%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU268+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 5.56s 1.77s
% Output : Refutation 5.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 16 unt; 0 def)
% Number of atoms : 151 ( 28 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 191 ( 73 ~; 72 |; 34 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 65 ( 56 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f34,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/sandbox/benchmark/theBenchmark.p',d1_wellord2) ).
fof(f86,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f157,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_wellord1) ).
fof(f197,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f259,conjecture,
! [X0] : reflexive(inclusion_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_wellord2) ).
fof(f260,negated_conjecture,
~ ! [X0] : reflexive(inclusion_relation(X0)),
inference(negated_conjecture,[status(cth)],[f259]) ).
fof(f352,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f197]) ).
fof(f392,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,[],[f34]) ).
fof(f393,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,[],[f392]) ).
fof(f484,plain,
! [X0] :
( ( reflexive(X0)
<=> ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f157]) ).
fof(f592,plain,
? [X0] : ~ reflexive(inclusion_relation(X0)),
inference(ennf_transformation,[],[f260]) ).
fof(f749,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,[],[f393]) ).
fof(f750,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,[],[f749]) ).
fof(f751,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,[],[f750]) ).
fof(f752,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ( ( ~ subset(sK31(X0,X1),sK32(X0,X1))
| ~ in(ordered_pair(sK31(X0,X1),sK32(X0,X1)),X1) )
& ( subset(sK31(X0,X1),sK32(X0,X1))
| in(ordered_pair(sK31(X0,X1),sK32(X0,X1)),X1) )
& in(sK31(X0,X1),X0)
& in(sK32(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,[sK31,sK32]),skolemize(X2,sK31(X0,X1)),skolemize(X3,sK32(X0,X1))],[f751]) ).
fof(f856,plain,
! [X0] :
( ( ( reflexive(X0)
| ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) ) )
& ( ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) )
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f484]) ).
fof(f857,plain,
! [X0] :
( ( ( reflexive(X0)
| ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) ) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0)) )
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f856]) ).
fof(f858,plain,
! [X0] :
( ( ( reflexive(X0)
| ( ~ in(ordered_pair(sK91(X0),sK91(X0)),X0)
& in(sK91(X0),relation_field(X0)) ) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0)) )
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(X1,sK91(X0))],[f857]) ).
fof(f916,plain,
~ reflexive(inclusion_relation(sK122)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(X0,sK122)],[f592]) ).
fof(f1073,plain,
! [X0,X1,X4,X5] :
( inclusion_relation(X0) != X1
| ~ subset(X4,X5)
| ~ in(X4,X0)
| ~ in(X5,X0)
| in(ordered_pair(X4,X5),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f752]) ).
fof(f1074,plain,
! [X0,X1] :
( inclusion_relation(X0) != X1
| relation_field(X1) = X0
| ~ relation(X1) ),
inference(cnf_transformation,[],[f752]) ).
fof(f1258,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f1342,plain,
! [X0] :
( in(sK91(X0),relation_field(X0))
| reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f858]) ).
fof(f1343,plain,
! [X0] :
( ~ in(ordered_pair(sK91(X0),sK91(X0)),X0)
| reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f858]) ).
fof(f1428,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f352]) ).
fof(f1517,plain,
~ reflexive(inclusion_relation(sK122)),
inference(cnf_transformation,[],[f916]) ).
fof(f1678,plain,
in(sK91(inclusion_relation(sK122)),relation_field(inclusion_relation(sK122))),
inference(unit_resulting_resolution,[],[f1342,f1258,f1517]) ).
fof(f1679,plain,
! [X0] :
( relation_field(inclusion_relation(X0)) = X0
| ~ relation(inclusion_relation(X0)) ),
inference(equality_resolution,[],[f1074]) ).
fof(f1680,plain,
! [X0] : relation_field(inclusion_relation(X0)) = X0,
inference(forward_subsumption_resolution,[],[f1679,f1258]) ).
fof(f1682,plain,
~ in(ordered_pair(sK91(inclusion_relation(sK122)),sK91(inclusion_relation(sK122))),inclusion_relation(sK122)),
inference(unit_resulting_resolution,[],[f1343,f1258,f1517]) ).
fof(f1694,plain,
in(sK91(inclusion_relation(sK122)),sK122),
inference(superposition,[],[f1678,f1680]) ).
fof(f1714,plain,
inclusion_relation(sK122) != inclusion_relation(sK122),
inference(unit_resulting_resolution,[],[f1073,f1258,f1694,f1428,f1682,f1694]) ).
fof(f1716,plain,
$false,
inference(trivial_inequality_removal,[],[f1714]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU268+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n008.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 04:24:39 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.70/1.58 % (1869679)Detected formulas, will run a generic FOF schedule.
% 3.70/1.58 % (1869685)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=1133832525:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.70/1.58 % (1869690)dis-21_1_sil=8000:lcm=predicate:random_seed=673490909: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)
% 3.70/1.58 % (1869687)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2320112760:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.70/1.58 % (1869686)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=2528732314:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.70/1.58 % (1869689)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4227897623:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.70/1.58 % (1869688)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3456735020:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.70/1.58 % (1869684)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=1269485280:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.70/1.58 % (1869687)Instruction limit reached!
% 3.70/1.58 % (1869687)------------------------------
% 3.70/1.58 % (1869687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.58 % (1869687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.58 % (1869687)CaDiCaL version: 2.1.3
% 3.70/1.58 % (1869687)Termination reason: Instruction limit
% 3.70/1.58 % (1869687)Termination phase: Saturation
% 3.70/1.58 % (1869687)Time elapsed: 0.068 s
% 3.70/1.58 % (1869687)Peak memory usage: 90 MB
% 3.70/1.58 % (1869687)Instructions burned: 109 (million)
% 3.70/1.58 % (1869690)Instruction limit reached!
% 3.70/1.58 % (1869690)------------------------------
% 3.70/1.58 % (1869690)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.58 % (1869690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.58 % (1869690)CaDiCaL version: 2.1.3
% 3.70/1.58 % (1869690)Termination reason: Instruction limit
% 3.70/1.58 % (1869690)Termination phase: Saturation
% 3.70/1.58 % (1869690)Time elapsed: 0.075 s
% 3.70/1.58 % (1869690)Peak memory usage: 90 MB
% 3.70/1.58 % (1869690)Instructions burned: 130 (million)
% 3.70/1.58 % (1869688)Instruction limit reached!
% 3.70/1.58 % (1869688)------------------------------
% 3.70/1.58 % (1869688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.58 % (1869688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.58 % (1869688)CaDiCaL version: 2.1.3
% 3.70/1.58 % (1869688)Termination reason: Instruction limit
% 3.70/1.58 % (1869688)Termination phase: Saturation
% 3.70/1.58 % (1869688)Time elapsed: 0.079 s
% 3.70/1.58 % (1869688)Peak memory usage: 90 MB
% 3.70/1.58 % (1869688)Instructions burned: 119 (million)
% 3.70/1.58 % (1869689)Instruction limit reached!
% 3.70/1.58 % (1869689)------------------------------
% 3.70/1.58 % (1869689)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.58 % (1869689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.58 % (1869689)CaDiCaL version: 2.1.3
% 3.70/1.58 % (1869689)Termination reason: Instruction limit
% 3.70/1.58 % (1869689)Termination phase: Saturation
% 3.70/1.58 % (1869689)Time elapsed: 0.095 s
% 3.70/1.58 % (1869689)Peak memory usage: 90 MB
% 3.70/1.58 % (1869689)Instructions burned: 139 (million)
% 3.70/1.58 % (1869698)lrs+10_1_sil=8000:sp=occurrence:random_seed=2005081402:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.70/1.58 % (1869700)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4153455080:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.70/1.58 % (1869699)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1848797894:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.70/1.58 % (1869699)Refutation not found, incomplete strategy
% 3.70/1.58 % (1869699)------------------------------
% 3.70/1.58 % (1869699)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.58 % (1869699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.77 % (1869699)CaDiCaL version: 2.1.3
% 5.56/1.77 % (1869699)Termination reason: Refutation not found, incomplete strategy
% 5.56/1.77 % (1869699)Time elapsed: 0.005 s
% 5.56/1.77 % (1869699)Peak memory usage: 89 MB
% 5.56/1.77 % (1869699)Instructions burned: 5 (million)
% 5.56/1.77 % (1869701)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1943864720:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.56/1.77 % (1869701)First to succeed.
% 5.56/1.77 % (1869701)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1869679"
% 5.56/1.77 % (1869698)Instruction limit reached!
% 5.56/1.77 % (1869698)------------------------------
% 5.56/1.77 % (1869698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.77 % (1869698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.77 % (1869698)CaDiCaL version: 2.1.3
% 5.56/1.77 % (1869698)Termination reason: Instruction limit
% 5.56/1.77 % (1869698)Termination phase: Saturation
% 5.56/1.77 % (1869698)Time elapsed: 0.184 s
% 5.56/1.77 % (1869698)Peak memory usage: 93 MB
% 5.56/1.77 % (1869698)Instructions burned: 285 (million)
% 5.56/1.77 % (1869685)Also succeeded, but the first one will report.
% 5.56/1.77 % (1869700)Instruction limit reached!
% 5.56/1.77 % (1869700)------------------------------
% 5.56/1.77 % (1869700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.77 % (1869700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.77 % (1869700)CaDiCaL version: 2.1.3
% 5.56/1.77 % (1869700)Termination reason: Instruction limit
% 5.56/1.77 % (1869700)Termination phase: Saturation
% 5.56/1.77 % (1869700)Time elapsed: 0.226 s
% 5.56/1.77 % (1869700)Peak memory usage: 93 MB
% 5.56/1.77 % (1869700)Instructions burned: 326 (million)
% 5.56/1.77 % (1869699)------------------------------
% 5.56/1.77 % (1869699)------------------------------
% 5.56/1.77 % (1869701)Refutation found. Thanks to Tanya!
% 5.56/1.77 % SZS status Theorem for theBenchmark
% 5.56/1.77 % SZS output start Proof for theBenchmark
% See solution above
% 5.56/1.77 % (1869701)------------------------------
% 5.56/1.77 % (1869701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.56/1.77 % (1869701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.56/1.77 % (1869701)CaDiCaL version: 2.1.3
% 5.56/1.77 % (1869701)Termination reason: Refutation
% 5.56/1.77 % (1869701)Time elapsed: 0.018 s
% 5.56/1.77 % (1869701)Peak memory usage: 89 MB
% 5.56/1.77 % (1869701)Instructions burned: 28 (million)
% 5.56/1.77 % (1869701)------------------------------
% 5.56/1.77 % (1869701)------------------------------
% 5.56/1.77 % (1869679)Success in time 0.712 s
% 5.56/1.77 % Vampire exiting
%------------------------------------------------------------------------------