TSTP Solution File: SEU045+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU045+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n020.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 : Thu Aug 31 17:55:05 EDT 2023
% Result : Theorem 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 46 ( 14 unt; 0 def)
% Number of atoms : 198 ( 53 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 240 ( 88 ~; 78 |; 49 &)
% ( 11 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 98 (; 85 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f482,plain,
$false,
inference(subsumption_resolution,[],[f481,f173]) ).
fof(f173,plain,
sF20 != sF21,
inference(definition_folding,[],[f108,f172,f171,f170]) ).
fof(f170,plain,
relation_rng_restriction(sK1,sK3) = sF19,
introduced(function_definition,[]) ).
fof(f171,plain,
apply(sF19,sK2) = sF20,
introduced(function_definition,[]) ).
fof(f172,plain,
apply(sK3,sK2) = sF21,
introduced(function_definition,[]) ).
fof(f108,plain,
apply(relation_rng_restriction(sK1,sK3),sK2) != apply(sK3,sK2),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
( apply(relation_rng_restriction(sK1,sK3),sK2) != apply(sK3,sK2)
& in(sK2,relation_dom(relation_rng_restriction(sK1,sK3)))
& function(sK3)
& relation(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f44,f71]) ).
fof(f71,plain,
( ? [X0,X1,X2] :
( apply(relation_rng_restriction(X0,X2),X1) != apply(X2,X1)
& in(X1,relation_dom(relation_rng_restriction(X0,X2)))
& function(X2)
& relation(X2) )
=> ( apply(relation_rng_restriction(sK1,sK3),sK2) != apply(sK3,sK2)
& in(sK2,relation_dom(relation_rng_restriction(sK1,sK3)))
& function(sK3)
& relation(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
? [X0,X1,X2] :
( apply(relation_rng_restriction(X0,X2),X1) != apply(X2,X1)
& in(X1,relation_dom(relation_rng_restriction(X0,X2)))
& function(X2)
& relation(X2) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
? [X0,X1,X2] :
( apply(relation_rng_restriction(X0,X2),X1) != apply(X2,X1)
& in(X1,relation_dom(relation_rng_restriction(X0,X2)))
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
=> apply(relation_rng_restriction(X0,X2),X1) = apply(X2,X1) ) ),
inference(negated_conjecture,[],[f33]) ).
fof(f33,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
=> apply(relation_rng_restriction(X0,X2),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NHbH9hKDI7/Vampire---4.8_4470',t87_funct_1) ).
fof(f481,plain,
sF20 = sF21,
inference(backward_demodulation,[],[f172,f480]) ).
fof(f480,plain,
apply(sK3,sK2) = sF20,
inference(forward_demodulation,[],[f476,f171]) ).
fof(f476,plain,
apply(sK3,sK2) = apply(sF19,sK2),
inference(resolution,[],[f473,f175]) ).
fof(f175,plain,
in(sK2,sF22),
inference(definition_folding,[],[f107,f174,f170]) ).
fof(f174,plain,
relation_dom(sF19) = sF22,
introduced(function_definition,[]) ).
fof(f107,plain,
in(sK2,relation_dom(relation_rng_restriction(sK1,sK3))),
inference(cnf_transformation,[],[f72]) ).
fof(f473,plain,
! [X0] :
( ~ in(X0,sF22)
| apply(sK3,X0) = apply(sF19,X0) ),
inference(forward_demodulation,[],[f472,f174]) ).
fof(f472,plain,
! [X0] :
( ~ in(X0,relation_dom(sF19))
| apply(sK3,X0) = apply(sF19,X0) ),
inference(superposition,[],[f451,f170]) ).
fof(f451,plain,
! [X10,X9] :
( ~ in(X9,relation_dom(relation_rng_restriction(X10,sK3)))
| apply(sK3,X9) = apply(relation_rng_restriction(X10,sK3),X9) ),
inference(subsumption_resolution,[],[f444,f105]) ).
fof(f105,plain,
relation(sK3),
inference(cnf_transformation,[],[f72]) ).
fof(f444,plain,
! [X10,X9] :
( ~ in(X9,relation_dom(relation_rng_restriction(X10,sK3)))
| apply(sK3,X9) = apply(relation_rng_restriction(X10,sK3),X9)
| ~ relation(sK3) ),
inference(resolution,[],[f177,f106]) ).
fof(f106,plain,
function(sK3),
inference(cnf_transformation,[],[f72]) ).
fof(f177,plain,
! [X2,X0,X4] :
( ~ function(X2)
| ~ in(X4,relation_dom(relation_rng_restriction(X0,X2)))
| apply(X2,X4) = apply(relation_rng_restriction(X0,X2),X4)
| ~ relation(X2) ),
inference(subsumption_resolution,[],[f176,f129]) ).
fof(f129,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.NHbH9hKDI7/Vampire---4.8_4470',dt_k8_relat_1) ).
fof(f176,plain,
! [X2,X0,X4] :
( apply(X2,X4) = apply(relation_rng_restriction(X0,X2),X4)
| ~ in(X4,relation_dom(relation_rng_restriction(X0,X2)))
| ~ function(X2)
| ~ relation(X2)
| ~ relation(relation_rng_restriction(X0,X2)) ),
inference(subsumption_resolution,[],[f164,f134]) ).
fof(f134,plain,
! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NHbH9hKDI7/Vampire---4.8_4470',fc5_funct_1) ).
fof(f164,plain,
! [X2,X0,X4] :
( apply(X2,X4) = apply(relation_rng_restriction(X0,X2),X4)
| ~ in(X4,relation_dom(relation_rng_restriction(X0,X2)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2)) ),
inference(equality_resolution,[],[f142]) ).
fof(f142,plain,
! [X2,X0,X1,X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1))
| relation_rng_restriction(X0,X2) != X1
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_rng_restriction(X0,X2) = X1
| ( apply(X2,sK8(X1,X2)) != apply(X1,sK8(X1,X2))
& in(sK8(X1,X2),relation_dom(X1)) )
| ~ sP0(X0,X2,X1) )
& ( ( ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) )
& sP0(X0,X2,X1) )
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f86,f87]) ).
fof(f87,plain,
! [X1,X2] :
( ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
=> ( apply(X2,sK8(X1,X2)) != apply(X1,sK8(X1,X2))
& in(sK8(X1,X2),relation_dom(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_rng_restriction(X0,X2) = X1
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| ~ sP0(X0,X2,X1) )
& ( ( ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) )
& sP0(X0,X2,X1) )
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_rng_restriction(X0,X2) = X1
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| ~ sP0(X0,X2,X1) )
& ( ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& sP0(X0,X2,X1) )
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_rng_restriction(X0,X2) = X1
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| ~ sP0(X0,X2,X1) )
& ( ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& sP0(X0,X2,X1) )
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& sP0(X0,X2,X1) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(definition_folding,[],[f62,f69]) ).
fof(f69,plain,
! [X0,X2,X1] :
( sP0(X0,X2,X1)
<=> ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f62,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X2,X3) = apply(X1,X3) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) ) ) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X2,X3) = apply(X1,X3) )
& ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NHbH9hKDI7/Vampire---4.8_4470',t85_funct_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU045+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 23 18:31:16 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.NHbH9hKDI7/Vampire---4.8_4470
% 0.15/0.36 % (4623)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (4630)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.21/0.42 % (4628)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.21/0.42 % (4627)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.21/0.42 % (4626)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.21/0.42 % (4629)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.21/0.42 % (4625)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.21/0.42 % (4624)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.21/0.43 % (4630)First to succeed.
% 0.21/0.43 % (4630)Refutation found. Thanks to Tanya!
% 0.21/0.43 % SZS status Theorem for Vampire---4
% 0.21/0.43 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.43 % (4630)------------------------------
% 0.21/0.43 % (4630)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.43 % (4630)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.43 % (4630)Termination reason: Refutation
% 0.21/0.43
% 0.21/0.43 % (4630)Memory used [KB]: 1407
% 0.21/0.43 % (4630)Time elapsed: 0.012 s
% 0.21/0.43 % (4630)------------------------------
% 0.21/0.43 % (4630)------------------------------
% 0.21/0.43 % (4623)Success in time 0.07 s
% 0.21/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------