%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO173+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 : n005.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 09:51:47 AM UTC 2026
% Result : Theorem 3.86s 1.54s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 111 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 113 ( 32 ~; 56 |; 20 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 59 ( 51 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ distinct_points(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
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(f13,conjecture,
! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& distinct_lines(X2,line_connecting(X0,X1)) )
=> ( apart_point_and_line(X0,X2)
| apart_point_and_line(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( distinct_points(X0,X1)
& convergent_lines(X2,X3)
& distinct_lines(X2,line_connecting(X0,X1)) )
=> ( apart_point_and_line(X0,X2)
| apart_point_and_line(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
? [X0,X1,X2,X3] :
( ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2)
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& distinct_lines(X2,line_connecting(X0,X1)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f16,plain,
? [X0,X1,X2,X3] :
( ~ apart_point_and_line(X0,X2)
& ~ apart_point_and_line(X1,X2)
& distinct_points(X0,X1)
& convergent_lines(X2,X3)
& distinct_lines(X2,line_connecting(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(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,[],[f9]) ).
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(f32,plain,
( ~ apart_point_and_line(sK0,sK2)
& ~ apart_point_and_line(sK1,sK2)
& distinct_points(sK0,sK1)
& convergent_lines(sK2,sK3)
& distinct_lines(sK2,line_connecting(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f16]) ).
fof(f33,plain,
distinct_lines(sK2,line_connecting(sK0,sK1)),
inference(cnf_transformation,[],[f32]) ).
fof(f35,plain,
distinct_points(sK0,sK1),
inference(cnf_transformation,[],[f32]) ).
fof(f36,plain,
~ apart_point_and_line(sK1,sK2),
inference(cnf_transformation,[],[f32]) ).
fof(f37,plain,
~ apart_point_and_line(sK0,sK2),
inference(cnf_transformation,[],[f32]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X1)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ apart_point_and_line(X2,line_connecting(X0,X1))
| distinct_points(X2,X0)
| ~ distinct_points(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f41,plain,
! [X0] : ~ distinct_points(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f43,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(f56,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(sK0,sK1))
| apart_point_and_line(X1,sK2)
| apart_point_and_line(X0,line_connecting(sK0,sK1))
| ~ distinct_points(X0,X1)
| apart_point_and_line(X0,sK2) ),
inference(resolution,[],[f33,f43]) ).
fof(f71,plain,
! [X0,X1] :
( apart_point_and_line(X0,sK2)
| apart_point_and_line(X1,line_connecting(sK0,sK1))
| ~ distinct_points(X1,X0)
| apart_point_and_line(X1,sK2)
| distinct_points(X0,sK1)
| ~ distinct_points(sK0,sK1) ),
inference(resolution,[],[f56,f38]) ).
fof(f78,plain,
! [X0,X1] :
( apart_point_and_line(X1,line_connecting(sK0,sK1))
| apart_point_and_line(X0,sK2)
| ~ distinct_points(X1,X0)
| apart_point_and_line(X1,sK2)
| distinct_points(X0,sK1) ),
inference(forward_subsumption_resolution,[],[f71,f35]) ).
fof(f141,plain,
! [X0,X1] :
( apart_point_and_line(X0,sK2)
| ~ distinct_points(X1,X0)
| apart_point_and_line(X1,sK2)
| distinct_points(X0,sK1)
| distinct_points(X1,sK0)
| ~ distinct_points(sK0,sK1) ),
inference(resolution,[],[f78,f39]) ).
fof(f144,plain,
! [X0,X1] :
( ~ distinct_points(X1,X0)
| apart_point_and_line(X0,sK2)
| apart_point_and_line(X1,sK2)
| distinct_points(X0,sK1)
| distinct_points(X1,sK0) ),
inference(forward_subsumption_resolution,[],[f141,f35]) ).
fof(f268,plain,
( apart_point_and_line(sK1,sK2)
| apart_point_and_line(sK0,sK2)
| distinct_points(sK1,sK1)
| distinct_points(sK0,sK0) ),
inference(resolution,[],[f144,f35]) ).
fof(f278,plain,
( apart_point_and_line(sK0,sK2)
| distinct_points(sK1,sK1)
| distinct_points(sK0,sK0) ),
inference(forward_subsumption_resolution,[],[f268,f36]) ).
fof(f281,plain,
( distinct_points(sK1,sK1)
| distinct_points(sK0,sK0) ),
inference(forward_subsumption_resolution,[],[f278,f37]) ).
fof(f290,plain,
distinct_points(sK1,sK1),
inference(forward_subsumption_resolution,[],[f281,f41]) ).
fof(f291,plain,
$false,
inference(forward_subsumption_resolution,[],[f290,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO173+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n005.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % 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 07:22:32 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.86/1.54 % (3648998)Detected formulas, will run a generic FOF schedule.
% 3.86/1.54 % (3649100)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=952907735:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.86/1.54 % (3649099)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=3992353206:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.86/1.54 % (3649098)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=3243299493:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.86/1.54 % (3649101)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2163542811:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.86/1.54 % (3649102)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2818925478:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.86/1.54 % (3649103)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=964941795:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.86/1.54 % (3649101)First to succeed.
% 3.86/1.54 % (3649101)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3648998"
% 3.86/1.54 % (3649103)Also succeeded, but the first one will report.
% 3.86/1.54 % (3649102)Also succeeded, but the first one will report.
% 3.86/1.54 % (3649104)dis-21_1_sil=8000:lcm=predicate:random_seed=2199269247: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)
% 3.86/1.54 % (3649104)Also succeeded, but the first one will report.
% 3.86/1.54 % (3649101)Refutation found. Thanks to Tanya!
% 3.86/1.54 % SZS status Theorem for theBenchmark
% 3.86/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 3.86/1.54 % (3649101)------------------------------
% 3.86/1.54 % (3649101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.86/1.54 % (3649101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/1.54 % (3649101)CaDiCaL version: 2.1.3
% 3.86/1.54 % (3649101)Termination reason: Refutation
% 3.86/1.54 % (3649101)Time elapsed: 0.008 s
% 3.86/1.54 % (3649101)Peak memory usage: 88 MB
% 3.86/1.54 % (3649101)Instructions burned: 10 (million)
% 3.86/1.54 % (3649101)------------------------------
% 3.86/1.54 % (3649101)------------------------------
% 3.86/1.54 % (3648998)Success in time 0.466 s
% 3.86/1.54 % Vampire exiting
%------------------------------------------------------------------------------