%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU209+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 : n005.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 12:47:45 PM UTC 2026
% Result : Theorem 0.14s 1.70s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 6 unt; 0 def)
% Number of atoms : 130 ( 9 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 159 ( 59 ~; 57 |; 30 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-3 aty)
% Number of variables : 89 ( 73 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f26,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f131,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
fof(f132,conjecture,
! [X0,X1] :
( relation(X1)
=> subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_relat_1) ).
fof(f133,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
inference(negated_conjecture,[status(cth)],[f132]) ).
fof(f209,plain,
? [X0,X1] :
( ~ subset(relation_inverse_image(X1,X0),relation_dom(X1))
& relation(X1) ),
inference(ennf_transformation,[],[f133]) ).
fof(f212,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f213,plain,
! [X0,X1,X2] :
( ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f131]) ).
fof(f225,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f226,plain,
( ~ subset(relation_inverse_image(sK1,sK0),relation_dom(sK1))
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f209]) ).
fof(f227,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f212]) ).
fof(f228,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f227]) ).
fof(f229,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK2(X0,X1),X1)
& in(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f228]) ).
fof(f232,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_rng(X2))
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,X1) ) )
& ( ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f213]) ).
fof(f233,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_rng(X2))
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,X1) ) )
& ( ? [X4] :
( in(X4,relation_rng(X2))
& in(ordered_pair(X0,X4),X2)
& in(X4,X1) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(rectify,[],[f232]) ).
fof(f234,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_rng(X2))
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,X1) ) )
& ( ( in(sK3(X0,X1,X2),relation_rng(X2))
& in(ordered_pair(X0,sK3(X0,X1,X2)),X2)
& in(sK3(X0,X1,X2),X1) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X1,X2))],[f233]) ).
fof(f239,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f225]) ).
fof(f240,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f239]) ).
fof(f241,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK7(X0,X1),X3),X0)
| ~ in(sK7(X0,X1),X1) )
& ( in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0)
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK9(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f240]) ).
fof(f242,plain,
relation(sK1),
inference(cnf_transformation,[],[f226]) ).
fof(f243,plain,
~ subset(relation_inverse_image(sK1,sK0),relation_dom(sK1)),
inference(cnf_transformation,[],[f226]) ).
fof(f247,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f229]) ).
fof(f248,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f229]) ).
fof(f253,plain,
! [X2,X0,X1] :
( in(ordered_pair(X0,sK3(X0,X1,X2)),X2)
| ~ in(X0,relation_inverse_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f234]) ).
fof(f276,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f284,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f276]) ).
fof(f298,plain,
in(sK2(relation_inverse_image(sK1,sK0),relation_dom(sK1)),relation_inverse_image(sK1,sK0)),
inference(unit_resulting_resolution,[],[f247,f243]) ).
fof(f299,plain,
~ in(sK2(relation_inverse_image(sK1,sK0),relation_dom(sK1)),relation_dom(sK1)),
inference(unit_resulting_resolution,[],[f248,f243]) ).
fof(f311,plain,
! [X0] : ~ in(ordered_pair(sK2(relation_inverse_image(sK1,sK0),relation_dom(sK1)),X0),sK1),
inference(unit_resulting_resolution,[],[f284,f242,f299]) ).
fof(f338,plain,
$false,
inference(unit_resulting_resolution,[],[f253,f242,f298,f311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU209+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 04:03:16 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 2.47/1.51 % (423829)Detected formulas, will run a generic FOF schedule.
% 2.47/1.51 % (423839)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3676832534:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.47/1.51 % (423836)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=3708964234:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.47/1.51 % (423834)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=3571954170:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.47/1.51 % (423837)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2117927217:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.47/1.51 % (423835)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=2939764942:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.47/1.51 % (423838)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1509887815:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.47/1.51 % (423839)Instruction limit reached!
% 2.47/1.51 % (423839)------------------------------
% 2.47/1.51 % (423839)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.51 % (423839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.51 % (423839)CaDiCaL version: 2.1.3
% 2.47/1.51 % (423839)Termination reason: Instruction limit
% 2.47/1.51 % (423839)Termination phase: Saturation
% 2.47/1.51 % (423839)Time elapsed: 0.054 s
% 2.47/1.51 % (423839)Peak memory usage: 90 MB
% 2.47/1.51 % (423839)Instructions burned: 142 (million)
% 2.47/1.51 % (423840)dis-21_1_sil=8000:lcm=predicate:random_seed=3215185437: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)
% 2.47/1.51 % (423837)Instruction limit reached!
% 2.47/1.51 % (423837)------------------------------
% 2.47/1.51 % (423837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.51 % (423837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.51 % (423837)CaDiCaL version: 2.1.3
% 2.47/1.51 % (423837)Termination reason: Instruction limit
% 2.47/1.51 % (423837)Termination phase: Saturation
% 2.47/1.51 % (423837)Time elapsed: 0.073 s
% 2.47/1.51 % (423837)Peak memory usage: 90 MB
% 2.47/1.51 % (423837)Instructions burned: 109 (million)
% 2.47/1.51 % (423838)Instruction limit reached!
% 2.47/1.51 % (423838)------------------------------
% 2.47/1.51 % (423838)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.51 % (423838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.51 % (423838)CaDiCaL version: 2.1.3
% 2.47/1.51 % (423838)Termination reason: Instruction limit
% 2.47/1.51 % (423838)Termination phase: Saturation
% 2.47/1.51 % (423838)Time elapsed: 0.080 s
% 2.47/1.51 % (423838)Peak memory usage: 89 MB
% 2.47/1.51 % (423838)Instructions burned: 119 (million)
% 2.47/1.51 % (423840)Instruction limit reached!
% 2.47/1.51 % (423840)------------------------------
% 2.47/1.51 % (423840)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.47/1.51 % (423840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/1.51 % (423840)CaDiCaL version: 2.1.3
% 2.47/1.51 % (423840)Termination reason: Instruction limit
% 2.47/1.51 % (423840)Termination phase: Saturation
% 2.47/1.51 % (423840)Time elapsed: 0.077 s
% 2.47/1.51 % (423840)Peak memory usage: 90 MB
% 2.47/1.51 % (423840)Instructions burned: 129 (million)
% 2.47/1.51 % (423848)lrs+10_1_sil=8000:sp=occurrence:random_seed=3361356182:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.47/1.51 % (423849)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3922164427:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.47/1.51 % (423850)lrs+1011_1_sil=32000:sp=occurrence:random_seed=710022780:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.47/1.51 % (423849)First to succeed.
% 2.47/1.51 % (423849)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-423829"
% 2.47/1.51 % (423848)Instruction limit reached!
% 2.47/1.51 % (423848)------------------------------
% 2.47/1.51 % (423848)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.70 % (423848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.70 % (423848)CaDiCaL version: 2.1.3
% 0.14/1.70 % (423848)Termination reason: Instruction limit
% 0.14/1.70 % (423848)Termination phase: Saturation
% 0.14/1.70 % (423848)Time elapsed: 0.102 s
% 0.14/1.70 % (423848)Peak memory usage: 93 MB
% 0.14/1.70 % (423848)Instructions burned: 286 (million)
% 0.14/1.70 % (423851)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=1512231094:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 0.14/1.70 % (423851)Also succeeded, but the first one will report.
% 0.14/1.70 % (423855)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3282083723:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 0.14/1.70 % (423850)Instruction limit reached!
% 0.14/1.70 % (423850)------------------------------
% 0.14/1.70 % (423850)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.70 % (423850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.70 % (423850)CaDiCaL version: 2.1.3
% 0.14/1.70 % (423850)Termination reason: Instruction limit
% 0.14/1.70 % (423850)Termination phase: Saturation
% 0.14/1.70 % (423850)Time elapsed: 0.220 s
% 0.14/1.70 % (423850)Peak memory usage: 93 MB
% 0.14/1.70 % (423850)Instructions burned: 327 (million)
% 0.14/1.70 % (423849)Refutation found. Thanks to Tanya!
% 0.14/1.70 % SZS status Theorem for theBenchmark
% 0.14/1.70 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/1.70 % (423849)------------------------------
% 0.14/1.70 % (423849)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.70 % (423849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.70 % (423849)CaDiCaL version: 2.1.3
% 0.14/1.70 % (423849)Termination reason: Refutation
% 0.14/1.70 % (423849)Time elapsed: 0.006 s
% 0.14/1.70 % (423849)Peak memory usage: 89 MB
% 0.14/1.70 % (423849)Instructions burned: 7 (million)
% 0.14/1.70 % (423849)------------------------------
% 0.14/1.70 % (423849)------------------------------
% 0.14/1.70 % (423829)Success in time 0.663 s
% 0.14/1.70 % Vampire exiting
%------------------------------------------------------------------------------