%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO093+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:53:33 AM UTC 2026
% Result : Theorem 0.07s 0.36s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 10 unt; 2 def)
% Number of atoms : 129 ( 20 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 120 ( 46 ~; 49 |; 15 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 74 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X1)
=> incident_c(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',part_of_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( X0 = sum(X1,X2)
<=> ! [X3] :
( incident_c(X3,X0)
<=> ( incident_c(X3,X1)
| incident_c(X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',sum_defn) ).
fof(f8,axiom,
! [X0,X1] :
( ( part_of(X1,X0)
& X1 != X0 )
=> open(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',c1) ).
fof(f17,conjecture,
! [X0,X1,X2,X3] :
( ( open(X0)
& part_of(X1,X0)
& part_of(X2,X0)
& meet(X3,X1,X2) )
=> open(sum(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',proposition_2_14_2) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( open(X0)
& part_of(X1,X0)
& part_of(X2,X0)
& meet(X3,X1,X2) )
=> open(sum(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0,X1] :
( open(X1)
| ~ part_of(X1,X0)
| X0 = X1 ),
inference(ennf_transformation,[],[f8]) ).
fof(f27,plain,
! [X0,X1] :
( open(X1)
| ~ part_of(X1,X0)
| X0 = X1 ),
inference(flattening,[],[f26]) ).
fof(f38,plain,
? [X0,X1,X2,X3] :
( ~ open(sum(X1,X2))
& open(X0)
& part_of(X1,X0)
& part_of(X2,X0)
& meet(X3,X1,X2) ),
inference(ennf_transformation,[],[f18]) ).
fof(f39,plain,
? [X0,X1,X2,X3] :
( ~ open(sum(X1,X2))
& open(X0)
& part_of(X1,X0)
& part_of(X2,X0)
& meet(X3,X1,X2) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ part_of(X1,X0)
| incident_c(X2,X0)
| ~ incident_c(X2,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f41,plain,
! [X0,X1] :
( part_of(X1,X0)
| incident_c(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f42,plain,
! [X0,X1] :
( part_of(X1,X0)
| ~ incident_c(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( incident_c(X3,X2)
| incident_c(X3,X1)
| ~ incident_c(X3,X0)
| sum(X1,X2) != X0 ),
inference(cnf_transformation,[],[f2]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( ~ incident_c(X3,X2)
| incident_c(X3,X0)
| sum(X1,X2) != X0 ),
inference(cnf_transformation,[],[f2]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( ~ incident_c(X3,X1)
| incident_c(X3,X0)
| sum(X1,X2) != X0 ),
inference(cnf_transformation,[],[f2]) ).
fof(f70,plain,
! [X0,X1] :
( open(X1)
| ~ part_of(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f83,plain,
part_of(sK15,sK13),
inference(cnf_transformation,[],[f39]) ).
fof(f84,plain,
part_of(sK14,sK13),
inference(cnf_transformation,[],[f39]) ).
fof(f85,plain,
open(sK13),
inference(cnf_transformation,[],[f39]) ).
fof(f86,plain,
~ open(sum(sK14,sK15)),
inference(cnf_transformation,[],[f39]) ).
fof(f87,plain,
! [X2,X3,X1] :
( incident_c(X3,sum(X1,X2))
| ~ incident_c(X3,X1) ),
inference(equality_resolution,[],[f48]) ).
fof(f88,plain,
! [X2,X3,X1] :
( incident_c(X3,sum(X1,X2))
| ~ incident_c(X3,X2) ),
inference(equality_resolution,[],[f47]) ).
fof(f89,plain,
! [X2,X3,X1] :
( ~ incident_c(X3,sum(X1,X2))
| incident_c(X3,X1)
| incident_c(X3,X2) ),
inference(equality_resolution,[],[f46]) ).
fof(f99,plain,
! [X0] :
( ~ part_of(sum(sK14,sK15),X0)
| sum(sK14,sK15) = X0 ),
inference(resolution,[],[f70,f86]) ).
fof(f101,plain,
! [X0] :
( ~ incident_c(sK0(X0,sum(sK14,sK15)),X0)
| sum(sK14,sK15) = X0 ),
inference(resolution,[],[f99,f42]) ).
fof(f102,plain,
! [X0] :
( incident_c(sK0(X0,sum(sK14,sK15)),sum(sK14,sK15))
| sum(sK14,sK15) = X0 ),
inference(resolution,[],[f99,f41]) ).
fof(f107,plain,
! [X0,X1] :
( ~ incident_c(sK0(sum(X0,X1),sum(sK14,sK15)),X0)
| sum(X0,X1) = sum(sK14,sK15) ),
inference(resolution,[],[f87,f101]) ).
fof(f111,plain,
! [X0] :
( sum(sK14,sK15) = sum(sum(sK14,sK15),X0)
| sum(sK14,sK15) = sum(sum(sK14,sK15),X0) ),
inference(resolution,[],[f107,f102]) ).
fof(f114,plain,
! [X0] : sum(sK14,sK15) = sum(sum(sK14,sK15),X0),
inference(duplicate_literal_removal,[],[f111]) ).
fof(f115,plain,
! [X0] :
( ~ incident_c(X0,sK15)
| incident_c(X0,sK13) ),
inference(resolution,[],[f40,f83]) ).
fof(f116,plain,
! [X0] :
( ~ incident_c(X0,sK14)
| incident_c(X0,sK13) ),
inference(resolution,[],[f40,f84]) ).
fof(f137,plain,
! [X0,X1] :
( incident_c(X0,sum(sK14,sK15))
| ~ incident_c(X0,X1) ),
inference(superposition,[],[f88,f114]) ).
fof(f149,plain,
! [X0,X1] :
( incident_c(X0,sK15)
| ~ incident_c(X0,X1)
| incident_c(X0,sK14) ),
inference(resolution,[],[f89,f137]) ).
fof(f164,plain,
! [X0,X1] :
( ~ incident_c(X0,X1)
| incident_c(X0,sK14)
| incident_c(X0,sK13) ),
inference(resolution,[],[f149,f115]) ).
fof(f171,plain,
! [X0,X1] :
( ~ incident_c(X0,X1)
| incident_c(X0,sK13) ),
inference(forward_subsumption_resolution,[],[f164,f116]) ).
fof(f195,plain,
! [X0] :
( ~ incident_c(sK0(sK13,sum(sK14,sK15)),X0)
| sK13 = sum(sK14,sK15) ),
inference(resolution,[],[f171,f101]) ).
fof(f198,definition,
( spl17_4
<=> sK13 = sum(sK14,sK15) ),
introduced(definition,[new_symbols(definition,[spl17_4])],[avatar_definition]) ).
fof(f199,plain,
( sK13 != sum(sK14,sK15)
| spl17_4 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f200,plain,
( sK13 = sum(sK14,sK15)
| ~ spl17_4 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f202,definition,
( spl17_5
<=> ! [X0] : ~ incident_c(sK0(sK13,sum(sK14,sK15)),X0) ),
introduced(definition,[new_symbols(definition,[spl17_5])],[avatar_definition]) ).
fof(f203,plain,
( ! [X0] : ~ incident_c(sK0(sK13,sum(sK14,sK15)),X0)
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f204,plain,
( spl17_4
| spl17_5 ),
inference(avatar_split_clause,[],[f195,f202,f198]) ).
fof(f207,plain,
( ~ open(sK13)
| ~ spl17_4 ),
inference(superposition,[],[f86,f200]) ).
fof(f219,plain,
( $false
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f207,f85]) ).
fof(f220,plain,
~ spl17_4,
inference(avatar_contradiction_clause,[],[f219]) ).
fof(f265,plain,
( sK13 = sum(sK14,sK15)
| ~ spl17_5 ),
inference(resolution,[],[f203,f102]) ).
fof(f271,plain,
( $false
| spl17_4
| ~ spl17_5 ),
inference(forward_subsumption_resolution,[],[f265,f199]) ).
fof(f272,plain,
( spl17_4
| ~ spl17_5 ),
inference(avatar_contradiction_clause,[],[f271]) ).
cnf(s2,plain,
( spl17_4
| spl17_5 ),
inference(sat_conversion,[],[f204]) ).
cnf(s3,plain,
~ spl17_4,
inference(sat_conversion,[],[f220]) ).
cnf(s4,plain,
( spl17_4
| ~ spl17_5 ),
inference(sat_conversion,[],[f272]) ).
cnf(s5,plain,
~ spl17_5,
inference(rat,[],[s4,s3]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s2,s5,s3]) ).
fof(f273,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO093+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 27 06:56:35 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.32 Running first-order model finding
% 0.03/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36 % (2022414)Will run a generic schedule for satisfiability detection.
% 0.07/0.36 % (2022420)% WARNING: option uhcvi not known.
% 0.07/0.36 % (2022423)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4275527579:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.36 % (2022420)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=487674030:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.36 % (2022419)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2498067904_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.36 % (2022425)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4269306604:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.36 % (2022421)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=605444469:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.36 % (2022422)dis+10_1_sil=32000:sp=arity:random_seed=1575192538:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.36 % (2022424)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1636390444:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.36 % TRYING [1]
% 0.07/0.36 % TRYING [2]
% 0.07/0.36 % TRYING [3]
% 0.07/0.36 % (2022423) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2022414-2022423"...
% 0.07/0.36 % TRYING [4]
% 0.07/0.36 % (2022423)...printing done.
% 0.07/0.36 % (2022423)Refutation found. Thanks to Tanya!
% 0.07/0.36 % SZS status Theorem for theBenchmark
% 0.07/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.36 % (2022423)------------------------------
% 0.07/0.36 % (2022423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.36 % (2022423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.36 % (2022423)CaDiCaL version: 2.1.3
% 0.07/0.36 % (2022423)Termination reason: Refutation
% 0.07/0.36 % (2022423)Time elapsed: 0.005 s
% 0.07/0.36 % (2022423)Peak memory usage: 12 MB
% 0.07/0.36 % (2022423)Instructions burned: 12 (million)
% 0.07/0.36 % (2022414)Success in time 0.032 s
% 0.07/0.36 % Vampire exiting
%------------------------------------------------------------------------------