%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO082+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 09:51:28 AM UTC 2026
% Result : Theorem 3.43s 1.35s
% Output : Refutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 5 unt; 0 def)
% Number of atoms : 94 ( 20 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 104 ( 39 ~; 41 |; 16 &)
% ( 3 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 49 !; 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/theBenchmark.p',part_of_defn) ).
fof(f16,axiom,
! [X0,X1] :
( ! [X2] :
( incident_c(X2,X0)
<=> incident_c(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c9) ).
fof(f17,conjecture,
! [X0,X1] :
( ( part_of(X0,X1)
& part_of(X1,X0) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_antisymmetry) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( part_of(X0,X1)
& part_of(X1,X0) )
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1] :
( X0 != X1
& part_of(X0,X1)
& part_of(X1,X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
? [X0,X1] :
( X0 != X1
& part_of(X0,X1)
& part_of(X1,X0) ),
inference(flattening,[],[f19]) ).
fof(f28,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f29,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( incident_c(X2,X0)
<~> incident_c(X2,X1) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f30,plain,
( sK0 != sK1
& part_of(sK0,sK1)
& part_of(sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f20]) ).
fof(f36,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,[],[f28]) ).
fof(f37,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,[],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ( ~ incident_c(sK5(X0,X1),X0)
& incident_c(sK5(X0,X1),X1) ) )
& ( ! [X3] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1) )
| ~ part_of(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ incident_c(X2,X1)
| ~ incident_c(X2,X0) )
& ( incident_c(X2,X1)
| incident_c(X2,X0) ) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f40,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ incident_c(sK6(X0,X1),X1)
| ~ incident_c(sK6(X0,X1),X0) )
& ( incident_c(sK6(X0,X1),X1)
| incident_c(sK6(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f39]) ).
fof(f41,plain,
part_of(sK1,sK0),
inference(cnf_transformation,[],[f30]) ).
fof(f42,plain,
part_of(sK0,sK1),
inference(cnf_transformation,[],[f30]) ).
fof(f43,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f30]) ).
fof(f56,plain,
! [X3,X0,X1] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1)
| ~ part_of(X1,X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f59,plain,
! [X0,X1] :
( incident_c(sK6(X0,X1),X1)
| X0 = X1
| incident_c(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f60,plain,
! [X0,X1] :
( ~ incident_c(sK6(X0,X1),X1)
| X0 = X1
| ~ incident_c(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ incident_c(sK6(X0,X1),X2)
| ~ incident_c(sK6(X0,X1),X0)
| X0 = X1
| ~ part_of(X2,X1) ),
inference(resolution,[],[f60,f56]) ).
fof(f102,plain,
! [X0,X1] :
( ~ incident_c(sK6(X0,X1),X0)
| X0 = X1
| ~ part_of(X0,X1) ),
inference(factoring,[],[f72]) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ incident_c(sK6(X0,X1),X2)
| ~ part_of(X0,X1)
| X0 = X1
| ~ part_of(X2,X0) ),
inference(resolution,[],[f102,f56]) ).
fof(f119,plain,
! [X0,X1] :
( ~ part_of(X0,X1)
| X0 = X1
| ~ part_of(X1,X0)
| X0 = X1
| incident_c(sK6(X0,X1),X0) ),
inference(resolution,[],[f105,f59]) ).
fof(f124,plain,
! [X0,X1] :
( ~ part_of(X0,X1)
| X0 = X1
| ~ part_of(X1,X0)
| incident_c(sK6(X0,X1),X0) ),
inference(duplicate_literal_removal,[],[f119]) ).
fof(f125,plain,
! [X0,X1] :
( ~ part_of(X1,X0)
| X0 = X1
| ~ part_of(X0,X1) ),
inference(forward_subsumption_resolution,[],[f124,f102]) ).
fof(f138,plain,
( sK0 = sK1
| ~ part_of(sK0,sK1) ),
inference(resolution,[],[f125,f41]) ).
fof(f142,plain,
~ part_of(sK0,sK1),
inference(forward_subsumption_resolution,[],[f138,f43]) ).
fof(f144,plain,
$false,
inference(forward_subsumption_resolution,[],[f142,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO082+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.37 % Computer : n011.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 27 06:53:16 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.43/1.35 % (2048747)Detected formulas, will run a generic FOF schedule.
% 3.43/1.35 % (2048754)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1269245707:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.43/1.35 % (2048755)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1371295863:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.43/1.35 % (2048752)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2079490719:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.43/1.35 % (2048758)dis-21_1_sil=8000:lcm=predicate:random_seed=3696002321:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.43/1.35 % (2048756)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2390074291:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.43/1.35 % (2048757)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2415079329:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.43/1.35 % (2048753)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2568073618:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.43/1.35 % (2048755)Refutation not found, incomplete strategy
% 3.43/1.35 % (2048755)------------------------------
% 3.43/1.35 % (2048755)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.35 % (2048755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.35 % (2048755)CaDiCaL version: 2.1.3
% 3.43/1.35 % (2048755)Termination reason: Refutation not found, incomplete strategy
% 3.43/1.35 % (2048755)Time elapsed: 0.002 s
% 3.43/1.35 % (2048755)Peak memory usage: 88 MB
% 3.43/1.35 % (2048755)Instructions burned: 1 (million)
% 3.43/1.35 % (2048756)First to succeed.
% 3.43/1.35 % (2048756)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2048747"
% 3.43/1.35 % (2048758)Also succeeded, but the first one will report.
% 3.43/1.35 % (2048757)Also succeeded, but the first one will report.
% 3.43/1.35 % (2048755)------------------------------
% 3.43/1.35 % (2048755)------------------------------
% 3.43/1.35 % (2048756)Refutation found. Thanks to Tanya!
% 3.43/1.35 % SZS status Theorem for theBenchmark
% 3.43/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.43/1.35 % (2048756)------------------------------
% 3.43/1.35 % (2048756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.35 % (2048756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.35 % (2048756)CaDiCaL version: 2.1.3
% 3.43/1.35 % (2048756)Termination reason: Refutation
% 3.43/1.35 % (2048756)Time elapsed: 0.005 s
% 3.43/1.35 % (2048756)Peak memory usage: 88 MB
% 3.43/1.35 % (2048756)Instructions burned: 5 (million)
% 3.43/1.35 % (2048756)------------------------------
% 3.43/1.35 % (2048756)------------------------------
% 3.43/1.35 % (2048747)Success in time 0.417 s
% 3.43/1.35 % Vampire exiting
%------------------------------------------------------------------------------