%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO266+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 09:52:17 AM UTC 2026
% Result : Theorem 0.42s 0.83s
% Output : Refutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 8 unt; 2 def)
% Number of atoms : 137 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 135 ( 60 ~; 60 |; 5 &)
% ( 6 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 67 ( 0 sgn 63 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
<=> unequally_directed_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_defns) ).
fof(f4,axiom,
! [X0,X1] :
( equally_directed_lines(X0,X1)
<=> ~ unequally_directed_lines(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4_defns) ).
fof(f15,axiom,
! [X0] : equally_directed_lines(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5_basics) ).
fof(f16,axiom,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X1)
=> ( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6_basics) ).
fof(f18,axiom,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| unequally_directed_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8_basics) ).
fof(f19,axiom,
! [X0,X1] :
( ( unequally_directed_lines(X0,X1)
& unequally_directed_lines(X0,reverse_line(X1)) )
=> ( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9_basics) ).
fof(f21,axiom,
! [X0,X1] :
~ ( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11_basics) ).
fof(f37,conjecture,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
<=> unequally_directed_opposite_lines(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(f38,negated_conjecture,
~ ! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
<=> unequally_directed_opposite_lines(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( equally_directed_lines(X0,X1)
=> ~ unequally_directed_lines(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f43,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,X1)
| ~ equally_directed_lines(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f49,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f50,plain,
! [X0,X1,X2] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(flattening,[],[f49]) ).
fof(f53,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f19]) ).
fof(f54,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(flattening,[],[f53]) ).
fof(f56,plain,
! [X0,X1] :
( ~ left_convergent_lines(X0,X1)
& ~ left_convergent_lines(X0,reverse_line(X1)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f78,plain,
? [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
<~> unequally_directed_opposite_lines(X1,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f79,plain,
! [X0,X1] :
( ( unequally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) )
& ( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f80,plain,
? [X0,X1] :
( ( ~ unequally_directed_opposite_lines(X1,X0)
| ~ unequally_directed_opposite_lines(X0,X1) )
& ( unequally_directed_opposite_lines(X1,X0)
| unequally_directed_opposite_lines(X0,X1) ) ),
inference(nnf_transformation,[],[f78]) ).
fof(f81,plain,
( ( ~ unequally_directed_opposite_lines(sK1,sK0)
| ~ unequally_directed_opposite_lines(sK0,sK1) )
& ( unequally_directed_opposite_lines(sK1,sK0)
| unequally_directed_opposite_lines(sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f83,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_opposite_lines(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f85,plain,
! [X0,X1] :
( ~ equally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f92,plain,
! [X0] : equally_directed_lines(X0,X0),
inference(cnf_transformation,[],[f15]) ).
fof(f93,plain,
! [X2,X0,X1] :
( unequally_directed_lines(X0,X2)
| unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f98,plain,
! [X0,X1] :
( unequally_directed_lines(X0,reverse_line(X1))
| unequally_directed_lines(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f99,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| left_convergent_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f103,plain,
! [X0,X1] : ~ left_convergent_lines(X0,X1),
inference(cnf_transformation,[],[f56]) ).
fof(f121,plain,
( unequally_directed_opposite_lines(sK1,sK0)
| unequally_directed_opposite_lines(sK0,sK1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f122,plain,
( ~ unequally_directed_opposite_lines(sK1,sK0)
| ~ unequally_directed_opposite_lines(sK0,sK1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f124,definition,
( spl2_1
<=> unequally_directed_opposite_lines(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f125,plain,
( ~ unequally_directed_opposite_lines(sK0,sK1)
| spl2_1 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f126,plain,
( unequally_directed_opposite_lines(sK0,sK1)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f128,definition,
( spl2_2
<=> unequally_directed_opposite_lines(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f129,plain,
( ~ unequally_directed_opposite_lines(sK1,sK0)
| spl2_2 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f130,plain,
( unequally_directed_opposite_lines(sK1,sK0)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f121,f128,f124]) ).
fof(f132,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f122,f128,f124]) ).
fof(f134,plain,
! [X0] : ~ unequally_directed_lines(X0,X0),
inference(resolution,[],[f85,f92]) ).
fof(f136,plain,
! [X0,X1] :
( unequally_directed_opposite_lines(X0,X1)
| unequally_directed_lines(X0,X1) ),
inference(resolution,[],[f98,f83]) ).
fof(f140,plain,
! [X0,X1] :
( unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X1,X0) ),
inference(resolution,[],[f93,f134]) ).
fof(f145,plain,
( unequally_directed_lines(sK0,sK1)
| spl2_1 ),
inference(resolution,[],[f136,f125]) ).
fof(f157,plain,
! [X0,X1] :
( left_convergent_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1)
| ~ unequally_directed_lines(X0,reverse_line(X1)) ),
inference(forward_subsumption_resolution,[],[f99,f103]) ).
fof(f158,plain,
! [X0,X1] :
( ~ unequally_directed_lines(X0,reverse_line(X1))
| ~ unequally_directed_lines(X0,X1) ),
inference(forward_subsumption_resolution,[],[f157,f103]) ).
fof(f164,plain,
! [X0,X1] :
( ~ unequally_directed_opposite_lines(X0,X1)
| ~ unequally_directed_lines(X0,X1) ),
inference(resolution,[],[f158,f82]) ).
fof(f199,plain,
( ~ unequally_directed_lines(sK1,sK0)
| ~ spl2_2 ),
inference(resolution,[],[f164,f130]) ).
fof(f202,plain,
( ~ unequally_directed_lines(sK0,sK1)
| ~ spl2_2 ),
inference(resolution,[],[f199,f140]) ).
fof(f204,plain,
( $false
| spl2_1
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f202,f145]) ).
fof(f205,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_contradiction_clause,[],[f204]) ).
fof(f206,plain,
( ~ unequally_directed_lines(sK0,sK1)
| ~ spl2_1 ),
inference(resolution,[],[f126,f164]) ).
fof(f207,plain,
( unequally_directed_lines(sK1,sK0)
| spl2_2 ),
inference(resolution,[],[f129,f136]) ).
fof(f208,plain,
( ~ unequally_directed_lines(sK1,sK0)
| ~ spl2_1 ),
inference(resolution,[],[f206,f140]) ).
fof(f210,plain,
( $false
| ~ spl2_1
| spl2_2 ),
inference(forward_subsumption_resolution,[],[f208,f207]) ).
fof(f211,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_contradiction_clause,[],[f210]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f131]) ).
cnf(s2,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f132]) ).
cnf(s4,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f205]) ).
cnf(s5,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f211]) ).
cnf(s6,plain,
spl2_1,
inference(rat,[],[s1,s4]) ).
cnf(s7,plain,
spl2_2,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s2,s7,s6]) ).
fof(f212,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO266+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 07:57:20 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 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
% 0.42/0.83 % (2045178)Detected formulas, will run a generic FOF schedule.
% 0.42/0.83 % (2045184)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=521078252:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.42/0.83 % (2045187)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1010410527:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.42/0.83 % (2045189)dis-21_1_sil=8000:lcm=predicate:random_seed=1041271677: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)
% 0.42/0.83 % (2045186)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=353565964:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.42/0.83 % (2045188)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=687292125:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.42/0.83 % (2045183)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=107723168:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.42/0.83 % (2045185)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=3826260503:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.42/0.83 % (2045186)Refutation not found, incomplete strategy
% 0.42/0.83 % (2045186)------------------------------
% 0.42/0.83 % (2045186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.42/0.83 % (2045186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.83 % (2045186)CaDiCaL version: 2.1.3
% 0.42/0.83 % (2045186)Termination reason: Refutation not found, incomplete strategy
% 0.42/0.83 % (2045186)Time elapsed: 0.0000 s
% 0.42/0.83 % (2045186)Peak memory usage: 87 MB
% 0.42/0.83 % (2045188)First to succeed.
% 0.42/0.83 % (2045188)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2045178"
% 0.42/0.83 % (2045189)Also succeeded, but the first one will report.
% 0.42/0.83 % (2045187)Instruction limit reached!
% 0.42/0.83 % (2045187)------------------------------
% 0.42/0.83 % (2045187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.42/0.83 % (2045187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.83 % (2045187)CaDiCaL version: 2.1.3
% 0.42/0.83 % (2045187)Termination reason: Instruction limit
% 0.42/0.83 % (2045187)Termination phase: Saturation
% 0.42/0.83 % (2045187)Time elapsed: 0.032 s
% 0.42/0.83 % (2045187)Peak memory usage: 87 MB
% 0.42/0.83 % (2045187)Instructions burned: 122 (million)
% 0.42/0.83 % (2045186)------------------------------
% 0.42/0.83 % (2045186)------------------------------
% 0.42/0.83 % (2045188)Refutation found. Thanks to Tanya!
% 0.42/0.83 % SZS status Theorem for theBenchmark
% 0.42/0.83 % SZS output start Proof for theBenchmark
% See solution above
% 2.31/0.93 % (2045188)------------------------------
% 2.31/0.93 % (2045188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.31/0.93 % (2045188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.93 % (2045188)CaDiCaL version: 2.1.3
% 2.31/0.93 % (2045188)Termination reason: Refutation
% 2.31/0.93 % (2045188)Time elapsed: 0.002 s
% 2.31/0.93 % (2045188)Peak memory usage: 89 MB
% 2.31/0.93 % (2045188)Instructions burned: 5 (million)
% 2.31/0.93 % (2045188)------------------------------
% 2.31/0.93 % (2045188)------------------------------
% 2.31/0.93 % (2045178)Success in time 0.295 s
% 2.31/0.93 % Vampire exiting
%------------------------------------------------------------------------------