TSTP Solution File: SEU160+2 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU160+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.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 15:22:41 EDT 2024
% Result : Theorem 0.19s 0.40s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 82 ( 23 unt; 0 def)
% Number of atoms : 181 ( 64 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 170 ( 71 ~; 63 |; 21 &)
% ( 6 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 109 ( 94 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2153,plain,
$false,
inference(avatar_sat_refutation,[],[f1692,f2058,f2143,f2145,f2152]) ).
fof(f2152,plain,
~ spl29_2,
inference(avatar_contradiction_clause,[],[f2151]) ).
fof(f2151,plain,
( $false
| ~ spl29_2 ),
inference(subsumption_resolution,[],[f2149,f424]) ).
fof(f424,plain,
empty_set != sK6,
inference(subsumption_resolution,[],[f409,f239]) ).
fof(f239,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f409,plain,
( empty_set != sK6
| ~ subset(empty_set,singleton(sK7)) ),
inference(inner_rewriting,[],[f236]) ).
fof(f236,plain,
( empty_set != sK6
| ~ subset(sK6,singleton(sK7)) ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
( ( ( sK6 != singleton(sK7)
& empty_set != sK6 )
| ~ subset(sK6,singleton(sK7)) )
& ( sK6 = singleton(sK7)
| empty_set = sK6
| subset(sK6,singleton(sK7)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f153,f154]) ).
fof(f154,plain,
( ? [X0,X1] :
( ( ( singleton(X1) != X0
& empty_set != X0 )
| ~ subset(X0,singleton(X1)) )
& ( singleton(X1) = X0
| empty_set = X0
| subset(X0,singleton(X1)) ) )
=> ( ( ( sK6 != singleton(sK7)
& empty_set != sK6 )
| ~ subset(sK6,singleton(sK7)) )
& ( sK6 = singleton(sK7)
| empty_set = sK6
| subset(sK6,singleton(sK7)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f153,plain,
? [X0,X1] :
( ( ( singleton(X1) != X0
& empty_set != X0 )
| ~ subset(X0,singleton(X1)) )
& ( singleton(X1) = X0
| empty_set = X0
| subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f152]) ).
fof(f152,plain,
? [X0,X1] :
( ( ( singleton(X1) != X0
& empty_set != X0 )
| ~ subset(X0,singleton(X1)) )
& ( singleton(X1) = X0
| empty_set = X0
| subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f99]) ).
fof(f99,plain,
? [X0,X1] :
( subset(X0,singleton(X1))
<~> ( singleton(X1) = X0
| empty_set = X0 ) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( singleton(X1) = X0
| empty_set = X0 ) ),
inference(negated_conjecture,[],[f70]) ).
fof(f70,conjecture,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( singleton(X1) = X0
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f2149,plain,
( empty_set = sK6
| ~ spl29_2 ),
inference(resolution,[],[f1691,f301]) ).
fof(f301,plain,
! [X0] :
( in(sK10(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f174]) ).
fof(f174,plain,
! [X0] :
( ( empty_set = X0
| in(sK10(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f172,f173]) ).
fof(f173,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK10(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f172,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f171]) ).
fof(f171,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f1691,plain,
( ! [X0] : ~ in(X0,sK6)
| ~ spl29_2 ),
inference(avatar_component_clause,[],[f1690]) ).
fof(f1690,plain,
( spl29_2
<=> ! [X0] : ~ in(X0,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_2])]) ).
fof(f2145,plain,
spl29_1,
inference(avatar_contradiction_clause,[],[f2144]) ).
fof(f2144,plain,
( $false
| spl29_1 ),
inference(subsumption_resolution,[],[f2112,f423]) ).
fof(f423,plain,
sK6 != singleton(sK7),
inference(subsumption_resolution,[],[f408,f303]) ).
fof(f303,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f408,plain,
( sK6 != singleton(sK7)
| ~ subset(sK6,sK6) ),
inference(inner_rewriting,[],[f237]) ).
fof(f237,plain,
( sK6 != singleton(sK7)
| ~ subset(sK6,singleton(sK7)) ),
inference(cnf_transformation,[],[f155]) ).
fof(f2112,plain,
( sK6 = singleton(sK7)
| spl29_1 ),
inference(superposition,[],[f1658,f2101]) ).
fof(f2101,plain,
( sK6 = set_union2(singleton(sK7),sK6)
| spl29_1 ),
inference(resolution,[],[f256,f1726]) ).
fof(f1726,plain,
( in(sK7,sK6)
| spl29_1 ),
inference(resolution,[],[f1688,f455]) ).
fof(f455,plain,
! [X0,X1] :
( disjoint(X1,singleton(X0))
| in(X0,X1) ),
inference(resolution,[],[f254,f314]) ).
fof(f314,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f254,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f1688,plain,
( ~ disjoint(sK6,singleton(sK7))
| spl29_1 ),
inference(avatar_component_clause,[],[f1686]) ).
fof(f1686,plain,
( spl29_1
<=> disjoint(sK6,singleton(sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_1])]) ).
fof(f256,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(f1658,plain,
singleton(sK7) = set_union2(singleton(sK7),sK6),
inference(superposition,[],[f928,f1626]) ).
fof(f1626,plain,
sK6 = set_intersection2(sK6,singleton(sK7)),
inference(resolution,[],[f1623,f257]) ).
fof(f257,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f1623,plain,
subset(sK6,singleton(sK7)),
inference(subsumption_resolution,[],[f1622,f424]) ).
fof(f1622,plain,
( empty_set = sK6
| subset(sK6,singleton(sK7)) ),
inference(subsumption_resolution,[],[f235,f423]) ).
fof(f235,plain,
( sK6 = singleton(sK7)
| empty_set = sK6
| subset(sK6,singleton(sK7)) ),
inference(cnf_transformation,[],[f155]) ).
fof(f928,plain,
! [X0,X1] : set_union2(X1,set_intersection2(X0,X1)) = X1,
inference(superposition,[],[f801,f309]) ).
fof(f309,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f801,plain,
! [X0,X1] : set_union2(set_intersection2(X0,X1),X1) = X1,
inference(resolution,[],[f258,f486]) ).
fof(f486,plain,
! [X0,X1] : subset(set_intersection2(X1,X0),X0),
inference(superposition,[],[f244,f308]) ).
fof(f308,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f244,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f258,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f2143,plain,
spl29_1,
inference(avatar_contradiction_clause,[],[f2142]) ).
fof(f2142,plain,
( $false
| spl29_1 ),
inference(subsumption_resolution,[],[f2109,f423]) ).
fof(f2109,plain,
( sK6 = singleton(sK7)
| spl29_1 ),
inference(superposition,[],[f2101,f1658]) ).
fof(f2058,plain,
( ~ spl29_3
| spl29_2 ),
inference(avatar_split_clause,[],[f2053,f1690,f2055]) ).
fof(f2055,plain,
( spl29_3
<=> disjoint(singleton(sK7),sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_3])]) ).
fof(f2053,plain,
! [X0] :
( ~ in(X0,sK6)
| ~ disjoint(singleton(sK7),sK6) ),
inference(superposition,[],[f642,f1626]) ).
fof(f642,plain,
! [X2,X0,X1] :
( ~ in(X2,set_intersection2(X1,X0))
| ~ disjoint(X0,X1) ),
inference(superposition,[],[f250,f308]) ).
fof(f250,plain,
! [X2,X0,X1] :
( ~ in(X2,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f157]) ).
fof(f157,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( in(sK8(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f101,f156]) ).
fof(f156,plain,
! [X0,X1] :
( ? [X3] : in(X3,set_intersection2(X0,X1))
=> in(sK8(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( ? [X3] : in(X3,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f79]) ).
fof(f79,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f1692,plain,
( ~ spl29_1
| spl29_2 ),
inference(avatar_split_clause,[],[f1642,f1690,f1686]) ).
fof(f1642,plain,
! [X0] :
( ~ in(X0,sK6)
| ~ disjoint(sK6,singleton(sK7)) ),
inference(superposition,[],[f250,f1626]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU160+2 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 29 20:35:55 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % (30766)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.36 % (30769)WARNING: value z3 for option sas not known
% 0.12/0.36 % (30769)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)
% 0.12/0.36 % (30772)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)
% 0.12/0.36 % (30770)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.36 % (30771)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)
% 0.12/0.36 % (30768)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.36 % (30773)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)
% 0.12/0.37 % (30767)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.37 TRYING [1]
% 0.12/0.37 TRYING [2]
% 0.12/0.38 TRYING [1]
% 0.12/0.38 TRYING [2]
% 0.12/0.38 TRYING [3]
% 0.12/0.38 TRYING [3]
% 0.19/0.40 % (30769)First to succeed.
% 0.19/0.40 TRYING [4]
% 0.19/0.40 % (30769)Refutation found. Thanks to Tanya!
% 0.19/0.40 % SZS status Theorem for theBenchmark
% 0.19/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.40 % (30769)------------------------------
% 0.19/0.40 % (30769)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.40 % (30769)Termination reason: Refutation
% 0.19/0.40
% 0.19/0.40 % (30769)Memory used [KB]: 1467
% 0.19/0.40 % (30769)Time elapsed: 0.040 s
% 0.19/0.40 % (30769)Instructions burned: 74 (million)
% 0.19/0.40 % (30769)------------------------------
% 0.19/0.40 % (30769)------------------------------
% 0.19/0.40 % (30766)Success in time 0.056 s
%------------------------------------------------------------------------------