TSTP Solution File: GEO083+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO083+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 : n029.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 05:15:24 EDT 2024
% Result : Theorem 3.51s 0.91s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 9 unt; 0 def)
% Number of atoms : 188 ( 6 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 218 ( 75 ~; 73 |; 54 &)
% ( 9 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 122 ( 103 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6576,plain,
$false,
inference(resolution,[],[f6566,f107]) ).
fof(f107,plain,
~ part_of(sum(sK3,sK4),sum(sK3,sK5)),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
( ~ part_of(sum(sK3,sK4),sum(sK3,sK5))
& meet(sK6,sK3,sK5)
& meet(sK6,sK3,sK4)
& part_of(sK4,sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f36,f62]) ).
fof(f62,plain,
( ? [X0,X1,X2,X3] :
( ~ part_of(sum(X0,X1),sum(X0,X2))
& meet(X3,X0,X2)
& meet(X3,X0,X1)
& part_of(X1,X2) )
=> ( ~ part_of(sum(sK3,sK4),sum(sK3,sK5))
& meet(sK6,sK3,sK5)
& meet(sK6,sK3,sK4)
& part_of(sK4,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
? [X0,X1,X2,X3] :
( ~ part_of(sum(X0,X1),sum(X0,X2))
& meet(X3,X0,X2)
& meet(X3,X0,X1)
& part_of(X1,X2) ),
inference(flattening,[],[f35]) ).
fof(f35,plain,
? [X0,X1,X2,X3] :
( ~ part_of(sum(X0,X1),sum(X0,X2))
& meet(X3,X0,X2)
& meet(X3,X0,X1)
& part_of(X1,X2) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X0,X1,X2,X3] :
( ( meet(X3,X0,X2)
& meet(X3,X0,X1)
& part_of(X1,X2) )
=> part_of(sum(X0,X1),sum(X0,X2)) ),
inference(rectify,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X1,X3,X5,X2] :
( ( meet(X2,X1,X5)
& meet(X2,X1,X3)
& part_of(X3,X5) )
=> part_of(sum(X1,X3),sum(X1,X5)) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X1,X3,X5,X2] :
( ( meet(X2,X1,X5)
& meet(X2,X1,X3)
& part_of(X3,X5) )
=> part_of(sum(X1,X3),sum(X1,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_6_1) ).
fof(f6566,plain,
part_of(sum(sK3,sK4),sum(sK3,sK5)),
inference(resolution,[],[f5133,f182]) ).
fof(f182,plain,
~ incident_c(sK17(sum(sK3,sK5),sum(sK3,sK4)),sK3),
inference(resolution,[],[f181,f158]) ).
fof(f158,plain,
~ incident_c(sK17(sum(sK3,sK5),sum(sK3,sK4)),sum(sK3,sK5)),
inference(resolution,[],[f134,f107]) ).
fof(f134,plain,
! [X0,X1] :
( part_of(X1,X0)
| ~ incident_c(sK17(X0,X1),X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ( ~ incident_c(sK17(X0,X1),X0)
& incident_c(sK17(X0,X1),X1) ) )
& ( ! [X3] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1) )
| ~ part_of(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f89,f90]) ).
fof(f90,plain,
! [X0,X1] :
( ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) )
=> ( ~ incident_c(sK17(X0,X1),X0)
& incident_c(sK17(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) ) )
& ( ! [X3] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1) )
| ~ part_of(X1,X0) ) ),
inference(rectify,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) ) )
& ( ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) )
| ~ part_of(X1,X0) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X1)
=> incident_c(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_defn) ).
fof(f181,plain,
! [X2,X0,X1] :
( incident_c(X0,sum(X1,X2))
| ~ incident_c(X0,X1) ),
inference(resolution,[],[f145,f155]) ).
fof(f155,plain,
! [X2,X1] : sP2(X2,X1,sum(X1,X2)),
inference(equality_resolution,[],[f150]) ).
fof(f150,plain,
! [X2,X0,X1] :
( sP2(X2,X1,X0)
| sum(X1,X2) != X0 ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) = X0
| ~ sP2(X2,X1,X0) )
& ( sP2(X2,X1,X0)
| sum(X1,X2) != X0 ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2] :
( sum(X1,X2) = X0
<=> sP2(X2,X1,X0) ),
inference(definition_folding,[],[f29,f60]) ).
fof(f60,plain,
! [X2,X1,X0] :
( sP2(X2,X1,X0)
<=> ! [X3] :
( incident_c(X3,X0)
<=> ( incident_c(X3,X2)
| incident_c(X3,X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f29,plain,
! [X0,X1,X2] :
( sum(X1,X2) = X0
<=> ! [X3] :
( incident_c(X3,X0)
<=> ( incident_c(X3,X2)
| incident_c(X3,X1) ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X3] :
( sum(X1,X3) = X0
<=> ! [X4] :
( incident_c(X4,X0)
<=> ( incident_c(X4,X3)
| incident_c(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_defn) ).
fof(f145,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ incident_c(X4,X1)
| incident_c(X4,X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ( ( ~ incident_c(sK19(X0,X1,X2),X0)
& ~ incident_c(sK19(X0,X1,X2),X1) )
| ~ incident_c(sK19(X0,X1,X2),X2) )
& ( incident_c(sK19(X0,X1,X2),X0)
| incident_c(sK19(X0,X1,X2),X1)
| incident_c(sK19(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( incident_c(X4,X2)
| ( ~ incident_c(X4,X0)
& ~ incident_c(X4,X1) ) )
& ( incident_c(X4,X0)
| incident_c(X4,X1)
| ~ incident_c(X4,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f100,f101]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ incident_c(X3,X0)
& ~ incident_c(X3,X1) )
| ~ incident_c(X3,X2) )
& ( incident_c(X3,X0)
| incident_c(X3,X1)
| incident_c(X3,X2) ) )
=> ( ( ( ~ incident_c(sK19(X0,X1,X2),X0)
& ~ incident_c(sK19(X0,X1,X2),X1) )
| ~ incident_c(sK19(X0,X1,X2),X2) )
& ( incident_c(sK19(X0,X1,X2),X0)
| incident_c(sK19(X0,X1,X2),X1)
| incident_c(sK19(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3] :
( ( ( ~ incident_c(X3,X0)
& ~ incident_c(X3,X1) )
| ~ incident_c(X3,X2) )
& ( incident_c(X3,X0)
| incident_c(X3,X1)
| incident_c(X3,X2) ) ) )
& ( ! [X4] :
( ( incident_c(X4,X2)
| ( ~ incident_c(X4,X0)
& ~ incident_c(X4,X1) ) )
& ( incident_c(X4,X0)
| incident_c(X4,X1)
| ~ incident_c(X4,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f99]) ).
fof(f99,plain,
! [X2,X1,X0] :
( ( sP2(X2,X1,X0)
| ? [X3] :
( ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| incident_c(X3,X0) ) ) )
& ( ! [X3] :
( ( incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| ~ incident_c(X3,X0) ) )
| ~ sP2(X2,X1,X0) ) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
! [X2,X1,X0] :
( ( sP2(X2,X1,X0)
| ? [X3] :
( ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| incident_c(X3,X0) ) ) )
& ( ! [X3] :
( ( incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| ~ incident_c(X3,X0) ) )
| ~ sP2(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f5133,plain,
( incident_c(sK17(sum(sK3,sK5),sum(sK3,sK4)),sK3)
| part_of(sum(sK3,sK4),sum(sK3,sK5)) ),
inference(resolution,[],[f788,f199]) ).
fof(f199,plain,
~ incident_c(sK17(sum(sK3,sK5),sum(sK3,sK4)),sK4),
inference(resolution,[],[f193,f104]) ).
fof(f104,plain,
part_of(sK4,sK5),
inference(cnf_transformation,[],[f63]) ).
fof(f193,plain,
! [X0] :
( ~ part_of(X0,sK5)
| ~ incident_c(sK17(sum(sK3,sK5),sum(sK3,sK4)),X0) ),
inference(resolution,[],[f192,f132]) ).
fof(f132,plain,
! [X3,X0,X1] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1)
| ~ part_of(X1,X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f192,plain,
~ incident_c(sK17(sum(sK3,sK5),sum(sK3,sK4)),sK5),
inference(resolution,[],[f187,f158]) ).
fof(f187,plain,
! [X2,X0,X1] :
( incident_c(X0,sum(X2,X1))
| ~ incident_c(X0,X1) ),
inference(resolution,[],[f146,f155]) ).
fof(f146,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ incident_c(X4,X0)
| incident_c(X4,X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f788,plain,
! [X2,X0,X1] :
( incident_c(sK17(X0,sum(X1,X2)),X2)
| incident_c(sK17(X0,sum(X1,X2)),X1)
| part_of(sum(X1,X2),X0) ),
inference(resolution,[],[f367,f133]) ).
fof(f133,plain,
! [X0,X1] :
( incident_c(sK17(X0,X1),X1)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f367,plain,
! [X2,X0,X1] :
( ~ incident_c(X0,sum(X1,X2))
| incident_c(X0,X1)
| incident_c(X0,X2) ),
inference(resolution,[],[f144,f155]) ).
fof(f144,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| incident_c(X4,X1)
| ~ incident_c(X4,X2)
| incident_c(X4,X0) ),
inference(cnf_transformation,[],[f102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO083+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n029.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 22:07:08 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (31780)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (31786)WARNING: value z3 for option sas not known
% 0.15/0.38 % (31784)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 % (31783)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (31787)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (31786)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 % (31789)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 % (31790)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 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.22/0.39 % (31788)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)
% 0.22/0.39 TRYING [3]
% 0.22/0.40 TRYING [1]
% 0.22/0.40 TRYING [2]
% 0.22/0.40 TRYING [4]
% 0.22/0.42 TRYING [3]
% 0.22/0.43 TRYING [5]
% 0.22/0.49 TRYING [6]
% 0.22/0.51 TRYING [4]
% 1.40/0.57 TRYING [7]
% 2.04/0.63 TRYING [5]
% 2.39/0.72 TRYING [8]
% 3.27/0.84 TRYING [1]
% 3.27/0.84 TRYING [2]
% 3.51/0.84 TRYING [3]
% 3.51/0.85 TRYING [4]
% 3.51/0.87 TRYING [5]
% 3.51/0.90 TRYING [6]
% 3.51/0.91 % (31789)First to succeed.
% 3.51/0.91 % (31789)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-31780"
% 3.51/0.91 % (31789)Refutation found. Thanks to Tanya!
% 3.51/0.91 % SZS status Theorem for theBenchmark
% 3.51/0.91 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/0.91 % (31789)------------------------------
% 3.51/0.91 % (31789)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 3.51/0.91 % (31789)Termination reason: Refutation
% 3.51/0.91
% 3.51/0.91 % (31789)Memory used [KB]: 5834
% 3.51/0.91 % (31789)Time elapsed: 0.529 s
% 3.51/0.91 % (31789)Instructions burned: 1777 (million)
% 3.51/0.91 % (31780)Success in time 0.536 s
%------------------------------------------------------------------------------