%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO112+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 : n003.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 09:51:34 AM UTC 2026
% Result : Theorem 3.44s 1.45s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 9 unt; 2 def)
% Number of atoms : 142 ( 14 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 188 ( 87 ~; 70 |; 26 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 80 ( 0 sgn 72 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1,X2,X3] :
( between_c(X0,X1,X2,X3)
<=> ( X1 != X3
& ? [X4] :
( part_of(X4,X0)
& end_point(X1,X4)
& end_point(X3,X4)
& inner_point(X2,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',between_c_defn) ).
fof(f18,conjecture,
! [X0,X1,X2,X3] :
( between_c(X0,X1,X2,X3)
=> between_c(X0,X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem_3_8_2) ).
fof(f19,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( between_c(X0,X1,X2,X3)
=> between_c(X0,X3,X2,X1) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0,X1,X2,X3] :
( ~ between_c(X0,X3,X2,X1)
& between_c(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
( ~ between_c(sK0,sK3,sK2,sK1)
& between_c(sK0,sK1,sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( between_c(X0,X1,X2,X3)
| X1 = X3
| ! [X4] :
( ~ part_of(X4,X0)
| ~ end_point(X1,X4)
| ~ end_point(X3,X4)
| ~ inner_point(X2,X4) ) )
& ( ( X1 != X3
& ? [X4] :
( part_of(X4,X0)
& end_point(X1,X4)
& end_point(X3,X4)
& inner_point(X2,X4) ) )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( ( between_c(X0,X1,X2,X3)
| X1 = X3
| ! [X4] :
( ~ part_of(X4,X0)
| ~ end_point(X1,X4)
| ~ end_point(X3,X4)
| ~ inner_point(X2,X4) ) )
& ( ( X1 != X3
& ? [X4] :
( part_of(X4,X0)
& end_point(X1,X4)
& end_point(X3,X4)
& inner_point(X2,X4) ) )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( ( between_c(X0,X1,X2,X3)
| X1 = X3
| ! [X4] :
( ~ part_of(X4,X0)
| ~ end_point(X1,X4)
| ~ end_point(X3,X4)
| ~ inner_point(X2,X4) ) )
& ( ( X1 != X3
& ? [X5] :
( part_of(X5,X0)
& end_point(X1,X5)
& end_point(X3,X5)
& inner_point(X2,X5) ) )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(rectify,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ( between_c(X0,X1,X2,X3)
| X1 = X3
| ! [X4] :
( ~ part_of(X4,X0)
| ~ end_point(X1,X4)
| ~ end_point(X3,X4)
| ~ inner_point(X2,X4) ) )
& ( ( X1 != X3
& part_of(sK4(X0,X1,X2,X3),X0)
& end_point(X1,sK4(X0,X1,X2,X3))
& end_point(X3,sK4(X0,X1,X2,X3))
& inner_point(X2,sK4(X0,X1,X2,X3)) )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X5,sK4(X0,X1,X2,X3))],[f24]) ).
fof(f26,plain,
between_c(sK0,sK1,sK2,sK3),
inference(cnf_transformation,[],[f21]) ).
fof(f27,plain,
~ between_c(sK0,sK3,sK2,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f28,plain,
! [X2,X3,X0,X1] :
( inner_point(X2,sK4(X0,X1,X2,X3))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f25]) ).
fof(f29,plain,
! [X2,X3,X0,X1] :
( end_point(X3,sK4(X0,X1,X2,X3))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f25]) ).
fof(f30,plain,
! [X2,X3,X0,X1] :
( end_point(X1,sK4(X0,X1,X2,X3))
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f25]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( part_of(sK4(X0,X1,X2,X3),X0)
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f25]) ).
fof(f32,plain,
! [X2,X3,X0,X1] :
( X1 != X3
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f25]) ).
fof(f33,plain,
! [X2,X3,X0,X1,X4] :
( between_c(X0,X1,X2,X3)
| X1 = X3
| ~ part_of(X4,X0)
| ~ end_point(X1,X4)
| ~ end_point(X3,X4)
| ~ inner_point(X2,X4) ),
inference(cnf_transformation,[],[f25]) ).
fof(f34,plain,
! [X2,X3,X0] : ~ between_c(X0,X3,X2,X3),
inference(equality_resolution,[],[f32]) ).
fof(f35,plain,
! [X0] :
( sK1 = sK3
| ~ part_of(X0,sK0)
| ~ end_point(sK3,X0)
| ~ end_point(sK1,X0)
| ~ inner_point(sK2,X0) ),
inference(resolution,[],[f27,f33]) ).
fof(f37,definition,
( spl5_1
<=> ! [X0] :
( ~ part_of(X0,sK0)
| ~ inner_point(sK2,X0)
| ~ end_point(sK1,X0)
| ~ end_point(sK3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f38,plain,
( ! [X0] :
( ~ inner_point(sK2,X0)
| ~ part_of(X0,sK0)
| ~ end_point(sK1,X0)
| ~ end_point(sK3,X0) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f40,definition,
( spl5_2
<=> sK1 = sK3 ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f42,plain,
( sK1 = sK3
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f43,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f35,f40,f37]) ).
fof(f45,plain,
( between_c(sK0,sK1,sK2,sK1)
| ~ spl5_2 ),
inference(superposition,[],[f26,f42]) ).
fof(f46,plain,
( $false
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f45,f34]) ).
fof(f47,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f46]) ).
fof(f48,plain,
( ! [X2,X0,X1] :
( ~ end_point(sK3,sK4(X0,X1,sK2,X2))
| ~ end_point(sK1,sK4(X0,X1,sK2,X2))
| ~ part_of(sK4(X0,X1,sK2,X2),sK0)
| ~ between_c(X0,X1,sK2,X2) )
| ~ spl5_1 ),
inference(resolution,[],[f38,f28]) ).
fof(f50,plain,
( ! [X0,X1] :
( ~ end_point(sK1,sK4(X0,X1,sK2,sK3))
| ~ part_of(sK4(X0,X1,sK2,sK3),sK0)
| ~ between_c(X0,X1,sK2,sK3)
| ~ between_c(X0,X1,sK2,sK3) )
| ~ spl5_1 ),
inference(resolution,[],[f48,f29]) ).
fof(f51,plain,
( ! [X0,X1] :
( ~ end_point(sK1,sK4(X0,X1,sK2,sK3))
| ~ part_of(sK4(X0,X1,sK2,sK3),sK0)
| ~ between_c(X0,X1,sK2,sK3) )
| ~ spl5_1 ),
inference(duplicate_literal_removal,[],[f50]) ).
fof(f53,plain,
( ! [X0] :
( ~ part_of(sK4(X0,sK1,sK2,sK3),sK0)
| ~ between_c(X0,sK1,sK2,sK3)
| ~ between_c(X0,sK1,sK2,sK3) )
| ~ spl5_1 ),
inference(resolution,[],[f51,f30]) ).
fof(f54,plain,
( ! [X0] :
( ~ part_of(sK4(X0,sK1,sK2,sK3),sK0)
| ~ between_c(X0,sK1,sK2,sK3) )
| ~ spl5_1 ),
inference(duplicate_literal_removal,[],[f53]) ).
fof(f57,plain,
( ~ between_c(sK0,sK1,sK2,sK3)
| ~ between_c(sK0,sK1,sK2,sK3)
| ~ spl5_1 ),
inference(resolution,[],[f54,f31]) ).
fof(f58,plain,
( ~ between_c(sK0,sK1,sK2,sK3)
| ~ spl5_1 ),
inference(duplicate_literal_removal,[],[f57]) ).
fof(f59,plain,
( $false
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f58,f26]) ).
fof(f60,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f59]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s2,plain,
~ spl5_2,
inference(sat_conversion,[],[f47]) ).
cnf(s3,plain,
~ spl5_1,
inference(sat_conversion,[],[f60]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f61,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO112+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % 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 07:05:11 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 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
% 3.44/1.45 % (159165)Detected formulas, will run a generic FOF schedule.
% 3.44/1.45 % (159171)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=2105845412:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.44/1.45 % (159174)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3118268611:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.44/1.45 % (159170)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=3486535196:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.44/1.45 % (159172)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=1790623663:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.44/1.45 % (159175)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=575899455:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.44/1.45 % (159173)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2129329556:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.44/1.45 % (159173)First to succeed.
% 3.44/1.45 % (159173)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-159165"
% 3.44/1.45 % (159174)Also succeeded, but the first one will report.
% 3.44/1.45 % (159176)dis-21_1_sil=8000:lcm=predicate:random_seed=2303403971: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)
% 3.44/1.45 % (159176)Instruction limit reached!
% 3.44/1.45 % (159176)------------------------------
% 3.44/1.45 % (159176)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.45 % (159176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.45 % (159176)CaDiCaL version: 2.1.3
% 3.44/1.45 % (159176)Termination reason: Instruction limit
% 3.44/1.45 % (159176)Termination phase: Saturation
% 3.44/1.45 % (159176)Time elapsed: 0.077 s
% 3.44/1.45 % (159176)Peak memory usage: 89 MB
% 3.44/1.45 % (159176)Instructions burned: 131 (million)
% 3.44/1.45 % (159175)Instruction limit reached!
% 3.44/1.45 % (159175)------------------------------
% 3.44/1.45 % (159175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.45 % (159175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.45 % (159175)CaDiCaL version: 2.1.3
% 3.44/1.45 % (159175)Termination reason: Instruction limit
% 3.44/1.45 % (159175)Termination phase: Saturation
% 3.44/1.45 % (159175)Time elapsed: 0.096 s
% 3.44/1.45 % (159175)Peak memory usage: 89 MB
% 3.44/1.45 % (159175)Instructions burned: 140 (million)
% 3.44/1.45 % (159185)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1547293742:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.44/1.45 % (159185)Also succeeded, but the first one will report.
% 3.44/1.45 % (159184)lrs+10_1_sil=8000:sp=occurrence:random_seed=4119349730:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.44/1.45 % (159173)Refutation found. Thanks to Tanya!
% 3.44/1.45 % SZS status Theorem for theBenchmark
% 3.44/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.44/1.45 % (159173)------------------------------
% 3.44/1.45 % (159173)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.45 % (159173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.45 % (159173)CaDiCaL version: 2.1.3
% 3.44/1.45 % (159173)Termination reason: Refutation
% 3.44/1.45 % (159173)Time elapsed: 0.003 s
% 3.44/1.45 % (159173)Peak memory usage: 89 MB
% 3.44/1.45 % (159173)Instructions burned: 2 (million)
% 3.44/1.45 % (159173)------------------------------
% 3.44/1.45 % (159173)------------------------------
% 3.44/1.45 % (159165)Success in time 0.404 s
% 3.44/1.45 % Vampire exiting
%------------------------------------------------------------------------------