%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n003.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 09:53:37 AM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% 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 : 101 ( 89 !; 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/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/sandbox2/benchmark/Axioms/GEO004+2.ax',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/Axioms/GEO004+2.ax',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(f57,plain,
? [X0,X1] : ordered_by(X0,X1,X1),
inference(ennf_transformation,[],[f29]) ).
fof(f86,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(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(flattening,[],[f86]) ).
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
& ? [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,[],[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
& 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))],[f88]) ).
fof(f90,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(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(flattening,[],[f90]) ).
fof(f94,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(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) ) )
& ( ? [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,[],[f94]) ).
fof(f96,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))],[f95]) ).
fof(f105,plain,
ordered_by(sK22,sK23,sK23),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23]),skolemize(X0,sK22),skolemize(X1,sK23)],[f57]) ).
fof(f152,plain,
! [X2,X3,X0,X1] :
( X1 != X3
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f89]) ).
fof(f159,plain,
! [X2,X3,X0,X1] :
( between_o(X0,X1,X2,X3)
| ~ ordered_by(X0,X1,X2)
| ~ ordered_by(X0,X2,X3) ),
inference(cnf_transformation,[],[f91]) ).
fof(f167,plain,
! [X2,X3,X0,X1] :
( between_c(sK16(X0,X1,X2,X3),X0,X1,X2)
| ~ between_o(X3,X0,X1,X2) ),
inference(cnf_transformation,[],[f96]) ).
fof(f182,plain,
ordered_by(sK22,sK23,sK23),
inference(cnf_transformation,[],[f105]) ).
fof(f187,plain,
! [X2,X3,X0] : ~ between_c(X0,X3,X2,X3),
inference(equality_resolution,[],[f152]) ).
fof(f363,plain,
! [X2,X0,X1] : ~ between_o(X0,X1,X2,X1),
inference(resolution,[],[f167,f187]) ).
fof(f364,plain,
! [X2,X0,X1] :
( ~ ordered_by(X0,X2,X1)
| ~ ordered_by(X0,X1,X2) ),
inference(resolution,[],[f363,f159]) ).
fof(f371,plain,
~ ordered_by(sK22,sK23,sK23),
inference(resolution,[],[f364,f182]) ).
fof(f374,plain,
$false,
inference(forward_subsumption_resolution,[],[f371,f182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % 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 SAT
% 0.11/0.37 % Computer : n003.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 07:06:25 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.45 % (160113)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (160121)dis+10_1_sil=32000:sp=arity:random_seed=12424269:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (160121) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-160113-160121"...
% 0.11/0.45 % (160119)% WARNING: option uhcvi not known.
% 0.11/0.45 % (160121)...printing done.
% 0.11/0.45 % (160121)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (160121)------------------------------
% 0.11/0.45 % (160121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (160121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (160121)CaDiCaL version: 2.1.3
% 0.11/0.45 % (160121)Termination reason: Refutation
% 0.11/0.45 % (160121)Time elapsed: 0.005 s
% 0.11/0.45 % (160121)Peak memory usage: 12 MB
% 0.11/0.45 % (160121)Instructions burned: 12 (million)
% 0.11/0.45 % (160113)Success in time 0.029 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------