166]) ).
tff(f166,plain,
~ spl4_17,
inference(avatar_contradiction_clause,[],[f165]) ).
tff(f165,plain,
( $false
| ~ spl4_17 ),
inference(equality_resolution,[],[f161]) ).
tff(f161,plain,
( ! [X0: $o] : ( $false != (X0) )
| ~ spl4_17 ),
inference(avatar_component_clause,[],[f160]) ).
tff(f160,plain,
( spl4_17
<=> ! [X0: $o] : ( $false != (X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).
tff(f162,plain,
( spl4_17
| spl4_5
| ~ spl4_15 ),
inference(avatar_split_clause,[],[f152,f143,f52,f160]) ).
tff(f52,plain,
( spl4_5
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
tff(f143,plain,
( spl4_15
<=> ! [X0: $o] : ( $true = (X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_15])]) ).
tff(f152,plain,
( ! [X0: $o] : ( $false != (X0) )
| spl4_5
| ~ spl4_15 ),
inference(superposition,[],[f54,f144]) ).
tff(f144,plain,
( ! [X0: $o] : ( $true = (X0) )
| ~ spl4_15 ),
inference(avatar_component_clause,[],[f143]) ).
tff(f54,plain,
( ( $true != $false )
| spl4_5 ),
inference(avatar_component_clause,[],[f52]) ).
tff(f158,plain,
( spl4_16
| ~ spl4_15 ),
inference(avatar_split_clause,[],[f146,f143,f156]) ).
tff(f156,plain,
( spl4_16
<=> ! [X0: $o,X1: $o] : ( (X0) = (X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_16])]) ).
tff(f146,plain,
( ! [X0: $o,X1: $o] : ( (X0) = (X1) )
| ~ spl4_15 ),
inference(superposition,[],[f144,f144]) ).
tff(f145,plain,
( spl4_2
| spl4_15
| ~ spl4_8
| ~ spl4_12 ),
inference(avatar_split_clause,[],[f92,f87,f69,f143,f37]) ).
tff(f37,plain,
( spl4_2
<=> in(sK3,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
tff(f69,plain,
( spl4_8
<=> ! [X2,X0: $o,X1,X3] :
( in(X2,X3)
| ~ sP0((X0),X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
tff(f87,plain,
( spl4_12
<=> ! [X0: $o] :
( ( $true = (X0) )
| sP0((X0),sK2,sK3,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).
tff(f92,plain,
( ! [X0: $o] :
( ( $true = (X0) )
| in(sK3,sK1) )
| ~ spl4_8
| ~ spl4_12 ),
inference(resolution,[],[f88,f70]) ).
tff(f70,plain,
( ! [X2: $i,X3: $i,X0: $o,X1: $i] :
( ~ sP0((X0),X1,X2,X3)
| in(X2,X3) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f69]) ).
tff(f88,plain,
( ! [X0: $o] :
( sP0((X0),sK2,sK3,sK1)
| ( $true = (X0) ) )
| ~ spl4_12 ),
inference(avatar_component_clause,[],[f87]) ).
tff(f101,plain,
( spl4_14
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f64,f61,f99]) ).
tff(f99,plain,
( spl4_14
<=> ! [X0: $o,X1: $o] :
( ( (X0) = (X1) )
| ( $false = (X1) )
| ( $false = (X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).
tff(f61,plain,
( spl4_7
<=> ! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
tff(f64,plain,
( ! [X0: $o,X1: $o] :
( ( (X0) = (X1) )
| ( $false = (X1) )
| ( $false = (X0) ) )
| ~ spl4_7 ),
inference(superposition,[],[f62,f62]) ).
tff(f62,plain,
( ! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f61]) ).
tff(f96,plain,
( spl4_13
| ~ spl4_6
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f65,f61,f57,f94]) ).
tff(f94,plain,
( spl4_13
<=> ! [X0: $o,X3,X2,X1] :
( ~ sP0((X0),X1,X2,X3)
| ( $false = (X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).
tff(f57,plain,
( spl4_6
<=> ! [X2,X1,X3] : ~ sP0($true,X1,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
tff(f65,plain,
( ! [X2: $i,X3: $i,X0: $o,X1: $i] :
( ~ sP0((X0),X1,X2,X3)
| ( $false = (X0) ) )
| ~ spl4_6
| ~ spl4_7 ),
inference(superposition,[],[f58,f62]) ).
tff(f58,plain,
( ! [X2: $i,X3: $i,X1: $i] : ~ sP0($true,X1,X2,X3)
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f57]) ).
tff(f89,plain,
( spl4_3
| spl4_12
| ~ spl4_4
| ~ spl4_11 ),
inference(avatar_split_clause,[],[f85,f82,f47,f87,f42]) ).
tff(f42,plain,
( spl4_3
<=> in(sK3,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
tff(f47,plain,
( spl4_4
<=> in(sK3,symdiff(sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
tff(f82,plain,
( spl4_11
<=> ! [X0,X3: $o,X2,X1] :
( ( $true = (X3) )
| ~ in(X2,symdiff(X0,X1))
| sP0((X3),X1,X2,X0)
| in(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
tff(f85,plain,
( ! [X0: $o] :
( ( $true = (X0) )
| sP0((X0),sK2,sK3,sK1)
| in(sK3,sK2) )
| ~ spl4_4
| ~ spl4_11 ),
inference(resolution,[],[f83,f49]) ).
tff(f49,plain,
( in(sK3,symdiff(sK1,sK2))
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f47]) ).
tff(f83,plain,
( ! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ~ in(X2,symdiff(X0,X1))
| ( $true = (X3) )
| sP0((X3),X1,X2,X0)
| in(X2,X1) )
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f82]) ).
tff(f84,plain,
( ~ spl4_1
| spl4_11 ),
inference(avatar_split_clause,[],[f27,f82,f32]) ).
tff(f32,plain,
( spl4_1
<=> symdiffE ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
tff(f27,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ( $true = (X3) )
| in(X2,X1)
| sP0((X3),X1,X2,X0)
| ~ in(X2,symdiff(X0,X1))
| ~ symdiffE ),
inference(cnf_transformation,[],[f14]) ).
tff(f14,plain,
( ! [X0,X1,X2] :
( ! [X3: $o] :
( ( $true = (X3) )
| ( ( $true != (X3) )
& in(X2,X1)
& ~ in(X2,X0) )
| sP0((X3),X1,X2,X0) )
| ~ in(X2,symdiff(X0,X1)) )
| ~ symdiffE ),
inference(definition_folding,[],[f12,f13]) ).
tff(f13,plain,
! [X3: $o,X1,X2,X0] :
( ( ( $true != (X3) )
& ~ in(X2,X1)
& in(X2,X0) )
| ~ sP0((X3),X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f12,plain,
( ! [X0,X1,X2] :
( ! [X3: $o] :
( ( $true = (X3) )
| ( ( $true != (X3) )
& in(X2,X1)
& ~ in(X2,X0) )
| ( ( $true != (X3) )
& ~ in(X2,X1)
& in(X2,X0) ) )
| ~ in(X2,symdiff(X0,X1)) )
| ~ symdiffE ),
inference(flattening,[],[f11]) ).
tff(f11,plain,
( ! [X0,X1,X2] :
( ! [X3: $o] :
( ( $true = (X3) )
| ( ( $true != (X3) )
& in(X2,X1)
& ~ in(X2,X0) )
| ( ( $true != (X3) )
& ~ in(X2,X1)
& in(X2,X0) ) )
| ~ in(X2,symdiff(X0,X1)) )
| ~ symdiffE ),
inference(ennf_transformation,[],[f8]) ).
tff(f8,plain,
( symdiffE
=> ! [X0,X1,X2] :
( in(X2,symdiff(X0,X1))
=> ! [X3: $o] :
( ( in(X2,X0)
=> ( ~ in(X2,X1)
=> ( $true = (X3) ) ) )
=> ( ( ~ in(X2,X0)
=> ( in(X2,X1)
=> ( $true = (X3) ) ) )
=> ( $true = (X3) ) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
tff(f7,plain,
( symdiffE
<=> ! [X0,X1,X2] :
( in(X2,symdiff(X0,X1))
=> ! [X3: $o] :
( ( in(X2,X0)
=> ( ~ in(X2,X1)
=> ( $true = (X3) ) ) )
=> ( ( ~ in(X2,X0)
=> ( in(X2,X1)
=> ( $true = (X3) ) ) )
=> ( $true = (X3) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
tff(f6,plain,
( symdiffE
= ( ! [X0,X1,X2] :
( in(X2,symdiff(X0,X1))
=> ! [X3: $o] :
( ( in(X2,X0)
=> ( ~ in(X2,X1)
=> (X3) ) )
=> ( ( ~ in(X2,X0)
=> ( in(X2,X1)
=> (X3) ) )
=> (X3) ) ) ) ) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
( symdiffE
= ( ! [X0,X1,X2] :
( in(X2,symdiff(X0,X1))
=> ! [X3: $o] :
( ( in(X2,X0)
=> ( ~ in(X2,X1)
=> (X3) ) )
=> ( ( ~ in(X2,X0)
=> ( in(X2,X1)
=> (X3) ) )
=> (X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
tff(f79,plain,
( ~ spl4_1
| spl4_10 ),
inference(avatar_split_clause,[],[f26,f77,f32]) ).
tff(f77,plain,
( spl4_10
<=> ! [X0,X3: $o,X2,X1] :
( ( $true = (X3) )
| ~ in(X2,symdiff(X0,X1))
| sP0((X3),X1,X2,X0)
| ~ in(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
tff(f26,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ( $true = (X3) )
| ~ in(X2,X0)
| sP0((X3),X1,X2,X0)
| ~ in(X2,symdiff(X0,X1))
| ~ symdiffE ),
inference(cnf_transformation,[],[f14]) ).
tff(f75,plain,
spl4_9,
inference(avatar_split_clause,[],[f24,f73]) ).
tff(f73,plain,
( spl4_9
<=> ! [X2,X0: $o,X1,X3] :
( ~ in(X2,X1)
| ~ sP0((X0),X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
tff(f24,plain,
! [X2: $i,X3: $i,X0: $o,X1: $i] :
( ~ in(X2,X1)
| ~ sP0((X0),X1,X2,X3) ),
inference(cnf_transformation,[],[f18]) ).
tff(f18,plain,
! [X0: $o,X1,X2,X3] :
( ( ( $true != (X0) )
& ~ in(X2,X1)
& in(X2,X3) )
| ~ sP0((X0),X1,X2,X3) ),
inference(rectify,[],[f17]) ).
tff(f17,plain,
! [X3: $o,X1,X2,X0] :
( ( ( $true != (X3) )
& ~ in(X2,X1)
& in(X2,X0) )
| ~ sP0((X3),X1,X2,X0) ),
inference(nnf_transformation,[],[f13]) ).
tff(f71,plain,
spl4_8,
inference(avatar_split_clause,[],[f23,f69]) ).
tff(f23,plain,
! [X2: $i,X3: $i,X0: $o,X1: $i] :
( in(X2,X3)
| ~ sP0((X0),X1,X2,X3) ),
inference(cnf_transformation,[],[f18]) ).
tff(f63,plain,
spl4_7,
inference(avatar_split_clause,[],[f5,f61]) ).
tff(f5,plain,
! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ),
introduced(fool_axiom,[]) ).
tff(f59,plain,
spl4_6,
inference(avatar_split_clause,[],[f29,f57]) ).
tff(f29,plain,
! [X2: $i,X3: $i,X1: $i] : ~ sP0($true,X1,X2,X3),
inference(equality_resolution,[],[f25]) ).
tff(f25,plain,
! [X2: $i,X3: $i,X0: $o,X1: $i] :
( ( $true != (X0) )
| ~ sP0((X0),X1,X2,X3) ),
inference(cnf_transformation,[],[f18]) ).
tff(f55,plain,
~ spl4_5,
inference(avatar_split_clause,[],[f4,f52]) ).
tff(f4,plain,
$true != $false,
introduced(fool_axiom,[]) ).
tff(f50,plain,
spl4_4,
inference(avatar_split_clause,[],[f22,f47]) ).
tff(f22,plain,
in(sK3,symdiff(sK1,sK2)),
inference(cnf_transformation,[],[f16]) ).
tff(f16,plain,
( in(sK3,symdiff(sK1,sK2))
& ~ in(sK3,sK2)
& ~ in(sK3,sK1)
& symdiffE ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f10,f15]) ).
tff(f15,plain,
( ? [X0,X1,X2] :
( in(X2,symdiff(X0,X1))
& ~ in(X2,X1)
& ~ in(X2,X0) )
=> ( in(sK3,symdiff(sK1,sK2))
& ~ in(sK3,sK2)
& ~ in(sK3,sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f10,plain,
( ? [X0,X1,X2] :
( in(X2,symdiff(X0,X1))
& ~ in(X2,X1)
& ~ in(X2,X0) )
& symdiffE ),
inference(flattening,[],[f9]) ).
tff(f9,plain,
( ? [X0,X1,X2] :
( in(X2,symdiff(X0,X1))
& ~ in(X2,X1)
& ~ in(X2,X0) )
& symdiffE ),
inference(ennf_transformation,[],[f3]) ).
tff(f3,negated_conjecture,
~ ( symdiffE
=> ! [X0,X1,X2] :
( ~ in(X2,X0)
=> ( ~ in(X2,X1)
=> ~ in(X2,symdiff(X0,X1)) ) ) ),
inference(negated_conjecture,[],[f2]) ).
tff(f2,conjecture,
( symdiffE
=> ! [X0,X1,X2] :
( ~ in(X2,X0)
=> ( ~ in(X2,X1)
=> ~ in(X2,symdiff(X0,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
tff(f45,plain,
~ spl4_3,
inference(avatar_split_clause,[],[f21,f42]) ).
tff(f21,plain,
~ in(sK3,sK2),
inference(cnf_transformation,[],[f16]) ).
tff(f40,plain,
~ spl4_2,
inference(avatar_split_clause,[],[f20,f37]) ).
tff(f20,plain,
~ in(sK3,sK1),
inference(cnf_transformation,[],[f16]) ).
tff(f35,plain,
spl4_1,
inference(avatar_split_clause,[],[f19,f32]) ).
tff(f19,plain,
symdiffE,
inference(cnf_transformation,[],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU615_8 : TPTP v8.2.0. Released v8.0.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n012.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 : Sun May 19 16:16:07 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % (31032)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (31035)WARNING: value z3 for option sas not known
% 0.13/0.37 % (31033)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % (31037)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 theBenchmark for (531ds/0Mi)
% 0.13/0.37 % (31035)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 theBenchmark for (569ds/0Mi)
% 0.13/0.37 % (31039)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 theBenchmark for (497ds/0Mi)
% 0.13/0.37 % (31034)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37 % (31036)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37 % (31038)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 theBenchmark for (522ds/0Mi)
% 0.13/0.37 TRYING [1]
% 0.13/0.37 TRYING [2]
% 0.13/0.37 TRYING [3]
% 0.13/0.37 TRYING [4]
% 0.13/0.37 Detected minimum model sizes of [1,1]
% 0.13/0.37 Detected maximum model sizes of [max,2]
% 0.13/0.37 TRYING [1,1]
% 0.13/0.37 TRYING [1,2]
% 0.13/0.37 TRYING [2,2]
% 0.13/0.37 TRYING [3,2]
% 0.13/0.37 % (31037)First to succeed.
% 0.13/0.37 TRYING [5]
% 0.13/0.37 TRYING [4,2]
% 0.13/0.37 Detected minimum model sizes of [1,1]
% 0.13/0.37 Detected maximum model sizes of [max,2]
% 0.13/0.37 TRYING [1,1]
% 0.13/0.37 TRYING [1,2]
% 0.13/0.37 TRYING [2,2]
% 0.13/0.37 TRYING [5,2]
% 0.13/0.38 TRYING [3,2]
% 0.13/0.38 % (31037)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-31032"
% 0.13/0.38 TRYING [4,2]
% 0.13/0.38 TRYING [6]
% 0.13/0.38 % (31037)Refutation found. Thanks to Tanya!
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38 % (31037)------------------------------
% 0.13/0.38 % (31037)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.38 % (31037)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (31037)Memory used [KB]: 793
% 0.13/0.38 % (31037)Time elapsed: 0.005 s
% 0.13/0.38 % (31037)Instructions burned: 7 (million)
% 0.13/0.38 % (31032)Success in time 0.02 s
%------------------------------------------------------------------------------