%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO006-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 09:51:09 AM UTC 2026
% Result : Unsatisfiable 4.05s 1.53s
% Output : Refutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 14 unt; 2 def)
% Number of atoms : 85 ( 14 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 98 ( 51 ~; 45 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 63 ( 0 sgn 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).
fof(f7,axiom,
! [X0,X1] :
( ~ between(X0,X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4] :
( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch1) ).
fof(f9,axiom,
! [X2,X3,X0,X1,X4] :
( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch2) ).
fof(f19,axiom,
a != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_c) ).
fof(f21,axiom,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_not_d) ).
fof(f22,axiom,
between(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_between_a_and_d) ).
fof(f23,negated_conjecture,
( between(c,a,d)
| between(a,d,c) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_not_between_others) ).
fof(f25,definition,
( spl0_1
<=> between(a,d,c) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f27,plain,
( between(a,d,c)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f29,definition,
( spl0_2
<=> between(c,a,d) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f32,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f23,f29,f25]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( inner_pasch(X3,X0,X2,X1,X0) = X0
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[],[f8,f7]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( inner_pasch(X1,X3,X2,X1,X0) = X1
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[],[f9,f7]) ).
fof(f36,plain,
! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0,
inference(resolution,[],[f5,f3]) ).
fof(f38,plain,
! [X0,X1] : between(X1,X0,X0),
inference(superposition,[],[f4,f36]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( between(X1,X0,X2)
| ~ between(X0,X1,X3)
| ~ between(X2,X0,X3)
| ~ between(X2,X0,X3)
| ~ between(X0,X1,X3) ),
inference(superposition,[],[f9,f33]) ).
fof(f70,plain,
! [X2,X3,X0,X1] :
( between(X1,X0,X2)
| ~ between(X0,X1,X3)
| ~ between(X2,X0,X3) ),
inference(duplicate_literal_removal,[],[f67]) ).
fof(f74,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ between(X0,X1,X2)
| ~ between(X1,X0,X2)
| ~ between(X0,X1,X2)
| ~ between(X1,X0,X2) ),
inference(superposition,[],[f33,f35]) ).
fof(f75,plain,
! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| X0 = X1
| ~ between(X1,X0,X2) ),
inference(duplicate_literal_removal,[],[f74]) ).
fof(f89,plain,
( a = c
| ~ between(c,a,d) ),
inference(resolution,[],[f75,f22]) ).
fof(f91,plain,
~ between(c,a,d),
inference(forward_subsumption_resolution,[],[f89,f19]) ).
fof(f97,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f91,f29]) ).
fof(f116,plain,
! [X2,X3,X0,X1] :
( ~ between(X0,X1,X3)
| ~ between(X3,X0,X2)
| X0 = X1
| ~ between(X0,X1,X2) ),
inference(resolution,[],[f70,f75]) ).
fof(f233,plain,
! [X2,X3,X0,X1,X4] :
( ~ between(X0,X3,X4)
| X1 = X3
| ~ between(X1,X3,X2)
| ~ between(X3,X1,X4)
| ~ between(X0,X1,X2) ),
inference(resolution,[],[f116,f70]) ).
fof(f913,plain,
( ! [X0,X1] :
( ~ between(d,X0,c)
| ~ between(X0,d,X1)
| d = X0
| ~ between(a,X0,X1) )
| ~ spl0_1 ),
inference(resolution,[],[f233,f27]) ).
fof(f1043,plain,
( ! [X0] :
( ~ between(c,d,X0)
| c = d
| ~ between(a,c,X0) )
| ~ spl0_1 ),
inference(resolution,[],[f913,f38]) ).
fof(f1049,plain,
( ! [X0] :
( ~ between(c,d,X0)
| ~ between(a,c,X0) )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f1043,f21]) ).
fof(f1061,plain,
( ~ between(a,c,d)
| ~ spl0_1 ),
inference(resolution,[],[f1049,f38]) ).
fof(f1067,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f1061,f22]) ).
fof(f1068,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f1067]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f32]) ).
cnf(s4,plain,
~ spl0_2,
inference(sat_conversion,[],[f97]) ).
cnf(s7,plain,
~ spl0_1,
inference(sat_conversion,[],[f1068]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s4,s7]) ).
fof(f1069,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n017.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 06:24:35 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 4.05/1.53 % (2182867)Input is clausal, will run a generic CNF schedule.
% 4.05/1.53 % (2182938)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=47877200:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.05/1.53 % (2182940)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2866659293:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.05/1.53 % (2182939)lrs+10_1_sil=8000:sp=occurrence:random_seed=4260911752:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.05/1.53 % (2182937)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3521208867:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.05/1.53 % (2182942)dis-21_1_sil=8000:lcm=predicate:random_seed=537938493: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)
% 4.05/1.53 % (2182936)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=1688812992:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.05/1.53 % (2182939)Refutation not found, incomplete strategy
% 4.05/1.53 % (2182939)------------------------------
% 4.05/1.53 % (2182939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.53 % (2182939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.53 % (2182939)CaDiCaL version: 2.1.3
% 4.05/1.53 % (2182939)Termination reason: Refutation not found, incomplete strategy
% 4.05/1.53 % (2182939)Time elapsed: 0.001 s
% 4.05/1.53 % (2182939)Peak memory usage: 88 MB
% 4.05/1.53 % (2182941)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=443170321:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.05/1.53 % (2182940)Instruction limit reached!
% 4.05/1.53 % (2182940)------------------------------
% 4.05/1.53 % (2182940)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.53 % (2182940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.53 % (2182940)CaDiCaL version: 2.1.3
% 4.05/1.53 % (2182940)Termination reason: Instruction limit
% 4.05/1.53 % (2182940)Termination phase: Saturation
% 4.05/1.53 % (2182940)Time elapsed: 0.063 s
% 4.05/1.53 % (2182940)Peak memory usage: 88 MB
% 4.05/1.53 % (2182940)Instructions burned: 115 (million)
% 4.05/1.53 % (2182942)Instruction limit reached!
% 4.05/1.53 % (2182942)------------------------------
% 4.05/1.53 % (2182942)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.53 % (2182942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.53 % (2182942)CaDiCaL version: 2.1.3
% 4.05/1.53 % (2182942)Termination reason: Instruction limit
% 4.05/1.53 % (2182942)Termination phase: Saturation
% 4.05/1.53 % (2182942)Time elapsed: 0.067 s
% 4.05/1.53 % (2182942)Peak memory usage: 88 MB
% 4.05/1.53 % (2182942)Instructions burned: 118 (million)
% 4.05/1.53 % (2182941)First to succeed.
% 4.05/1.53 % (2182941)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2182867"
% 4.05/1.53 % (2182950)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=989267127:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.05/1.53 % (2182951)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2755713782:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 4.05/1.53 % (2182950)Refutation not found, incomplete strategy
% 4.05/1.53 % (2182950)------------------------------
% 4.05/1.53 % (2182950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.53 % (2182950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.53 % (2182950)CaDiCaL version: 2.1.3
% 4.05/1.53 % (2182950)Termination reason: Refutation not found, incomplete strategy
% 4.05/1.53 % (2182950)Time elapsed: 0.002 s
% 4.05/1.53 % (2182950)Peak memory usage: 88 MB
% 4.05/1.53 % (2182950)Instructions burned: 1 (million)
% 4.05/1.53 % (2182939)------------------------------
% 4.05/1.53 % (2182939)------------------------------
% 4.05/1.53 % (2182951)Instruction limit reached!
% 4.05/1.53 % (2182951)------------------------------
% 4.05/1.53 % (2182951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.53 % (2182951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.53 % (2182951)CaDiCaL version: 2.1.3
% 4.05/1.53 % (2182951)Termination reason: Instruction limit
% 4.05/1.53 % (2182951)Termination phase: Saturation
% 4.05/1.53 % (2182951)Time elapsed: 0.104 s
% 4.05/1.53 % (2182951)Peak memory usage: 90 MB
% 4.05/1.53 % (2182951)Instructions burned: 190 (million)
% 4.05/1.53 % (2182941)Refutation found. Thanks to Tanya!
% 4.05/1.53 % SZS status Unsatisfiable for theBenchmark
% 4.05/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 4.05/1.53 % (2182941)------------------------------
% 4.05/1.53 % (2182941)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.53 % (2182941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.53 % (2182941)CaDiCaL version: 2.1.3
% 4.05/1.53 % (2182941)Termination reason: Refutation
% 4.05/1.53 % (2182941)Time elapsed: 0.077 s
% 4.05/1.53 % (2182941)Peak memory usage: 90 MB
% 4.05/1.53 % (2182941)Instructions burned: 104 (million)
% 4.05/1.53 % (2182941)------------------------------
% 4.05/1.53 % (2182941)------------------------------
% 4.05/1.53 % (2182867)Success in time 0.48 s
% 4.05/1.53 % Vampire exiting
%------------------------------------------------------------------------------