%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO068-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 09:51:26 AM UTC 2026
% Result : Unsatisfiable 4.10s 1.54s
% Output : Refutation 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 23
% Syntax : Number of formulae : 84 ( 22 unt; 8 def)
% Number of atoms : 172 ( 4 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 165 ( 77 ~; 80 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| colinear(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity1) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| colinear(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity3) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ colinear(X0,X1,X2)
| between(X0,X1,X2)
| between(X1,X2,X0)
| between(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity4) ).
fof(f29,axiom,
! [X2,X3,X0,X1] :
( ~ equidistant(X0,X1,X2,X3)
| equidistant(X1,X0,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_2) ).
fof(f56,axiom,
! [X0,X1] : between(X0,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
fof(f58,axiom,
! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| between(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
fof(f60,axiom,
! [X2,X0,X1] :
( ~ between(X1,X0,X2)
| ~ between(X0,X1,X2)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).
fof(f89,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X1,X2,X3)
| ~ equidistant(X0,X4,X2,X5)
| ~ between(X0,X1,X4)
| between(X2,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b11) ).
fof(f98,axiom,
! [X2,X0,X1] :
( ~ between(X0,X1,X2)
| colinear(X0,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_2) ).
fof(f102,axiom,
! [X2,X0,X1] :
( ~ colinear(X0,X1,X2)
| colinear(X0,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_3) ).
fof(f110,axiom,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
fof(f111,axiom,
equidistant(v,w,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).
fof(f112,axiom,
equidistant(u,w,u1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_w_equals_u1_to_w1) ).
fof(f113,axiom,
colinear(u,v,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uvw_colinear) ).
fof(f114,negated_conjecture,
~ colinear(u1,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_u1v1w1_colinear) ).
fof(f146,plain,
colinear(u,w,v),
inference(resolution,[],[f102,f113]) ).
fof(f214,plain,
equidistant(w,u,w1,u1),
inference(resolution,[],[f29,f112]) ).
fof(f215,plain,
equidistant(w,v,w1,v1),
inference(resolution,[],[f29,f111]) ).
fof(f410,plain,
( between(u,v,w)
| between(v,w,u)
| between(w,u,v) ),
inference(resolution,[],[f22,f113]) ).
fof(f411,plain,
( between(u,w,v)
| between(w,v,u)
| between(v,u,w) ),
inference(resolution,[],[f22,f146]) ).
fof(f417,definition,
( spl0_1
<=> between(v,w,u) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f421,definition,
( spl0_2
<=> between(u,v,w) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f422,plain,
( ~ between(u,v,w)
| spl0_2 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f423,plain,
( between(u,v,w)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f425,definition,
( spl0_3
<=> between(w,u,v) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f427,plain,
( between(w,u,v)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f430,definition,
( spl0_4
<=> between(u,w,v) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f432,plain,
( between(u,w,v)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f434,definition,
( spl0_5
<=> between(v,u,w) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f436,plain,
( between(v,u,w)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f438,definition,
( spl0_6
<=> between(w,v,u) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f440,plain,
( between(w,v,u)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f438]) ).
fof(f444,plain,
( spl0_5
| spl0_6
| spl0_4 ),
inference(avatar_split_clause,[],[f411,f430,f438,f434]) ).
fof(f445,plain,
( spl0_3
| spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f410,f421,f417,f425]) ).
fof(f484,plain,
( between(w,u,v)
| ~ spl0_5 ),
inference(resolution,[],[f436,f58]) ).
fof(f511,plain,
( spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f484,f434,f425]) ).
fof(f522,plain,
( ~ between(v,w,u)
| v = w
| ~ spl0_6 ),
inference(resolution,[],[f440,f60]) ).
fof(f536,definition,
( spl0_13
<=> v = w ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f538,plain,
( v = w
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f536]) ).
fof(f548,plain,
( spl0_13
| ~ spl0_1
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f522,f438,f417,f536]) ).
fof(f694,plain,
! [X0,X1] :
( ~ equidistant(X0,v,X1,v1)
| ~ equidistant(X0,u,X1,u1)
| ~ between(X0,u,v)
| between(X1,u1,v1) ),
inference(resolution,[],[f89,f110]) ).
fof(f698,plain,
! [X0,X1] :
( ~ equidistant(X0,w,X1,w1)
| ~ equidistant(X0,v,X1,v1)
| ~ between(X0,v,w)
| between(X1,v1,w1) ),
inference(resolution,[],[f89,f111]) ).
fof(f712,plain,
! [X0,X1] :
( ~ equidistant(X0,w,X1,w1)
| ~ equidistant(X0,v,X1,v1)
| ~ between(X0,w,v)
| between(X1,w1,v1) ),
inference(resolution,[],[f89,f215]) ).
fof(f1275,plain,
( ~ equidistant(w,u,w1,u1)
| ~ between(w,u,v)
| between(w1,u1,v1) ),
inference(resolution,[],[f694,f215]) ).
fof(f1278,plain,
( ~ between(w,u,v)
| between(w1,u1,v1) ),
inference(forward_subsumption_resolution,[],[f1275,f214]) ).
fof(f1281,plain,
( between(w1,u1,v1)
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f1278,f427]) ).
fof(f1290,plain,
( colinear(u1,v1,w1)
| ~ spl0_3 ),
inference(resolution,[],[f1281,f21]) ).
fof(f1342,definition,
( spl0_33
<=> between(u1,w1,v1) ),
introduced(definition,[new_symbols(definition,[spl0_33])],[avatar_definition]) ).
fof(f1343,plain,
( between(u1,w1,v1)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f1342]) ).
fof(f1346,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f1290,f114]) ).
fof(f1347,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f1346]) ).
fof(f1481,plain,
( ~ equidistant(u,v,u1,v1)
| ~ between(u,v,w)
| between(u1,v1,w1) ),
inference(resolution,[],[f698,f112]) ).
fof(f1483,plain,
( ~ between(u,v,w)
| between(u1,v1,w1) ),
inference(forward_subsumption_resolution,[],[f1481,f110]) ).
fof(f1486,plain,
( between(u1,v1,w1)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1483,f423]) ).
fof(f2020,plain,
( colinear(u1,v1,w1)
| ~ spl0_2 ),
inference(resolution,[],[f1486,f19]) ).
fof(f2071,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f2020,f114]) ).
fof(f2072,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f2071]) ).
fof(f2073,plain,
( ~ between(u,v,v)
| spl0_2
| ~ spl0_13 ),
inference(forward_demodulation,[],[f422,f538]) ).
fof(f2078,plain,
( $false
| spl0_2
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f2073,f56]) ).
fof(f2079,plain,
( spl0_2
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f2078]) ).
fof(f3256,plain,
( ~ equidistant(u,v,u1,v1)
| ~ between(u,w,v)
| between(u1,w1,v1) ),
inference(resolution,[],[f712,f112]) ).
fof(f3258,plain,
( ~ between(u,w,v)
| between(u1,w1,v1) ),
inference(forward_subsumption_resolution,[],[f3256,f110]) ).
fof(f3259,plain,
( between(u1,w1,v1)
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f3258,f432]) ).
fof(f3260,plain,
( spl0_33
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f3259,f430,f1342]) ).
fof(f3279,plain,
( colinear(u1,v1,w1)
| ~ spl0_33 ),
inference(resolution,[],[f1343,f98]) ).
fof(f3281,plain,
( $false
| ~ spl0_33 ),
inference(forward_subsumption_resolution,[],[f3279,f114]) ).
fof(f3282,plain,
~ spl0_33,
inference(avatar_contradiction_clause,[],[f3281]) ).
cnf(s5,plain,
( spl0_4
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f444]) ).
cnf(s6,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f445]) ).
cnf(s14,plain,
( spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f511]) ).
cnf(s19,plain,
( ~ spl0_1
| ~ spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f548]) ).
cnf(s42,plain,
~ spl0_3,
inference(sat_conversion,[],[f1347]) ).
cnf(s115,plain,
~ spl0_2,
inference(sat_conversion,[],[f2072]) ).
cnf(s116,plain,
( spl0_2
| ~ spl0_13 ),
inference(sat_conversion,[],[f2079]) ).
cnf(s220,plain,
( ~ spl0_4
| spl0_33 ),
inference(sat_conversion,[],[f3260]) ).
cnf(s221,plain,
~ spl0_33,
inference(sat_conversion,[],[f3282]) ).
cnf(s227,plain,
~ spl0_4,
inference(rat,[],[s220,s221]) ).
cnf(s228,plain,
~ spl0_13,
inference(rat,[],[s116,s115]) ).
cnf(s235,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(rat,[],[s19,s228]) ).
cnf(s238,plain,
~ spl0_5,
inference(rat,[],[s14,s42]) ).
cnf(s242,plain,
spl0_1,
inference(rat,[],[s6,s42,s115]) ).
cnf(s243,plain,
~ spl0_6,
inference(rat,[],[s235,s242]) ).
cnf(s245,plain,
$false,
inference(rat,[],[s5,s243,s238,s227]) ).
fof(f3303,plain,
$false,
inference(avatar_sat_refutation,[],[s245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO068-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 06:55:30 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 3.13/1.34 % (3210736)Input is clausal, will run a generic CNF schedule.
% 3.13/1.34 % (3210745)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2296418727:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.13/1.34 % (3210745)Instruction limit reached!
% 3.13/1.34 % (3210745)------------------------------
% 3.13/1.34 % (3210745)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.34 % (3210745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.34 % (3210745)CaDiCaL version: 2.1.3
% 3.13/1.34 % (3210745)Termination reason: Instruction limit
% 3.13/1.34 % (3210745)Termination phase: Saturation
% 3.13/1.34 % (3210745)Time elapsed: 0.034 s
% 3.13/1.34 % (3210745)Peak memory usage: 88 MB
% 3.13/1.34 % (3210745)Instructions burned: 115 (million)
% 3.13/1.34 % (3210747)dis-21_1_sil=8000:lcm=predicate:random_seed=4025513507: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)
% 3.13/1.34 % (3210744)lrs+10_1_sil=8000:sp=occurrence:random_seed=653445681:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.13/1.34 % (3210741)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=1735039482:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.13/1.34 % (3210742)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2757839767:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.13/1.34 % (3210743)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1796187232:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.13/1.34 % (3210746)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2734278803:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.13/1.34 % (3210744)First to succeed.
% 3.13/1.34 % (3210744)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3210736"
% 3.13/1.34 % (3210747)Instruction limit reached!
% 3.13/1.34 % (3210747)------------------------------
% 3.13/1.34 % (3210747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.34 % (3210747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.34 % (3210747)CaDiCaL version: 2.1.3
% 3.13/1.34 % (3210747)Termination reason: Instruction limit
% 3.13/1.34 % (3210747)Termination phase: Saturation
% 3.13/1.34 % (3210747)Time elapsed: 0.070 s
% 3.13/1.34 % (3210747)Peak memory usage: 89 MB
% 3.13/1.34 % (3210747)Instructions burned: 118 (million)
% 3.13/1.34 % (3210749)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=330892800:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.13/1.34 % (3210746)Instruction limit reached!
% 3.13/1.34 % (3210746)------------------------------
% 3.13/1.34 % (3210746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.34 % (3210746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.34 % (3210746)CaDiCaL version: 2.1.3
% 3.13/1.34 % (3210746)Termination reason: Instruction limit
% 3.13/1.34 % (3210746)Termination phase: Saturation
% 3.13/1.34 % (3210746)Time elapsed: 0.118 s
% 3.13/1.34 % (3210746)Peak memory usage: 90 MB
% 3.13/1.34 % (3210746)Instructions burned: 181 (million)
% 3.13/1.34 % (3210749)Instruction limit reached!
% 3.13/1.34 % (3210749)------------------------------
% 3.13/1.34 % (3210749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.34 % (3210749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.34 % (3210749)CaDiCaL version: 2.1.3
% 3.13/1.34 % (3210749)Termination reason: Instruction limit
% 3.13/1.34 % (3210749)Termination phase: Saturation
% 3.13/1.34 % (3210749)Time elapsed: 0.049 s
% 3.13/1.34 % (3210749)Peak memory usage: 89 MB
% 3.13/1.34 % (3210749)Instructions burned: 144 (million)
% 3.13/1.34 % (3210756)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=840607172: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)
% 3.13/1.34 % (3210758)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1122021660:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.13/1.34 % (3210759)lrs+10_64_to=lpo:sil=8000:random_seed=3947232217:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 4.10/1.54 % (3210756)Also succeeded, but the first one will report.
% 4.10/1.54 % (3210744)Refutation found. Thanks to Tanya!
% 4.10/1.54 % SZS status Unsatisfiable for theBenchmark
% 4.10/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 4.10/1.54 % (3210744)------------------------------
% 4.10/1.54 % (3210744)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.10/1.54 % (3210744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.10/1.54 % (3210744)CaDiCaL version: 2.1.3
% 4.10/1.54 % (3210744)Termination reason: Refutation
% 4.10/1.54 % (3210744)Time elapsed: 0.059 s
% 4.10/1.54 % (3210744)Peak memory usage: 90 MB
% 4.10/1.54 % (3210744)Instructions burned: 100 (million)
% 4.10/1.54 % (3210744)------------------------------
% 4.10/1.54 % (3210744)------------------------------
% 4.10/1.54 % (3210736)Success in time 0.495 s
% 4.10/1.54 % Vampire exiting
%------------------------------------------------------------------------------