%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU180+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:52:16 PM UTC 2026
% Result : Theorem 1.51s 0.69s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 21 unt; 2 def)
% Number of atoms : 95 ( 12 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 81 ( 33 ~; 28 |; 9 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 62 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f24,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f25,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f99,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f108,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f109,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f108]) ).
fof(f139,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f172,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f216,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f99]) ).
fof(f217,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f216]) ).
fof(f226,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_field(X2))
| ~ in(X1,relation_field(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(ennf_transformation,[],[f109]) ).
fof(f227,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_field(X2))
| ~ in(X1,relation_field(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(flattening,[],[f226]) ).
fof(f306,plain,
! [X2,X3,X0,X1] :
( ~ in(X3,X1)
| in(X3,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f14]) ).
fof(f307,plain,
! [X2,X3,X0,X1] :
( ~ in(X3,X0)
| in(X3,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f14]) ).
fof(f347,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f348,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(cnf_transformation,[],[f172]) ).
fof(f427,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X1,relation_rng(X2)) ),
inference(cnf_transformation,[],[f217]) ).
fof(f428,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f217]) ).
fof(f439,plain,
( ~ in(sK39,relation_field(sK40))
| ~ in(sK38,relation_field(sK40)) ),
inference(cnf_transformation,[],[f227]) ).
fof(f440,plain,
relation(sK40),
inference(cnf_transformation,[],[f227]) ).
fof(f441,plain,
in(ordered_pair(sK38,sK39),sK40),
inference(cnf_transformation,[],[f227]) ).
fof(f484,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f139]) ).
fof(f501,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f347,f484]) ).
fof(f551,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X0,relation_dom(X2)) ),
inference(definition_unfolding,[],[f428,f501]) ).
fof(f552,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X1,relation_rng(X2)) ),
inference(definition_unfolding,[],[f427,f501]) ).
fof(f556,plain,
in(unordered_pair(unordered_pair(sK38,sK39),unordered_pair(sK38,sK38)),sK40),
inference(definition_unfolding,[],[f441,f501]) ).
fof(f592,plain,
! [X3,X0,X1] :
( ~ in(X3,X0)
| in(X3,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f307]) ).
fof(f593,plain,
! [X3,X0,X1] :
( ~ in(X3,X1)
| in(X3,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f306]) ).
fof(f639,definition,
( spl45_1
<=> in(sK38,relation_field(sK40)) ),
introduced(definition,[new_symbols(definition,[spl45_1])],[avatar_definition]) ).
fof(f643,definition,
( spl45_2
<=> in(sK39,relation_field(sK40)) ),
introduced(definition,[new_symbols(definition,[spl45_2])],[avatar_definition]) ).
fof(f646,plain,
( ~ spl45_1
| ~ spl45_2 ),
inference(avatar_split_clause,[],[f439,f643,f639]) ).
fof(f1337,plain,
relation_field(sK40) = set_union2(relation_dom(sK40),relation_rng(sK40)),
inference(resolution,[],[f348,f440]) ).
fof(f2175,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK40)
| in(X0,relation_dom(sK40)) ),
inference(resolution,[],[f551,f440]) ).
fof(f2181,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK40)
| in(X1,relation_rng(sK40)) ),
inference(resolution,[],[f552,f440]) ).
fof(f3365,plain,
in(sK38,relation_dom(sK40)),
inference(resolution,[],[f2175,f556]) ).
fof(f3387,plain,
in(sK39,relation_rng(sK40)),
inference(resolution,[],[f2181,f556]) ).
fof(f3453,plain,
! [X0] : in(sK38,set_union2(relation_dom(sK40),X0)),
inference(resolution,[],[f3365,f592]) ).
fof(f3615,plain,
! [X0] : in(sK39,set_union2(X0,relation_rng(sK40))),
inference(resolution,[],[f3387,f593]) ).
fof(f7853,plain,
in(sK38,relation_field(sK40)),
inference(superposition,[],[f3453,f1337]) ).
fof(f8376,plain,
in(sK39,relation_field(sK40)),
inference(superposition,[],[f3615,f1337]) ).
fof(f8383,plain,
spl45_2,
inference(avatar_split_clause,[],[f8376,f643]) ).
fof(f8384,plain,
spl45_1,
inference(avatar_split_clause,[],[f7853,f639]) ).
cnf(s1,plain,
( ~ spl45_1
| ~ spl45_2 ),
inference(sat_conversion,[],[f646]) ).
cnf(s150,plain,
spl45_2,
inference(sat_conversion,[],[f8383]) ).
cnf(s151,plain,
spl45_1,
inference(sat_conversion,[],[f8384]) ).
cnf(s174,plain,
$false,
inference(rat,[],[s1,s150,s151]) ).
fof(f8388,plain,
$false,
inference(avatar_sat_refutation,[],[s174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU180+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:55:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.51/0.69 % (1851466)Will run a generic schedule for satisfiability detection.
% 1.51/0.69 % (1851476)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3894955870:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.51/0.69 % (1851472)% WARNING: option uhcvi not known.
% 1.51/0.69 % (1851471)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1635135305_2999 on theBenchmark for (2999ds/0Mi)
% 1.51/0.69 % (1851472)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4117365134:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.51/0.69 % (1851473)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1345167302:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.51/0.69 % (1851474)dis+10_1_sil=32000:sp=arity:random_seed=3709150333:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.51/0.69 % (1851475)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3824390666:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.51/0.69 % (1851477)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1334093112:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.51/0.69 % TRYING [1]
% 1.51/0.69 % TRYING [2]
% 1.51/0.69 % TRYING [3]
% 1.51/0.69 % (1851476)Instruction limit reached!
% 1.51/0.69 % (1851476)------------------------------
% 1.51/0.69 % (1851476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.69 % (1851476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.69 % (1851476)CaDiCaL version: 2.1.3
% 1.51/0.69 % (1851476)Termination reason: Instruction limit
% 1.51/0.69 % (1851476)Termination phase: Saturation
% 1.51/0.69 % (1851476)Time elapsed: 0.048 s
% 1.51/0.69 % (1851476)Peak memory usage: 13 MB
% 1.51/0.69 % (1851476)Instructions burned: 133 (million)
% 1.51/0.69 % (1851485)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=470354891:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.51/0.69 % TRYING [1]
% 1.51/0.69 % TRYING [2]
% 1.51/0.69 % TRYING [3]
% 1.51/0.69 % TRYING [4]
% 1.51/0.69 % (1851474)Instruction limit reached!
% 1.51/0.69 % (1851474)------------------------------
% 1.51/0.69 % (1851474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.69 % (1851474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.69 % (1851474)CaDiCaL version: 2.1.3
% 1.51/0.69 % (1851474)Termination reason: Instruction limit
% 1.51/0.69 % (1851474)Termination phase: Saturation
% 1.51/0.69 % (1851474)Time elapsed: 0.070 s
% 1.51/0.69 % (1851474)Peak memory usage: 13 MB
% 1.51/0.69 % (1851474)Instructions burned: 104 (million)
% 1.51/0.69 % (1851475)Instruction limit reached!
% 1.51/0.69 % (1851475)------------------------------
% 1.51/0.69 % (1851475)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.69 % (1851475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.69 % (1851475)CaDiCaL version: 2.1.3
% 1.51/0.69 % (1851475)Termination reason: Instruction limit
% 1.51/0.69 % (1851475)Termination phase: Saturation
% 1.51/0.69 % (1851475)Time elapsed: 0.076 s
% 1.51/0.69 % (1851475)Peak memory usage: 13 MB
% 1.51/0.69 % (1851475)Instructions burned: 116 (million)
% 1.51/0.69 % TRYING [4]
% 1.51/0.69 % (1851487)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3274389176:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.51/0.69 % (1851488)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=37487248:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.51/0.69 % (1851477)Instruction limit reached!
% 1.51/0.69 % (1851477)------------------------------
% 1.51/0.69 % (1851477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.69 % (1851477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.69 % (1851477)CaDiCaL version: 2.1.3
% 1.51/0.69 % (1851477)Termination reason: Instruction limit
% 1.51/0.69 % (1851477)Termination phase: Saturation
% 1.51/0.69 % (1851477)Time elapsed: 0.110 s
% 1.51/0.69 % (1851477)Peak memory usage: 14 MB
% 1.51/0.69 % (1851477)Instructions burned: 159 (million)
% 1.51/0.69 % (1851491)ott-21_1_sil=16000:fs=off:random_seed=3140912111:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.51/0.69 % TRYING [5]
% 1.51/0.69 % (1851487)Instruction limit reached!
% 1.51/0.69 % (1851487)------------------------------
% 1.51/0.69 % (1851487)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.69 % (1851487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.69 % (1851487)CaDiCaL version: 2.1.3
% 1.51/0.69 % (1851487)Termination reason: Instruction limit
% 1.51/0.69 % (1851487)Termination phase: Saturation
% 1.51/0.69 % (1851487)Time elapsed: 0.089 s
% 1.51/0.69 % (1851487)Peak memory usage: 13 MB
% 1.51/0.69 % (1851487)Instructions burned: 132 (million)
% 1.51/0.69 % (1851485)Instruction limit reached!
% 1.51/0.69 % (1851485)------------------------------
% 1.51/0.69 % (1851485)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.69 % (1851485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.69 % (1851485)CaDiCaL version: 2.1.3
% 1.51/0.69 % (1851485)Termination reason: Instruction limit
% 1.51/0.69 % (1851485)Termination phase: Finite model building constraint generation
% 1.51/0.69 % (1851485)Time elapsed: 0.146 s
% 1.51/0.69 % (1851485)Peak memory usage: 33 MB
% 1.51/0.69 % (1851485)Instructions burned: 718 (million)
% 1.51/0.69 % (1851493)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1634986101:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.51/0.69 % TRYING [5]
% 1.51/0.69 % (1851495)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2172341509:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.51/0.69 % TRYING [1]
% 1.51/0.69 % TRYING [2]
% 1.51/0.69 % (1851472) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1851466-1851472"...
% 1.51/0.69 % TRYING [3]
% 1.51/0.69 % (1851472)...printing done.
% 1.51/0.69 % (1851491)Instruction limit reached!
% 1.51/0.69 % (1851491)------------------------------
% 1.51/0.69 % (1851491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.69 % (1851491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.69 % (1851491)CaDiCaL version: 2.1.3
% 1.51/0.69 % (1851491)Termination reason: Instruction limit
% 1.51/0.69 % (1851491)Termination phase: Saturation
% 1.51/0.69 % (1851491)Time elapsed: 0.102 s
% 1.51/0.69 % (1851491)Peak memory usage: 13 MB
% 1.51/0.69 % (1851491)Instructions burned: 180 (million)
% 1.51/0.69 % (1851472)Refutation found. Thanks to Tanya!
% 1.51/0.69 % SZS status Theorem for theBenchmark
% 1.51/0.69 % SZS output start Proof for theBenchmark
% See solution above
% 1.51/0.69 % (1851472)------------------------------
% 1.51/0.69 % (1851472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.69 % (1851472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.69 % (1851472)CaDiCaL version: 2.1.3
% 1.51/0.69 % (1851472)Termination reason: Refutation
% 1.51/0.69 % (1851472)Time elapsed: 0.232 s
% 1.51/0.69 % (1851472)Peak memory usage: 16 MB
% 1.51/0.69 % (1851472)Instructions burned: 354 (million)
% 1.51/0.69 % (1851466)Success in time 0.276 s
% 1.51/0.69 % Vampire exiting
%------------------------------------------------------------------------------