%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO027-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 09:51:15 AM UTC 2026
% Result : Unsatisfiable 6.71s 2.03s
% Output : Refutation 6.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 21 ( 4 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 28 ( 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3)
| equidistant(X2,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : between(X0,X1,extension(X0,X1,X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ equidistant(X1,X6,X3,X7)
| ~ equidistant(X1,X4,X3,X5)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X0,X1,X2,X3)
| ~ between(X0,X1,X4)
| ~ between(X2,X3,X5)
| X0 = X1
| equidistant(X4,X6,X5,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).
fof(f19,axiom,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f20,axiom,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
fof(f21,negated_conjecture,
w != extension(u,v,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_w_is_an_extension) ).
fof(f23,plain,
! [X0] : ~ equidistant(extension(u,v,v,w),w,X0,X0),
inference(unit_resulting_resolution,[],[f3,f21]) ).
fof(f48,plain,
! [X0,X1] : equidistant(X0,X1,X0,X1),
inference(unit_resulting_resolution,[],[f2,f5,f5]) ).
fof(f207,plain,
$false,
inference(unit_resulting_resolution,[],[f6,f20,f19,f48,f48,f4,f23,f5,f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO027-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n002.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 06:40:07 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 6.71/1.92 % (3181785)Input is clausal, will run a generic CNF schedule.
% 6.71/1.92 % (3181795)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1466005273:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.71/1.92 % (3181796)dis-21_1_sil=8000:lcm=predicate:random_seed=3113640122: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)
% 6.71/1.92 % (3181793)lrs+10_1_sil=8000:sp=occurrence:random_seed=1455055206:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.71/1.92 % (3181791)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=98710106:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.71/1.92 % (3181792)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4032137287:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.71/1.92 % (3181790)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=489857005:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.71/1.92 % (3181794)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1347884781:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.71/1.92 % (3181795)Instruction limit reached!
% 6.71/1.92 % (3181795)------------------------------
% 6.71/1.92 % (3181795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.92 % (3181795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.92 % (3181795)CaDiCaL version: 2.1.3
% 6.71/1.92 % (3181795)Termination reason: Instruction limit
% 6.71/1.92 % (3181795)Termination phase: Saturation
% 6.71/1.92 % (3181795)Time elapsed: 0.055 s
% 6.71/1.92 % (3181795)Peak memory usage: 89 MB
% 6.71/1.92 % (3181795)Instructions burned: 181 (million)
% 6.71/1.92 % (3181793)Instruction limit reached!
% 6.71/1.92 % (3181793)------------------------------
% 6.71/1.92 % (3181793)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.92 % (3181793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.92 % (3181793)CaDiCaL version: 2.1.3
% 6.71/1.92 % (3181793)Termination reason: Instruction limit
% 6.71/1.92 % (3181793)Termination phase: Saturation
% 6.71/1.92 % (3181793)Time elapsed: 0.069 s
% 6.71/1.92 % (3181793)Peak memory usage: 88 MB
% 6.71/1.92 % (3181793)Instructions burned: 108 (million)
% 6.71/1.92 % (3181796)Instruction limit reached!
% 6.71/1.92 % (3181796)------------------------------
% 6.71/1.92 % (3181796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.92 % (3181796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.92 % (3181796)CaDiCaL version: 2.1.3
% 6.71/1.92 % (3181796)Termination reason: Instruction limit
% 6.71/1.92 % (3181796)Termination phase: Saturation
% 6.71/1.92 % (3181796)Time elapsed: 0.074 s
% 6.71/1.92 % (3181796)Peak memory usage: 89 MB
% 6.71/1.92 % (3181796)Instructions burned: 118 (million)
% 6.71/1.92 % (3181794)Instruction limit reached!
% 6.71/1.92 % (3181794)------------------------------
% 6.71/1.92 % (3181794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.92 % (3181794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.92 % (3181794)CaDiCaL version: 2.1.3
% 6.71/1.92 % (3181794)Termination reason: Instruction limit
% 6.71/1.92 % (3181794)Termination phase: Saturation
% 6.71/1.92 % (3181794)Time elapsed: 0.070 s
% 6.71/1.92 % (3181794)Peak memory usage: 88 MB
% 6.71/1.92 % (3181794)Instructions burned: 115 (million)
% 6.71/1.92 % (3181804)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=3974406691:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 6.71/1.92 % (3181804)Refutation not found, incomplete strategy
% 6.71/1.92 % (3181804)------------------------------
% 6.71/1.92 % (3181804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/1.92 % (3181804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.92 % (3181804)CaDiCaL version: 2.1.3
% 6.71/1.92 % (3181804)Termination reason: Refutation not found, incomplete strategy
% 6.71/1.92 % (3181804)Time elapsed: 0.001 s
% 6.71/1.92 % (3181804)Peak memory usage: 87 MB
% 6.71/1.92 % (3181804)Instructions burned: 1 (million)
% 6.71/1.92 % (3181805)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=71035000: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)
% 6.71/2.03 % (3181806)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3236279529:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 6.71/2.03 % (3181806)Refutation not found, incomplete strategy
% 6.71/2.03 % (3181806)------------------------------
% 6.71/2.03 % (3181806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/2.03 % (3181806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/2.03 % (3181806)CaDiCaL version: 2.1.3
% 6.71/2.03 % (3181806)Termination reason: Refutation not found, incomplete strategy
% 6.71/2.03 % (3181806)Time elapsed: 0.001 s
% 6.71/2.03 % (3181806)Peak memory usage: 87 MB
% 6.71/2.03 % (3181807)lrs+10_64_to=lpo:sil=8000:random_seed=2993167903:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 6.71/2.03 % (3181804)------------------------------
% 6.71/2.03 % (3181804)------------------------------
% 6.71/2.03 % (3181807)Instruction limit reached!
% 6.71/2.03 % (3181807)------------------------------
% 6.71/2.03 % (3181807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/2.03 % (3181807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/2.03 % (3181807)CaDiCaL version: 2.1.3
% 6.71/2.03 % (3181807)Termination reason: Instruction limit
% 6.71/2.03 % (3181807)Termination phase: Saturation
% 6.71/2.03 % (3181807)Time elapsed: 0.082 s
% 6.71/2.03 % (3181807)Peak memory usage: 88 MB
% 6.71/2.03 % (3181807)Instructions burned: 127 (million)
% 6.71/2.03 % (3181805)Instruction limit reached!
% 6.71/2.03 % (3181805)------------------------------
% 6.71/2.03 % (3181805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/2.03 % (3181805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/2.03 % (3181805)CaDiCaL version: 2.1.3
% 6.71/2.03 % (3181805)Termination reason: Instruction limit
% 6.71/2.03 % (3181805)Termination phase: Saturation
% 6.71/2.03 % (3181805)Time elapsed: 0.117 s
% 6.71/2.03 % (3181805)Peak memory usage: 89 MB
% 6.71/2.03 % (3181805)Instructions burned: 189 (million)
% 6.71/2.03 % (3181812)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3999226974:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 6.71/2.03 % (3181813)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=348403242:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 6.71/2.03 % (3181814)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2578189160:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 6.71/2.03 % (3181812)Instruction limit reached!
% 6.71/2.03 % (3181812)------------------------------
% 6.71/2.03 % (3181812)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/2.03 % (3181812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/2.03 % (3181812)CaDiCaL version: 2.1.3
% 6.71/2.03 % (3181812)Termination reason: Instruction limit
% 6.71/2.03 % (3181812)Termination phase: Saturation
% 6.71/2.03 % (3181812)Time elapsed: 0.065 s
% 6.71/2.03 % (3181812)Peak memory usage: 89 MB
% 6.71/2.03 % (3181812)Instructions burned: 196 (million)
% 6.71/2.03 % (3181806)------------------------------
% 6.71/2.03 % (3181806)------------------------------
% 6.71/2.03 % (3181813)Instruction limit reached!
% 6.71/2.03 % (3181813)------------------------------
% 6.71/2.03 % (3181813)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/2.03 % (3181813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/2.03 % (3181813)CaDiCaL version: 2.1.3
% 6.71/2.03 % (3181813)Termination reason: Instruction limit
% 6.71/2.03 % (3181813)Termination phase: Saturation
% 6.71/2.03 % (3181813)Time elapsed: 0.107 s
% 6.71/2.03 % (3181813)Peak memory usage: 90 MB
% 6.71/2.03 % (3181813)Instructions burned: 158 (million)
% 6.71/2.03 % (3181818)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=2302970114:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2994 on theBenchmark for (2994ds/106Mi)
% 6.71/2.03 % (3181818)Instruction limit reached!
% 6.71/2.03 % (3181818)------------------------------
% 6.71/2.03 % (3181818)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/2.03 % (3181818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/2.03 % (3181818)CaDiCaL version: 2.1.3
% 6.71/2.03 % (3181818)Termination reason: Instruction limit
% 6.71/2.03 % (3181818)Termination phase: Saturation
% 6.71/2.03 % (3181818)Time elapsed: 0.033 s
% 6.71/2.03 % (3181818)Peak memory usage: 88 MB
% 6.71/2.03 % (3181818)Instructions burned: 109 (million)
% 6.71/2.03 % (3181819)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=756494519:i=107_2993 on theBenchmark for (2993ds/107Mi)
% 6.71/2.03 % (3181819)Refutation not found, incomplete strategy
% 6.71/2.03 % (3181819)------------------------------
% 6.71/2.03 % (3181819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/2.03 % (3181819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/2.03 % (3181819)CaDiCaL version: 2.1.3
% 6.71/2.03 % (3181819)Termination reason: Refutation not found, incomplete strategy
% 6.71/2.03 % (3181819)Time elapsed: 0.001 s
% 6.71/2.03 % (3181819)Peak memory usage: 87 MB
% 6.71/2.03 % (3181791)First to succeed.
% 6.71/2.03 % (3181791)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3181785"
% 6.71/2.03 % (3181790)Also succeeded, but the first one will report.
% 6.71/2.03 % (3181822)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=1029273141:cond=fast:i=5208:av=off_2992 on theBenchmark for (2992ds/5208Mi)
% 6.71/2.03 % (3181821)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=3232395579:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2993 on theBenchmark for (2993ds/242Mi)
% 6.71/2.03 % (3181821)Instruction limit reached!
% 6.71/2.03 % (3181821)------------------------------
% 6.71/2.03 % (3181821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/2.03 % (3181821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/2.03 % (3181821)CaDiCaL version: 2.1.3
% 6.71/2.03 % (3181821)Termination reason: Instruction limit
% 6.71/2.03 % (3181821)Termination phase: Saturation
% 6.71/2.03 % (3181821)Time elapsed: 0.154 s
% 6.71/2.03 % (3181821)Peak memory usage: 90 MB
% 6.71/2.03 % (3181821)Instructions burned: 244 (million)
% 6.71/2.03 % (3181819)------------------------------
% 6.71/2.03 % (3181819)------------------------------
% 6.71/2.03 % (3181791)Refutation found. Thanks to Tanya!
% 6.71/2.03 % SZS status Unsatisfiable for theBenchmark
% 6.71/2.03 % SZS output start Proof for theBenchmark
% See solution above
% 6.71/2.03 % (3181791)------------------------------
% 6.71/2.03 % (3181791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.71/2.03 % (3181791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/2.03 % (3181791)CaDiCaL version: 2.1.3
% 6.71/2.03 % (3181791)Termination reason: Refutation
% 6.71/2.03 % (3181791)Time elapsed: 0.643 s
% 6.71/2.03 % (3181791)Peak memory usage: 127 MB
% 6.71/2.03 % (3181791)Instructions burned: 947 (million)
% 6.71/2.03 % (3181791)------------------------------
% 6.71/2.03 % (3181791)------------------------------
% 6.71/2.03 % (3181785)Success in time 1.055 s
% 6.71/2.03 % Vampire exiting
%------------------------------------------------------------------------------