TSTP Solution File: SEU008+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU008+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n011.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 : Sun May 5 09:26:37 EDT 2024
% Result : Theorem 2.00s 0.70s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 17 unt; 0 def)
% Number of atoms : 266 ( 73 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 331 ( 126 ~; 120 |; 65 &)
% ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 129 ( 112 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7255,plain,
$false,
inference(trivial_inequality_removal,[],[f7254]) ).
fof(f7254,plain,
apply(sK3,sK2) != apply(sK3,sK2),
inference(superposition,[],[f117,f7252]) ).
fof(f7252,plain,
apply(sK3,sK2) = apply(relation_composition(identity_relation(sK1),sK3),sK2),
inference(resolution,[],[f7250,f114]) ).
fof(f114,plain,
relation(sK3),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
( apply(sK3,sK2) != apply(relation_composition(identity_relation(sK1),sK3),sK2)
& in(sK2,set_intersection2(relation_dom(sK3),sK1))
& function(sK3)
& relation(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f49,f83]) ).
fof(f83,plain,
( ? [X0,X1,X2] :
( apply(X2,X1) != apply(relation_composition(identity_relation(X0),X2),X1)
& in(X1,set_intersection2(relation_dom(X2),X0))
& function(X2)
& relation(X2) )
=> ( apply(sK3,sK2) != apply(relation_composition(identity_relation(sK1),sK3),sK2)
& in(sK2,set_intersection2(relation_dom(sK3),sK1))
& function(sK3)
& relation(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
? [X0,X1,X2] :
( apply(X2,X1) != apply(relation_composition(identity_relation(X0),X2),X1)
& in(X1,set_intersection2(relation_dom(X2),X0))
& function(X2)
& relation(X2) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
? [X0,X1,X2] :
( apply(X2,X1) != apply(relation_composition(identity_relation(X0),X2),X1)
& in(X1,set_intersection2(relation_dom(X2),X0))
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,set_intersection2(relation_dom(X2),X0))
=> apply(X2,X1) = apply(relation_composition(identity_relation(X0),X2),X1) ) ),
inference(negated_conjecture,[],[f35]) ).
fof(f35,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,set_intersection2(relation_dom(X2),X0))
=> apply(X2,X1) = apply(relation_composition(identity_relation(X0),X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_1) ).
fof(f7250,plain,
( ~ relation(sK3)
| apply(sK3,sK2) = apply(relation_composition(identity_relation(sK1),sK3),sK2) ),
inference(resolution,[],[f7118,f124]) ).
fof(f124,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f7118,plain,
( ~ relation(identity_relation(sK1))
| ~ relation(sK3)
| apply(sK3,sK2) = apply(relation_composition(identity_relation(sK1),sK3),sK2) ),
inference(forward_demodulation,[],[f7112,f1246]) ).
fof(f1246,plain,
sK2 = apply(identity_relation(sK1),sK2),
inference(resolution,[],[f1223,f124]) ).
fof(f1223,plain,
( ~ relation(identity_relation(sK1))
| sK2 = apply(identity_relation(sK1),sK2) ),
inference(resolution,[],[f593,f373]) ).
fof(f373,plain,
in(sK2,sK1),
inference(resolution,[],[f349,f210]) ).
fof(f210,plain,
in(sK2,set_intersection2(sK1,relation_dom(sK3))),
inference(superposition,[],[f116,f141]) ).
fof(f141,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f116,plain,
in(sK2,set_intersection2(relation_dom(sK3),sK1)),
inference(cnf_transformation,[],[f84]) ).
fof(f349,plain,
! [X2,X0,X1] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) ),
inference(resolution,[],[f162,f184]) ).
fof(f184,plain,
! [X0,X1] : sP0(X1,X0,set_intersection2(X0,X1)),
inference(equality_resolution,[],[f168]) ).
fof(f168,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f5,f81]) ).
fof(f81,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f162,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ~ in(sK8(X0,X1,X2),X0)
| ~ in(sK8(X0,X1,X2),X1)
| ~ in(sK8(X0,X1,X2),X2) )
& ( ( in(sK8(X0,X1,X2),X0)
& in(sK8(X0,X1,X2),X1) )
| in(sK8(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f98,f99]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( ~ in(sK8(X0,X1,X2),X0)
| ~ in(sK8(X0,X1,X2),X1)
| ~ in(sK8(X0,X1,X2),X2) )
& ( ( in(sK8(X0,X1,X2),X0)
& in(sK8(X0,X1,X2),X1) )
| in(sK8(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f97]) ).
fof(f97,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f96]) ).
fof(f96,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f593,plain,
! [X0,X1] :
( ~ in(X0,X1)
| apply(identity_relation(X1),X0) = X0
| ~ relation(identity_relation(X1)) ),
inference(resolution,[],[f182,f127]) ).
fof(f127,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f182,plain,
! [X3,X0] :
( ~ function(identity_relation(X0))
| ~ in(X3,X0)
| apply(identity_relation(X0),X3) = X3
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f152]) ).
fof(f152,plain,
! [X3,X0,X1] :
( apply(X1,X3) = X3
| ~ in(X3,X0)
| identity_relation(X0) != X1
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ( sK7(X0,X1) != apply(X1,sK7(X0,X1))
& in(sK7(X0,X1),X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f93,f94]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
=> ( sK7(X0,X1) != apply(X1,sK7(X0,X1))
& in(sK7(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( identity_relation(X0) = X1
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f7112,plain,
( ~ relation(sK3)
| apply(relation_composition(identity_relation(sK1),sK3),sK2) = apply(sK3,apply(identity_relation(sK1),sK2))
| ~ relation(identity_relation(sK1)) ),
inference(resolution,[],[f1550,f373]) ).
fof(f1550,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ relation(sK3)
| apply(relation_composition(identity_relation(X1),sK3),X0) = apply(sK3,apply(identity_relation(X1),X0))
| ~ relation(identity_relation(X1)) ),
inference(forward_demodulation,[],[f1545,f452]) ).
fof(f452,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(resolution,[],[f431,f124]) ).
fof(f431,plain,
! [X0] :
( ~ relation(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(resolution,[],[f183,f127]) ).
fof(f183,plain,
! [X0] :
( ~ function(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f151]) ).
fof(f151,plain,
! [X0,X1] :
( relation_dom(X1) = X0
| identity_relation(X0) != X1
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f1545,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(identity_relation(X1)))
| ~ relation(sK3)
| apply(relation_composition(identity_relation(X1),sK3),X0) = apply(sK3,apply(identity_relation(X1),X0))
| ~ relation(identity_relation(X1)) ),
inference(resolution,[],[f996,f127]) ).
fof(f996,plain,
! [X0,X1] :
( ~ function(X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(sK3)
| apply(relation_composition(X0,sK3),X1) = apply(sK3,apply(X0,X1))
| ~ relation(X0) ),
inference(resolution,[],[f155,f115]) ).
fof(f115,plain,
function(sK3),
inference(cnf_transformation,[],[f84]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ function(X1)
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f117,plain,
apply(sK3,sK2) != apply(relation_composition(identity_relation(sK1),sK3),sK2),
inference(cnf_transformation,[],[f84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU008+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n011.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 : Fri May 3 11:39:19 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (18977)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (18980)WARNING: value z3 for option sas not known
% 0.15/0.38 % (18978)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (18979)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 % (18980)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 % (18981)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (18982)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 % (18983)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 % (18984)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 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.40 TRYING [4]
% 0.22/0.42 TRYING [3]
% 0.22/0.42 TRYING [5]
% 0.22/0.47 TRYING [4]
% 0.22/0.48 TRYING [6]
% 0.22/0.57 TRYING [5]
% 0.22/0.57 TRYING [7]
% 2.00/0.69 % (18983)First to succeed.
% 2.00/0.69 % (18983)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18977"
% 2.00/0.70 % (18983)Refutation found. Thanks to Tanya!
% 2.00/0.70 % SZS status Theorem for theBenchmark
% 2.00/0.70 % SZS output start Proof for theBenchmark
% See solution above
% 2.00/0.70 % (18983)------------------------------
% 2.00/0.70 % (18983)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.00/0.70 % (18983)Termination reason: Refutation
% 2.00/0.70
% 2.00/0.70 % (18983)Memory used [KB]: 4706
% 2.00/0.70 % (18983)Time elapsed: 0.316 s
% 2.00/0.70 % (18983)Instructions burned: 853 (million)
% 2.00/0.70 % (18977)Success in time 0.32 s
%------------------------------------------------------------------------------