%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU204+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 : n015.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 12:47:43 PM UTC 2026
% Result : Theorem 5.27s 1.75s
% Output : Refutation 5.27s
% 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(f23,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f29,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f124,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_dom(X2))
& in(ordered_pair(X3,X0),X2)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
fof(f125,conjecture,
! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_relat_1) ).
fof(f126,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_image(X1,X0),relation_rng(X1)) ),
inference(negated_conjecture,[status(cth)],[f125]) ).
fof(f202,plain,
? [X0,X1] :
( ~ subset(relation_image(X1,X0),relation_rng(X1))
& relation(X1) ),
inference(ennf_transformation,[],[f126]) ).
fof(f205,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f206,plain,
! [X0,X1,X2] :
( ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_dom(X2))
& in(ordered_pair(X3,X0),X2)
& in(X3,X1) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f124]) ).
fof(f211,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f212,plain,
( ~ subset(relation_image(sK1,sK0),relation_rng(sK1))
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f202]) ).
fof(f213,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,[],[f205]) ).
fof(f214,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,[],[f213]) ).
fof(f215,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))],[f214]) ).
fof(f218,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_dom(X2))
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,X1) ) )
& ( ? [X3] :
( in(X3,relation_dom(X2))
& in(ordered_pair(X3,X0),X2)
& in(X3,X1) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f206]) ).
fof(f219,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_dom(X2))
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,X1) ) )
& ( ? [X4] :
( in(X4,relation_dom(X2))
& in(ordered_pair(X4,X0),X2)
& in(X4,X1) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(rectify,[],[f218]) ).
fof(f220,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_dom(X2))
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,X1) ) )
& ( ( in(sK3(X0,X1,X2),relation_dom(X2))
& in(ordered_pair(sK3(X0,X1,X2),X0),X2)
& in(sK3(X0,X1,X2),X1) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X1,X2))],[f219]) ).
fof(f224,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f211]) ).
fof(f225,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f224]) ).
fof(f226,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK7(X0,X1)),X0)
| ~ in(sK7(X0,X1),X1) )
& ( in(ordered_pair(sK8(X0,X1),sK7(X0,X1)),X0)
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK9(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(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))],[f225]) ).
fof(f227,plain,
relation(sK1),
inference(cnf_transformation,[],[f212]) ).
fof(f228,plain,
~ subset(relation_image(sK1,sK0),relation_rng(sK1)),
inference(cnf_transformation,[],[f212]) ).
fof(f232,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f215]) ).
fof(f233,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f215]) ).
fof(f238,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK3(X0,X1,X2),X0),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f220]) ).
fof(f251,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f226]) ).
fof(f259,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X6,X5),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f251]) ).
fof(f261,plain,
in(sK2(relation_image(sK1,sK0),relation_rng(sK1)),relation_image(sK1,sK0)),
inference(unit_resulting_resolution,[],[f232,f228]) ).
fof(f262,plain,
~ in(sK2(relation_image(sK1,sK0),relation_rng(sK1)),relation_rng(sK1)),
inference(unit_resulting_resolution,[],[f233,f228]) ).
fof(f270,plain,
! [X0] : ~ in(ordered_pair(X0,sK2(relation_image(sK1,sK0),relation_rng(sK1))),sK1),
inference(unit_resulting_resolution,[],[f259,f227,f262]) ).
fof(f281,plain,
$false,
inference(unit_resulting_resolution,[],[f238,f227,f261,f270]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU204+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 % Computer : n015.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Mon Sep 28 04:05:47 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.45 Running first-order theorem proving
% 0.12/0.45 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
% 3.66/1.56 % (2246026)Detected formulas, will run a generic FOF schedule.
% 3.66/1.56 % (2246032)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=1241780542:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.66/1.56 % (2246033)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=3926943880:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.66/1.56 % (2246031)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=3944556044:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.66/1.56 % (2246034)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2533102859:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.66/1.56 % (2246036)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3187627991:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.66/1.56 % (2246037)dis-21_1_sil=8000:lcm=predicate:random_seed=1823869264: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)
% 3.66/1.56 % (2246035)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3567036323:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.66/1.56 % (2246034)Instruction limit reached!
% 3.66/1.56 % (2246034)------------------------------
% 3.66/1.56 % (2246034)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.56 % (2246034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.56 % (2246034)CaDiCaL version: 2.1.3
% 3.66/1.56 % (2246034)Termination reason: Instruction limit
% 3.66/1.56 % (2246034)Termination phase: Saturation
% 3.66/1.56 % (2246034)Time elapsed: 0.071 s
% 3.66/1.56 % (2246034)Peak memory usage: 90 MB
% 3.66/1.56 % (2246034)Instructions burned: 109 (million)
% 3.66/1.56 % (2246037)Instruction limit reached!
% 3.66/1.56 % (2246037)------------------------------
% 3.66/1.56 % (2246037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.56 % (2246037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.56 % (2246037)CaDiCaL version: 2.1.3
% 3.66/1.56 % (2246037)Termination reason: Instruction limit
% 3.66/1.56 % (2246037)Termination phase: Saturation
% 3.66/1.56 % (2246037)Time elapsed: 0.077 s
% 3.66/1.56 % (2246037)Peak memory usage: 90 MB
% 3.66/1.56 % (2246037)Instructions burned: 130 (million)
% 3.66/1.56 % (2246035)Instruction limit reached!
% 3.66/1.56 % (2246035)------------------------------
% 3.66/1.56 % (2246035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.56 % (2246035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.56 % (2246035)CaDiCaL version: 2.1.3
% 3.66/1.56 % (2246035)Termination reason: Instruction limit
% 3.66/1.56 % (2246035)Termination phase: Saturation
% 3.66/1.56 % (2246035)Time elapsed: 0.078 s
% 3.66/1.56 % (2246035)Peak memory usage: 89 MB
% 3.66/1.56 % (2246035)Instructions burned: 119 (million)
% 3.66/1.56 % (2246036)Instruction limit reached!
% 3.66/1.56 % (2246036)------------------------------
% 3.66/1.56 % (2246036)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.56 % (2246036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.56 % (2246036)CaDiCaL version: 2.1.3
% 3.66/1.56 % (2246036)Termination reason: Instruction limit
% 3.66/1.56 % (2246036)Termination phase: Saturation
% 3.66/1.56 % (2246036)Time elapsed: 0.097 s
% 3.66/1.56 % (2246036)Peak memory usage: 90 MB
% 3.66/1.56 % (2246036)Instructions burned: 139 (million)
% 3.66/1.56 % (2246046)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3060649178:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.66/1.56 % (2246045)lrs+10_1_sil=8000:sp=occurrence:random_seed=131592354:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.66/1.56 % (2246047)lrs+1011_1_sil=32000:sp=occurrence:random_seed=98268213:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.66/1.56 % (2246046)First to succeed.
% 3.66/1.56 % (2246046)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2246026"
% 3.66/1.56 % (2246048)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=1047551930:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.27/1.75 % (2246048)Also succeeded, but the first one will report.
% 5.27/1.75 % (2246032)Also succeeded, but the first one will report.
% 5.27/1.75 % (2246045)Instruction limit reached!
% 5.27/1.75 % (2246045)------------------------------
% 5.27/1.75 % (2246045)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.75 % (2246045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.75 % (2246045)CaDiCaL version: 2.1.3
% 5.27/1.75 % (2246045)Termination reason: Instruction limit
% 5.27/1.75 % (2246045)Termination phase: Saturation
% 5.27/1.75 % (2246045)Time elapsed: 0.186 s
% 5.27/1.75 % (2246045)Peak memory usage: 92 MB
% 5.27/1.75 % (2246045)Instructions burned: 286 (million)
% 5.27/1.75 % (2246047)Instruction limit reached!
% 5.27/1.75 % (2246047)------------------------------
% 5.27/1.75 % (2246047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.75 % (2246047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.75 % (2246047)CaDiCaL version: 2.1.3
% 5.27/1.75 % (2246047)Termination reason: Instruction limit
% 5.27/1.75 % (2246047)Termination phase: Saturation
% 5.27/1.75 % (2246047)Time elapsed: 0.217 s
% 5.27/1.75 % (2246047)Peak memory usage: 92 MB
% 5.27/1.75 % (2246047)Instructions burned: 326 (million)
% 5.27/1.75 % (2246046)Refutation found. Thanks to Tanya!
% 5.27/1.75 % SZS status Theorem for theBenchmark
% 5.27/1.75 % SZS output start Proof for theBenchmark
% See solution above
% 5.27/1.75 % (2246046)------------------------------
% 5.27/1.75 % (2246046)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.27/1.75 % (2246046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.27/1.75 % (2246046)CaDiCaL version: 2.1.3
% 5.27/1.75 % (2246046)Termination reason: Refutation
% 5.27/1.75 % (2246046)Time elapsed: 0.005 s
% 5.27/1.75 % (2246046)Peak memory usage: 89 MB
% 5.27/1.75 % (2246046)Instructions burned: 5 (million)
% 5.27/1.75 % (2246046)------------------------------
% 5.27/1.75 % (2246046)------------------------------
% 5.27/1.75 % (2246026)Success in time 0.664 s
% 5.27/1.75 % Vampire exiting
%------------------------------------------------------------------------------