%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU224+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 : n019.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 12:47:51 PM UTC 2026
% Result : Theorem 3.50s 1.38s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 6 unt; 3 def)
% Number of atoms : 155 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 167 ( 62 ~; 65 |; 28 &)
% ( 7 <=>; 3 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 29 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f117,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<=> ( in(X1,relation_dom(X2))
& in(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
fof(f118,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<=> ( in(X1,relation_dom(X2))
& in(X1,X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f117]) ).
fof(f228,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,X1)
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
fof(f335,plain,
? [X0,X1,X2] :
( ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<~> ( in(X1,relation_dom(X2))
& in(X1,X0) ) )
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f118]) ).
fof(f336,plain,
? [X0,X1,X2] :
( ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
<~> ( in(X1,relation_dom(X2))
& in(X1,X0) ) )
& relation(X2)
& function(X2) ),
inference(flattening,[],[f335]) ).
fof(f445,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,X1)
& in(X0,relation_dom(X2)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f228]) ).
fof(f558,plain,
? [X0,X1,X2] :
( ( ~ in(X1,relation_dom(X2))
| ~ in(X1,X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X0))) )
& ( ( in(X1,relation_dom(X2))
& in(X1,X0) )
| in(X1,relation_dom(relation_dom_restriction(X2,X0))) )
& relation(X2)
& function(X2) ),
inference(nnf_transformation,[],[f336]) ).
fof(f559,plain,
? [X0,X1,X2] :
( ( ~ in(X1,relation_dom(X2))
| ~ in(X1,X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X2,X0))) )
& ( ( in(X1,relation_dom(X2))
& in(X1,X0) )
| in(X1,relation_dom(relation_dom_restriction(X2,X0))) )
& relation(X2)
& function(X2) ),
inference(flattening,[],[f558]) ).
fof(f560,plain,
( ( ~ in(sK57,relation_dom(sK58))
| ~ in(sK57,sK56)
| ~ in(sK57,relation_dom(relation_dom_restriction(sK58,sK56))) )
& ( ( in(sK57,relation_dom(sK58))
& in(sK57,sK56) )
| in(sK57,relation_dom(relation_dom_restriction(sK58,sK56))) )
& relation(sK58)
& function(sK58) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56,sK57,sK58]),skolemize(X0,sK56),skolemize(X1,sK57),skolemize(X2,sK58)],[f559]) ).
fof(f617,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,X1)
| ~ in(X0,relation_dom(X2)) )
& ( ( in(X0,X1)
& in(X0,relation_dom(X2)) )
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f445]) ).
fof(f618,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,X1)
| ~ in(X0,relation_dom(X2)) )
& ( ( in(X0,X1)
& in(X0,relation_dom(X2)) )
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) )
| ~ relation(X2) ),
inference(flattening,[],[f617]) ).
fof(f855,plain,
relation(sK58),
inference(cnf_transformation,[],[f560]) ).
fof(f856,plain,
( in(sK57,sK56)
| in(sK57,relation_dom(relation_dom_restriction(sK58,sK56))) ),
inference(cnf_transformation,[],[f560]) ).
fof(f857,plain,
( in(sK57,relation_dom(sK58))
| in(sK57,relation_dom(relation_dom_restriction(sK58,sK56))) ),
inference(cnf_transformation,[],[f560]) ).
fof(f858,plain,
( ~ in(sK57,relation_dom(sK58))
| ~ in(sK57,sK56)
| ~ in(sK57,relation_dom(relation_dom_restriction(sK58,sK56))) ),
inference(cnf_transformation,[],[f560]) ).
fof(f1037,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| in(X0,relation_dom(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f618]) ).
fof(f1038,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| in(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f618]) ).
fof(f1039,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f618]) ).
fof(f1149,definition,
( spl83_1
<=> in(sK57,relation_dom(relation_dom_restriction(sK58,sK56))) ),
introduced(definition,[new_symbols(definition,[spl83_1])],[avatar_definition]) ).
fof(f1150,plain,
( ~ in(sK57,relation_dom(relation_dom_restriction(sK58,sK56)))
| spl83_1 ),
inference(avatar_component_clause,[],[f1149]) ).
fof(f1151,plain,
( in(sK57,relation_dom(relation_dom_restriction(sK58,sK56)))
| ~ spl83_1 ),
inference(avatar_component_clause,[],[f1149]) ).
fof(f1153,definition,
( spl83_2
<=> in(sK57,sK56) ),
introduced(definition,[new_symbols(definition,[spl83_2])],[avatar_definition]) ).
fof(f1155,plain,
( in(sK57,sK56)
| ~ spl83_2 ),
inference(avatar_component_clause,[],[f1153]) ).
fof(f1156,plain,
( spl83_1
| spl83_2 ),
inference(avatar_split_clause,[],[f856,f1153,f1149]) ).
fof(f1158,definition,
( spl83_3
<=> in(sK57,relation_dom(sK58)) ),
introduced(definition,[new_symbols(definition,[spl83_3])],[avatar_definition]) ).
fof(f1160,plain,
( in(sK57,relation_dom(sK58))
| ~ spl83_3 ),
inference(avatar_component_clause,[],[f1158]) ).
fof(f1161,plain,
( spl83_1
| spl83_3 ),
inference(avatar_split_clause,[],[f857,f1158,f1149]) ).
fof(f1162,plain,
( ~ spl83_1
| ~ spl83_2
| ~ spl83_3 ),
inference(avatar_split_clause,[],[f858,f1158,f1153,f1149]) ).
fof(f1417,plain,
( ! [X0] :
( ~ in(sK57,X0)
| in(sK57,relation_dom(relation_dom_restriction(sK58,X0)))
| ~ relation(sK58) )
| ~ spl83_3 ),
inference(resolution,[],[f1039,f1160]) ).
fof(f1425,plain,
( ! [X0] :
( ~ in(sK57,X0)
| in(sK57,relation_dom(relation_dom_restriction(sK58,X0))) )
| ~ spl83_3 ),
inference(forward_subsumption_resolution,[],[f1417,f855]) ).
fof(f1518,plain,
( in(sK57,relation_dom(relation_dom_restriction(sK58,sK56)))
| ~ spl83_2
| ~ spl83_3 ),
inference(resolution,[],[f1425,f1155]) ).
fof(f1523,plain,
( $false
| spl83_1
| ~ spl83_2
| ~ spl83_3 ),
inference(forward_subsumption_resolution,[],[f1518,f1150]) ).
fof(f1524,plain,
( spl83_1
| ~ spl83_2
| ~ spl83_3 ),
inference(avatar_contradiction_clause,[],[f1523]) ).
fof(f1525,plain,
( in(sK57,relation_dom(sK58))
| ~ relation(sK58)
| ~ spl83_1 ),
inference(resolution,[],[f1151,f1037]) ).
fof(f1526,plain,
( in(sK57,sK56)
| ~ relation(sK58)
| ~ spl83_1 ),
inference(resolution,[],[f1151,f1038]) ).
fof(f1556,plain,
( in(sK57,relation_dom(sK58))
| ~ spl83_1 ),
inference(forward_subsumption_resolution,[],[f1525,f855]) ).
fof(f1557,plain,
( in(sK57,sK56)
| ~ spl83_1 ),
inference(forward_subsumption_resolution,[],[f1526,f855]) ).
fof(f1558,plain,
( spl83_3
| ~ spl83_1 ),
inference(avatar_split_clause,[],[f1556,f1149,f1158]) ).
fof(f1559,plain,
( spl83_2
| ~ spl83_1 ),
inference(avatar_split_clause,[],[f1557,f1149,f1153]) ).
cnf(s1,plain,
( spl83_1
| spl83_2 ),
inference(sat_conversion,[],[f1156]) ).
cnf(s2,plain,
( spl83_1
| spl83_3 ),
inference(sat_conversion,[],[f1161]) ).
cnf(s3,plain,
( ~ spl83_1
| ~ spl83_2
| ~ spl83_3 ),
inference(sat_conversion,[],[f1162]) ).
cnf(s7,plain,
( spl83_1
| ~ spl83_2
| ~ spl83_3 ),
inference(sat_conversion,[],[f1524]) ).
cnf(s12,plain,
( ~ spl83_1
| spl83_3 ),
inference(sat_conversion,[],[f1558]) ).
cnf(s13,plain,
( ~ spl83_1
| spl83_2 ),
inference(sat_conversion,[],[f1559]) ).
cnf(s14,plain,
spl83_1,
inference(rat,[],[s7,s1,s2]) ).
cnf(s15,plain,
spl83_2,
inference(rat,[],[s13,s14]) ).
cnf(s16,plain,
spl83_3,
inference(rat,[],[s12,s14]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s3,s15,s16,s14]) ).
fof(f1560,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU224+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 04:09:49 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 3.50/1.38 % (3650125)Detected formulas, will run a generic FOF schedule.
% 3.50/1.38 % (3650132)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=2576441047:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.50/1.38 % (3650134)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=339909600:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.50/1.38 % (3650136)dis-21_1_sil=8000:lcm=predicate:random_seed=2299664985: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)
% 3.50/1.38 % (3650130)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=2783024837:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.50/1.38 % (3650133)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4011477067:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.50/1.38 % (3650131)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=4165878634:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.50/1.38 % (3650135)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=625190520:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.50/1.38 % (3650135)First to succeed.
% 3.50/1.38 % (3650135)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3650125"
% 3.50/1.38 % (3650136)Instruction limit reached!
% 3.50/1.38 % (3650136)------------------------------
% 3.50/1.38 % (3650136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (3650136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (3650136)CaDiCaL version: 2.1.3
% 3.50/1.38 % (3650136)Termination reason: Instruction limit
% 3.50/1.38 % (3650136)Termination phase: Saturation
% 3.50/1.38 % (3650136)Time elapsed: 0.068 s
% 3.50/1.38 % (3650136)Peak memory usage: 90 MB
% 3.50/1.38 % (3650136)Instructions burned: 130 (million)
% 3.50/1.38 % (3650133)Instruction limit reached!
% 3.50/1.38 % (3650133)------------------------------
% 3.50/1.38 % (3650133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (3650133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (3650133)CaDiCaL version: 2.1.3
% 3.50/1.38 % (3650133)Termination reason: Instruction limit
% 3.50/1.38 % (3650133)Termination phase: Saturation
% 3.50/1.38 % (3650133)Time elapsed: 0.071 s
% 3.50/1.38 % (3650133)Peak memory usage: 90 MB
% 3.50/1.38 % (3650133)Instructions burned: 110 (million)
% 3.50/1.38 % (3650134)Instruction limit reached!
% 3.50/1.38 % (3650134)------------------------------
% 3.50/1.38 % (3650134)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (3650134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (3650134)CaDiCaL version: 2.1.3
% 3.50/1.38 % (3650134)Termination reason: Instruction limit
% 3.50/1.38 % (3650134)Termination phase: Saturation
% 3.50/1.38 % (3650134)Time elapsed: 0.080 s
% 3.50/1.38 % (3650134)Peak memory usage: 89 MB
% 3.50/1.38 % (3650134)Instructions burned: 120 (million)
% 3.50/1.38 % (3650144)lrs+10_1_sil=8000:sp=occurrence:random_seed=3350115882:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.50/1.38 % (3650145)lrs+10_1_sil=32000:urr=on:br=off:random_seed=852135555:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.50/1.38 % (3650145)Also succeeded, but the first one will report.
% 3.50/1.38 % (3650146)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3136710309:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.50/1.38 % (3650135)Refutation found. Thanks to Tanya!
% 3.50/1.38 % SZS status Theorem for theBenchmark
% 3.50/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.38 % (3650135)------------------------------
% 3.50/1.38 % (3650135)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (3650135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (3650135)CaDiCaL version: 2.1.3
% 3.50/1.38 % (3650135)Termination reason: Refutation
% 3.50/1.38 % (3650135)Time elapsed: 0.026 s
% 3.50/1.38 % (3650135)Peak memory usage: 90 MB
% 3.50/1.38 % (3650135)Instructions burned: 35 (million)
% 3.50/1.38 % (3650135)------------------------------
% 3.50/1.38 % (3650135)------------------------------
% 3.50/1.38 % (3650125)Success in time 0.434 s
% 3.50/1.38 % Vampire exiting
%------------------------------------------------------------------------------