TSTP Solution File: GEO118+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO118+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n008.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 11:14:07 EDT 2024
% Result : Theorem 0.12s 0.36s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 8 unt; 0 def)
% Number of atoms : 226 ( 11 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 271 ( 90 ~; 82 |; 79 &)
% ( 13 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 178 ( 157 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f450,plain,
$false,
inference(resolution,[],[f444,f166]) ).
fof(f166,plain,
ordered_by(sK5,sK6,sK7),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
( ordered_by(sK5,sK7,sK6)
& ordered_by(sK5,sK6,sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f57,f92]) ).
fof(f92,plain,
( ? [X0,X1,X2] :
( ordered_by(X0,X2,X1)
& ordered_by(X0,X1,X2) )
=> ( ordered_by(sK5,sK7,sK6)
& ordered_by(sK5,sK6,sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
? [X0,X1,X2] :
( ordered_by(X0,X2,X1)
& ordered_by(X0,X1,X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,plain,
~ ! [X0,X1,X2] :
( ordered_by(X0,X1,X2)
=> ~ ordered_by(X0,X2,X1) ),
inference(rectify,[],[f29]) ).
fof(f29,negated_conjecture,
~ ! [X8,X2,X4] :
( ordered_by(X8,X2,X4)
=> ~ ordered_by(X8,X4,X2) ),
inference(negated_conjecture,[],[f28]) ).
fof(f28,conjecture,
! [X8,X2,X4] :
( ordered_by(X8,X2,X4)
=> ~ ordered_by(X8,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_5) ).
fof(f444,plain,
~ ordered_by(sK5,sK6,sK7),
inference(resolution,[],[f440,f167]) ).
fof(f167,plain,
ordered_by(sK5,sK7,sK6),
inference(cnf_transformation,[],[f93]) ).
fof(f440,plain,
! [X2,X0,X1] :
( ~ ordered_by(X0,X1,X2)
| ~ ordered_by(X0,X2,X1) ),
inference(resolution,[],[f439,f244]) ).
fof(f244,plain,
! [X2,X3,X0,X1] :
( sP3(X0,X1,X2,X3)
| ~ ordered_by(X2,X1,X0)
| ~ ordered_by(X2,X3,X1) ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0,X1,X2,X3] :
( ( sP3(X0,X1,X2,X3)
| ( ( ~ ordered_by(X2,X1,X0)
| ~ ordered_by(X2,X3,X1) )
& ( ~ ordered_by(X2,X1,X3)
| ~ ordered_by(X2,X0,X1) ) ) )
& ( ( ordered_by(X2,X1,X0)
& ordered_by(X2,X3,X1) )
| ( ordered_by(X2,X1,X3)
& ordered_by(X2,X0,X1) )
| ~ sP3(X0,X1,X2,X3) ) ),
inference(rectify,[],[f157]) ).
fof(f157,plain,
! [X1,X2,X0,X3] :
( ( sP3(X1,X2,X0,X3)
| ( ( ~ ordered_by(X0,X2,X1)
| ~ ordered_by(X0,X3,X2) )
& ( ~ ordered_by(X0,X2,X3)
| ~ ordered_by(X0,X1,X2) ) ) )
& ( ( ordered_by(X0,X2,X1)
& ordered_by(X0,X3,X2) )
| ( ordered_by(X0,X2,X3)
& ordered_by(X0,X1,X2) )
| ~ sP3(X1,X2,X0,X3) ) ),
inference(flattening,[],[f156]) ).
fof(f156,plain,
! [X1,X2,X0,X3] :
( ( sP3(X1,X2,X0,X3)
| ( ( ~ ordered_by(X0,X2,X1)
| ~ ordered_by(X0,X3,X2) )
& ( ~ ordered_by(X0,X2,X3)
| ~ ordered_by(X0,X1,X2) ) ) )
& ( ( ordered_by(X0,X2,X1)
& ordered_by(X0,X3,X2) )
| ( ordered_by(X0,X2,X3)
& ordered_by(X0,X1,X2) )
| ~ sP3(X1,X2,X0,X3) ) ),
inference(nnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X1,X2,X0,X3] :
( sP3(X1,X2,X0,X3)
<=> ( ( ordered_by(X0,X2,X1)
& ordered_by(X0,X3,X2) )
| ( ordered_by(X0,X2,X3)
& ordered_by(X0,X1,X2) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f439,plain,
! [X2,X0,X1] : ~ sP3(X0,X1,X2,X0),
inference(resolution,[],[f437,f246]) ).
fof(f246,plain,
! [X2,X3,X0,X1] :
( between_o(X0,X1,X2,X3)
| ~ sP3(X1,X2,X0,X3) ),
inference(cnf_transformation,[],[f159]) ).
fof(f159,plain,
! [X0,X1,X2,X3] :
( ( between_o(X0,X1,X2,X3)
| ~ sP3(X1,X2,X0,X3) )
& ( sP3(X1,X2,X0,X3)
| ~ between_o(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2,X3] :
( between_o(X0,X1,X2,X3)
<=> sP3(X1,X2,X0,X3) ),
inference(definition_folding,[],[f53,f88]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( between_o(X0,X1,X2,X3)
<=> ( ( ordered_by(X0,X2,X1)
& ordered_by(X0,X3,X2) )
| ( ordered_by(X0,X2,X3)
& ordered_by(X0,X1,X2) ) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X8,X2,X4,X6] :
( between_o(X8,X2,X4,X6)
<=> ( ( ordered_by(X8,X4,X2)
& ordered_by(X8,X6,X4) )
| ( ordered_by(X8,X4,X6)
& ordered_by(X8,X2,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_o_defn) ).
fof(f437,plain,
! [X2,X0,X1] : ~ between_o(X0,X1,X2,X1),
inference(resolution,[],[f432,f252]) ).
fof(f252,plain,
! [X2,X3,X0,X1] :
( sP4(X2,X1,X0,X3)
| ~ between_o(X3,X0,X1,X2) ),
inference(cnf_transformation,[],[f165]) ).
fof(f165,plain,
! [X0,X1,X2,X3] :
( ( between_o(X3,X0,X1,X2)
| ~ sP4(X2,X1,X0,X3) )
& ( sP4(X2,X1,X0,X3)
| ~ between_o(X3,X0,X1,X2) ) ),
inference(nnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( between_o(X3,X0,X1,X2)
<=> sP4(X2,X1,X0,X3) ),
inference(definition_folding,[],[f54,f90]) ).
fof(f90,plain,
! [X2,X1,X0,X3] :
( sP4(X2,X1,X0,X3)
<=> ? [X4] :
( between_c(X4,X0,X1,X2)
& ! [X5] :
( incident_o(X5,X3)
<=> incident_c(X5,X4) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( between_o(X3,X0,X1,X2)
<=> ? [X4] :
( between_c(X4,X0,X1,X2)
& ! [X5] :
( incident_o(X5,X3)
<=> incident_c(X5,X4) ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X2,X4,X6,X8] :
( between_o(X8,X2,X4,X6)
<=> ? [X0] :
( between_c(X0,X2,X4,X6)
& ! [X2] :
( incident_o(X2,X8)
<=> incident_c(X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o3) ).
fof(f432,plain,
! [X2,X0,X1] : ~ sP4(X0,X1,X0,X2),
inference(resolution,[],[f249,f258]) ).
fof(f258,plain,
! [X2,X3,X0] : ~ between_c(X0,X3,X2,X3),
inference(equality_resolution,[],[f233]) ).
fof(f233,plain,
! [X2,X3,X0,X1] :
( X1 != X3
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0,X1,X2,X3] :
( ( between_c(X0,X1,X2,X3)
| ! [X4] :
( ~ inner_point(X2,X4)
| ~ end_point(X3,X4)
| ~ end_point(X1,X4)
| ~ part_of(X4,X0) )
| X1 = X3 )
& ( ( inner_point(X2,sK27(X0,X1,X2,X3))
& end_point(X3,sK27(X0,X1,X2,X3))
& end_point(X1,sK27(X0,X1,X2,X3))
& part_of(sK27(X0,X1,X2,X3),X0)
& X1 != X3 )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f153,f154]) ).
fof(f154,plain,
! [X0,X1,X2,X3] :
( ? [X5] :
( inner_point(X2,X5)
& end_point(X3,X5)
& end_point(X1,X5)
& part_of(X5,X0) )
=> ( inner_point(X2,sK27(X0,X1,X2,X3))
& end_point(X3,sK27(X0,X1,X2,X3))
& end_point(X1,sK27(X0,X1,X2,X3))
& part_of(sK27(X0,X1,X2,X3),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f153,plain,
! [X0,X1,X2,X3] :
( ( between_c(X0,X1,X2,X3)
| ! [X4] :
( ~ inner_point(X2,X4)
| ~ end_point(X3,X4)
| ~ end_point(X1,X4)
| ~ part_of(X4,X0) )
| X1 = X3 )
& ( ( ? [X5] :
( inner_point(X2,X5)
& end_point(X3,X5)
& end_point(X1,X5)
& part_of(X5,X0) )
& X1 != X3 )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(rectify,[],[f152]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( ( between_c(X0,X1,X2,X3)
| ! [X4] :
( ~ inner_point(X2,X4)
| ~ end_point(X3,X4)
| ~ end_point(X1,X4)
| ~ part_of(X4,X0) )
| X1 = X3 )
& ( ( ? [X4] :
( inner_point(X2,X4)
& end_point(X3,X4)
& end_point(X1,X4)
& part_of(X4,X0) )
& X1 != X3 )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(flattening,[],[f151]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( ( between_c(X0,X1,X2,X3)
| ! [X4] :
( ~ inner_point(X2,X4)
| ~ end_point(X3,X4)
| ~ end_point(X1,X4)
| ~ part_of(X4,X0) )
| X1 = X3 )
& ( ( ? [X4] :
( inner_point(X2,X4)
& end_point(X3,X4)
& end_point(X1,X4)
& part_of(X4,X0) )
& X1 != X3 )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( between_c(X0,X1,X2,X3)
<=> ( ? [X4] :
( inner_point(X2,X4)
& end_point(X3,X4)
& end_point(X1,X4)
& part_of(X4,X0) )
& X1 != X3 ) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X0,X2,X4,X6] :
( between_c(X0,X2,X4,X6)
<=> ( ? [X7] :
( inner_point(X4,X7)
& end_point(X6,X7)
& end_point(X2,X7)
& part_of(X7,X0) )
& X2 != X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn) ).
fof(f249,plain,
! [X2,X3,X0,X1] :
( between_c(sK29(X0,X1,X2,X3),X2,X1,X0)
| ~ sP4(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
! [X0,X1,X2,X3] :
( ( sP4(X0,X1,X2,X3)
| ! [X4] :
( ~ between_c(X4,X2,X1,X0)
| ( ( ~ incident_c(sK28(X3,X4),X4)
| ~ incident_o(sK28(X3,X4),X3) )
& ( incident_c(sK28(X3,X4),X4)
| incident_o(sK28(X3,X4),X3) ) ) ) )
& ( ( between_c(sK29(X0,X1,X2,X3),X2,X1,X0)
& ! [X7] :
( ( incident_o(X7,X3)
| ~ incident_c(X7,sK29(X0,X1,X2,X3)) )
& ( incident_c(X7,sK29(X0,X1,X2,X3))
| ~ incident_o(X7,X3) ) ) )
| ~ sP4(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f161,f163,f162]) ).
fof(f162,plain,
! [X3,X4] :
( ? [X5] :
( ( ~ incident_c(X5,X4)
| ~ incident_o(X5,X3) )
& ( incident_c(X5,X4)
| incident_o(X5,X3) ) )
=> ( ( ~ incident_c(sK28(X3,X4),X4)
| ~ incident_o(sK28(X3,X4),X3) )
& ( incident_c(sK28(X3,X4),X4)
| incident_o(sK28(X3,X4),X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f163,plain,
! [X0,X1,X2,X3] :
( ? [X6] :
( between_c(X6,X2,X1,X0)
& ! [X7] :
( ( incident_o(X7,X3)
| ~ incident_c(X7,X6) )
& ( incident_c(X7,X6)
| ~ incident_o(X7,X3) ) ) )
=> ( between_c(sK29(X0,X1,X2,X3),X2,X1,X0)
& ! [X7] :
( ( incident_o(X7,X3)
| ~ incident_c(X7,sK29(X0,X1,X2,X3)) )
& ( incident_c(X7,sK29(X0,X1,X2,X3))
| ~ incident_o(X7,X3) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f161,plain,
! [X0,X1,X2,X3] :
( ( sP4(X0,X1,X2,X3)
| ! [X4] :
( ~ between_c(X4,X2,X1,X0)
| ? [X5] :
( ( ~ incident_c(X5,X4)
| ~ incident_o(X5,X3) )
& ( incident_c(X5,X4)
| incident_o(X5,X3) ) ) ) )
& ( ? [X6] :
( between_c(X6,X2,X1,X0)
& ! [X7] :
( ( incident_o(X7,X3)
| ~ incident_c(X7,X6) )
& ( incident_c(X7,X6)
| ~ incident_o(X7,X3) ) ) )
| ~ sP4(X0,X1,X2,X3) ) ),
inference(rectify,[],[f160]) ).
fof(f160,plain,
! [X2,X1,X0,X3] :
( ( sP4(X2,X1,X0,X3)
| ! [X4] :
( ~ between_c(X4,X0,X1,X2)
| ? [X5] :
( ( ~ incident_c(X5,X4)
| ~ incident_o(X5,X3) )
& ( incident_c(X5,X4)
| incident_o(X5,X3) ) ) ) )
& ( ? [X4] :
( between_c(X4,X0,X1,X2)
& ! [X5] :
( ( incident_o(X5,X3)
| ~ incident_c(X5,X4) )
& ( incident_c(X5,X4)
| ~ incident_o(X5,X3) ) ) )
| ~ sP4(X2,X1,X0,X3) ) ),
inference(nnf_transformation,[],[f90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GEO118+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.32 % Computer : n008.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Apr 30 05:45:42 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % (9146)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.34 % (9149)WARNING: value z3 for option sas not known
% 0.12/0.34 % (9148)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.34 % (9151)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)
% 0.12/0.34 % (9149)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)
% 0.12/0.34 % (9150)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.34 % (9152)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)
% 0.12/0.34 % (9153)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)
% 0.12/0.35 % (9147)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.35 TRYING [1]
% 0.12/0.35 TRYING [2]
% 0.12/0.36 % (9152)First to succeed.
% 0.12/0.36 TRYING [3]
% 0.12/0.36 TRYING [1]
% 0.12/0.36 TRYING [2]
% 0.12/0.36 % (9152)Refutation found. Thanks to Tanya!
% 0.12/0.36 % SZS status Theorem for theBenchmark
% 0.12/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.36 % (9152)------------------------------
% 0.12/0.36 % (9152)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.12/0.36 % (9152)Termination reason: Refutation
% 0.12/0.36
% 0.12/0.36 % (9152)Memory used [KB]: 1175
% 0.12/0.36 % (9152)Time elapsed: 0.014 s
% 0.12/0.36 % (9152)Instructions burned: 22 (million)
% 0.12/0.36 % (9152)------------------------------
% 0.12/0.36 % (9152)------------------------------
% 0.12/0.36 % (9146)Success in time 0.03 s
%------------------------------------------------------------------------------