TSTP Solution File: GEO084+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO084+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 : Tue Apr 30 11:14:00 EDT 2024
% Result : Theorem 0.24s 0.43s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 10 unt; 0 def)
% Number of atoms : 161 ( 6 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 180 ( 61 ~; 55 |; 47 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 111 ( 93 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1254,plain,
$false,
inference(unit_resulting_resolution,[],[f655,f211,f159,f147]) ).
fof(f147,plain,
! [X2,X0,X1,X4] :
( ~ sP3(X0,X1,X2)
| ~ incident_c(X4,X2)
| sP2(X1,X4,X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ( ( ~ sP2(X1,sK20(X0,X1,X2),X0)
| ~ incident_c(sK20(X0,X1,X2),X2) )
& ( sP2(X1,sK20(X0,X1,X2),X0)
| incident_c(sK20(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( incident_c(X4,X2)
| ~ sP2(X1,X4,X0) )
& ( sP2(X1,X4,X0)
| ~ incident_c(X4,X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f100,f101]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ sP2(X1,X3,X0)
| ~ incident_c(X3,X2) )
& ( sP2(X1,X3,X0)
| incident_c(X3,X2) ) )
=> ( ( ~ sP2(X1,sK20(X0,X1,X2),X0)
| ~ incident_c(sK20(X0,X1,X2),X2) )
& ( sP2(X1,sK20(X0,X1,X2),X0)
| incident_c(sK20(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ? [X3] :
( ( ~ sP2(X1,X3,X0)
| ~ incident_c(X3,X2) )
& ( sP2(X1,X3,X0)
| incident_c(X3,X2) ) ) )
& ( ! [X4] :
( ( incident_c(X4,X2)
| ~ sP2(X1,X4,X0) )
& ( sP2(X1,X4,X0)
| ~ incident_c(X4,X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(rectify,[],[f99]) ).
fof(f99,plain,
! [X1,X2,X0] :
( ( sP3(X1,X2,X0)
| ? [X3] :
( ( ~ sP2(X2,X3,X1)
| ~ incident_c(X3,X0) )
& ( sP2(X2,X3,X1)
| incident_c(X3,X0) ) ) )
& ( ! [X3] :
( ( incident_c(X3,X0)
| ~ sP2(X2,X3,X1) )
& ( sP2(X2,X3,X1)
| ~ incident_c(X3,X0) ) )
| ~ sP3(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X1,X2,X0] :
( sP3(X1,X2,X0)
<=> ! [X3] :
( incident_c(X3,X0)
<=> sP2(X2,X3,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f159,plain,
! [X2,X1] : sP3(X1,X2,sum(X1,X2)),
inference(equality_resolution,[],[f154]) ).
fof(f154,plain,
! [X2,X0,X1] :
( sP3(X1,X2,X0)
| sum(X1,X2) != X0 ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) = X0
| ~ sP3(X1,X2,X0) )
& ( sP3(X1,X2,X0)
| sum(X1,X2) != X0 ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2] :
( sum(X1,X2) = X0
<=> sP3(X1,X2,X0) ),
inference(definition_folding,[],[f29,f61,f60]) ).
fof(f60,plain,
! [X2,X3,X1] :
( sP2(X2,X3,X1)
<=> ( 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/sandbox/benchmark/theBenchmark.p',sum_defn) ).
fof(f211,plain,
incident_c(sK18(sK6,sum(sK4,sK5)),sum(sK4,sK5)),
inference(unit_resulting_resolution,[],[f110,f136]) ).
fof(f136,plain,
! [X0,X1] :
( incident_c(sK18(X0,X1),X1)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ( ~ incident_c(sK18(X0,X1),X0)
& incident_c(sK18(X0,X1),X1) ) )
& ( ! [X3] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1) )
| ~ part_of(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f90,f91]) ).
fof(f91,plain,
! [X0,X1] :
( ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) )
=> ( ~ incident_c(sK18(X0,X1),X0)
& incident_c(sK18(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f90,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,[],[f89]) ).
fof(f89,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/sandbox/benchmark/theBenchmark.p',part_of_defn) ).
fof(f110,plain,
~ part_of(sum(sK4,sK5),sK6),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
( ~ part_of(sum(sK4,sK5),sK6)
& meet(sK7,sK4,sK5)
& part_of(sK5,sK6)
& part_of(sK4,sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f36,f63]) ).
fof(f63,plain,
( ? [X0,X1,X2,X3] :
( ~ part_of(sum(X0,X1),X2)
& meet(X3,X0,X1)
& part_of(X1,X2)
& part_of(X0,X2) )
=> ( ~ part_of(sum(sK4,sK5),sK6)
& meet(sK7,sK4,sK5)
& part_of(sK5,sK6)
& part_of(sK4,sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
? [X0,X1,X2,X3] :
( ~ part_of(sum(X0,X1),X2)
& meet(X3,X0,X1)
& part_of(X1,X2)
& part_of(X0,X2) ),
inference(flattening,[],[f35]) ).
fof(f35,plain,
? [X0,X1,X2,X3] :
( ~ part_of(sum(X0,X1),X2)
& meet(X3,X0,X1)
& part_of(X1,X2)
& part_of(X0,X2) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X0,X1,X2,X3] :
( ( meet(X3,X0,X1)
& part_of(X1,X2)
& part_of(X0,X2) )
=> part_of(sum(X0,X1),X2) ),
inference(rectify,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X1,X3,X5,X2] :
( ( meet(X2,X1,X3)
& part_of(X3,X5)
& part_of(X1,X5) )
=> part_of(sum(X1,X3),X5) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X1,X3,X5,X2] :
( ( meet(X2,X1,X3)
& part_of(X3,X5)
& part_of(X1,X5) )
=> part_of(sum(X1,X3),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_6_2) ).
fof(f655,plain,
~ sP2(sK5,sK18(sK6,sum(sK4,sK5)),sK4),
inference(unit_resulting_resolution,[],[f294,f293,f151]) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| incident_c(X1,X2)
| incident_c(X1,X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ~ incident_c(X1,X0)
& ~ incident_c(X1,X2) ) )
& ( incident_c(X1,X0)
| incident_c(X1,X2)
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f104]) ).
fof(f104,plain,
! [X2,X3,X1] :
( ( sP2(X2,X3,X1)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| ~ sP2(X2,X3,X1) ) ),
inference(flattening,[],[f103]) ).
fof(f103,plain,
! [X2,X3,X1] :
( ( sP2(X2,X3,X1)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| ~ sP2(X2,X3,X1) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f293,plain,
~ incident_c(sK18(sK6,sum(sK4,sK5)),sK4),
inference(unit_resulting_resolution,[],[f107,f214,f135]) ).
fof(f135,plain,
! [X3,X0,X1] :
( ~ incident_c(X3,X1)
| incident_c(X3,X0)
| ~ part_of(X1,X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f214,plain,
~ incident_c(sK18(sK6,sum(sK4,sK5)),sK6),
inference(unit_resulting_resolution,[],[f110,f137]) ).
fof(f137,plain,
! [X0,X1] :
( ~ incident_c(sK18(X0,X1),X0)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f107,plain,
part_of(sK4,sK6),
inference(cnf_transformation,[],[f64]) ).
fof(f294,plain,
~ incident_c(sK18(sK6,sum(sK4,sK5)),sK5),
inference(unit_resulting_resolution,[],[f108,f214,f135]) ).
fof(f108,plain,
part_of(sK5,sK6),
inference(cnf_transformation,[],[f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GEO084+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.38 % Computer : n029.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Tue Apr 30 06:04:50 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.16/0.38 % (24695)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.40 % (24698)WARNING: value z3 for option sas not known
% 0.24/0.40 % (24698)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)
% 0.24/0.40 % (24697)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.24/0.40 % (24699)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.24/0.40 % (24700)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)
% 0.24/0.40 % (24701)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)
% 0.24/0.40 % (24702)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)
% 0.24/0.40 TRYING [1]
% 0.24/0.40 TRYING [2]
% 0.24/0.40 % (24696)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.24/0.41 TRYING [3]
% 0.24/0.42 TRYING [4]
% 0.24/0.42 TRYING [1]
% 0.24/0.42 TRYING [2]
% 0.24/0.43 % (24702)First to succeed.
% 0.24/0.43 % (24702)Refutation found. Thanks to Tanya!
% 0.24/0.43 % SZS status Theorem for theBenchmark
% 0.24/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.43 % (24702)------------------------------
% 0.24/0.43 % (24702)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.24/0.43 % (24702)Termination reason: Refutation
% 0.24/0.43
% 0.24/0.43 % (24702)Memory used [KB]: 1298
% 0.24/0.43 % (24702)Time elapsed: 0.028 s
% 0.24/0.43 % (24702)Instructions burned: 48 (million)
% 0.24/0.43 % (24702)------------------------------
% 0.24/0.43 % (24702)------------------------------
% 0.24/0.43 % (24695)Success in time 0.043 s
%------------------------------------------------------------------------------