%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEO126+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 : n007.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 09:53:39 AM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 16 unt; 0 def)
% Number of atoms : 207 ( 17 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 240 ( 88 ~; 86 |; 55 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 116 ( 98 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( end_point(X0,X1)
<=> ( incident_c(X0,X1)
& ! [X2,X3] :
( ( part_of(X2,X1)
& part_of(X3,X1)
& incident_c(X0,X2)
& incident_c(X0,X3) )
=> ( part_of(X2,X3)
| part_of(X3,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',end_point_defn) ).
fof(f4,axiom,
! [X0,X1] :
( inner_point(X0,X1)
<=> ( incident_c(X0,X1)
& ~ end_point(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',inner_point_defn) ).
fof(f7,axiom,
! [X0] :
( open(X0)
<=> ? [X1] : end_point(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',open_defn) ).
fof(f10,axiom,
! [X0] :
? [X1] : inner_point(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',c3) ).
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(f22,axiom,
! [X0] :
? [X1] :
( open(X1)
& ! [X2] :
( incident_o(X2,X0)
<=> incident_c(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',o2) ).
fof(f24,axiom,
! [X0] :
? [X1] : start_point(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',o4) ).
fof(f28,conjecture,
! [X0] :
? [X1,X2] :
( ordered_by(X0,X1,X2)
& X1 != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_11) ).
fof(f29,negated_conjecture,
~ ! [X0] :
? [X1,X2] :
( ordered_by(X0,X1,X2)
& X1 != X2 ),
inference(negated_conjecture,[status(cth)],[f28]) ).
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(f34,plain,
! [X0,X1] :
( end_point(X0,X1)
<=> ( incident_c(X0,X1)
& ! [X2,X3] :
( part_of(X2,X3)
| part_of(X3,X2)
| ~ part_of(X2,X1)
| ~ part_of(X3,X1)
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X3) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f35,plain,
! [X0,X1] :
( end_point(X0,X1)
<=> ( incident_c(X0,X1)
& ! [X2,X3] :
( part_of(X2,X3)
| part_of(X3,X2)
| ~ part_of(X2,X1)
| ~ part_of(X3,X1)
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X3) ) ) ),
inference(flattening,[],[f34]) ).
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(f57,plain,
? [X0] :
! [X1,X2] :
( ~ ordered_by(X0,X1,X2)
| X1 = X2 ),
inference(ennf_transformation,[],[f29]) ).
fof(f65,plain,
! [X0,X1] :
( ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| ? [X2,X3] :
( ~ part_of(X2,X3)
& ~ part_of(X3,X2)
& part_of(X2,X1)
& part_of(X3,X1)
& incident_c(X0,X2)
& incident_c(X0,X3) ) )
& ( ( incident_c(X0,X1)
& ! [X2,X3] :
( part_of(X2,X3)
| part_of(X3,X2)
| ~ part_of(X2,X1)
| ~ part_of(X3,X1)
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X3) ) )
| ~ end_point(X0,X1) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f66,plain,
! [X0,X1] :
( ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| ? [X2,X3] :
( ~ part_of(X2,X3)
& ~ part_of(X3,X2)
& part_of(X2,X1)
& part_of(X3,X1)
& incident_c(X0,X2)
& incident_c(X0,X3) ) )
& ( ( incident_c(X0,X1)
& ! [X2,X3] :
( part_of(X2,X3)
| part_of(X3,X2)
| ~ part_of(X2,X1)
| ~ part_of(X3,X1)
| ~ incident_c(X0,X2)
| ~ incident_c(X0,X3) ) )
| ~ end_point(X0,X1) ) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| ? [X2,X3] :
( ~ part_of(X2,X3)
& ~ part_of(X3,X2)
& part_of(X2,X1)
& part_of(X3,X1)
& incident_c(X0,X2)
& incident_c(X0,X3) ) )
& ( ( incident_c(X0,X1)
& ! [X4,X5] :
( part_of(X4,X5)
| part_of(X5,X4)
| ~ part_of(X4,X1)
| ~ part_of(X5,X1)
| ~ incident_c(X0,X4)
| ~ incident_c(X0,X5) ) )
| ~ end_point(X0,X1) ) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ( end_point(X0,X1)
| ~ incident_c(X0,X1)
| ( ~ part_of(sK2(X0,X1),sK3(X0,X1))
& ~ part_of(sK3(X0,X1),sK2(X0,X1))
& part_of(sK2(X0,X1),X1)
& part_of(sK3(X0,X1),X1)
& incident_c(X0,sK2(X0,X1))
& incident_c(X0,sK3(X0,X1)) ) )
& ( ( incident_c(X0,X1)
& ! [X4,X5] :
( part_of(X4,X5)
| part_of(X5,X4)
| ~ part_of(X4,X1)
| ~ part_of(X5,X1)
| ~ incident_c(X0,X4)
| ~ incident_c(X0,X5) ) )
| ~ end_point(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1))],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ( inner_point(X0,X1)
| ~ incident_c(X0,X1)
| end_point(X0,X1) )
& ( ( incident_c(X0,X1)
& ~ end_point(X0,X1) )
| ~ inner_point(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f70,plain,
! [X0,X1] :
( ( inner_point(X0,X1)
| ~ incident_c(X0,X1)
| end_point(X0,X1) )
& ( ( incident_c(X0,X1)
& ~ end_point(X0,X1) )
| ~ inner_point(X0,X1) ) ),
inference(flattening,[],[f69]) ).
fof(f76,plain,
! [X0] :
( ( open(X0)
| ! [X1] : ~ end_point(X1,X0) )
& ( ? [X1] : end_point(X1,X0)
| ~ open(X0) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f77,plain,
! [X0] :
( ( open(X0)
| ! [X1] : ~ end_point(X1,X0) )
& ( ? [X2] : end_point(X2,X0)
| ~ open(X0) ) ),
inference(rectify,[],[f76]) ).
fof(f78,plain,
! [X0] :
( ( open(X0)
| ! [X1] : ~ end_point(X1,X0) )
& ( end_point(sK6(X0),X0)
| ~ open(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0))],[f77]) ).
fof(f79,plain,
! [X0] : inner_point(sK7(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f10]) ).
fof(f92,plain,
! [X0] :
? [X1] :
( open(X1)
& ! [X2] :
( ( incident_o(X2,X0)
| ~ incident_c(X2,X1) )
& ( incident_c(X2,X1)
| ~ incident_o(X2,X0) ) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f93,plain,
! [X0] :
( open(sK14(X0))
& ! [X2] :
( ( incident_o(X2,X0)
| ~ incident_c(X2,sK14(X0)) )
& ( incident_c(X2,sK14(X0))
| ~ incident_o(X2,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X1,sK14(X0))],[f92]) ).
fof(f97,plain,
! [X0] : start_point(sK17(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X1,sK17(X0))],[f24]) ).
fof(f105,plain,
! [X1,X2] :
( ~ ordered_by(sK22,X1,X2)
| X1 = X2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(X0,sK22)],[f57]) ).
fof(f116,plain,
! [X0,X1] :
( ~ end_point(X0,X1)
| incident_c(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f123,plain,
! [X0,X1] :
( ~ inner_point(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f124,plain,
! [X0,X1] :
( ~ inner_point(X0,X1)
| incident_c(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f134,plain,
! [X0] :
( end_point(sK6(X0),X0)
| ~ open(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f138,plain,
! [X0] : inner_point(sK7(X0),X0),
inference(cnf_transformation,[],[f79]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ordered_by(X1,X0,X2)
| X0 = X2
| ~ incident_o(X2,X1)
| ~ start_point(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f165,plain,
! [X2,X0] :
( ~ incident_c(X2,sK14(X0))
| incident_o(X2,X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f166,plain,
! [X0] : open(sK14(X0)),
inference(cnf_transformation,[],[f93]) ).
fof(f172,plain,
! [X0] : start_point(sK17(X0),X0),
inference(cnf_transformation,[],[f97]) ).
fof(f182,plain,
! [X2,X1] :
( ~ ordered_by(sK22,X1,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f105]) ).
fof(f190,plain,
! [X0] : ~ end_point(sK7(X0),X0),
inference(resolution,[],[f123,f138]) ).
fof(f191,plain,
! [X0] : incident_c(sK7(X0),X0),
inference(resolution,[],[f124,f138]) ).
fof(f194,plain,
! [X0] :
( incident_c(sK6(X0),X0)
| ~ open(X0) ),
inference(resolution,[],[f134,f116]) ).
fof(f198,plain,
! [X0] : incident_o(sK7(sK14(X0)),X0),
inference(resolution,[],[f165,f191]) ).
fof(f200,plain,
! [X0] :
( incident_o(sK6(sK14(X0)),X0)
| ~ open(sK14(X0)) ),
inference(resolution,[],[f165,f194]) ).
fof(f201,plain,
! [X0] : incident_o(sK6(sK14(X0)),X0),
inference(forward_subsumption_resolution,[],[f200,f166]) ).
fof(f349,plain,
! [X0,X1] :
( X0 = X1
| ~ incident_o(X1,sK22)
| ~ start_point(X0,sK22)
| X0 = X1 ),
inference(resolution,[],[f160,f182]) ).
fof(f352,plain,
! [X0,X1] :
( ~ incident_o(X1,sK22)
| X0 = X1
| ~ start_point(X0,sK22) ),
inference(duplicate_literal_removal,[],[f349]) ).
fof(f355,plain,
! [X0] :
( ~ start_point(X0,sK22)
| sK6(sK14(sK22)) = X0 ),
inference(resolution,[],[f352,f201]) ).
fof(f357,plain,
! [X0] :
( ~ start_point(X0,sK22)
| sK7(sK14(sK22)) = X0 ),
inference(resolution,[],[f352,f198]) ).
fof(f457,plain,
sK6(sK14(sK22)) = sK17(sK22),
inference(resolution,[],[f355,f172]) ).
fof(f461,plain,
( end_point(sK17(sK22),sK14(sK22))
| ~ open(sK14(sK22)) ),
inference(superposition,[],[f134,f457]) ).
fof(f462,plain,
end_point(sK17(sK22),sK14(sK22)),
inference(forward_subsumption_resolution,[],[f461,f166]) ).
fof(f489,plain,
sK7(sK14(sK22)) = sK17(sK22),
inference(resolution,[],[f357,f172]) ).
fof(f502,plain,
~ end_point(sK17(sK22),sK14(sK22)),
inference(superposition,[],[f190,f489]) ).
fof(f504,plain,
$false,
inference(forward_subsumption_resolution,[],[f502,f462]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO126+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n007.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
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 07:05:55 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.16/0.48 % (1062910)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (1062915)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2787959752_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (1062916)% WARNING: option uhcvi not known.
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % (1062918)dis+10_1_sil=32000:sp=arity:random_seed=3304038244:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (1062916)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=387632701:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (1062919)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=575596458:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (1062917)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3631003657:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (1062921)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=719985846:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % (1062920)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1036465772:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % TRYING [4]
% 0.16/0.48 % (1062918) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1062910-1062918"...
% 0.16/0.48 % (1062918)...printing done.
% 0.16/0.48 % (1062918)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (1062918)------------------------------
% 0.16/0.48 % (1062918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (1062918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (1062918)CaDiCaL version: 2.1.3
% 0.16/0.48 % (1062918)Termination reason: Refutation
% 0.16/0.48 % (1062918)Time elapsed: 0.013 s
% 0.16/0.48 % (1062918)Peak memory usage: 12 MB
% 0.16/0.48 % (1062918)Instructions burned: 17 (million)
% 0.16/0.48 % (1062910)Success in time 0.052 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------