%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEO117+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 09:51:35 AM UTC 2026
% Result : Theorem 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 141 ( 10 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 181 ( 66 ~; 61 |; 48 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-4 aty)
% Number of variables : 103 ( 91 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1,X2,X3] :
( between_c(X0,X1,X2,X3)
<=> ( X1 != X3
& ? [X4] :
( part_of(X4,X0)
& end_point(X1,X4)
& end_point(X3,X4)
& inner_point(X2,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',between_c_defn) ).
fof(f18,axiom,
! [X0,X1,X2,X3] :
( between_o(X0,X1,X2,X3)
<=> ( ( ordered_by(X0,X1,X2)
& ordered_by(X0,X2,X3) )
| ( ordered_by(X0,X3,X2)
& ordered_by(X0,X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',between_o_defn) ).
fof(f23,axiom,
! [X0,X1,X2,X3] :
( between_o(X3,X0,X1,X2)
<=> ? [X4] :
( ! [X0] :
( incident_o(X0,X3)
<=> incident_c(X0,X4) )
& between_c(X4,X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',o3) ).
fof(f28,conjecture,
! [X0,X1] : ~ ordered_by(X0,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem_4_4) ).
fof(f29,negated_conjecture,
~ ! [X0,X1] : ~ ordered_by(X0,X1,X1),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( between_o(X3,X0,X1,X2)
<=> ? [X4] :
( ! [X5] :
( incident_o(X5,X3)
<=> incident_c(X5,X4) )
& between_c(X4,X0,X1,X2) ) ),
inference(rectify,[],[f23]) ).
fof(f33,plain,
? [X0,X1] : ordered_by(X0,X1,X1),
inference(ennf_transformation,[],[f29]) ).
fof(f58,plain,
ordered_by(sK0,sK1,sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f33]) ).
fof(f63,plain,
! [X0,X1,X2,X3] :
( ( between_o(X0,X1,X2,X3)
| ( ( ~ ordered_by(X0,X1,X2)
| ~ ordered_by(X0,X2,X3) )
& ( ~ ordered_by(X0,X3,X2)
| ~ ordered_by(X0,X2,X1) ) ) )
& ( ( ordered_by(X0,X1,X2)
& ordered_by(X0,X2,X3) )
| ( ordered_by(X0,X3,X2)
& ordered_by(X0,X2,X1) )
| ~ between_o(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( ( between_o(X0,X1,X2,X3)
| ( ( ~ ordered_by(X0,X1,X2)
| ~ ordered_by(X0,X2,X3) )
& ( ~ ordered_by(X0,X3,X2)
| ~ ordered_by(X0,X2,X1) ) ) )
& ( ( ordered_by(X0,X1,X2)
& ordered_by(X0,X2,X3) )
| ( ordered_by(X0,X3,X2)
& ordered_by(X0,X2,X1) )
| ~ between_o(X0,X1,X2,X3) ) ),
inference(flattening,[],[f63]) ).
fof(f75,plain,
! [X0,X1,X2,X3] :
( ( between_o(X3,X0,X1,X2)
| ! [X4] :
( ? [X5] :
( ( ~ incident_c(X5,X4)
| ~ incident_o(X5,X3) )
& ( incident_c(X5,X4)
| incident_o(X5,X3) ) )
| ~ between_c(X4,X0,X1,X2) ) )
& ( ? [X4] :
( ! [X5] :
( ( incident_o(X5,X3)
| ~ incident_c(X5,X4) )
& ( incident_c(X5,X4)
| ~ incident_o(X5,X3) ) )
& between_c(X4,X0,X1,X2) )
| ~ between_o(X3,X0,X1,X2) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f76,plain,
! [X0,X1,X2,X3] :
( ( between_o(X3,X0,X1,X2)
| ! [X4] :
( ? [X5] :
( ( ~ incident_c(X5,X4)
| ~ incident_o(X5,X3) )
& ( incident_c(X5,X4)
| incident_o(X5,X3) ) )
| ~ between_c(X4,X0,X1,X2) ) )
& ( ? [X6] :
( ! [X7] :
( ( incident_o(X7,X3)
| ~ incident_c(X7,X6) )
& ( incident_c(X7,X6)
| ~ incident_o(X7,X3) ) )
& between_c(X6,X0,X1,X2) )
| ~ between_o(X3,X0,X1,X2) ) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( ( between_o(X3,X0,X1,X2)
| ! [X4] :
( ( ( ~ incident_c(sK11(X3,X4),X4)
| ~ incident_o(sK11(X3,X4),X3) )
& ( incident_c(sK11(X3,X4),X4)
| incident_o(sK11(X3,X4),X3) ) )
| ~ between_c(X4,X0,X1,X2) ) )
& ( ( ! [X7] :
( ( incident_o(X7,X3)
| ~ incident_c(X7,sK12(X0,X1,X2,X3)) )
& ( incident_c(X7,sK12(X0,X1,X2,X3))
| ~ incident_o(X7,X3) ) )
& between_c(sK12(X0,X1,X2,X3),X0,X1,X2) )
| ~ between_o(X3,X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X5,sK11(X3,X4)),skolemize(X6,sK12(X0,X1,X2,X3))],[f76]) ).
fof(f97,plain,
! [X0,X1,X2,X3] :
( ( between_c(X0,X1,X2,X3)
| X1 = X3
| ! [X4] :
( ~ part_of(X4,X0)
| ~ end_point(X1,X4)
| ~ end_point(X3,X4)
| ~ inner_point(X2,X4) ) )
& ( ( X1 != X3
& ? [X4] :
( part_of(X4,X0)
& end_point(X1,X4)
& end_point(X3,X4)
& inner_point(X2,X4) ) )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f98,plain,
! [X0,X1,X2,X3] :
( ( between_c(X0,X1,X2,X3)
| X1 = X3
| ! [X4] :
( ~ part_of(X4,X0)
| ~ end_point(X1,X4)
| ~ end_point(X3,X4)
| ~ inner_point(X2,X4) ) )
& ( ( X1 != X3
& ? [X4] :
( part_of(X4,X0)
& end_point(X1,X4)
& end_point(X3,X4)
& inner_point(X2,X4) ) )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
! [X0,X1,X2,X3] :
( ( between_c(X0,X1,X2,X3)
| X1 = X3
| ! [X4] :
( ~ part_of(X4,X0)
| ~ end_point(X1,X4)
| ~ end_point(X3,X4)
| ~ inner_point(X2,X4) ) )
& ( ( X1 != X3
& ? [X5] :
( part_of(X5,X0)
& end_point(X1,X5)
& end_point(X3,X5)
& inner_point(X2,X5) ) )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(rectify,[],[f98]) ).
fof(f100,plain,
! [X0,X1,X2,X3] :
( ( between_c(X0,X1,X2,X3)
| X1 = X3
| ! [X4] :
( ~ part_of(X4,X0)
| ~ end_point(X1,X4)
| ~ end_point(X3,X4)
| ~ inner_point(X2,X4) ) )
& ( ( X1 != X3
& part_of(sK20(X0,X1,X2,X3),X0)
& end_point(X1,sK20(X0,X1,X2,X3))
& end_point(X3,sK20(X0,X1,X2,X3))
& inner_point(X2,sK20(X0,X1,X2,X3)) )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X5,sK20(X0,X1,X2,X3))],[f99]) ).
fof(f103,plain,
ordered_by(sK0,sK1,sK1),
inference(cnf_transformation,[],[f58]) ).
fof(f118,plain,
! [X2,X3,X0,X1] :
( between_o(X0,X1,X2,X3)
| ~ ordered_by(X0,X1,X2)
| ~ ordered_by(X0,X2,X3) ),
inference(cnf_transformation,[],[f64]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( between_c(sK12(X0,X1,X2,X3),X0,X1,X2)
| ~ between_o(X3,X0,X1,X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f171,plain,
! [X2,X3,X0,X1] :
( X1 != X3
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f100]) ).
fof(f180,plain,
! [X2,X3,X0] : ~ between_c(X0,X3,X2,X3),
inference(equality_resolution,[],[f171]) ).
fof(f296,plain,
! [X2,X0,X1] : ~ between_o(X0,X1,X2,X1),
inference(resolution,[],[f134,f180]) ).
fof(f302,plain,
! [X2,X0,X1] :
( ~ ordered_by(X0,X1,X2)
| ~ ordered_by(X0,X2,X1) ),
inference(resolution,[],[f296,f118]) ).
fof(f306,plain,
! [X0,X1] : ~ ordered_by(X0,X1,X1),
inference(factoring,[],[f302]) ).
fof(f309,plain,
$false,
inference(resolution,[],[f306,f103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO117+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 07:07:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.17/1.50 % (3196543)Detected formulas, will run a generic FOF schedule.
% 0.17/1.50 % (3196552)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3468446645:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.50 % (3196552)Refutation not found, incomplete strategy
% 0.17/1.50 % (3196552)------------------------------
% 0.17/1.50 % (3196552)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3196552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3196552)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3196552)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (3196552)Time elapsed: 0.001 s
% 0.17/1.50 % (3196552)Peak memory usage: 88 MB
% 0.17/1.50 % (3196551)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=252069763:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.50 % (3196548)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=1068320691:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.50 % (3196550)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=1760412523:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.50 % (3196549)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=824696538:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.50 % (3196551)Refutation not found, incomplete strategy
% 0.17/1.50 % (3196551)------------------------------
% 0.17/1.50 % (3196551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3196551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3196551)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3196551)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (3196551)Time elapsed: 0.001 s
% 0.17/1.50 % (3196551)Peak memory usage: 88 MB
% 0.17/1.50 % (3196554)dis-21_1_sil=8000:lcm=predicate:random_seed=580509151: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)
% 0.17/1.50 % (3196553)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=811499459:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.50 % (3196554)First to succeed.
% 0.17/1.50 % (3196554)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3196543"
% 0.17/1.50 % (3196553)Also succeeded, but the first one will report.
% 0.17/1.50 % (3196552)------------------------------
% 0.17/1.50 % (3196552)------------------------------
% 0.17/1.50 % (3196551)------------------------------
% 0.17/1.50 % (3196551)------------------------------
% 0.17/1.50 % (3196554)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Theorem for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (3196554)------------------------------
% 0.17/1.50 % (3196554)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3196554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3196554)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3196554)Termination reason: Refutation
% 0.17/1.50 % (3196554)Time elapsed: 0.007 s
% 0.17/1.50 % (3196554)Peak memory usage: 88 MB
% 0.17/1.50 % (3196554)Instructions burned: 8 (million)
% 0.17/1.50 % (3196554)------------------------------
% 0.17/1.50 % (3196554)------------------------------
% 0.17/1.50 % (3196543)Success in time 0.445 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------