TSTP Solution File: SEU515_8 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU515_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.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 Apr 30 15:34:50 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 58 ( 11 unt; 1 typ; 0 def)
% Number of atoms : 315 ( 68 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 202 ( 66 ~; 67 |; 26 &)
% ( 16 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 164 ( 131 fml; 33 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 21 ( 18 usr; 18 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 73 ( 59 !; 14 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_6,type,
sK3: $o ).
tff(f90,plain,
$false,
inference(avatar_sat_refutation,[],[f31,f36,f41,f46,f51,f56,f60,f64,f73,f77,f85,f89]) ).
tff(f89,plain,
( spl4_4
| spl4_5
| ~ spl4_3
| ~ spl4_10 ),
inference(avatar_split_clause,[],[f78,f75,f38,f48,f43]) ).
tff(f43,plain,
( spl4_4
<=> ( sK0 = sK2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
tff(f48,plain,
( spl4_5
<=> in(sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
tff(f38,plain,
( spl4_3
<=> in(sK2,setadjoin(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
tff(f75,plain,
( spl4_10
<=> ! [X2,X0,X1] :
( in(X2,X1)
| ~ in(X2,setadjoin(X0,X1))
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
tff(f78,plain,
( in(sK2,sK1)
| ( sK0 = sK2 )
| ~ spl4_3
| ~ spl4_10 ),
inference(resolution,[],[f76,f40]) ).
tff(f40,plain,
( in(sK2,setadjoin(sK0,sK1))
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f38]) ).
tff(f76,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ~ in(X2,setadjoin(X0,X1))
| in(X2,X1)
| ( X0 = X2 ) )
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f75]) ).
tff(f85,plain,
( spl4_11
| spl4_2
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f69,f58,f33,f82]) ).
tff(f82,plain,
( spl4_11
<=> ( $false = sK3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
tff(f33,plain,
( spl4_2
<=> ( $true = sK3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
tff(f58,plain,
( spl4_7
<=> ! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
tff(f69,plain,
( ( $false = sK3 )
| spl4_2
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f67]) ).
tff(f67,plain,
( ( $true != $true )
| ( $false = sK3 )
| spl4_2
| ~ spl4_7 ),
inference(superposition,[],[f35,f59]) ).
tff(f59,plain,
( ! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f58]) ).
tff(f35,plain,
( ( $true != sK3 )
| spl4_2 ),
inference(avatar_component_clause,[],[f33]) ).
tff(f77,plain,
( ~ spl4_1
| spl4_10 ),
inference(avatar_split_clause,[],[f23,f75,f28]) ).
tff(f28,plain,
( spl4_1
<=> setadjoinAx ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
tff(f23,plain,
! [X2: $i,X0: $i,X1: $i] :
( in(X2,X1)
| ( X0 = X2 )
| ~ in(X2,setadjoin(X0,X1))
| ~ setadjoinAx ),
inference(cnf_transformation,[],[f17]) ).
tff(f17,plain,
( ! [X0,X1,X2] :
( ( in(X2,setadjoin(X0,X1))
| ( ~ in(X2,X1)
& ( X0 != X2 ) ) )
& ( in(X2,X1)
| ( X0 = X2 )
| ~ in(X2,setadjoin(X0,X1)) ) )
| ~ setadjoinAx ),
inference(flattening,[],[f16]) ).
tff(f16,plain,
( ! [X0,X1,X2] :
( ( in(X2,setadjoin(X0,X1))
| ( ~ in(X2,X1)
& ( X0 != X2 ) ) )
& ( in(X2,X1)
| ( X0 = X2 )
| ~ in(X2,setadjoin(X0,X1)) ) )
| ~ setadjoinAx ),
inference(nnf_transformation,[],[f12]) ).
tff(f12,plain,
( ! [X0,X1,X2] :
( in(X2,setadjoin(X0,X1))
<=> ( in(X2,X1)
| ( X0 = X2 ) ) )
| ~ setadjoinAx ),
inference(ennf_transformation,[],[f9]) ).
tff(f9,plain,
( setadjoinAx
=> ! [X0,X1,X2] :
( in(X2,setadjoin(X0,X1))
<=> ( in(X2,X1)
| ( X0 = X2 ) ) ) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
tff(f8,plain,
( setadjoinAx
<=> ! [X0,X1,X2] :
( in(X2,setadjoin(X0,X1))
<=> ( in(X2,X1)
| ( X0 = X2 ) ) ) ),
inference(fool_elimination,[],[f1]) ).
tff(f1,axiom,
( setadjoinAx
= ( ! [X0,X1,X2] :
( in(X2,setadjoin(X0,X1))
<=> ( in(X2,X1)
| ( X0 = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
tff(f73,plain,
( ~ spl4_1
| spl4_9 ),
inference(avatar_split_clause,[],[f25,f71,f28]) ).
tff(f71,plain,
( spl4_9
<=> ! [X2,X0,X1] :
( in(X2,setadjoin(X0,X1))
| ~ in(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
tff(f25,plain,
! [X2: $i,X0: $i,X1: $i] :
( in(X2,setadjoin(X0,X1))
| ~ in(X2,X1)
| ~ setadjoinAx ),
inference(cnf_transformation,[],[f17]) ).
tff(f64,plain,
( ~ spl4_1
| spl4_8 ),
inference(avatar_split_clause,[],[f26,f62,f28]) ).
tff(f62,plain,
( spl4_8
<=> ! [X2,X1] : in(X2,setadjoin(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
tff(f26,plain,
! [X2: $i,X1: $i] :
( in(X2,setadjoin(X2,X1))
| ~ setadjoinAx ),
inference(equality_resolution,[],[f24]) ).
tff(f24,plain,
! [X2: $i,X0: $i,X1: $i] :
( in(X2,setadjoin(X0,X1))
| ( X0 != X2 )
| ~ setadjoinAx ),
inference(cnf_transformation,[],[f17]) ).
tff(f60,plain,
spl4_7,
inference(avatar_split_clause,[],[f5,f58]) ).
tff(f5,plain,
! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ),
introduced(fool_axiom,[]) ).
tff(f56,plain,
~ spl4_6,
inference(avatar_split_clause,[],[f4,f53]) ).
tff(f53,plain,
( spl4_6
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
tff(f4,plain,
$true != $false,
introduced(fool_axiom,[]) ).
tff(f51,plain,
( ~ spl4_5
| spl4_2 ),
inference(avatar_split_clause,[],[f21,f33,f48]) ).
tff(f21,plain,
( ( $true = sK3 )
| ~ in(sK2,sK1) ),
inference(cnf_transformation,[],[f15]) ).
tff(f15,plain,
( ( $true != sK3 )
& ( ( $true = sK3 )
| ~ in(sK2,sK1) )
& ( ( $true = sK3 )
| ( sK0 != sK2 ) )
& in(sK2,setadjoin(sK0,sK1))
& setadjoinAx ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f11,f14,f13]) ).
tff(f13,plain,
( ? [X0,X1,X2] :
( ? [X3: $o] :
( ( $true != (X3) )
& ( ( $true = (X3) )
| ~ in(X2,X1) )
& ( ( $true = (X3) )
| ( X0 != X2 ) ) )
& in(X2,setadjoin(X0,X1)) )
=> ( ? [X3: $o] :
( ( $true != (X3) )
& ( ( $true = (X3) )
| ~ in(sK2,sK1) )
& ( ( $true = (X3) )
| ( sK0 != sK2 ) ) )
& in(sK2,setadjoin(sK0,sK1)) ) ),
introduced(choice_axiom,[]) ).
tff(f14,plain,
( ? [X3: $o] :
( ( $true != (X3) )
& ( ( $true = (X3) )
| ~ in(sK2,sK1) )
& ( ( $true = (X3) )
| ( sK0 != sK2 ) ) )
=> ( ( $true != sK3 )
& ( ( $true = sK3 )
| ~ in(sK2,sK1) )
& ( ( $true = sK3 )
| ( sK0 != sK2 ) ) ) ),
introduced(choice_axiom,[]) ).
tff(f11,plain,
( ? [X0,X1,X2] :
( ? [X3: $o] :
( ( $true != (X3) )
& ( ( $true = (X3) )
| ~ in(X2,X1) )
& ( ( $true = (X3) )
| ( X0 != X2 ) ) )
& in(X2,setadjoin(X0,X1)) )
& setadjoinAx ),
inference(flattening,[],[f10]) ).
tff(f10,plain,
( ? [X0,X1,X2] :
( ? [X3: $o] :
( ( $true != (X3) )
& ( ( $true = (X3) )
| ~ in(X2,X1) )
& ( ( $true = (X3) )
| ( X0 != X2 ) ) )
& in(X2,setadjoin(X0,X1)) )
& setadjoinAx ),
inference(ennf_transformation,[],[f7]) ).
tff(f7,plain,
~ ( setadjoinAx
=> ! [X0,X1,X2] :
( in(X2,setadjoin(X0,X1))
=> ! [X3: $o] :
( ( ( X0 = X2 )
=> ( $true = (X3) ) )
=> ( ( in(X2,X1)
=> ( $true = (X3) ) )
=> ( $true = (X3) ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
tff(f6,plain,
~ ( setadjoinAx
=> ! [X0,X1,X2] :
( in(X2,setadjoin(X0,X1))
=> ! [X3: $o] :
( ( ( X0 = X2 )
=> (X3) )
=> ( ( in(X2,X1)
=> (X3) )
=> (X3) ) ) ) ),
inference(rectify,[],[f3]) ).
tff(f3,negated_conjecture,
~ ( setadjoinAx
=> ! [X0,X1,X2] :
( in(X2,setadjoin(X0,X1))
=> ! [X3: $o] :
( ( ( X0 = X2 )
=> (X3) )
=> ( ( in(X2,X1)
=> (X3) )
=> (X3) ) ) ) ),
inference(negated_conjecture,[],[f2]) ).
tff(f2,conjecture,
( setadjoinAx
=> ! [X0,X1,X2] :
( in(X2,setadjoin(X0,X1))
=> ! [X3: $o] :
( ( ( X0 = X2 )
=> (X3) )
=> ( ( in(X2,X1)
=> (X3) )
=> (X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
tff(f46,plain,
( ~ spl4_4
| spl4_2 ),
inference(avatar_split_clause,[],[f20,f33,f43]) ).
tff(f20,plain,
( ( $true = sK3 )
| ( sK0 != sK2 ) ),
inference(cnf_transformation,[],[f15]) ).
tff(f41,plain,
spl4_3,
inference(avatar_split_clause,[],[f19,f38]) ).
tff(f19,plain,
in(sK2,setadjoin(sK0,sK1)),
inference(cnf_transformation,[],[f15]) ).
tff(f36,plain,
~ spl4_2,
inference(avatar_split_clause,[],[f22,f33]) ).
tff(f22,plain,
$true != sK3,
inference(cnf_transformation,[],[f15]) ).
tff(f31,plain,
spl4_1,
inference(avatar_split_clause,[],[f18,f28]) ).
tff(f18,plain,
setadjoinAx,
inference(cnf_transformation,[],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU515_8 : TPTP v8.1.2. Released v8.0.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Apr 29 20:48:39 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % (1342)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (1345)WARNING: value z3 for option sas not known
% 0.15/0.38 % (1343)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (1344)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (1346)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (1345)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)
% 0.15/0.38 % (1347)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)
% 0.15/0.38 % (1348)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)
% 0.15/0.38 % (1349)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)
% 0.15/0.38 Detected minimum model sizes of [1,1]
% 0.15/0.38 Detected maximum model sizes of [max,3]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [1,1]
% 0.15/0.39 TRYING [1,2]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [2,2]
% 0.15/0.39 % (1347)First to succeed.
% 0.15/0.39 TRYING [1,3]
% 0.15/0.39 TRYING [2,3]
% 0.15/0.39 TRYING [3,2]
% 0.15/0.39 % (1348)Also succeeded, but the first one will report.
% 0.15/0.39 TRYING [3]
% 0.15/0.39 Detected minimum model sizes of [1,1]
% 0.15/0.39 Detected maximum model sizes of [max,3]
% 0.15/0.39 TRYING [1,1]
% 0.15/0.39 TRYING [1,2]
% 0.15/0.39 TRYING [3,3]
% 0.15/0.39 TRYING [1,3]
% 0.15/0.39 TRYING [2,3]
% 0.15/0.39 % (1345)Also succeeded, but the first one will report.
% 0.15/0.39 % (1347)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39 % (1347)------------------------------
% 0.15/0.39 % (1347)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39 % (1347)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (1347)Memory used [KB]: 777
% 0.15/0.39 % (1347)Time elapsed: 0.005 s
% 0.15/0.39 % (1347)Instructions burned: 5 (million)
% 0.15/0.39 % (1347)------------------------------
% 0.15/0.39 % (1347)------------------------------
% 0.15/0.39 % (1342)Success in time 0.02 s
%------------------------------------------------------------------------------