%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO111-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 : Unsatisfiable 1.19s 1.00s
% Output : Refutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 70 ( 22 unt; 6 def)
% Number of atoms : 137 ( 10 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 130 ( 63 ~; 61 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 44 ( 0 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( incident_c(X2,X1)
| ~ incident_c(X2,X0)
| ~ part_of(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn_1) ).
fof(f22,axiom,
! [X0,X1] :
( ~ end_point(X0,X1)
| incident_c(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',end_point_defn_13) ).
fof(f30,axiom,
! [X0,X1] :
( ~ inner_point(X0,X1)
| incident_c(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn_21) ).
fof(f31,axiom,
! [X0,X1] :
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn_22) ).
fof(f66,axiom,
! [X2,X3,X0,X1] :
( ~ between_c(X0,X1,X2,X3)
| X1 != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn_1) ).
fof(f67,axiom,
! [X2,X3,X0,X1] :
( part_of(ax1_sk1(X3,X2,X1,X0),X0)
| ~ between_c(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn_2) ).
fof(f68,axiom,
! [X2,X3,X0,X1] :
( ~ between_c(X0,X1,X2,X3)
| end_point(X1,ax1_sk1(X3,X2,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn_3) ).
fof(f69,axiom,
! [X2,X3,X0,X1] :
( ~ between_c(X0,X1,X2,X3)
| end_point(X3,ax1_sk1(X3,X2,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn_4) ).
fof(f70,axiom,
! [X2,X3,X0,X1] :
( ~ between_c(X0,X1,X2,X3)
| inner_point(X2,ax1_sk1(X3,X2,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn_5) ).
fof(f72,negated_conjecture,
between_c(sk15,sk16,sk17,sk18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_3_8_1_77) ).
fof(f73,negated_conjecture,
( ~ incident_c(sk16,sk15)
| ~ incident_c(sk17,sk15)
| ~ incident_c(sk18,sk15)
| sk16 = sk17
| sk17 = sk18
| sk16 = sk18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_3_8_1_78) ).
fof(f78,plain,
! [X2,X3,X0] : ~ between_c(X0,X3,X2,X3),
inference(equality_resolution,[],[f66]) ).
fof(f80,definition,
( spl0_1
<=> sk16 = sk18 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f82,plain,
( sk16 = sk18
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f84,definition,
( spl0_2
<=> sk17 = sk18 ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f86,plain,
( sk17 = sk18
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f88,definition,
( spl0_3
<=> sk16 = sk17 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f90,plain,
( sk16 = sk17
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f92,definition,
( spl0_4
<=> incident_c(sk18,sk15) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f94,plain,
( ~ incident_c(sk18,sk15)
| spl0_4 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f96,definition,
( spl0_5
<=> incident_c(sk17,sk15) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f98,plain,
( ~ incident_c(sk17,sk15)
| spl0_5 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f100,definition,
( spl0_6
<=> incident_c(sk16,sk15) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f102,plain,
( ~ incident_c(sk16,sk15)
| spl0_6 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f103,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f73,f100,f96,f92,f88,f84,f80]) ).
fof(f139,plain,
( ! [X0] :
( ~ part_of(X0,sk15)
| ~ incident_c(sk16,X0) )
| spl0_6 ),
inference(resolution,[],[f102,f1]) ).
fof(f147,plain,
( ! [X2,X0,X1] :
( ~ between_c(sk15,X0,X1,X2)
| ~ incident_c(sk16,ax1_sk1(X2,X1,X0,sk15)) )
| spl0_6 ),
inference(resolution,[],[f67,f139]) ).
fof(f153,plain,
end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolution,[],[f68,f72]) ).
fof(f158,plain,
incident_c(sk16,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolution,[],[f153,f22]) ).
fof(f159,plain,
end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolution,[],[f69,f72]) ).
fof(f164,plain,
incident_c(sk18,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolution,[],[f159,f22]) ).
fof(f165,plain,
inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolution,[],[f70,f72]) ).
fof(f167,plain,
incident_c(sk17,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolution,[],[f165,f30]) ).
fof(f326,plain,
( ~ incident_c(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| spl0_6 ),
inference(resolution,[],[f147,f72]) ).
fof(f327,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f326,f158]) ).
fof(f328,plain,
spl0_6,
inference(avatar_contradiction_clause,[],[f327]) ).
fof(f330,plain,
( ! [X0] :
( ~ part_of(X0,sk15)
| ~ incident_c(sk17,X0) )
| spl0_5 ),
inference(resolution,[],[f98,f1]) ).
fof(f334,plain,
( ! [X2,X0,X1] :
( ~ between_c(sk15,X2,X1,X0)
| ~ incident_c(sk17,ax1_sk1(X0,X1,X2,sk15)) )
| spl0_5 ),
inference(resolution,[],[f330,f67]) ).
fof(f472,plain,
( ~ incident_c(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| spl0_5 ),
inference(resolution,[],[f334,f72]) ).
fof(f473,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f472,f167]) ).
fof(f474,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f473]) ).
fof(f475,plain,
( between_c(sk15,sk16,sk16,sk18)
| ~ spl0_3 ),
inference(superposition,[],[f72,f90]) ).
fof(f485,plain,
( inner_point(sk16,ax1_sk1(sk18,sk16,sk16,sk15))
| ~ spl0_3 ),
inference(resolution,[],[f475,f70]) ).
fof(f487,plain,
( end_point(sk16,ax1_sk1(sk18,sk16,sk16,sk15))
| ~ spl0_3 ),
inference(resolution,[],[f475,f68]) ).
fof(f502,plain,
( ~ inner_point(sk16,ax1_sk1(sk18,sk16,sk16,sk15))
| ~ spl0_3 ),
inference(resolution,[],[f487,f31]) ).
fof(f509,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f502,f485]) ).
fof(f510,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f509]) ).
fof(f511,plain,
( between_c(sk15,sk16,sk17,sk17)
| ~ spl0_2 ),
inference(superposition,[],[f72,f86]) ).
fof(f522,plain,
( inner_point(sk17,ax1_sk1(sk17,sk17,sk16,sk15))
| ~ spl0_2 ),
inference(resolution,[],[f511,f70]) ).
fof(f523,plain,
( end_point(sk17,ax1_sk1(sk17,sk17,sk16,sk15))
| ~ spl0_2 ),
inference(resolution,[],[f511,f69]) ).
fof(f530,plain,
( ~ inner_point(sk17,ax1_sk1(sk17,sk17,sk16,sk15))
| ~ spl0_2 ),
inference(resolution,[],[f523,f31]) ).
fof(f537,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f530,f522]) ).
fof(f538,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f537]) ).
fof(f540,plain,
( ! [X0] :
( ~ part_of(X0,sk15)
| ~ incident_c(sk18,X0) )
| spl0_4 ),
inference(resolution,[],[f94,f1]) ).
fof(f544,plain,
( ! [X2,X0,X1] :
( ~ between_c(sk15,X2,X1,X0)
| ~ incident_c(sk18,ax1_sk1(X0,X1,X2,sk15)) )
| spl0_4 ),
inference(resolution,[],[f540,f67]) ).
fof(f577,plain,
( ~ incident_c(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| spl0_4 ),
inference(resolution,[],[f544,f72]) ).
fof(f578,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f577,f164]) ).
fof(f579,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f578]) ).
fof(f580,plain,
( between_c(sk15,sk16,sk17,sk16)
| ~ spl0_1 ),
inference(superposition,[],[f72,f82]) ).
fof(f590,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f580,f78]) ).
fof(f591,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f590]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f103]) ).
cnf(s3,plain,
spl0_6,
inference(sat_conversion,[],[f328]) ).
cnf(s4,plain,
spl0_5,
inference(sat_conversion,[],[f474]) ).
cnf(s5,plain,
~ spl0_3,
inference(sat_conversion,[],[f510]) ).
cnf(s7,plain,
~ spl0_2,
inference(sat_conversion,[],[f538]) ).
cnf(s8,plain,
spl0_4,
inference(sat_conversion,[],[f579]) ).
cnf(s9,plain,
~ spl0_1,
inference(sat_conversion,[],[f591]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s3,s4,s8,s5,s7,s9]) ).
fof(f592,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO111-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n014.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 07:03:17 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.19/1.00 % (462212)Input is clausal, will run a generic CNF schedule.
% 1.19/1.00 % (462222)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=228049668:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.19/1.00 % (462221)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1396663785:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.19/1.00 % (462220)lrs+10_1_sil=8000:sp=occurrence:random_seed=4232146065:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.19/1.00 % (462218)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2872826536:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.19/1.00 % (462219)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=609476346:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.19/1.00 % (462217)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=2992516551:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.19/1.00 % (462223)dis-21_1_sil=8000:lcm=predicate:random_seed=4143706389:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 1.19/1.00 % (462222)First to succeed.
% 1.19/1.00 % (462222)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-462212"
% 1.19/1.00 % (462221)Instruction limit reached!
% 1.19/1.00 % (462221)------------------------------
% 1.19/1.00 % (462221)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.19/1.00 % (462221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/1.00 % (462221)CaDiCaL version: 2.1.3
% 1.19/1.00 % (462221)Termination reason: Instruction limit
% 1.19/1.00 % (462221)Termination phase: Saturation
% 1.19/1.00 % (462221)Time elapsed: 0.043 s
% 1.19/1.00 % (462221)Peak memory usage: 88 MB
% 1.19/1.00 % (462221)Instructions burned: 115 (million)
% 1.19/1.00 % (462223)Instruction limit reached!
% 1.19/1.00 % (462223)------------------------------
% 1.19/1.00 % (462223)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.19/1.00 % (462223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/1.00 % (462223)CaDiCaL version: 2.1.3
% 1.19/1.00 % (462223)Termination reason: Instruction limit
% 1.19/1.00 % (462223)Termination phase: Saturation
% 1.19/1.00 % (462223)Time elapsed: 0.049 s
% 1.19/1.00 % (462223)Peak memory usage: 88 MB
% 1.19/1.00 % (462223)Instructions burned: 119 (million)
% 1.19/1.00 % (462220)Instruction limit reached!
% 1.19/1.00 % (462220)------------------------------
% 1.19/1.00 % (462220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.19/1.00 % (462220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/1.00 % (462220)CaDiCaL version: 2.1.3
% 1.19/1.00 % (462220)Termination reason: Instruction limit
% 1.19/1.00 % (462220)Termination phase: Saturation
% 1.19/1.00 % (462220)Time elapsed: 0.072 s
% 1.19/1.00 % (462220)Peak memory usage: 89 MB
% 1.19/1.00 % (462220)Instructions burned: 108 (million)
% 1.19/1.00 % (462222)Refutation found. Thanks to Tanya!
% 1.19/1.00 % SZS status Unsatisfiable for theBenchmark
% 1.19/1.00 % SZS output start Proof for theBenchmark
% See solution above
% 1.19/1.00 % (462222)------------------------------
% 1.19/1.00 % (462222)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.19/1.00 % (462222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/1.00 % (462222)CaDiCaL version: 2.1.3
% 1.19/1.00 % (462222)Termination reason: Refutation
% 1.19/1.00 % (462222)Time elapsed: 0.012 s
% 1.19/1.00 % (462222)Peak memory usage: 89 MB
% 1.19/1.00 % (462222)Instructions burned: 28 (million)
% 1.19/1.00 % (462222)------------------------------
% 1.19/1.00 % (462222)------------------------------
% 1.19/1.00 % (462212)Success in time 0.299 s
% 1.19/1.00 % Vampire exiting
%------------------------------------------------------------------------------