TSTP Solution File: SEU204+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU204+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 : n025.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 15:23:48 EDT 2024
% Result : Theorem 0.19s 0.39s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 50 ( 7 unt; 0 def)
% Number of atoms : 215 ( 15 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 262 ( 97 ~; 89 |; 50 &)
% ( 13 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 160 ( 126 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f805,plain,
$false,
inference(resolution,[],[f801,f100]) ).
fof(f100,plain,
~ subset(relation_image(sK3,sK2),relation_rng(sK3)),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
( ~ subset(relation_image(sK3,sK2),relation_rng(sK3))
& relation(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f43,f65]) ).
fof(f65,plain,
( ? [X0,X1] :
( ~ subset(relation_image(X1,X0),relation_rng(X1))
& relation(X1) )
=> ( ~ subset(relation_image(sK3,sK2),relation_rng(sK3))
& relation(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
? [X0,X1] :
( ~ subset(relation_image(X1,X0),relation_rng(X1))
& relation(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
inference(negated_conjecture,[],[f32]) ).
fof(f32,conjecture,
! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
fof(f801,plain,
subset(relation_image(sK3,sK2),relation_rng(sK3)),
inference(resolution,[],[f799,f138]) ).
fof(f138,plain,
! [X0,X1] :
( in(sK13(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK13(X0,X1),X1)
& in(sK13(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f87,f88]) ).
fof(f88,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK13(X0,X1),X1)
& in(sK13(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f799,plain,
! [X0] : ~ in(sK13(relation_image(sK3,sK2),relation_rng(sK3)),relation_image(sK3,X0)),
inference(resolution,[],[f747,f99]) ).
fof(f99,plain,
relation(sK3),
inference(cnf_transformation,[],[f66]) ).
fof(f747,plain,
! [X0] :
( ~ relation(sK3)
| ~ in(sK13(relation_image(sK3,sK2),relation_rng(sK3)),relation_image(sK3,X0)) ),
inference(resolution,[],[f703,f120]) ).
fof(f120,plain,
! [X0] :
( sP1(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( sP1(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f46,f63,f62]) ).
fof(f62,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f63,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> sP0(X1,X0,X2) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f46,plain,
! [X0] :
( ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation_image(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f703,plain,
! [X0] :
( ~ sP1(sK3)
| ~ in(sK13(relation_image(sK3,sK2),relation_rng(sK3)),relation_image(sK3,X0)) ),
inference(resolution,[],[f700,f154]) ).
fof(f154,plain,
! [X0,X1] :
( sP0(X1,X0,relation_image(X0,X1))
| ~ sP1(X0) ),
inference(equality_resolution,[],[f112]) ).
fof(f112,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| relation_image(X0,X1) != X2
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_image(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| relation_image(X0,X1) != X2 ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f63]) ).
fof(f700,plain,
! [X0,X1] :
( ~ sP0(X1,sK3,X0)
| ~ in(sK13(relation_image(sK3,sK2),relation_rng(sK3)),X0) ),
inference(resolution,[],[f697,f114]) ).
fof(f114,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(sK10(X0,X1,X6),X6),X1)
| ~ in(X6,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X4,sK8(X0,X1,X2)),X1) )
| ~ in(sK8(X0,X1,X2),X2) )
& ( ( in(sK9(X0,X1,X2),X0)
& in(ordered_pair(sK9(X0,X1,X2),sK8(X0,X1,X2)),X1) )
| in(sK8(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X0)
| ~ in(ordered_pair(X7,X6),X1) ) )
& ( ( in(sK10(X0,X1,X6),X0)
& in(ordered_pair(sK10(X0,X1,X6),X6),X1) )
| ~ in(X6,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f77,f80,f79,f78]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X4,X3),X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X5,X3),X1) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X4,sK8(X0,X1,X2)),X1) )
| ~ in(sK8(X0,X1,X2),X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X5,sK8(X0,X1,X2)),X1) )
| in(sK8(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X5,sK8(X0,X1,X2)),X1) )
=> ( in(sK9(X0,X1,X2),X0)
& in(ordered_pair(sK9(X0,X1,X2),sK8(X0,X1,X2)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0,X1,X6] :
( ? [X8] :
( in(X8,X0)
& in(ordered_pair(X8,X6),X1) )
=> ( in(sK10(X0,X1,X6),X0)
& in(ordered_pair(sK10(X0,X1,X6),X6),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X0)
| ~ in(ordered_pair(X4,X3),X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,X0)
& in(ordered_pair(X5,X3),X1) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,X0)
| ~ in(ordered_pair(X7,X6),X1) ) )
& ( ? [X8] :
( in(X8,X0)
& in(ordered_pair(X8,X6),X1) )
| ~ in(X6,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f76]) ).
fof(f76,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0) ) )
& ( ? [X4] :
( in(X4,X1)
& in(ordered_pair(X4,X3),X0) )
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f697,plain,
! [X0] : ~ in(ordered_pair(X0,sK13(relation_image(sK3,sK2),relation_rng(sK3))),sK3),
inference(resolution,[],[f440,f99]) ).
fof(f440,plain,
! [X0] :
( ~ relation(sK3)
| ~ in(ordered_pair(X0,sK13(relation_image(sK3,sK2),relation_rng(sK3))),sK3) ),
inference(resolution,[],[f152,f227]) ).
fof(f227,plain,
~ in(sK13(relation_image(sK3,sK2),relation_rng(sK3)),relation_rng(sK3)),
inference(resolution,[],[f139,f100]) ).
fof(f139,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK13(X0,X1),X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f152,plain,
! [X0,X6,X5] :
( in(X5,relation_rng(X0))
| ~ in(ordered_pair(X6,X5),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f109]) ).
fof(f109,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK5(X0,X1)),X0)
| ~ in(sK5(X0,X1),X1) )
& ( in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0)
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK7(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f70,f73,f72,f71]) ).
fof(f71,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,sK5(X0,X1)),X0)
| ~ in(sK5(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK5(X0,X1)),X0)
| in(sK5(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK5(X0,X1)),X0)
=> in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK7(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(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) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(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) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,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) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU204+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 20:36:11 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (3331)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.36 % (3334)WARNING: value z3 for option sas not known
% 0.19/0.36 % (3334)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)
% 0.19/0.36 % (3336)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)
% 0.19/0.36 % (3338)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)
% 0.19/0.36 % (3337)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)
% 0.19/0.36 % (3335)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.36 % (3333)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.37 % (3332)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.37 TRYING [1]
% 0.19/0.37 TRYING [2]
% 0.19/0.37 TRYING [3]
% 0.19/0.38 TRYING [1]
% 0.19/0.38 TRYING [2]
% 0.19/0.38 % (3337)First to succeed.
% 0.19/0.39 % (3337)Refutation found. Thanks to Tanya!
% 0.19/0.39 % SZS status Theorem for theBenchmark
% 0.19/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.39 % (3337)------------------------------
% 0.19/0.39 % (3337)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.39 % (3337)Termination reason: Refutation
% 0.19/0.39
% 0.19/0.39 % (3337)Memory used [KB]: 1171
% 0.19/0.39 % (3337)Time elapsed: 0.022 s
% 0.19/0.39 % (3337)Instructions burned: 37 (million)
% 0.19/0.39 % (3337)------------------------------
% 0.19/0.39 % (3337)------------------------------
% 0.19/0.39 % (3331)Success in time 0.036 s
%------------------------------------------------------------------------------