%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO182+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 09:51:50 AM UTC 2026
% Result : Theorem 1.63s 1.12s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 74 ( 20 unt; 5 def)
% Number of atoms : 192 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 191 ( 73 ~; 93 |; 10 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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 : 105 ( 0 sgn 99 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
fof(f4,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( distinct_points(X0,X2)
| distinct_points(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart4) ).
fof(f7,axiom,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> ( distinct_points(X2,X0)
& distinct_points(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con1) ).
fof(f9,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/sandbox/benchmark/theBenchmark.p',cu1) ).
fof(f10,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_points(X0,X2)
| apart_point_and_line(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq1) ).
fof(f11,axiom,
! [X0,X1,X2] :
( apart_point_and_line(X0,X1)
=> ( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq2) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> apart_point_and_line(X2,line_connecting(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( distinct_points(X0,X1)
=> ( apart_point_and_line(X2,line_connecting(X0,X1))
=> apart_point_and_line(X2,line_connecting(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X2,line_connecting(X1,X0))
& apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f16,plain,
? [X0,X1,X2] :
( ~ apart_point_and_line(X2,line_connecting(X1,X0))
& apart_point_and_line(X2,line_connecting(X0,X1))
& distinct_points(X0,X1) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X0)
& distinct_points(X2,X1) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( distinct_points(X2,X0)
& distinct_points(X2,X1) )
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f20,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f19]) ).
fof(f21,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,[],[f9]) ).
fof(f22,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,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f24,plain,
! [X0,X1,X2] :
( distinct_points(X0,X2)
| distinct_points(X1,X2)
| ~ distinct_points(X0,X1) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f26,plain,
! [X0,X1,X2] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(flattening,[],[f25]) ).
fof(f34,plain,
( ~ apart_point_and_line(sK2,line_connecting(sK1,sK0))
& apart_point_and_line(sK2,line_connecting(sK0,sK1))
& distinct_points(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f16]) ).
fof(f35,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f36,plain,
apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f34]) ).
fof(f37,plain,
~ apart_point_and_line(sK2,line_connecting(sK1,sK0)),
inference(cnf_transformation,[],[f34]) ).
fof(f38,plain,
! [X2,X0,X1] :
( distinct_points(X2,X1)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f39,plain,
! [X2,X0,X1] :
( distinct_points(X2,X0)
| ~ apart_point_and_line(X2,line_connecting(X0,X1))
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f40,plain,
! [X2,X0,X1] :
( distinct_points(X0,X2)
| apart_point_and_line(X2,X1)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f41,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,[],[f22]) ).
fof(f42,plain,
! [X2,X0,X1] :
( distinct_points(X1,X2)
| distinct_points(X0,X2)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f43,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f44,plain,
! [X2,X0,X1] :
( distinct_lines(X1,X2)
| apart_point_and_line(X0,X2)
| ~ apart_point_and_line(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f59,plain,
! [X0,X1] :
( ~ distinct_points(X1,X0)
| ~ apart_point_and_line(X0,line_connecting(X1,X0)) ),
inference(resolution,[],[f38,f43]) ).
fof(f60,plain,
~ apart_point_and_line(sK1,line_connecting(sK0,sK1)),
inference(resolution,[],[f59,f35]) ).
fof(f62,plain,
! [X2,X0,X1] :
( distinct_points(X2,X0)
| ~ apart_point_and_line(X0,line_connecting(X1,X0))
| ~ distinct_points(X2,X1) ),
inference(resolution,[],[f59,f42]) ).
fof(f64,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X0,X1)) ),
inference(resolution,[],[f39,f43]) ).
fof(f67,plain,
~ apart_point_and_line(sK0,line_connecting(sK0,sK1)),
inference(resolution,[],[f64,f35]) ).
fof(f71,plain,
! [X2,X0,X1] :
( apart_point_and_line(X1,X2)
| ~ apart_point_and_line(X0,line_connecting(X0,X1))
| ~ apart_point_and_line(X0,X2) ),
inference(resolution,[],[f64,f40]) ).
fof(f75,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,[],[f41,f44]) ).
fof(f76,plain,
! [X0,X1] :
( ~ distinct_points(X0,X1)
| ~ apart_point_and_line(X0,line_connecting(X1,X0)) ),
inference(resolution,[],[f62,f43]) ).
fof(f82,plain,
~ apart_point_and_line(sK0,line_connecting(sK1,sK0)),
inference(resolution,[],[f76,f35]) ).
fof(f99,plain,
! [X2,X0,X1] :
( apart_point_and_line(X2,X1)
| apart_point_and_line(sK1,X1)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK1,X0)
| ~ apart_point_and_line(X2,X0) ),
inference(resolution,[],[f75,f35]) ).
fof(f113,plain,
! [X0] :
( apart_point_and_line(sK1,line_connecting(sK1,sK0))
| apart_point_and_line(sK0,line_connecting(sK1,sK0))
| apart_point_and_line(sK0,X0)
| apart_point_and_line(sK1,X0)
| ~ apart_point_and_line(sK2,X0) ),
inference(resolution,[],[f99,f37]) ).
fof(f116,definition,
( spl3_1
<=> ! [X1] :
( apart_point_and_line(sK0,X1)
| ~ apart_point_and_line(sK2,X1)
| apart_point_and_line(sK1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f117,plain,
( ! [X1] :
( ~ apart_point_and_line(sK2,X1)
| apart_point_and_line(sK0,X1)
| apart_point_and_line(sK1,X1) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f123,definition,
( spl3_3
<=> apart_point_and_line(sK0,line_connecting(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f124,plain,
( apart_point_and_line(sK0,line_connecting(sK1,sK0))
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f126,definition,
( spl3_4
<=> apart_point_and_line(sK1,line_connecting(sK1,sK0)) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f127,plain,
( apart_point_and_line(sK1,line_connecting(sK1,sK0))
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f128,plain,
( spl3_1
| spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f113,f126,f123,f116]) ).
fof(f133,plain,
( $false
| ~ spl3_3 ),
inference(resolution,[],[f124,f82]) ).
fof(f134,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f133]) ).
fof(f150,plain,
! [X0] :
( ~ apart_point_and_line(X0,line_connecting(X0,sK0))
| ~ apart_point_and_line(X0,line_connecting(sK1,sK0)) ),
inference(resolution,[],[f71,f82]) ).
fof(f253,plain,
~ apart_point_and_line(sK1,line_connecting(sK1,sK0)),
inference(factoring,[],[f150]) ).
fof(f258,plain,
( $false
| ~ spl3_4 ),
inference(resolution,[],[f253,f127]) ).
fof(f262,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[],[f258]) ).
fof(f267,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl3_1 ),
inference(resolution,[],[f117,f36]) ).
fof(f275,definition,
( spl3_7
<=> apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f276,plain,
( apart_point_and_line(sK1,line_connecting(sK0,sK1))
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f278,definition,
( spl3_8
<=> apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
fof(f279,plain,
( apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f280,plain,
( spl3_7
| spl3_8
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f267,f116,f278,f275]) ).
fof(f281,plain,
( $false
| ~ spl3_7 ),
inference(resolution,[],[f276,f60]) ).
fof(f285,plain,
~ spl3_7,
inference(avatar_contradiction_clause,[],[f281]) ).
fof(f312,plain,
( $false
| ~ spl3_8 ),
inference(resolution,[],[f279,f67]) ).
fof(f315,plain,
~ spl3_8,
inference(avatar_contradiction_clause,[],[f312]) ).
cnf(s2,plain,
( spl3_1
| spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f128]) ).
cnf(s4,plain,
~ spl3_3,
inference(sat_conversion,[],[f134]) ).
cnf(s5,plain,
~ spl3_4,
inference(sat_conversion,[],[f262]) ).
cnf(s9,plain,
( ~ spl3_1
| spl3_7
| spl3_8 ),
inference(sat_conversion,[],[f280]) ).
cnf(s10,plain,
~ spl3_7,
inference(sat_conversion,[],[f285]) ).
cnf(s14,plain,
~ spl3_8,
inference(sat_conversion,[],[f315]) ).
cnf(s16,plain,
~ spl3_1,
inference(rat,[],[s9,s14,s10]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s2,s5,s4,s16]) ).
fof(f316,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO182+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 07:24:10 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 1.63/1.12 % (1070034)Detected formulas, will run a generic FOF schedule.
% 1.63/1.12 % (1070045)dis-21_1_sil=8000:lcm=predicate:random_seed=3631777492: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)
% 1.63/1.12 % (1070045)First to succeed.
% 1.63/1.12 % (1070045)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1070034"
% 1.63/1.12 % (1070044)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2725766623:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.63/1.12 % (1070040)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=733327156:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.63/1.12 % (1070039)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=2674665207:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.63/1.12 % (1070042)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1022196893:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.63/1.12 % (1070043)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2670041366:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.63/1.12 % (1070041)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=3274354767:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.63/1.12 % (1070044)Also succeeded, but the first one will report.
% 1.63/1.12 % (1070043)Instruction limit reached!
% 1.63/1.12 % (1070043)------------------------------
% 1.63/1.12 % (1070043)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.63/1.12 % (1070043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/1.12 % (1070043)CaDiCaL version: 2.1.3
% 1.63/1.12 % (1070043)Termination reason: Instruction limit
% 1.63/1.12 % (1070043)Termination phase: Saturation
% 1.63/1.12 % (1070043)Time elapsed: 0.048 s
% 1.63/1.12 % (1070043)Peak memory usage: 87 MB
% 1.63/1.12 % (1070043)Instructions burned: 121 (million)
% 1.63/1.12 % (1070042)Instruction limit reached!
% 1.63/1.12 % (1070042)------------------------------
% 1.63/1.12 % (1070042)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.63/1.12 % (1070042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/1.12 % (1070042)CaDiCaL version: 2.1.3
% 1.63/1.12 % (1070042)Termination reason: Instruction limit
% 1.63/1.12 % (1070042)Termination phase: Saturation
% 1.63/1.12 % (1070042)Time elapsed: 0.054 s
% 1.63/1.12 % (1070042)Peak memory usage: 88 MB
% 1.63/1.12 % (1070042)Instructions burned: 109 (million)
% 1.63/1.12 % (1070045)Refutation found. Thanks to Tanya!
% 1.63/1.12 % SZS status Theorem for theBenchmark
% 1.63/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.31 % (1070045)------------------------------
% 2.65/1.31 % (1070045)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.31 % (1070045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.31 % (1070045)CaDiCaL version: 2.1.3
% 2.65/1.31 % (1070045)Termination reason: Refutation
% 2.65/1.31 % (1070045)Time elapsed: 0.004 s
% 2.65/1.31 % (1070045)Peak memory usage: 89 MB
% 2.65/1.31 % (1070045)Instructions burned: 9 (million)
% 2.65/1.31 % (1070045)------------------------------
% 2.65/1.31 % (1070045)------------------------------
% 2.65/1.31 % (1070034)Success in time 0.288 s
% 2.65/1.31 % Vampire exiting
%------------------------------------------------------------------------------