TSTP Solution File: SEU177+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU177+1 : 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 : n021.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 09:28:02 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 56 ( 11 unt; 0 def)
% Number of atoms : 203 ( 12 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 235 ( 88 ~; 82 |; 36 &)
% ( 16 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 151 ( 114 !; 37 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f262,plain,
$false,
inference(unit_resulting_resolution,[],[f214,f241,f150,f107]) ).
fof(f107,plain,
! [X0,X1,X5] :
( ~ sP2(X0,X1)
| in(X5,X1)
| sP18(X5,X0) ),
inference(cnf_transformation,[],[f107_D]) ).
fof(f107_D,plain,
! [X0,X5] :
( ! [X1] :
( ~ sP2(X0,X1)
| in(X5,X1) )
<=> ~ sP18(X5,X0) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP18])]) ).
fof(f150,plain,
sP2(sK6,relation_rng(sK6)),
inference(unit_resulting_resolution,[],[f113,f104]) ).
fof(f104,plain,
! [X0] :
( ~ sP3(X0)
| sP2(X0,relation_rng(X0)) ),
inference(equality_resolution,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( sP2(X0,X1)
| relation_rng(X0) != X1
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ~ sP2(X0,X1) )
& ( sP2(X0,X1)
| relation_rng(X0) != X1 ) )
| ~ sP3(X0) ),
inference(nnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> sP2(X0,X1) )
| ~ sP3(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f113,plain,
sP3(sK6),
inference(unit_resulting_resolution,[],[f69,f87]) ).
fof(f87,plain,
! [X0] :
( ~ relation(X0)
| sP3(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( sP3(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f31,f43,f42]) ).
fof(f42,plain,
! [X0,X1] :
( sP2(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f31,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f69,plain,
relation(sK6),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
( ( ~ in(sK5,relation_rng(sK6))
| ~ in(sK4,relation_dom(sK6)) )
& in(ordered_pair(sK4,sK5),sK6)
& relation(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f29,f45]) ).
fof(f45,plain,
( ? [X0,X1,X2] :
( ( ~ in(X1,relation_rng(X2))
| ~ in(X0,relation_dom(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) )
=> ( ( ~ in(sK5,relation_rng(sK6))
| ~ in(sK4,relation_dom(sK6)) )
& in(ordered_pair(sK4,sK5),sK6)
& relation(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
? [X0,X1,X2] :
( ( ~ in(X1,relation_rng(X2))
| ~ in(X0,relation_dom(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
? [X0,X1,X2] :
( ( ~ in(X1,relation_rng(X2))
| ~ in(X0,relation_dom(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
inference(negated_conjecture,[],[f24]) ).
fof(f24,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f241,plain,
~ in(sK5,relation_rng(sK6)),
inference(unit_resulting_resolution,[],[f238,f71]) ).
fof(f71,plain,
( ~ in(sK5,relation_rng(sK6))
| ~ in(sK4,relation_dom(sK6)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f238,plain,
in(sK4,relation_dom(sK6)),
inference(unit_resulting_resolution,[],[f213,f142,f105]) ).
fof(f105,plain,
! [X0,X1,X5] :
( ~ sP0(X0,X1)
| in(X5,X1)
| sP17(X5,X0) ),
inference(cnf_transformation,[],[f105_D]) ).
fof(f105_D,plain,
! [X0,X5] :
( ! [X1] :
( ~ sP0(X0,X1)
| in(X5,X1) )
<=> ~ sP17(X5,X0) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP17])]) ).
fof(f142,plain,
sP0(sK6,relation_dom(sK6)),
inference(unit_resulting_resolution,[],[f109,f103]) ).
fof(f103,plain,
! [X0] :
( ~ sP1(X0)
| sP0(X0,relation_dom(X0)) ),
inference(equality_resolution,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( sP0(X0,X1)
| relation_dom(X0) != X1
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| relation_dom(X0) != X1 ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> sP0(X0,X1) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f109,plain,
sP1(sK6),
inference(unit_resulting_resolution,[],[f69,f80]) ).
fof(f80,plain,
! [X0] :
( ~ relation(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( sP1(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f30,f40,f39]) ).
fof(f39,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f213,plain,
~ sP17(sK4,sK6),
inference(unit_resulting_resolution,[],[f70,f106]) ).
fof(f106,plain,
! [X0,X6,X5] :
( ~ sP17(X5,X0)
| ~ in(ordered_pair(X5,X6),X0) ),
inference(general_splitting,[],[f77,f105_D]) ).
fof(f77,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ! [X3] : ~ in(ordered_pair(sK7(X0,X1),X3),X0)
| ~ in(sK7(X0,X1),X1) )
& ( in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0)
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK9(X0,X5)),X0)
| ~ in(X5,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f49,f52,f51,f50]) ).
fof(f50,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(sK7(X0,X1),X3),X0)
| ~ in(sK7(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK7(X0,X1),X4),X0)
| in(sK7(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK7(X0,X1),X4),X0)
=> in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK9(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f70,plain,
in(ordered_pair(sK4,sK5),sK6),
inference(cnf_transformation,[],[f46]) ).
fof(f214,plain,
~ sP18(sK5,sK6),
inference(unit_resulting_resolution,[],[f70,f108]) ).
fof(f108,plain,
! [X0,X6,X5] :
( ~ sP18(X5,X0)
| ~ in(ordered_pair(X6,X5),X0) ),
inference(general_splitting,[],[f84,f107_D]) ).
fof(f84,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK10(X0,X1)),X0)
| ~ in(sK10(X0,X1),X1) )
& ( in(ordered_pair(sK11(X0,X1),sK10(X0,X1)),X0)
| in(sK10(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK12(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| ~ sP2(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f56,f59,f58,f57]) ).
fof(f57,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(X3,sK10(X0,X1)),X0)
| ~ in(sK10(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK10(X0,X1)),X0)
| in(sK10(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK10(X0,X1)),X0)
=> in(ordered_pair(sK11(X0,X1),sK10(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK12(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| ~ sP2(X0,X1) ) ),
inference(nnf_transformation,[],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU177+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n021.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 11:13:28 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (9913)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (9919)WARNING: value z3 for option sas not known
% 0.15/0.38 % (9917)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 % (9915)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (9920)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (9921)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 % (9919)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 % (9923)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 % (9922)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 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 % (9923)First to succeed.
% 0.15/0.38 % (9919)Also succeeded, but the first one will report.
% 0.15/0.39 TRYING [3]
% 0.15/0.39 % (9923)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9913"
% 0.15/0.39 TRYING [3]
% 0.15/0.39 % (9923)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 % (9923)------------------------------
% 0.15/0.39 % (9923)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39 % (9923)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (9923)Memory used [KB]: 846
% 0.15/0.39 % (9923)Time elapsed: 0.008 s
% 0.15/0.39 % (9923)Instructions burned: 10 (million)
% 0.15/0.39 % (9913)Success in time 0.024 s
%------------------------------------------------------------------------------