%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU242+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:47:58 PM UTC 2026
% Result : Theorem 1.86s 1.10s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of formulae : 51 ( 5 unt; 0 def)
% Number of atoms : 258 ( 25 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 354 ( 147 ~; 143 |; 53 &)
% ( 6 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 80 ( 66 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_connected_in(X0,X1)
<=> ! [X2,X3] :
~ ( in(X2,X1)
& in(X3,X1)
& X2 != X3
& ~ in(ordered_pair(X2,X3),X0)
& ~ in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_2) ).
fof(f25,conjecture,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> ! [X1,X2] :
~ ( in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2
& ~ in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_wellord1) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( connected(X0)
<=> ! [X1,X2] :
~ ( in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2
& ~ in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X2,X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f38,plain,
? [X0] :
( ( connected(X0)
<~> ! [X1,X2] :
( ~ in(X1,relation_field(X0))
| ~ in(X2,relation_field(X0))
| X1 = X2
| in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X2,X1),X0) ) )
& relation(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f42,plain,
! [X0] :
( ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( is_connected_in(X0,X1)
<=> ! [X2,X3] :
( ~ in(X2,X1)
| ~ in(X3,X1)
| X2 = X3
| in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f44,plain,
? [X0] :
( ( ? [X1,X2] :
( in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2
& ~ in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X2,X1),X0) )
| ~ connected(X0) )
& ( ! [X1,X2] :
( ~ in(X1,relation_field(X0))
| ~ in(X2,relation_field(X0))
| X1 = X2
| in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X2,X1),X0) )
| connected(X0) )
& relation(X0) ),
inference(nnf_transformation,[],[f38]) ).
fof(f45,plain,
? [X0] :
( ( ? [X1,X2] :
( in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2
& ~ in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X2,X1),X0) )
| ~ connected(X0) )
& ( ! [X1,X2] :
( ~ in(X1,relation_field(X0))
| ~ in(X2,relation_field(X0))
| X1 = X2
| in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X2,X1),X0) )
| connected(X0) )
& relation(X0) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
? [X0] :
( ( ? [X1,X2] :
( in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2
& ~ in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X2,X1),X0) )
| ~ connected(X0) )
& ( ! [X3,X4] :
( ~ in(X3,relation_field(X0))
| ~ in(X4,relation_field(X0))
| X3 = X4
| in(ordered_pair(X3,X4),X0)
| in(ordered_pair(X4,X3),X0) )
| connected(X0) )
& relation(X0) ),
inference(rectify,[],[f45]) ).
fof(f47,plain,
( ( ( in(sK1,relation_field(sK0))
& in(sK2,relation_field(sK0))
& sK1 != sK2
& ~ in(ordered_pair(sK1,sK2),sK0)
& ~ in(ordered_pair(sK2,sK1),sK0) )
| ~ connected(sK0) )
& ( ! [X3,X4] :
( ~ in(X3,relation_field(sK0))
| ~ in(X4,relation_field(sK0))
| X3 = X4
| in(ordered_pair(X3,X4),sK0)
| in(ordered_pair(X4,X3),sK0) )
| connected(sK0) )
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f46]) ).
fof(f48,plain,
! [X0] :
( ( ( connected(X0)
| ~ is_connected_in(X0,relation_field(X0)) )
& ( is_connected_in(X0,relation_field(X0))
| ~ connected(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f42]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( ( is_connected_in(X0,X1)
| ? [X2,X3] :
( in(X2,X1)
& in(X3,X1)
& X2 != X3
& ~ in(ordered_pair(X2,X3),X0)
& ~ in(ordered_pair(X3,X2),X0) ) )
& ( ! [X2,X3] :
( ~ in(X2,X1)
| ~ in(X3,X1)
| X2 = X3
| in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X3,X2),X0) )
| ~ is_connected_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f43]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ( is_connected_in(X0,X1)
| ? [X2,X3] :
( in(X2,X1)
& in(X3,X1)
& X2 != X3
& ~ in(ordered_pair(X2,X3),X0)
& ~ in(ordered_pair(X3,X2),X0) ) )
& ( ! [X4,X5] :
( ~ in(X4,X1)
| ~ in(X5,X1)
| X4 = X5
| in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X5,X4),X0) )
| ~ is_connected_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f51]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ( is_connected_in(X0,X1)
| ( in(sK5(X0,X1),X1)
& in(sK6(X0,X1),X1)
& sK5(X0,X1) != sK6(X0,X1)
& ~ in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0)
& ~ in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0) ) )
& ( ! [X4,X5] :
( ~ in(X4,X1)
| ~ in(X5,X1)
| X4 = X5
| in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X5,X4),X0) )
| ~ is_connected_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X2,sK5(X0,X1)),skolemize(X3,sK6(X0,X1))],[f52]) ).
fof(f54,plain,
relation(sK0),
inference(cnf_transformation,[],[f47]) ).
fof(f55,plain,
! [X3,X4] :
( in(ordered_pair(X4,X3),sK0)
| ~ in(X4,relation_field(sK0))
| X3 = X4
| in(ordered_pair(X3,X4),sK0)
| ~ in(X3,relation_field(sK0))
| connected(sK0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f56,plain,
( ~ in(ordered_pair(sK2,sK1),sK0)
| ~ connected(sK0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f57,plain,
( ~ in(ordered_pair(sK1,sK2),sK0)
| ~ connected(sK0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f58,plain,
( sK1 != sK2
| ~ connected(sK0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f59,plain,
( in(sK2,relation_field(sK0))
| ~ connected(sK0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f60,plain,
( in(sK1,relation_field(sK0))
| ~ connected(sK0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f65,plain,
! [X0] :
( is_connected_in(X0,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f66,plain,
! [X0] :
( ~ is_connected_in(X0,relation_field(X0))
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f69,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X5,X4),X0)
| ~ in(X5,X1)
| X4 = X5
| in(ordered_pair(X4,X5),X0)
| ~ in(X4,X1)
| ~ is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f70,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f71,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f72,plain,
! [X0,X1] :
( sK5(X0,X1) != sK6(X0,X1)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f73,plain,
! [X0,X1] :
( in(sK6(X0,X1),X1)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f74,plain,
! [X0,X1] :
( in(sK5(X0,X1),X1)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f134,plain,
! [X0] :
( is_connected_in(sK0,X0)
| ~ relation(sK0)
| ~ in(sK5(sK0,X0),relation_field(sK0))
| sK5(sK0,X0) = sK6(sK0,X0)
| in(ordered_pair(sK6(sK0,X0),sK5(sK0,X0)),sK0)
| ~ in(sK6(sK0,X0),relation_field(sK0))
| connected(sK0) ),
inference(resolution,[],[f71,f55]) ).
fof(f139,plain,
! [X0] :
( is_connected_in(sK0,X0)
| ~ relation(sK0)
| ~ in(sK5(sK0,X0),relation_field(sK0))
| in(ordered_pair(sK6(sK0,X0),sK5(sK0,X0)),sK0)
| ~ in(sK6(sK0,X0),relation_field(sK0))
| connected(sK0) ),
inference(forward_subsumption_resolution,[],[f134,f72]) ).
fof(f141,plain,
! [X0] :
( is_connected_in(sK0,X0)
| ~ relation(sK0)
| ~ in(sK5(sK0,X0),relation_field(sK0))
| ~ in(sK6(sK0,X0),relation_field(sK0))
| connected(sK0) ),
inference(forward_subsumption_resolution,[],[f139,f70]) ).
fof(f143,plain,
! [X0] :
( is_connected_in(sK0,X0)
| ~ in(sK5(sK0,X0),relation_field(sK0))
| ~ in(sK6(sK0,X0),relation_field(sK0))
| connected(sK0) ),
inference(forward_subsumption_resolution,[],[f141,f54]) ).
fof(f145,plain,
! [X0] :
( ~ in(sK1,X0)
| sK1 = sK2
| in(ordered_pair(sK2,sK1),sK0)
| ~ in(sK2,X0)
| ~ is_connected_in(sK0,X0)
| ~ relation(sK0)
| ~ connected(sK0) ),
inference(resolution,[],[f69,f57]) ).
fof(f157,plain,
! [X0] :
( ~ in(sK1,X0)
| in(ordered_pair(sK2,sK1),sK0)
| ~ in(sK2,X0)
| ~ is_connected_in(sK0,X0)
| ~ relation(sK0)
| ~ connected(sK0) ),
inference(forward_subsumption_resolution,[],[f145,f58]) ).
fof(f161,plain,
! [X0] :
( ~ in(sK1,X0)
| ~ in(sK2,X0)
| ~ is_connected_in(sK0,X0)
| ~ relation(sK0)
| ~ connected(sK0) ),
inference(forward_subsumption_resolution,[],[f157,f56]) ).
fof(f163,plain,
! [X0] :
( ~ is_connected_in(sK0,X0)
| ~ in(sK2,X0)
| ~ in(sK1,X0)
| ~ connected(sK0) ),
inference(forward_subsumption_resolution,[],[f161,f54]) ).
fof(f165,plain,
( ~ in(sK2,relation_field(sK0))
| ~ in(sK1,relation_field(sK0))
| ~ connected(sK0)
| ~ connected(sK0)
| ~ relation(sK0) ),
inference(resolution,[],[f163,f65]) ).
fof(f168,plain,
( ~ in(sK2,relation_field(sK0))
| ~ in(sK1,relation_field(sK0))
| ~ connected(sK0)
| ~ relation(sK0) ),
inference(duplicate_literal_removal,[],[f165]) ).
fof(f169,plain,
( ~ in(sK1,relation_field(sK0))
| ~ connected(sK0)
| ~ relation(sK0) ),
inference(forward_subsumption_resolution,[],[f168,f59]) ).
fof(f170,plain,
( ~ connected(sK0)
| ~ relation(sK0) ),
inference(forward_subsumption_resolution,[],[f169,f60]) ).
fof(f171,plain,
~ connected(sK0),
inference(forward_subsumption_resolution,[],[f170,f54]) ).
fof(f173,plain,
! [X0] :
( ~ in(sK6(sK0,X0),relation_field(sK0))
| ~ in(sK5(sK0,X0),relation_field(sK0))
| is_connected_in(sK0,X0) ),
inference(forward_subsumption_resolution,[],[f143,f171]) ).
fof(f174,plain,
( ~ in(sK5(sK0,relation_field(sK0)),relation_field(sK0))
| is_connected_in(sK0,relation_field(sK0))
| is_connected_in(sK0,relation_field(sK0))
| ~ relation(sK0) ),
inference(resolution,[],[f173,f73]) ).
fof(f177,plain,
( ~ in(sK5(sK0,relation_field(sK0)),relation_field(sK0))
| is_connected_in(sK0,relation_field(sK0))
| ~ relation(sK0) ),
inference(duplicate_literal_removal,[],[f174]) ).
fof(f178,plain,
( is_connected_in(sK0,relation_field(sK0))
| ~ relation(sK0) ),
inference(forward_subsumption_resolution,[],[f177,f74]) ).
fof(f179,plain,
is_connected_in(sK0,relation_field(sK0)),
inference(forward_subsumption_resolution,[],[f178,f54]) ).
fof(f181,plain,
( connected(sK0)
| ~ relation(sK0) ),
inference(resolution,[],[f179,f66]) ).
fof(f182,plain,
~ relation(sK0),
inference(forward_subsumption_resolution,[],[f181,f171]) ).
fof(f183,plain,
$false,
inference(forward_subsumption_resolution,[],[f182,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU242+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 28 04:17:20 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 1.86/1.10 % (4019002)Detected formulas, will run a generic FOF schedule.
% 1.86/1.10 % (4019011)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=786358529:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.86/1.10 % (4019011)First to succeed.
% 1.86/1.10 % (4019011)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4019002"
% 1.86/1.10 % (4019009)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=2582606529:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.86/1.10 % (4019012)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2044672842:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.86/1.10 % (4019008)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=786374870:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.86/1.10 % (4019007)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=3294900642:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.86/1.10 % (4019013)dis-21_1_sil=8000:lcm=predicate:random_seed=3732323202: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)
% 1.86/1.10 % (4019010)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2508495245:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.86/1.10 % (4019010)Refutation not found, incomplete strategy
% 1.86/1.10 % (4019010)------------------------------
% 1.86/1.10 % (4019010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.86/1.10 % (4019010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.86/1.10 % (4019010)CaDiCaL version: 2.1.3
% 1.86/1.10 % (4019010)Termination reason: Refutation not found, incomplete strategy
% 1.86/1.10 % (4019010)Time elapsed: 0.001 s
% 1.86/1.10 % (4019010)Peak memory usage: 88 MB
% 1.86/1.10 % (4019013)Also succeeded, but the first one will report.
% 1.86/1.10 % (4019012)Also succeeded, but the first one will report.
% 1.86/1.10 % (4019011)Refutation found. Thanks to Tanya!
% 1.86/1.10 % SZS status Theorem for theBenchmark
% 1.86/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.30 % (4019011)------------------------------
% 0.15/1.30 % (4019011)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.30 % (4019011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.30 % (4019011)CaDiCaL version: 2.1.3
% 0.15/1.30 % (4019011)Termination reason: Refutation
% 0.15/1.30 % (4019011)Time elapsed: 0.003 s
% 0.15/1.30 % (4019011)Peak memory usage: 88 MB
% 0.15/1.30 % (4019011)Instructions burned: 7 (million)
% 0.15/1.30 % (4019011)------------------------------
% 0.15/1.30 % (4019011)------------------------------
% 0.15/1.30 % (4019002)Success in time 0.275 s
% 0.15/1.30 % Vampire exiting
%------------------------------------------------------------------------------