TSTP Solution File: SET800+4 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET800+4 : 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 : n006.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 15:13:14 EDT 2024
% Result : Theorem 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 10 unt; 0 def)
% Number of atoms : 198 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 206 ( 56 ~; 40 |; 82 &)
% ( 7 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 149 ( 113 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f426,plain,
$false,
inference(subsumption_resolution,[],[f423,f137]) ).
fof(f137,plain,
! [X0] : subset(X0,X0),
inference(duplicate_literal_removal,[],[f135]) ).
fof(f135,plain,
! [X0] :
( subset(X0,X0)
| subset(X0,X0) ),
inference(resolution,[],[f98,f97]) ).
fof(f97,plain,
! [X0,X1] :
( member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK6(X0,X1),X1)
& member(sK6(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f60,f61]) ).
fof(f61,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK6(X0,X1),X1)
& member(sK6(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f98,plain,
! [X0,X1] :
( ~ member(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f423,plain,
~ subset(sK3,sK3),
inference(resolution,[],[f422,f184]) ).
fof(f184,plain,
! [X0] :
( member(sK4,X0)
| ~ subset(sK3,X0) ),
inference(resolution,[],[f155,f88]) ).
fof(f88,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
( ~ apply(sK0,sK5,sK4)
& greatest_lower_bound(sK5,sK3,sK0,sK1)
& greatest_lower_bound(sK4,sK2,sK0,sK1)
& subset(sK2,sK3)
& subset(sK3,sK1)
& subset(sK2,sK1)
& order(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f47,f57,f56,f55]) ).
fof(f55,plain,
( ? [X0,X1] :
( ? [X2,X3] :
( ? [X4,X5] :
( ~ apply(X0,X5,X4)
& greatest_lower_bound(X5,X3,X0,X1)
& greatest_lower_bound(X4,X2,X0,X1) )
& subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
& order(X0,X1) )
=> ( ? [X3,X2] :
( ? [X5,X4] :
( ~ apply(sK0,X5,X4)
& greatest_lower_bound(X5,X3,sK0,sK1)
& greatest_lower_bound(X4,X2,sK0,sK1) )
& subset(X2,X3)
& subset(X3,sK1)
& subset(X2,sK1) )
& order(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
( ? [X3,X2] :
( ? [X5,X4] :
( ~ apply(sK0,X5,X4)
& greatest_lower_bound(X5,X3,sK0,sK1)
& greatest_lower_bound(X4,X2,sK0,sK1) )
& subset(X2,X3)
& subset(X3,sK1)
& subset(X2,sK1) )
=> ( ? [X5,X4] :
( ~ apply(sK0,X5,X4)
& greatest_lower_bound(X5,sK3,sK0,sK1)
& greatest_lower_bound(X4,sK2,sK0,sK1) )
& subset(sK2,sK3)
& subset(sK3,sK1)
& subset(sK2,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
( ? [X5,X4] :
( ~ apply(sK0,X5,X4)
& greatest_lower_bound(X5,sK3,sK0,sK1)
& greatest_lower_bound(X4,sK2,sK0,sK1) )
=> ( ~ apply(sK0,sK5,sK4)
& greatest_lower_bound(sK5,sK3,sK0,sK1)
& greatest_lower_bound(sK4,sK2,sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4,X5] :
( ~ apply(X0,X5,X4)
& greatest_lower_bound(X5,X3,X0,X1)
& greatest_lower_bound(X4,X2,X0,X1) )
& subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
& order(X0,X1) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4,X5] :
( ~ apply(X0,X5,X4)
& greatest_lower_bound(X5,X3,X0,X1)
& greatest_lower_bound(X4,X2,X0,X1) )
& subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
& order(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( subset(X2,X3)
& subset(X3,X1)
& subset(X2,X1) )
=> ! [X4,X5] :
( ( greatest_lower_bound(X5,X3,X0,X1)
& greatest_lower_bound(X4,X2,X0,X1) )
=> apply(X0,X5,X4) ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,negated_conjecture,
~ ! [X5,X3] :
( order(X5,X3)
=> ! [X8,X9] :
( ( subset(X8,X9)
& subset(X9,X3)
& subset(X8,X3) )
=> ! [X10,X11] :
( ( greatest_lower_bound(X11,X9,X5,X3)
& greatest_lower_bound(X10,X8,X5,X3) )
=> apply(X5,X11,X10) ) ) ),
inference(negated_conjecture,[],[f22]) ).
fof(f22,conjecture,
! [X5,X3] :
( order(X5,X3)
=> ! [X8,X9] :
( ( subset(X8,X9)
& subset(X9,X3)
& subset(X8,X3) )
=> ! [X10,X11] :
( ( greatest_lower_bound(X11,X9,X5,X3)
& greatest_lower_bound(X10,X8,X5,X3) )
=> apply(X5,X11,X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV12) ).
fof(f155,plain,
! [X0,X1] :
( ~ subset(sK2,X0)
| member(sK4,X1)
| ~ subset(X0,X1) ),
inference(resolution,[],[f153,f96]) ).
fof(f96,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f153,plain,
! [X0] :
( member(sK4,X0)
| ~ subset(sK2,X0) ),
inference(resolution,[],[f144,f96]) ).
fof(f144,plain,
member(sK4,sK2),
inference(resolution,[],[f124,f89]) ).
fof(f89,plain,
greatest_lower_bound(sK4,sK2,sK0,sK1),
inference(cnf_transformation,[],[f58]) ).
fof(f124,plain,
! [X2,X3,X0,X1] :
( ~ greatest_lower_bound(X0,X1,X2,X3)
| member(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( ( ! [X4] :
( apply(X2,X4,X0)
| ~ lower_bound(X4,X2,X1)
| ~ member(X4,X3) )
& lower_bound(X0,X2,X1)
& member(X0,X1) )
| ~ greatest_lower_bound(X0,X1,X2,X3) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( ( ! [X4] :
( apply(X2,X4,X0)
| ~ lower_bound(X4,X2,X1)
| ~ member(X4,X3) )
& lower_bound(X0,X2,X1)
& member(X0,X1) )
| ~ greatest_lower_bound(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( greatest_lower_bound(X0,X1,X2,X3)
=> ( ! [X4] :
( ( lower_bound(X4,X2,X1)
& member(X4,X3) )
=> apply(X2,X4,X0) )
& lower_bound(X0,X2,X1)
& member(X0,X1) ) ),
inference(unused_predicate_definition_removal,[],[f43]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( greatest_lower_bound(X0,X1,X2,X3)
<=> ( ! [X4] :
( ( lower_bound(X4,X2,X1)
& member(X4,X3) )
=> apply(X2,X4,X0) )
& lower_bound(X0,X2,X1)
& member(X0,X1) ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X0,X2,X5,X3] :
( greatest_lower_bound(X0,X2,X5,X3)
<=> ( ! [X7] :
( ( lower_bound(X7,X5,X2)
& member(X7,X3) )
=> apply(X5,X7,X0) )
& lower_bound(X0,X5,X2)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greatest_lower_bound) ).
fof(f422,plain,
~ member(sK4,sK3),
inference(resolution,[],[f417,f91]) ).
fof(f91,plain,
~ apply(sK0,sK5,sK4),
inference(cnf_transformation,[],[f58]) ).
fof(f417,plain,
! [X0] :
( apply(sK0,sK5,X0)
| ~ member(X0,sK3) ),
inference(resolution,[],[f109,f246]) ).
fof(f246,plain,
lower_bound(sK5,sK0,sK3),
inference(resolution,[],[f125,f90]) ).
fof(f90,plain,
greatest_lower_bound(sK5,sK3,sK0,sK1),
inference(cnf_transformation,[],[f58]) ).
fof(f125,plain,
! [X2,X3,X0,X1] :
( ~ greatest_lower_bound(X0,X1,X2,X3)
| lower_bound(X0,X2,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f109,plain,
! [X2,X0,X1,X4] :
( ~ lower_bound(X2,X0,X1)
| ~ member(X4,X1)
| apply(X0,X2,X4) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ( lower_bound(X2,X0,X1)
| ( ~ apply(X0,X2,sK9(X0,X1,X2))
& member(sK9(X0,X1,X2),X1) ) )
& ( ! [X4] :
( apply(X0,X2,X4)
| ~ member(X4,X1) )
| ~ lower_bound(X2,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f74,f75]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ apply(X0,X2,X3)
& member(X3,X1) )
=> ( ~ apply(X0,X2,sK9(X0,X1,X2))
& member(sK9(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( lower_bound(X2,X0,X1)
| ? [X3] :
( ~ apply(X0,X2,X3)
& member(X3,X1) ) )
& ( ! [X4] :
( apply(X0,X2,X4)
| ~ member(X4,X1) )
| ~ lower_bound(X2,X0,X1) ) ),
inference(rectify,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( lower_bound(X2,X0,X1)
| ? [X3] :
( ~ apply(X0,X2,X3)
& member(X3,X1) ) )
& ( ! [X3] :
( apply(X0,X2,X3)
| ~ member(X3,X1) )
| ~ lower_bound(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2] :
( lower_bound(X2,X0,X1)
<=> ! [X3] :
( apply(X0,X2,X3)
| ~ member(X3,X1) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( lower_bound(X2,X0,X1)
<=> ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X5,X3,X7] :
( lower_bound(X7,X5,X3)
<=> ! [X2] :
( member(X2,X3)
=> apply(X5,X7,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_bound) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET800+4 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n006.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 : Tue Apr 30 01:04:50 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (6028)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (6031)WARNING: value z3 for option sas not known
% 0.15/0.38 % (6029)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (6030)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 % (6032)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (6033)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 % (6034)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 % (6031)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 % (6035)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)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [4]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 % (6031)First to succeed.
% 0.15/0.40 % (6034)Also succeeded, but the first one will report.
% 0.15/0.40 % (6031)Refutation found. Thanks to Tanya!
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40 % (6031)------------------------------
% 0.15/0.40 % (6031)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.40 % (6031)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (6031)Memory used [KB]: 979
% 0.15/0.40 % (6031)Time elapsed: 0.015 s
% 0.15/0.40 % (6031)Instructions burned: 20 (million)
% 0.15/0.40 % (6031)------------------------------
% 0.15/0.40 % (6031)------------------------------
% 0.15/0.40 % (6028)Success in time 0.032 s
%------------------------------------------------------------------------------