%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU239+2 : 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 : n001.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 12:47:57 PM UTC 2026
% Result : Theorem 3.83s 1.28s
% Output : Refutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 6 unt; 4 def)
% Number of atoms : 173 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 194 ( 77 ~; 79 |; 20 &)
% ( 10 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 39 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,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(f58,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_relat_2) ).
fof(f127,conjecture,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_wellord1) ).
fof(f128,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f127]) ).
fof(f320,plain,
! [X0] :
( ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f345,plain,
! [X0] :
( ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f393,plain,
? [X0] :
( ( reflexive(X0)
<~> ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) ) )
& relation(X0) ),
inference(ennf_transformation,[],[f128]) ).
fof(f590,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,[],[f320]) ).
fof(f591,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,[],[f590]) ).
fof(f592,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ( ~ in(ordered_pair(sK21(X0,X1),sK21(X0,X1)),X0)
& in(sK21(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,[sK21]),skolemize(X2,sK21(X0,X1))],[f591]) ).
fof(f670,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,[],[f345]) ).
fof(f672,plain,
? [X0] :
( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
| ~ reflexive(X0) )
& ( ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) )
| reflexive(X0) )
& relation(X0) ),
inference(nnf_transformation,[],[f393]) ).
fof(f673,plain,
? [X0] :
( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
| ~ reflexive(X0) )
& ( ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) )
| reflexive(X0) )
& relation(X0) ),
inference(flattening,[],[f672]) ).
fof(f674,plain,
? [X0] :
( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
| ~ reflexive(X0) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0)) )
| reflexive(X0) )
& relation(X0) ),
inference(rectify,[],[f673]) ).
fof(f675,plain,
( ( ( ~ in(ordered_pair(sK68,sK68),sK67)
& in(sK68,relation_field(sK67)) )
| ~ reflexive(sK67) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),sK67)
| ~ in(X2,relation_field(sK67)) )
| reflexive(sK67) )
& relation(sK67) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67,sK68]),skolemize(X0,sK67),skolemize(X1,sK68)],[f674]) ).
fof(f835,plain,
! [X3,X0,X1] :
( ~ is_reflexive_in(X0,X1)
| ~ in(X3,X1)
| in(ordered_pair(X3,X3),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f592]) ).
fof(f836,plain,
! [X0,X1] :
( in(sK21(X0,X1),X1)
| is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f592]) ).
fof(f837,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK21(X0,X1),sK21(X0,X1)),X0)
| is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f592]) ).
fof(f968,plain,
! [X0] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f670]) ).
fof(f969,plain,
! [X0] :
( ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f670]) ).
fof(f1044,plain,
relation(sK67),
inference(cnf_transformation,[],[f675]) ).
fof(f1045,plain,
! [X2] :
( in(ordered_pair(X2,X2),sK67)
| ~ in(X2,relation_field(sK67))
| reflexive(sK67) ),
inference(cnf_transformation,[],[f675]) ).
fof(f1046,plain,
( in(sK68,relation_field(sK67))
| ~ reflexive(sK67) ),
inference(cnf_transformation,[],[f675]) ).
fof(f1047,plain,
( ~ in(ordered_pair(sK68,sK68),sK67)
| ~ reflexive(sK67) ),
inference(cnf_transformation,[],[f675]) ).
fof(f1321,definition,
( spl103_3
<=> reflexive(sK67) ),
introduced(definition,[new_symbols(definition,[spl103_3])],[avatar_definition]) ).
fof(f1322,plain,
( ~ reflexive(sK67)
| spl103_3 ),
inference(avatar_component_clause,[],[f1321]) ).
fof(f1323,plain,
( reflexive(sK67)
| ~ spl103_3 ),
inference(avatar_component_clause,[],[f1321]) ).
fof(f1325,definition,
( spl103_4
<=> ! [X2] :
( in(ordered_pair(X2,X2),sK67)
| ~ in(X2,relation_field(sK67)) ) ),
introduced(definition,[new_symbols(definition,[spl103_4])],[avatar_definition]) ).
fof(f1326,plain,
( ! [X2] :
( in(ordered_pair(X2,X2),sK67)
| ~ in(X2,relation_field(sK67)) )
| ~ spl103_4 ),
inference(avatar_component_clause,[],[f1325]) ).
fof(f1327,plain,
( spl103_3
| spl103_4 ),
inference(avatar_split_clause,[],[f1045,f1325,f1321]) ).
fof(f1329,definition,
( spl103_5
<=> in(sK68,relation_field(sK67)) ),
introduced(definition,[new_symbols(definition,[spl103_5])],[avatar_definition]) ).
fof(f1331,plain,
( in(sK68,relation_field(sK67))
| ~ spl103_5 ),
inference(avatar_component_clause,[],[f1329]) ).
fof(f1332,plain,
( ~ spl103_3
| spl103_5 ),
inference(avatar_split_clause,[],[f1046,f1329,f1321]) ).
fof(f1334,definition,
( spl103_6
<=> in(ordered_pair(sK68,sK68),sK67) ),
introduced(definition,[new_symbols(definition,[spl103_6])],[avatar_definition]) ).
fof(f1336,plain,
( ~ in(ordered_pair(sK68,sK68),sK67)
| spl103_6 ),
inference(avatar_component_clause,[],[f1334]) ).
fof(f1337,plain,
( ~ spl103_3
| ~ spl103_6 ),
inference(avatar_split_clause,[],[f1047,f1334,f1321]) ).
fof(f1338,plain,
( ~ is_reflexive_in(sK67,relation_field(sK67))
| spl103_3 ),
inference(unit_resulting_resolution,[],[f969,f1044,f1322]) ).
fof(f1687,plain,
( in(sK21(sK67,relation_field(sK67)),relation_field(sK67))
| spl103_3 ),
inference(unit_resulting_resolution,[],[f836,f1044,f1338]) ).
fof(f1879,plain,
( ~ in(ordered_pair(sK21(sK67,relation_field(sK67)),sK21(sK67,relation_field(sK67))),sK67)
| spl103_3 ),
inference(unit_resulting_resolution,[],[f837,f1044,f1338]) ).
fof(f2109,plain,
( ~ in(sK21(sK67,relation_field(sK67)),relation_field(sK67))
| spl103_3
| ~ spl103_4 ),
inference(unit_resulting_resolution,[],[f1326,f1879]) ).
fof(f2135,plain,
( $false
| spl103_3
| ~ spl103_4 ),
inference(forward_subsumption_resolution,[],[f2109,f1687]) ).
fof(f2136,plain,
( spl103_3
| ~ spl103_4 ),
inference(avatar_contradiction_clause,[],[f2135]) ).
fof(f2137,plain,
( is_reflexive_in(sK67,relation_field(sK67))
| ~ spl103_3 ),
inference(unit_resulting_resolution,[],[f968,f1044,f1323]) ).
fof(f2192,plain,
( ~ relation(sK67)
| ~ spl103_3
| ~ spl103_5
| spl103_6 ),
inference(unit_resulting_resolution,[],[f835,f1331,f1336,f2137]) ).
fof(f2199,plain,
( $false
| ~ spl103_3
| ~ spl103_5
| spl103_6 ),
inference(forward_subsumption_resolution,[],[f2192,f1044]) ).
fof(f2200,plain,
( ~ spl103_3
| ~ spl103_5
| spl103_6 ),
inference(avatar_contradiction_clause,[],[f2199]) ).
cnf(s2,plain,
( spl103_3
| spl103_4 ),
inference(sat_conversion,[],[f1327]) ).
cnf(s3,plain,
( ~ spl103_3
| spl103_5 ),
inference(sat_conversion,[],[f1332]) ).
cnf(s4,plain,
( ~ spl103_3
| ~ spl103_6 ),
inference(sat_conversion,[],[f1337]) ).
cnf(s9,plain,
( spl103_3
| ~ spl103_4 ),
inference(sat_conversion,[],[f2136]) ).
cnf(s14,plain,
( ~ spl103_3
| ~ spl103_5
| spl103_6 ),
inference(sat_conversion,[],[f2200]) ).
cnf(s15,plain,
spl103_3,
inference(rat,[],[s2,s9]) ).
cnf(s16,plain,
~ spl103_6,
inference(rat,[],[s4,s15]) ).
cnf(s17,plain,
spl103_5,
inference(rat,[],[s3,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s14,s16,s15,s17]) ).
fof(f2201,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU239+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n001.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 04:21:47 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.39 Running first-order theorem proving
% 0.04/0.39 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
% 3.29/1.08 % (13316)Detected formulas, will run a generic FOF schedule.
% 3.29/1.08 % (13324)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=604919364:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.29/1.08 % (13325)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2102544020:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.29/1.08 % (13327)dis-21_1_sil=8000:lcm=predicate:random_seed=1049638020: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)
% 3.29/1.08 % (13322)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=930607208:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.29/1.08 % (13323)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=2586001995:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.29/1.08 % (13321)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=4098906838:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.29/1.08 % (13326)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1581082004:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.29/1.08 % (13327)Instruction limit reached!
% 3.29/1.08 % (13327)------------------------------
% 3.29/1.08 % (13327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.29/1.08 % (13327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/1.08 % (13327)CaDiCaL version: 2.1.3
% 3.29/1.08 % (13327)Termination reason: Instruction limit
% 3.29/1.08 % (13327)Termination phase: Saturation
% 3.29/1.08 % (13327)Time elapsed: 0.063 s
% 3.29/1.08 % (13327)Peak memory usage: 90 MB
% 3.29/1.08 % (13327)Instructions burned: 131 (million)
% 3.29/1.08 % (13324)Instruction limit reached!
% 3.29/1.08 % (13324)------------------------------
% 3.29/1.08 % (13324)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.29/1.08 % (13324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/1.08 % (13324)CaDiCaL version: 2.1.3
% 3.29/1.08 % (13324)Termination reason: Instruction limit
% 3.29/1.08 % (13324)Termination phase: Saturation
% 3.29/1.08 % (13324)Time elapsed: 0.068 s
% 3.29/1.08 % (13324)Peak memory usage: 90 MB
% 3.29/1.08 % (13324)Instructions burned: 109 (million)
% 3.29/1.08 % (13325)Instruction limit reached!
% 3.29/1.08 % (13325)------------------------------
% 3.29/1.08 % (13325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.29/1.08 % (13325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/1.08 % (13325)CaDiCaL version: 2.1.3
% 3.29/1.08 % (13325)Termination reason: Instruction limit
% 3.29/1.08 % (13325)Termination phase: Saturation
% 3.29/1.08 % (13325)Time elapsed: 0.079 s
% 3.29/1.08 % (13325)Peak memory usage: 89 MB
% 3.29/1.08 % (13325)Instructions burned: 120 (million)
% 3.29/1.08 % (13326)Instruction limit reached!
% 3.29/1.08 % (13326)------------------------------
% 3.29/1.08 % (13326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.29/1.08 % (13326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.29/1.08 % (13326)CaDiCaL version: 2.1.3
% 3.29/1.08 % (13326)Termination reason: Instruction limit
% 3.29/1.08 % (13326)Termination phase: Saturation
% 3.29/1.08 % (13326)Time elapsed: 0.077 s
% 3.29/1.08 % (13326)Peak memory usage: 90 MB
% 3.29/1.08 % (13326)Instructions burned: 140 (million)
% 3.29/1.08 % (13338)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=3049278580:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 3.29/1.08 % (13335)lrs+10_1_sil=8000:sp=occurrence:random_seed=827829398:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.29/1.08 % (13338)First to succeed.
% 3.29/1.08 % (13338)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13316"
% 3.29/1.08 % (13337)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2024054537:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.29/1.08 % (13336)lrs+10_1_sil=32000:urr=on:br=off:random_seed=982639656:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.29/1.08 % (13336)Refutation not found, incomplete strategy
% 3.83/1.28 % (13336)------------------------------
% 3.83/1.28 % (13336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.83/1.28 % (13336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.83/1.28 % (13336)CaDiCaL version: 2.1.3
% 3.83/1.28 % (13336)Termination reason: Refutation not found, incomplete strategy
% 3.83/1.28 % (13336)Time elapsed: 0.005 s
% 3.83/1.28 % (13336)Peak memory usage: 89 MB
% 3.83/1.28 % (13336)Instructions burned: 6 (million)
% 3.83/1.28 % (13338)Refutation found. Thanks to Tanya!
% 3.83/1.28 % SZS status Theorem for theBenchmark
% 3.83/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.83/1.28 % (13338)------------------------------
% 3.83/1.28 % (13338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.83/1.28 % (13338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.83/1.28 % (13338)CaDiCaL version: 2.1.3
% 3.83/1.28 % (13338)Termination reason: Refutation
% 3.83/1.28 % (13338)Time elapsed: 0.019 s
% 3.83/1.28 % (13338)Peak memory usage: 91 MB
% 3.83/1.28 % (13338)Instructions burned: 51 (million)
% 3.83/1.28 % (13338)------------------------------
% 3.83/1.28 % (13338)------------------------------
% 3.83/1.28 % (13316)Success in time 0.497 s
% 3.83/1.28 % Vampire exiting
%------------------------------------------------------------------------------