%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO189+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 09:51:53 AM UTC 2026
% Result : Theorem 1.75s 1.11s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 63 ( 20 unt; 5 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 160 ( 61 ~; 69 |; 19 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 57 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci1) ).
fof(f8,axiom,
! [X0,X1] :
( distinct_points(X0,X1)
=> ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci2) ).
fof(f11,axiom,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& distinct_lines(X2,X3) )
=> ( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cu1) ).
fof(f13,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq2) ).
fof(f15,conjecture,
! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) )
=> ~ apart_point_and_line(X1,line_connecting(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) )
=> ~ apart_point_and_line(X1,line_connecting(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
? [X0,X1,X2] :
( apart_point_and_line(X1,line_connecting(X0,X2))
& distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f18,plain,
? [X0,X1,X2] :
( apart_point_and_line(X1,line_connecting(X0,X2))
& distinct_points(X0,X1)
& distinct_points(X0,X2)
& distinct_points(X1,X2)
& ~ apart_point_and_line(X2,line_connecting(X0,X1)) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ~ apart_point_and_line(X1,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f20,plain,
! [X0,X1] :
( ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(ennf_transformation,[],[f11]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( apart_point_and_line(X0,X2)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| ~ distinct_lines(X2,X3) ),
inference(flattening,[],[f23]) ).
fof(f27,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f28,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f27]) ).
fof(f37,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK2))
& distinct_points(sK0,sK1)
& distinct_points(sK0,sK2)
& distinct_points(sK1,sK2)
& ~ apart_point_and_line(sK2,line_connecting(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f18]) ).
fof(f38,plain,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f37]) ).
fof(f40,plain,
distinct_points(sK0,sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f41,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f42,plain,
apart_point_and_line(sK1,line_connecting(sK0,sK2)),
inference(cnf_transformation,[],[f37]) ).
fof(f43,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X1,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( ~ distinct_lines(X2,X3)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| ~ distinct_points(X0,X1)
| apart_point_and_line(X0,X2) ),
inference(cnf_transformation,[],[f24]) ).
fof(f49,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f58,plain,
~ apart_point_and_line(sK2,line_connecting(sK0,sK2)),
inference(resolution,[],[f43,f40]) ).
fof(f59,plain,
~ apart_point_and_line(sK1,line_connecting(sK0,sK1)),
inference(resolution,[],[f43,f41]) ).
fof(f61,plain,
~ apart_point_and_line(sK0,line_connecting(sK0,sK2)),
inference(resolution,[],[f44,f40]) ).
fof(f62,plain,
~ apart_point_and_line(sK0,line_connecting(sK0,sK1)),
inference(resolution,[],[f44,f41]) ).
fof(f84,plain,
! [X2,X3,X0,X1,X4] :
( ~ distinct_points(X0,X2)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X1)
| apart_point_and_line(X0,X1)
| apart_point_and_line(X0,X3)
| apart_point_and_line(X4,X1)
| ~ apart_point_and_line(X4,X3) ),
inference(resolution,[],[f46,f49]) ).
fof(f146,plain,
! [X2,X0,X1] :
( apart_point_and_line(X2,X1)
| apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK2,X0)
| ~ apart_point_and_line(X2,X0) ),
inference(resolution,[],[f84,f40]) ).
fof(f236,definition,
( spl3_7
<=> apart_point_and_line(sK2,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f237,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK1))
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f263,plain,
( $false
| ~ spl3_7 ),
inference(resolution,[],[f237,f38]) ).
fof(f266,plain,
~ spl3_7,
inference(avatar_contradiction_clause,[],[f263]) ).
fof(f345,definition,
( spl3_17
<=> apart_point_and_line(sK1,line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_17])],[avatar_definition]) ).
fof(f346,plain,
( ~ apart_point_and_line(sK1,line_connecting(sK0,sK2))
| spl3_17 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f348,plain,
( $false
| spl3_17 ),
inference(resolution,[],[f346,f42]) ).
fof(f352,plain,
spl3_17,
inference(avatar_contradiction_clause,[],[f348]) ).
fof(f468,plain,
! [X0] :
( apart_point_and_line(sK2,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK2,X0)
| ~ apart_point_and_line(sK1,X0) ),
inference(resolution,[],[f146,f59]) ).
fof(f479,definition,
( spl3_21
<=> ! [X1] :
( apart_point_and_line(sK0,X1)
| ~ apart_point_and_line(sK1,X1)
| apart_point_and_line(sK2,X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_21])],[avatar_definition]) ).
fof(f480,plain,
( ! [X1] :
( apart_point_and_line(sK2,X1)
| ~ apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X1) )
| ~ spl3_21 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f495,definition,
( spl3_25
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_25])],[avatar_definition]) ).
fof(f496,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_25 ),
inference(avatar_component_clause,[],[f495]) ).
fof(f497,plain,
( spl3_21
| spl3_25
| spl3_7 ),
inference(avatar_split_clause,[],[f468,f236,f495,f479]) ).
fof(f517,plain,
( $false
| ~ spl3_25 ),
inference(resolution,[],[f496,f62]) ).
fof(f520,plain,
~ spl3_25,
inference(avatar_contradiction_clause,[],[f517]) ).
fof(f522,plain,
( ~ apart_point_and_line(sK1,line_connecting(sK0,sK2))
| apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ spl3_21 ),
inference(resolution,[],[f480,f58]) ).
fof(f543,definition,
( spl3_28
<=> apart_point_and_line(sK0,line_connecting(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl3_28])],[avatar_definition]) ).
fof(f544,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ spl3_28 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f545,plain,
( spl3_28
| ~ spl3_17
| ~ spl3_21 ),
inference(avatar_split_clause,[],[f522,f479,f345,f543]) ).
fof(f546,plain,
( $false
| ~ spl3_28 ),
inference(resolution,[],[f544,f61]) ).
fof(f550,plain,
~ spl3_28,
inference(avatar_contradiction_clause,[],[f546]) ).
cnf(s10,plain,
~ spl3_7,
inference(sat_conversion,[],[f266]) ).
cnf(s19,plain,
spl3_17,
inference(sat_conversion,[],[f352]) ).
cnf(s28,plain,
( spl3_7
| spl3_21
| spl3_25 ),
inference(sat_conversion,[],[f497]) ).
cnf(s36,plain,
~ spl3_25,
inference(sat_conversion,[],[f520]) ).
cnf(s37,plain,
( ~ spl3_17
| ~ spl3_21
| spl3_28 ),
inference(sat_conversion,[],[f545]) ).
cnf(s38,plain,
~ spl3_28,
inference(sat_conversion,[],[f550]) ).
cnf(s39,plain,
( ~ spl3_17
| ~ spl3_21 ),
inference(rat,[],[s37,s38]) ).
cnf(s44,plain,
( spl3_7
| spl3_21 ),
inference(rat,[],[s28,s36]) ).
cnf(s46,plain,
~ spl3_21,
inference(rat,[],[s39,s19]) ).
cnf(s47,plain,
spl3_7,
inference(rat,[],[s44,s46]) ).
cnf(s55,plain,
$false,
inference(rat,[],[s10,s47]) ).
fof(f551,plain,
$false,
inference(avatar_sat_refutation,[],[s55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO189+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 07:32:30 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 1.75/1.11 % (1317985)Detected formulas, will run a generic FOF schedule.
% 1.75/1.11 % (1317996)dis-21_1_sil=8000:lcm=predicate:random_seed=1873514894: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)
% 1.75/1.11 % (1317996)First to succeed.
% 1.75/1.11 % (1317996)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1317985"
% 1.75/1.11 % (1317992)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=879579842:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.75/1.11 % (1317991)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=2117834384:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.75/1.11 % (1317990)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=805761498:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.75/1.11 % (1317995)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2437791796:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.75/1.11 % (1317994)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1203351815:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.75/1.11 % (1317993)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3721390311:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.75/1.11 % (1317995)Also succeeded, but the first one will report.
% 1.75/1.11 % (1317994)Instruction limit reached!
% 1.75/1.11 % (1317994)------------------------------
% 1.75/1.11 % (1317994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.75/1.11 % (1317994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.75/1.11 % (1317994)CaDiCaL version: 2.1.3
% 1.75/1.11 % (1317994)Termination reason: Instruction limit
% 1.75/1.11 % (1317994)Termination phase: Saturation
% 1.75/1.11 % (1317994)Time elapsed: 0.047 s
% 1.75/1.11 % (1317994)Peak memory usage: 87 MB
% 1.75/1.11 % (1317994)Instructions burned: 122 (million)
% 1.75/1.11 % (1317993)Instruction limit reached!
% 1.75/1.11 % (1317993)------------------------------
% 1.75/1.11 % (1317993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.75/1.11 % (1317993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.75/1.11 % (1317993)CaDiCaL version: 2.1.3
% 1.75/1.11 % (1317993)Termination reason: Instruction limit
% 1.75/1.11 % (1317993)Termination phase: Saturation
% 1.75/1.11 % (1317993)Time elapsed: 0.054 s
% 1.75/1.11 % (1317993)Peak memory usage: 88 MB
% 1.75/1.11 % (1317993)Instructions burned: 111 (million)
% 1.75/1.11 % (1317996)Refutation found. Thanks to Tanya!
% 1.75/1.11 % SZS status Theorem for theBenchmark
% 1.75/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.30 % (1317996)------------------------------
% 0.15/1.30 % (1317996)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.30 % (1317996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.30 % (1317996)CaDiCaL version: 2.1.3
% 0.15/1.30 % (1317996)Termination reason: Refutation
% 0.15/1.30 % (1317996)Time elapsed: 0.005 s
% 0.15/1.30 % (1317996)Peak memory usage: 89 MB
% 0.15/1.30 % (1317996)Instructions burned: 13 (million)
% 0.15/1.30 % (1317996)------------------------------
% 0.15/1.30 % (1317996)------------------------------
% 0.15/1.30 % (1317985)Success in time 0.27 s
% 0.15/1.30 % Vampire exiting
%------------------------------------------------------------------------------