%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n026.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 09:51:38 AM UTC 2026
% Result : Theorem 2.78s 1.28s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 16 unt; 0 def)
% Number of atoms : 200 ( 17 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 231 ( 83 ~; 82 |; 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 : 113 ( 95 !; 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/theBenchmark.p',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/theBenchmark.p',inner_point_defn) ).
fof(f7,axiom,
! [X0] :
( open(X0)
<=> ? [X1] : end_point(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_defn) ).
fof(f10,axiom,
! [X0] :
? [X1] : inner_point(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/theBenchmark.p',start_point_defn) ).
fof(f22,axiom,
! [X0] :
? [X1] :
( open(X1)
& ! [X2] :
( incident_o(X2,X0)
<=> incident_c(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o2) ).
fof(f24,axiom,
! [X0] :
? [X1] : start_point(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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] :
( ~ end_point(X0,X1)
| ~ inner_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] :
( ~ open(X0)
| end_point(sK6(X0),X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f138,plain,
! [X0] : inner_point(sK7(X0),X0),
inference(cnf_transformation,[],[f79]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ~ start_point(X0,X1)
| X0 = X2
| ~ incident_o(X2,X1)
| ordered_by(X1,X0,X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f165,plain,
! [X2,X0] :
( incident_o(X2,X0)
| ~ incident_c(X2,sK14(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(f191,plain,
! [X0] : incident_c(sK7(X0),X0),
inference(resolution,[],[f124,f138]) ).
fof(f193,plain,
! [X0] : end_point(sK6(sK14(X0)),sK14(X0)),
inference(resolution,[],[f134,f166]) ).
fof(f197,plain,
! [X0] : ~ inner_point(sK6(sK14(X0)),sK14(X0)),
inference(resolution,[],[f193,f123]) ).
fof(f198,plain,
! [X0] : incident_c(sK6(sK14(X0)),sK14(X0)),
inference(resolution,[],[f193,f116]) ).
fof(f226,plain,
! [X0,X1] :
( ordered_by(X0,sK17(X0),X1)
| ~ incident_o(X1,X0)
| sK17(X0) = X1 ),
inference(resolution,[],[f160,f172]) ).
fof(f397,plain,
! [X0] :
( ~ incident_o(X0,sK22)
| sK17(sK22) = X0
| sK17(sK22) = X0 ),
inference(resolution,[],[f226,f182]) ).
fof(f402,plain,
! [X0] :
( ~ incident_o(X0,sK22)
| sK17(sK22) = X0 ),
inference(duplicate_literal_removal,[],[f397]) ).
fof(f408,plain,
! [X0] :
( ~ incident_c(X0,sK14(sK22))
| sK17(sK22) = X0 ),
inference(resolution,[],[f402,f165]) ).
fof(f514,plain,
sK17(sK22) = sK6(sK14(sK22)),
inference(resolution,[],[f408,f198]) ).
fof(f515,plain,
sK17(sK22) = sK7(sK14(sK22)),
inference(resolution,[],[f408,f191]) ).
fof(f535,plain,
~ inner_point(sK17(sK22),sK14(sK22)),
inference(superposition,[],[f197,f514]) ).
fof(f602,plain,
inner_point(sK17(sK22),sK14(sK22)),
inference(superposition,[],[f138,f515]) ).
fof(f603,plain,
$false,
inference(forward_subsumption_resolution,[],[f602,f535]) ).
%------------------------------------------------------------------------------
%----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 THM
% 0.10/0.38 % Computer : n026.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 07:10:42 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.78/1.28 % (2481633)Detected formulas, will run a generic FOF schedule.
% 2.78/1.28 % (2481639)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=345082303:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.78/1.28 % (2481642)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3705608210:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.78/1.28 % (2481641)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=951425233:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.78/1.28 % (2481638)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=2234569368:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.78/1.28 % (2481643)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=890388348:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.78/1.28 % (2481640)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=3406539252:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.78/1.28 % (2481644)dis-21_1_sil=8000:lcm=predicate:random_seed=3759843208: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)
% 2.78/1.28 % (2481642)Refutation not found, incomplete strategy
% 2.78/1.28 % (2481642)------------------------------
% 2.78/1.28 % (2481642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.28 % (2481641)Refutation not found, incomplete strategy
% 2.78/1.28 % (2481641)------------------------------
% 2.78/1.28 % (2481641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.28 % (2481642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.28 % (2481641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.28 % (2481642)CaDiCaL version: 2.1.3
% 2.78/1.28 % (2481641)CaDiCaL version: 2.1.3
% 2.78/1.28 % (2481642)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.28 % (2481642)Time elapsed: 0.001 s
% 2.78/1.28 % (2481641)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.28 % (2481641)Time elapsed: 0.001 s
% 2.78/1.28 % (2481642)Peak memory usage: 88 MB
% 2.78/1.28 % (2481641)Peak memory usage: 88 MB
% 2.78/1.28 % (2481643)First to succeed.
% 2.78/1.28 % (2481643)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2481633"
% 2.78/1.28 % (2481644)Instruction limit reached!
% 2.78/1.28 % (2481644)------------------------------
% 2.78/1.28 % (2481644)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.28 % (2481644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.28 % (2481644)CaDiCaL version: 2.1.3
% 2.78/1.28 % (2481644)Termination reason: Instruction limit
% 2.78/1.28 % (2481644)Termination phase: Saturation
% 2.78/1.28 % (2481644)Time elapsed: 0.079 s
% 2.78/1.28 % (2481644)Peak memory usage: 90 MB
% 2.78/1.28 % (2481644)Instructions burned: 130 (million)
% 2.78/1.28 % (2481652)lrs+10_1_sil=8000:sp=occurrence:random_seed=2180616905:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.78/1.28 % (2481641)------------------------------
% 2.78/1.28 % (2481641)------------------------------
% 2.78/1.28 % (2481642)------------------------------
% 2.78/1.28 % (2481642)------------------------------
% 2.78/1.28 % (2481643)Refutation found. Thanks to Tanya!
% 2.78/1.28 % SZS status Theorem for theBenchmark
% 2.78/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.52/1.37 % (2481643)------------------------------
% 3.52/1.37 % (2481643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.37 % (2481643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.37 % (2481643)CaDiCaL version: 2.1.3
% 3.52/1.37 % (2481643)Termination reason: Refutation
% 3.52/1.37 % (2481643)Time elapsed: 0.025 s
% 3.52/1.37 % (2481643)Peak memory usage: 89 MB
% 3.52/1.37 % (2481643)Instructions burned: 30 (million)
% 3.52/1.37 % (2481643)------------------------------
% 3.52/1.37 % (2481643)------------------------------
% 3.52/1.37 % (2481633)Success in time 0.432 s
% 3.52/1.37 % Vampire exiting
%------------------------------------------------------------------------------