TSTP Solution File: SEU019+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU019+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 : n007.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 15:21:52 EDT 2024
% Result : Theorem 0.14s 0.43s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 10
% Syntax : Number of formulae : 68 ( 15 unt; 0 def)
% Number of atoms : 249 ( 90 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 315 ( 134 ~; 125 |; 41 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 86 ( 74 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1523,plain,
$false,
inference(resolution,[],[f1521,f100]) ).
fof(f100,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f1521,plain,
~ relation(identity_relation(sK2)),
inference(resolution,[],[f1520,f102]) ).
fof(f102,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f1520,plain,
( ~ function(identity_relation(sK2))
| ~ relation(identity_relation(sK2)) ),
inference(resolution,[],[f1519,f159]) ).
fof(f159,plain,
( ~ sP0(identity_relation(sK2))
| ~ relation(identity_relation(sK2))
| ~ function(identity_relation(sK2)) ),
inference(resolution,[],[f118,f158]) ).
fof(f158,plain,
( ~ sP1(identity_relation(sK2))
| ~ sP0(identity_relation(sK2)) ),
inference(resolution,[],[f112,f93]) ).
fof(f93,plain,
~ one_to_one(identity_relation(sK2)),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
~ one_to_one(identity_relation(sK2)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f38,f63]) ).
fof(f63,plain,
( ? [X0] : ~ one_to_one(identity_relation(X0))
=> ~ one_to_one(identity_relation(sK2)) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
? [X0] : ~ one_to_one(identity_relation(X0)),
inference(ennf_transformation,[],[f29]) ).
fof(f29,negated_conjecture,
~ ! [X0] : one_to_one(identity_relation(X0)),
inference(negated_conjecture,[],[f28]) ).
fof(f28,conjecture,
! [X0] : one_to_one(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_1) ).
fof(f112,plain,
! [X0] :
( one_to_one(X0)
| ~ sP0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ( ( one_to_one(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ one_to_one(X0) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ( one_to_one(X0)
<=> sP0(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f118,plain,
! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f47,f61,f60]) ).
fof(f60,plain,
! [X0] :
( sP0(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f47,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f1519,plain,
sP0(identity_relation(sK2)),
inference(trivial_inequality_removal,[],[f1517]) ).
fof(f1517,plain,
( sK4(identity_relation(sK2)) != sK4(identity_relation(sK2))
| sP0(identity_relation(sK2)) ),
inference(superposition,[],[f117,f1450]) ).
fof(f1450,plain,
sK4(identity_relation(sK2)) = sK5(identity_relation(sK2)),
inference(resolution,[],[f1448,f100]) ).
fof(f1448,plain,
( ~ relation(identity_relation(sK2))
| sK4(identity_relation(sK2)) = sK5(identity_relation(sK2)) ),
inference(resolution,[],[f1441,f102]) ).
fof(f1441,plain,
( ~ function(identity_relation(sK2))
| ~ relation(identity_relation(sK2))
| sK4(identity_relation(sK2)) = sK5(identity_relation(sK2)) ),
inference(backward_demodulation,[],[f1419,f1438]) ).
fof(f1438,plain,
sK5(identity_relation(sK2)) = apply(identity_relation(sK2),sK5(identity_relation(sK2))),
inference(resolution,[],[f1426,f100]) ).
fof(f1426,plain,
( ~ relation(identity_relation(sK2))
| sK5(identity_relation(sK2)) = apply(identity_relation(sK2),sK5(identity_relation(sK2))) ),
inference(resolution,[],[f1382,f102]) ).
fof(f1382,plain,
( ~ function(identity_relation(sK2))
| ~ relation(identity_relation(sK2))
| sK5(identity_relation(sK2)) = apply(identity_relation(sK2),sK5(identity_relation(sK2))) ),
inference(forward_demodulation,[],[f1381,f323]) ).
fof(f323,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(resolution,[],[f321,f100]) ).
fof(f321,plain,
! [X0] :
( ~ relation(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(resolution,[],[f147,f102]) ).
fof(f147,plain,
! [X0] :
( ~ function(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f126]) ).
fof(f126,plain,
! [X0,X1] :
( relation_dom(X1) = X0
| identity_relation(X0) != X1
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ( sK8(X0,X1) != apply(X1,sK8(X0,X1))
& in(sK8(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,[sK8])],[f78,f79]) ).
fof(f79,plain,
! [X0,X1] :
( ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
=> ( sK8(X0,X1) != apply(X1,sK8(X0,X1))
& in(sK8(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f78,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,[],[f77]) ).
fof(f77,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,[],[f76]) ).
fof(f76,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,[],[f53]) ).
fof(f53,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,[],[f52]) ).
fof(f52,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,[],[f25]) ).
fof(f25,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/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f1381,plain,
( ~ relation(identity_relation(sK2))
| sK5(identity_relation(sK2)) = apply(identity_relation(relation_dom(identity_relation(sK2))),sK5(identity_relation(sK2)))
| ~ function(identity_relation(sK2)) ),
inference(duplicate_literal_removal,[],[f1380]) ).
fof(f1380,plain,
( ~ relation(identity_relation(sK2))
| sK5(identity_relation(sK2)) = apply(identity_relation(relation_dom(identity_relation(sK2))),sK5(identity_relation(sK2)))
| ~ relation(identity_relation(sK2))
| ~ function(identity_relation(sK2)) ),
inference(forward_demodulation,[],[f1379,f323]) ).
fof(f1379,plain,
( ~ relation(identity_relation(relation_dom(identity_relation(sK2))))
| sK5(identity_relation(sK2)) = apply(identity_relation(relation_dom(identity_relation(sK2))),sK5(identity_relation(sK2)))
| ~ relation(identity_relation(sK2))
| ~ function(identity_relation(sK2)) ),
inference(resolution,[],[f560,f159]) ).
fof(f560,plain,
! [X0] :
( sP0(X0)
| ~ relation(identity_relation(relation_dom(X0)))
| sK5(X0) = apply(identity_relation(relation_dom(X0)),sK5(X0)) ),
inference(resolution,[],[f355,f115]) ).
fof(f115,plain,
! [X0] :
( in(sK5(X0),relation_dom(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ( sP0(X0)
| ( sK4(X0) != sK5(X0)
& apply(X0,sK4(X0)) = apply(X0,sK5(X0))
& in(sK5(X0),relation_dom(X0))
& in(sK4(X0),relation_dom(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0)) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f69,f70]) ).
fof(f70,plain,
! [X0] :
( ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> ( sK4(X0) != sK5(X0)
& apply(X0,sK4(X0)) = apply(X0,sK5(X0))
& in(sK5(X0),relation_dom(X0))
& in(sK4(X0),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X0] :
( ( sP0(X0)
| ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0)) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ( sP0(X0)
| ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) ) )
& ( ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f355,plain,
! [X0,X1] :
( ~ in(X0,X1)
| apply(identity_relation(X1),X0) = X0
| ~ relation(identity_relation(X1)) ),
inference(resolution,[],[f146,f102]) ).
fof(f146,plain,
! [X3,X0] :
( ~ function(identity_relation(X0))
| ~ in(X3,X0)
| apply(identity_relation(X0),X3) = X3
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f127]) ).
fof(f127,plain,
! [X3,X0,X1] :
( apply(X1,X3) = X3
| ~ in(X3,X0)
| identity_relation(X0) != X1
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f1419,plain,
( sK4(identity_relation(sK2)) = apply(identity_relation(sK2),sK5(identity_relation(sK2)))
| ~ relation(identity_relation(sK2))
| ~ function(identity_relation(sK2)) ),
inference(backward_demodulation,[],[f286,f1416]) ).
fof(f1416,plain,
sK4(identity_relation(sK2)) = apply(identity_relation(sK2),sK4(identity_relation(sK2))),
inference(resolution,[],[f1414,f100]) ).
fof(f1414,plain,
( ~ relation(identity_relation(sK2))
| sK4(identity_relation(sK2)) = apply(identity_relation(sK2),sK4(identity_relation(sK2))) ),
inference(resolution,[],[f1370,f102]) ).
fof(f1370,plain,
( ~ function(identity_relation(sK2))
| ~ relation(identity_relation(sK2))
| sK4(identity_relation(sK2)) = apply(identity_relation(sK2),sK4(identity_relation(sK2))) ),
inference(forward_demodulation,[],[f1369,f323]) ).
fof(f1369,plain,
( ~ relation(identity_relation(sK2))
| sK4(identity_relation(sK2)) = apply(identity_relation(relation_dom(identity_relation(sK2))),sK4(identity_relation(sK2)))
| ~ function(identity_relation(sK2)) ),
inference(duplicate_literal_removal,[],[f1368]) ).
fof(f1368,plain,
( ~ relation(identity_relation(sK2))
| sK4(identity_relation(sK2)) = apply(identity_relation(relation_dom(identity_relation(sK2))),sK4(identity_relation(sK2)))
| ~ relation(identity_relation(sK2))
| ~ function(identity_relation(sK2)) ),
inference(forward_demodulation,[],[f1367,f323]) ).
fof(f1367,plain,
( ~ relation(identity_relation(relation_dom(identity_relation(sK2))))
| sK4(identity_relation(sK2)) = apply(identity_relation(relation_dom(identity_relation(sK2))),sK4(identity_relation(sK2)))
| ~ relation(identity_relation(sK2))
| ~ function(identity_relation(sK2)) ),
inference(resolution,[],[f559,f159]) ).
fof(f559,plain,
! [X0] :
( sP0(X0)
| ~ relation(identity_relation(relation_dom(X0)))
| sK4(X0) = apply(identity_relation(relation_dom(X0)),sK4(X0)) ),
inference(resolution,[],[f355,f114]) ).
fof(f114,plain,
! [X0] :
( in(sK4(X0),relation_dom(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f286,plain,
( apply(identity_relation(sK2),sK4(identity_relation(sK2))) = apply(identity_relation(sK2),sK5(identity_relation(sK2)))
| ~ relation(identity_relation(sK2))
| ~ function(identity_relation(sK2)) ),
inference(resolution,[],[f116,f159]) ).
fof(f116,plain,
! [X0] :
( sP0(X0)
| apply(X0,sK4(X0)) = apply(X0,sK5(X0)) ),
inference(cnf_transformation,[],[f71]) ).
fof(f117,plain,
! [X0] :
( sK4(X0) != sK5(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU019+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 20:27:17 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (4692)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (4695)WARNING: value z3 for option sas not known
% 0.14/0.38 % (4696)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (4699)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)
% 0.14/0.38 % (4694)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (4693)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (4697)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)
% 0.14/0.38 % (4698)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)
% 0.14/0.38 % (4695)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)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [4]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [5]
% 0.14/0.40 TRYING [3]
% 0.14/0.41 TRYING [6]
% 0.14/0.42 TRYING [1]
% 0.14/0.42 TRYING [2]
% 0.14/0.42 TRYING [3]
% 0.14/0.42 TRYING [4]
% 0.14/0.43 % (4698)First to succeed.
% 0.14/0.43 TRYING [4]
% 0.14/0.43 % (4698)Refutation found. Thanks to Tanya!
% 0.14/0.43 % SZS status Theorem for theBenchmark
% 0.14/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.43 % (4698)------------------------------
% 0.14/0.43 % (4698)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.43 % (4698)Termination reason: Refutation
% 0.14/0.43
% 0.14/0.43 % (4698)Memory used [KB]: 1462
% 0.14/0.43 % (4698)Time elapsed: 0.053 s
% 0.14/0.43 % (4698)Instructions burned: 90 (million)
% 0.14/0.43 % (4698)------------------------------
% 0.14/0.43 % (4698)------------------------------
% 0.14/0.43 % (4692)Success in time 0.06 s
%------------------------------------------------------------------------------