%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO124+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 09:53:38 AM UTC 2026
% Result : Theorem 0.15s 0.48s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 7 unt; 0 def)
% Number of atoms : 209 ( 29 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 257 ( 92 ~; 88 |; 64 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 149 ( 133 !; 16 ?)
% 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/sandbox/benchmark/Axioms/GEO004+1.ax',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/sandbox/benchmark/Axioms/GEO004+2.ax',between_o_defn) ).
fof(f19,axiom,
! [X0,X1] :
( start_point(X0,X1)
<=> ( incident_o(X0,X1)
& ! [X2] :
( ( X0 != X2
& incident_o(X2,X1) )
=> ordered_by(X1,X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',start_point_defn) ).
fof(f21,axiom,
! [X0,X1,X2] :
( ordered_by(X0,X1,X2)
=> ( incident_o(X1,X0)
& incident_o(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',o1) ).
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/sandbox/benchmark/Axioms/GEO004+2.ax',o3) ).
fof(f28,conjecture,
! [X0,X1,X2] :
( ( start_point(X1,X0)
& start_point(X2,X0) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_4_10_1) ).
fof(f29,negated_conjecture,
~ ! [X0,X1,X2] :
( ( start_point(X1,X0)
& start_point(X2,X0) )
=> X1 = X2 ),
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(f31,plain,
! [X0,X1] :
( start_point(X0,X1)
=> ( incident_o(X0,X1)
& ! [X2] :
( ( X0 != X2
& incident_o(X2,X1) )
=> ordered_by(X1,X0,X2) ) ) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f51,plain,
! [X0,X1] :
( ( incident_o(X0,X1)
& ! [X2] :
( ordered_by(X1,X0,X2)
| X0 = X2
| ~ incident_o(X2,X1) ) )
| ~ start_point(X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f52,plain,
! [X0,X1] :
( ( incident_o(X0,X1)
& ! [X2] :
( ordered_by(X1,X0,X2)
| X0 = X2
| ~ incident_o(X2,X1) ) )
| ~ start_point(X0,X1) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( incident_o(X1,X0)
& incident_o(X2,X0) )
| ~ ordered_by(X0,X1,X2) ),
inference(ennf_transformation,[],[f21]) ).
fof(f57,plain,
? [X0,X1,X2] :
( X1 != X2
& start_point(X1,X0)
& start_point(X2,X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f58,plain,
? [X0,X1,X2] :
( X1 != X2
& start_point(X1,X0)
& start_point(X2,X0) ),
inference(flattening,[],[f57]) ).
fof(f87,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(f88,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,[],[f87]) ).
fof(f89,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,[],[f88]) ).
fof(f90,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(sK13(X0,X1,X2,X3),X0)
& end_point(X1,sK13(X0,X1,X2,X3))
& end_point(X3,sK13(X0,X1,X2,X3))
& inner_point(X2,sK13(X0,X1,X2,X3)) )
| ~ between_c(X0,X1,X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X5,sK13(X0,X1,X2,X3))],[f89]) ).
fof(f91,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(f92,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,[],[f91]) ).
fof(f95,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(f96,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,[],[f95]) ).
fof(f97,plain,
! [X0,X1,X2,X3] :
( ( between_o(X3,X0,X1,X2)
| ! [X4] :
( ( ( ~ incident_c(sK15(X3,X4),X4)
| ~ incident_o(sK15(X3,X4),X3) )
& ( incident_c(sK15(X3,X4),X4)
| incident_o(sK15(X3,X4),X3) ) )
| ~ between_c(X4,X0,X1,X2) ) )
& ( ( ! [X7] :
( ( incident_o(X7,X3)
| ~ incident_c(X7,sK16(X0,X1,X2,X3)) )
& ( incident_c(X7,sK16(X0,X1,X2,X3))
| ~ incident_o(X7,X3) ) )
& between_c(sK16(X0,X1,X2,X3),X0,X1,X2) )
| ~ between_o(X3,X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X5,sK15(X3,X4)),skolemize(X6,sK16(X0,X1,X2,X3))],[f96]) ).
fof(f106,plain,
( sK23 != sK24
& start_point(sK23,sK22)
& start_point(sK24,sK22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23,sK24]),skolemize(X0,sK22),skolemize(X1,sK23),skolemize(X2,sK24)],[f58]) ).
fof(f153,plain,
! [X2,X3,X0,X1] :
( X1 != X3
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f90]) ).
fof(f160,plain,
! [X2,X3,X0,X1] :
( between_o(X0,X1,X2,X3)
| ~ ordered_by(X0,X1,X2)
| ~ ordered_by(X0,X2,X3) ),
inference(cnf_transformation,[],[f92]) ).
fof(f161,plain,
! [X2,X0,X1] :
( ordered_by(X1,X0,X2)
| X0 = X2
| ~ incident_o(X2,X1)
| ~ start_point(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f162,plain,
! [X0,X1] :
( ~ start_point(X0,X1)
| incident_o(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f164,plain,
! [X2,X0,X1] :
( ~ ordered_by(X0,X1,X2)
| incident_o(X1,X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f168,plain,
! [X2,X3,X0,X1] :
( between_c(sK16(X0,X1,X2,X3),X0,X1,X2)
| ~ between_o(X3,X0,X1,X2) ),
inference(cnf_transformation,[],[f97]) ).
fof(f183,plain,
start_point(sK24,sK22),
inference(cnf_transformation,[],[f106]) ).
fof(f184,plain,
start_point(sK23,sK22),
inference(cnf_transformation,[],[f106]) ).
fof(f185,plain,
sK23 != sK24,
inference(cnf_transformation,[],[f106]) ).
fof(f190,plain,
! [X2,X3,X0] : ~ between_c(X0,X3,X2,X3),
inference(equality_resolution,[],[f153]) ).
fof(f361,plain,
! [X2,X0,X1] : ~ between_o(X0,X1,X2,X1),
inference(resolution,[],[f168,f190]) ).
fof(f362,plain,
! [X2,X0,X1] :
( ~ ordered_by(X0,X2,X1)
| ~ ordered_by(X0,X1,X2) ),
inference(resolution,[],[f361,f160]) ).
fof(f369,plain,
! [X2,X0,X1] :
( ~ ordered_by(X0,X1,X2)
| X1 = X2
| ~ incident_o(X1,X0)
| ~ start_point(X2,X0) ),
inference(resolution,[],[f362,f161]) ).
fof(f370,plain,
! [X2,X0,X1] :
( ~ ordered_by(X0,X1,X2)
| X1 = X2
| ~ start_point(X2,X0) ),
inference(forward_subsumption_resolution,[],[f369,f164]) ).
fof(f407,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ start_point(X1,X2)
| X0 = X1
| ~ incident_o(X1,X2)
| ~ start_point(X0,X2) ),
inference(resolution,[],[f370,f161]) ).
fof(f408,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ start_point(X1,X2)
| ~ incident_o(X1,X2)
| ~ start_point(X0,X2) ),
inference(duplicate_literal_removal,[],[f407]) ).
fof(f409,plain,
! [X2,X0,X1] :
( ~ start_point(X1,X2)
| X0 = X1
| ~ start_point(X0,X2) ),
inference(forward_subsumption_resolution,[],[f408,f162]) ).
fof(f425,plain,
! [X0] :
( ~ start_point(X0,sK22)
| sK24 = X0 ),
inference(resolution,[],[f409,f183]) ).
fof(f429,plain,
sK23 = sK24,
inference(resolution,[],[f425,f184]) ).
fof(f431,plain,
$false,
inference(forward_subsumption_resolution,[],[f429,f185]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO124+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n011.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 07:07:45 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.48 % (2053763)Will run a generic schedule for satisfiability detection.
% 0.15/0.48 % (2053768)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=500311353_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.48 % TRYING [1]
% 0.15/0.48 % (2053769)% WARNING: option uhcvi not known.
% 0.15/0.48 % TRYING [2]
% 0.15/0.48 % TRYING [3]
% 0.15/0.48 % (2053769)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3351756673:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.48 % (2053772)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=449445300:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.48 % (2053770)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2654505300:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.48 % (2053771)dis+10_1_sil=32000:sp=arity:random_seed=1729772433:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.48 % (2053773)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1838875027:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.48 % (2053774)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3212145984:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.48 % TRYING [4]
% 0.15/0.48 % (2053771) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2053763-2053771"...
% 0.15/0.48 % (2053771)...printing done.
% 0.15/0.48 % (2053771)Refutation found. Thanks to Tanya!
% 0.15/0.48 % SZS status Theorem for theBenchmark
% 0.15/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48 % (2053771)------------------------------
% 0.15/0.48 % (2053771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.48 % (2053771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.48 % (2053771)CaDiCaL version: 2.1.3
% 0.15/0.48 % (2053771)Termination reason: Refutation
% 0.15/0.48 % (2053771)Time elapsed: 0.010 s
% 0.15/0.48 % (2053771)Peak memory usage: 12 MB
% 0.15/0.48 % (2053771)Instructions burned: 15 (million)
% 0.15/0.48 % (2053763)Success in time 0.049 s
% 0.15/0.48 % Vampire exiting
%------------------------------------------------------------------------------