%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU268+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 : 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 12:48:05 PM UTC 2026
% Result : Theorem 2.38s 1.15s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 14 unt; 0 def)
% Number of atoms : 196 ( 27 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 250 ( 99 ~; 101 |; 35 &)
% ( 10 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 96 ( 87 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(X2,X1)
=> in(ordered_pair(X2,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).
fof(f10,axiom,
! [X0,X1] :
( relation(X1)
=> ( X1 = inclusion_relation(X0)
<=> ( relation_field(X1) = X0
& ! [X2,X3] :
( ( in(X2,X0)
& in(X3,X0) )
=> ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_wellord2) ).
fof(f13,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
fof(f16,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f41,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f45,conjecture,
! [X0] : reflexive(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_wellord2) ).
fof(f46,negated_conjecture,
~ ! [X0] : reflexive(inclusion_relation(X0)),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f53,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f41]) ).
fof(f54,plain,
? [X0] : ~ reflexive(inclusion_relation(X0)),
inference(ennf_transformation,[],[f46]) ).
fof(f55,plain,
! [X0,X1] :
( ( X1 = inclusion_relation(X0)
<=> ( relation_field(X1) = X0
& ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) )
| ~ in(X2,X0)
| ~ in(X3,X0) ) ) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f56,plain,
! [X0,X1] :
( ( X1 = inclusion_relation(X0)
<=> ( relation_field(X1) = X0
& ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) )
| ~ in(X2,X0)
| ~ in(X3,X0) ) ) )
| ~ relation(X1) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f68,plain,
~ reflexive(inclusion_relation(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f54]) ).
fof(f69,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X2,X0)
& in(X3,X0) ) )
& ( ( relation_field(X1) = X0
& ! [X2,X3] :
( ( ( in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) )
& ( subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ in(X2,X0)
| ~ in(X3,X0) ) )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f56]) ).
fof(f70,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X2,X0)
& in(X3,X0) ) )
& ( ( relation_field(X1) = X0
& ! [X2,X3] :
( ( ( in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) )
& ( subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ in(X2,X0)
| ~ in(X3,X0) ) )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X2,X0)
& in(X3,X0) ) )
& ( ( relation_field(X1) = X0
& ! [X4,X5] :
( ( ( in(ordered_pair(X4,X5),X1)
| ~ subset(X4,X5) )
& ( subset(X4,X5)
| ~ in(ordered_pair(X4,X5),X1) ) )
| ~ in(X4,X0)
| ~ in(X5,X0) ) )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ( ( ~ subset(sK1(X0,X1),sK2(X0,X1))
| ~ in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X1) )
& ( subset(sK1(X0,X1),sK2(X0,X1))
| in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X1) )
& in(sK1(X0,X1),X0)
& in(sK2(X0,X1),X0) ) )
& ( ( relation_field(X1) = X0
& ! [X4,X5] :
( ( ( in(ordered_pair(X4,X5),X1)
| ~ subset(X4,X5) )
& ( subset(X4,X5)
| ~ in(ordered_pair(X4,X5),X1) ) )
| ~ in(X4,X0)
| ~ in(X5,X0) ) )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X2,sK1(X0,X1)),skolemize(X3,sK2(X0,X1))],[f71]) ).
fof(f73,plain,
! [X0] :
( ( ( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0)) )
& ( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f57]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) ) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f61]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) ) )
& ( ! [X3] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ( ~ in(ordered_pair(sK3(X0,X1),sK3(X0,X1)),X0)
& in(sK3(X0,X1),X1) ) )
& ( ! [X3] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f76]) ).
fof(f81,plain,
~ reflexive(inclusion_relation(sK0)),
inference(cnf_transformation,[],[f68]) ).
fof(f82,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f16]) ).
fof(f84,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ subset(X4,X5)
| ~ in(X4,X0)
| ~ in(X5,X0)
| inclusion_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f85,plain,
! [X0,X1] :
( relation_field(X1) = X0
| inclusion_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f91,plain,
! [X0] :
( ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f98,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f53]) ).
fof(f100,plain,
! [X0,X1] :
( in(sK3(X0,X1),X1)
| is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f101,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK3(X0,X1),sK3(X0,X1)),X0)
| is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f113,plain,
! [X0] :
( relation_field(inclusion_relation(X0)) = X0
| ~ relation(inclusion_relation(X0)) ),
inference(equality_resolution,[],[f85]) ).
fof(f114,plain,
! [X0,X4,X5] :
( in(ordered_pair(X4,X5),inclusion_relation(X0))
| ~ subset(X4,X5)
| ~ in(X4,X0)
| ~ in(X5,X0)
| ~ relation(inclusion_relation(X0)) ),
inference(equality_resolution,[],[f84]) ).
fof(f128,plain,
! [X0] : relation_field(inclusion_relation(X0)) = X0,
inference(forward_subsumption_resolution,[],[f113,f82]) ).
fof(f129,plain,
! [X0] :
( ~ is_reflexive_in(inclusion_relation(X0),X0)
| reflexive(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0)) ),
inference(superposition,[],[f91,f128]) ).
fof(f132,plain,
! [X0] :
( ~ is_reflexive_in(inclusion_relation(X0),X0)
| reflexive(inclusion_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f129,f82]) ).
fof(f174,plain,
! [X0,X4,X5] :
( in(ordered_pair(X4,X5),inclusion_relation(X0))
| ~ subset(X4,X5)
| ~ in(X4,X0)
| ~ in(X5,X0) ),
inference(forward_subsumption_resolution,[],[f114,f82]) ).
fof(f179,plain,
! [X0,X1] :
( ~ subset(sK3(inclusion_relation(X0),X1),sK3(inclusion_relation(X0),X1))
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| is_reflexive_in(inclusion_relation(X0),X1)
| ~ relation(inclusion_relation(X0)) ),
inference(resolution,[],[f174,f101]) ).
fof(f182,plain,
! [X0,X1] :
( ~ subset(sK3(inclusion_relation(X0),X1),sK3(inclusion_relation(X0),X1))
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| is_reflexive_in(inclusion_relation(X0),X1)
| ~ relation(inclusion_relation(X0)) ),
inference(duplicate_literal_removal,[],[f179]) ).
fof(f183,plain,
! [X0,X1] :
( ~ in(sK3(inclusion_relation(X0),X1),X0)
| is_reflexive_in(inclusion_relation(X0),X1)
| ~ relation(inclusion_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f182,f98]) ).
fof(f184,plain,
! [X0,X1] :
( ~ in(sK3(inclusion_relation(X0),X1),X0)
| is_reflexive_in(inclusion_relation(X0),X1) ),
inference(forward_subsumption_resolution,[],[f183,f82]) ).
fof(f267,plain,
! [X0] :
( is_reflexive_in(inclusion_relation(X0),X0)
| is_reflexive_in(inclusion_relation(X0),X0)
| ~ relation(inclusion_relation(X0)) ),
inference(resolution,[],[f184,f100]) ).
fof(f270,plain,
! [X0] :
( is_reflexive_in(inclusion_relation(X0),X0)
| ~ relation(inclusion_relation(X0)) ),
inference(duplicate_literal_removal,[],[f267]) ).
fof(f271,plain,
! [X0] : is_reflexive_in(inclusion_relation(X0),X0),
inference(forward_subsumption_resolution,[],[f270,f82]) ).
fof(f275,plain,
! [X0] : reflexive(inclusion_relation(X0)),
inference(resolution,[],[f271,f132]) ).
fof(f279,plain,
$false,
inference(resolution,[],[f275,f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU268+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n011.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 : Mon Sep 28 04:24:15 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.42 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
% 2.38/1.15 % (3015900)Detected formulas, will run a generic FOF schedule.
% 2.38/1.15 % (3015909)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1857930597:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.38/1.15 % (3015909)First to succeed.
% 2.38/1.15 % (3015909)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3015900"
% 2.38/1.15 % (3015906)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=2439817616:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.38/1.15 % (3015911)dis-21_1_sil=8000:lcm=predicate:random_seed=2458787558: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)
% 2.38/1.15 % (3015905)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=905311452:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.38/1.15 % (3015907)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=2030783488:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.38/1.15 % (3015908)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1048953995:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.38/1.15 % (3015910)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3772650360:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.38/1.15 % (3015908)Refutation not found, incomplete strategy
% 2.38/1.15 % (3015908)------------------------------
% 2.38/1.15 % (3015908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.38/1.15 % (3015908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/1.15 % (3015908)CaDiCaL version: 2.1.3
% 2.38/1.15 % (3015908)Termination reason: Refutation not found, incomplete strategy
% 2.38/1.15 % (3015908)Time elapsed: 0.002 s
% 2.38/1.15 % (3015908)Peak memory usage: 88 MB
% 2.38/1.15 % (3015908)Instructions burned: 1 (million)
% 2.38/1.15 % (3015910)Also succeeded, but the first one will report.
% 2.38/1.15 % (3015911)Instruction limit reached!
% 2.38/1.15 % (3015911)------------------------------
% 2.38/1.15 % (3015911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.38/1.15 % (3015911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/1.15 % (3015911)CaDiCaL version: 2.1.3
% 2.38/1.15 % (3015911)Termination reason: Instruction limit
% 2.38/1.15 % (3015911)Termination phase: Saturation
% 2.38/1.15 % (3015911)Time elapsed: 0.082 s
% 2.38/1.15 % (3015911)Peak memory usage: 89 MB
% 2.38/1.15 % (3015911)Instructions burned: 130 (million)
% 2.38/1.15 % (3015909)Refutation found. Thanks to Tanya!
% 2.38/1.15 % SZS status Theorem for theBenchmark
% 2.38/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.35 % (3015909)------------------------------
% 2.69/1.35 % (3015909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.35 % (3015909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.35 % (3015909)CaDiCaL version: 2.1.3
% 2.69/1.35 % (3015909)Termination reason: Refutation
% 2.69/1.35 % (3015909)Time elapsed: 0.004 s
% 2.69/1.35 % (3015909)Peak memory usage: 88 MB
% 2.69/1.35 % (3015909)Instructions burned: 9 (million)
% 2.69/1.35 % (3015909)------------------------------
% 2.69/1.35 % (3015909)------------------------------
% 2.69/1.35 % (3015900)Success in time 0.295 s
% 2.69/1.35 % Vampire exiting
%------------------------------------------------------------------------------