%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU162+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 12:52:11 PM UTC 2026
% Result : Theorem 0.98s 0.63s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 9 unt; 2 def)
% Number of atoms : 139 ( 29 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 133 ( 59 ~; 54 |; 8 &)
% ( 9 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 78 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f16,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f40,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f50,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f77,axiom,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f79,axiom,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ~ ( ? [X2] : in(X2,set_intersection2(X0,X1))
& disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f82,conjecture,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f83,negated_conjecture,
~ ! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f82]) ).
fof(f84,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f89,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f99,plain,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X0,X1))
& disjoint(X0,X1) ) ),
inference(rectify,[],[f79]) ).
fof(f110,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f114,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f130,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f99]) ).
fof(f134,plain,
? [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<~> ~ in(X1,X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f151,plain,
! [X2,X0,X1] :
( X0 != X2
| in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f7]) ).
fof(f199,plain,
! [X2,X3,X0,X1] :
( ~ in(X3,X1)
| ~ in(X3,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f200,plain,
! [X2,X3,X0,X1] :
( in(X3,X0)
| ~ in(X3,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f216,plain,
! [X0,X1] :
( in(X0,X1)
| disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f232,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f269,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f77]) ).
fof(f271,plain,
! [X0,X1] :
( in(sK20(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f275,plain,
( ~ in(sK22,sK21)
| sK21 = set_difference(sK21,singleton(sK22)) ),
inference(cnf_transformation,[],[f134]) ).
fof(f276,plain,
( in(sK22,sK21)
| sK21 != set_difference(sK21,singleton(sK22)) ),
inference(cnf_transformation,[],[f134]) ).
fof(f277,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f84]) ).
fof(f283,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 ),
inference(cnf_transformation,[],[f89]) ).
fof(f293,plain,
! [X2,X0,X1] :
( X0 != X2
| in(X2,X1)
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f151,f277]) ).
fof(f311,plain,
! [X0,X1] :
( disjoint(unordered_pair(X0,X0),X1)
| in(X0,X1) ),
inference(definition_unfolding,[],[f216,f277]) ).
fof(f336,plain,
! [X0,X1] :
( in(sK20(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ),
inference(definition_unfolding,[],[f271,f269]) ).
fof(f337,plain,
( in(sK22,sK21)
| sK21 != set_difference(sK21,unordered_pair(sK22,sK22)) ),
inference(definition_unfolding,[],[f276,f277]) ).
fof(f338,plain,
( ~ in(sK22,sK21)
| sK21 = set_difference(sK21,unordered_pair(sK22,sK22)) ),
inference(definition_unfolding,[],[f275,f277]) ).
fof(f345,plain,
! [X2,X1] :
( in(X2,X1)
| unordered_pair(X2,X2) != X1 ),
inference(equality_resolution,[],[f293]) ).
fof(f346,plain,
! [X2] : in(X2,unordered_pair(X2,X2)),
inference(equality_resolution,[],[f345]) ).
fof(f370,plain,
! [X3,X0,X1] :
( ~ in(X3,set_difference(X0,X1))
| in(X3,X0) ),
inference(equality_resolution,[],[f200]) ).
fof(f371,plain,
! [X3,X0,X1] :
( ~ in(X3,set_difference(X0,X1))
| ~ in(X3,X1) ),
inference(equality_resolution,[],[f199]) ).
fof(f426,definition,
( spl23_1
<=> sK21 = set_difference(sK21,unordered_pair(sK22,sK22)) ),
introduced(definition,[new_symbols(definition,[spl23_1])],[avatar_definition]) ).
fof(f427,plain,
( sK21 != set_difference(sK21,unordered_pair(sK22,sK22))
| spl23_1 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f428,plain,
( sK21 = set_difference(sK21,unordered_pair(sK22,sK22))
| ~ spl23_1 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f430,definition,
( spl23_2
<=> in(sK22,sK21) ),
introduced(definition,[new_symbols(definition,[spl23_2])],[avatar_definition]) ).
fof(f431,plain,
( in(sK22,sK21)
| ~ spl23_2 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f432,plain,
( ~ in(sK22,sK21)
| spl23_2 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f433,plain,
( spl23_1
| ~ spl23_2 ),
inference(avatar_split_clause,[],[f338,f430,f426]) ).
fof(f434,plain,
( ~ spl23_1
| spl23_2 ),
inference(avatar_split_clause,[],[f337,f430,f426]) ).
fof(f519,plain,
! [X0,X1] :
( in(X0,X1)
| unordered_pair(X0,X0) = set_difference(unordered_pair(X0,X0),X1) ),
inference(resolution,[],[f311,f283]) ).
fof(f965,plain,
! [X0,X1] :
( ~ in(sK20(X0,X1),set_difference(X0,X1))
| disjoint(X0,X1) ),
inference(resolution,[],[f336,f371]) ).
fof(f966,plain,
! [X0,X1] :
( in(sK20(X0,X1),X0)
| disjoint(X0,X1) ),
inference(resolution,[],[f336,f370]) ).
fof(f5338,plain,
( unordered_pair(sK22,sK22) = set_difference(unordered_pair(sK22,sK22),sK21)
| spl23_2 ),
inference(resolution,[],[f519,f432]) ).
fof(f5389,plain,
( ~ in(sK20(unordered_pair(sK22,sK22),sK21),unordered_pair(sK22,sK22))
| disjoint(unordered_pair(sK22,sK22),sK21)
| spl23_2 ),
inference(superposition,[],[f965,f5338]) ).
fof(f5398,plain,
( disjoint(unordered_pair(sK22,sK22),sK21)
| spl23_2 ),
inference(forward_subsumption_resolution,[],[f5389,f966]) ).
fof(f5459,plain,
( disjoint(sK21,unordered_pair(sK22,sK22))
| spl23_2 ),
inference(resolution,[],[f5398,f232]) ).
fof(f6040,plain,
( sK21 = set_difference(sK21,unordered_pair(sK22,sK22))
| spl23_2 ),
inference(resolution,[],[f5459,f283]) ).
fof(f6042,plain,
( $false
| spl23_1
| spl23_2 ),
inference(forward_subsumption_resolution,[],[f6040,f427]) ).
fof(f6043,plain,
( spl23_1
| spl23_2 ),
inference(avatar_contradiction_clause,[],[f6042]) ).
fof(f6064,plain,
( ! [X0] :
( ~ in(X0,sK21)
| ~ in(X0,unordered_pair(sK22,sK22)) )
| ~ spl23_1 ),
inference(superposition,[],[f371,f428]) ).
fof(f6307,plain,
( ~ in(sK22,unordered_pair(sK22,sK22))
| ~ spl23_1
| ~ spl23_2 ),
inference(resolution,[],[f6064,f431]) ).
fof(f6375,plain,
( $false
| ~ spl23_1
| ~ spl23_2 ),
inference(forward_subsumption_resolution,[],[f6307,f346]) ).
fof(f6376,plain,
( ~ spl23_1
| ~ spl23_2 ),
inference(avatar_contradiction_clause,[],[f6375]) ).
cnf(s1,plain,
( spl23_1
| ~ spl23_2 ),
inference(sat_conversion,[],[f433]) ).
cnf(s2,plain,
( ~ spl23_1
| spl23_2 ),
inference(sat_conversion,[],[f434]) ).
cnf(s8,plain,
( spl23_1
| spl23_2 ),
inference(sat_conversion,[],[f6043]) ).
cnf(s10,plain,
( ~ spl23_1
| ~ spl23_2 ),
inference(sat_conversion,[],[f6376]) ).
cnf(s11,plain,
spl23_1,
inference(rat,[],[s1,s8]) ).
cnf(s12,plain,
~ spl23_2,
inference(rat,[],[s10,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s2,s12,s11]) ).
fof(f6380,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU162+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n004.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 03:49:37 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.98/0.63 % (4132871)Will run a generic schedule for satisfiability detection.
% 0.98/0.63 % (4132876)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2153816529_2999 on theBenchmark for (2999ds/0Mi)
% 0.98/0.63 % (4132877)% WARNING: option uhcvi not known.
% 0.98/0.63 % TRYING [1]
% 0.98/0.63 % TRYING [2]
% 0.98/0.63 % (4132877)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3491590600:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.98/0.63 % (4132878)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3773969849:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.98/0.63 % (4132881)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2168531383:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.98/0.63 % (4132879)dis+10_1_sil=32000:sp=arity:random_seed=946859968:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.98/0.63 % (4132880)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=750201448:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.98/0.63 % TRYING [3]
% 0.98/0.63 % (4132882)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3611289806:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.98/0.63 % TRYING [4]
% 0.98/0.63 % TRYING [5]
% 0.98/0.63 % (4132879)Instruction limit reached!
% 0.98/0.63 % (4132879)------------------------------
% 0.98/0.63 % (4132879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.63 % (4132879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.63 % (4132879)CaDiCaL version: 2.1.3
% 0.98/0.63 % (4132879)Termination reason: Instruction limit
% 0.98/0.63 % (4132879)Termination phase: Saturation
% 0.98/0.63 % (4132879)Time elapsed: 0.066 s
% 0.98/0.63 % (4132879)Peak memory usage: 12 MB
% 0.98/0.63 % (4132879)Instructions burned: 104 (million)
% 0.98/0.63 % (4132880)Instruction limit reached!
% 0.98/0.63 % (4132880)------------------------------
% 0.98/0.63 % (4132880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.63 % (4132880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.63 % (4132880)CaDiCaL version: 2.1.3
% 0.98/0.63 % (4132880)Termination reason: Instruction limit
% 0.98/0.63 % (4132880)Termination phase: Saturation
% 0.98/0.63 % (4132880)Time elapsed: 0.072 s
% 0.98/0.63 % (4132880)Peak memory usage: 13 MB
% 0.98/0.63 % (4132880)Instructions burned: 116 (million)
% 0.98/0.63 % (4132881)Instruction limit reached!
% 0.98/0.63 % (4132881)------------------------------
% 0.98/0.63 % (4132881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.63 % (4132881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.63 % (4132881)CaDiCaL version: 2.1.3
% 0.98/0.63 % (4132881)Termination reason: Instruction limit
% 0.98/0.63 % (4132881)Termination phase: Saturation
% 0.98/0.63 % (4132881)Time elapsed: 0.081 s
% 0.98/0.63 % (4132881)Peak memory usage: 13 MB
% 0.98/0.63 % (4132881)Instructions burned: 131 (million)
% 0.98/0.63 % (4132890)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2270329437:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 0.98/0.63 % (4132891)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3834045967:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.98/0.63 % TRYING [1]
% 0.98/0.63 % TRYING [2]
% 0.98/0.63 % (4132892)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=1443161835:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.98/0.63 % TRYING [3]
% 0.98/0.63 % (4132882)Instruction limit reached!
% 0.98/0.63 % (4132882)------------------------------
% 0.98/0.63 % (4132882)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.63 % (4132882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.63 % (4132882)CaDiCaL version: 2.1.3
% 0.98/0.63 % (4132882)Termination reason: Instruction limit
% 0.98/0.63 % (4132882)Termination phase: Saturation
% 0.98/0.63 % (4132882)Time elapsed: 0.104 s
% 0.98/0.63 % (4132882)Peak memory usage: 13 MB
% 0.98/0.63 % (4132882)Instructions burned: 159 (million)
% 0.98/0.63 % TRYING [4]
% 0.98/0.63 % (4132896)ott-21_1_sil=16000:fs=off:random_seed=3522510310:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.98/0.63 % (4132877) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4132871-4132877"...
% 0.98/0.63 % (4132877)...printing done.
% 0.98/0.63 % (4132877)Refutation found. Thanks to Tanya!
% 0.98/0.63 % SZS status Theorem for theBenchmark
% 0.98/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.63 % (4132877)------------------------------
% 0.16/0.63 % (4132877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.63 % (4132877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.63 % (4132877)CaDiCaL version: 2.1.3
% 0.16/0.63 % (4132877)Termination reason: Refutation
% 0.16/0.63 % (4132877)Time elapsed: 0.169 s
% 0.16/0.63 % (4132877)Peak memory usage: 15 MB
% 0.16/0.63 % (4132877)Instructions burned: 266 (million)
% 0.16/0.63 % (4132871)Success in time 0.218 s
% 0.16/0.63 % Vampire exiting
%------------------------------------------------------------------------------