%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET927+1 : TPTP v9.3.1. Released v3.2.0.
% 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 12:42:21 PM UTC 2026
% Result : Theorem 3.37s 1.23s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 69 ( 12 unt; 9 def)
% Number of atoms : 191 ( 44 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 208 ( 86 ~; 93 |; 19 &)
% ( 9 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 29 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,conjecture,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f8,plain,
? [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<~> ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f10,plain,
? [X0,X1,X2] :
( ( in(X0,X2)
| ( ~ in(X1,X2)
& X0 != X1 )
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) )
& ( ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) )
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f11,plain,
? [X0,X1,X2] :
( ( in(X0,X2)
| ( ~ in(X1,X2)
& X0 != X1 )
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) )
& ( ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) )
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
( ( in(sK0,sK2)
| ( ~ in(sK1,sK2)
& sK0 != sK1 )
| set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0) )
& ( ( ~ in(sK0,sK2)
& ( in(sK1,sK2)
| sK0 = sK1 ) )
| set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| in(X0,X2)
| ( ~ in(X1,X2)
& X0 != X1 ) )
& ( ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) )
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| in(X0,X2)
| ( ~ in(X1,X2)
& X0 != X1 ) )
& ( ( ~ in(X0,X2)
& ( in(X1,X2)
| X0 = X1 ) )
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
( in(sK1,sK2)
| sK0 = sK1
| set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f16,plain,
( ~ in(sK0,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f17,plain,
( in(sK0,sK2)
| sK0 != sK1
| set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
( in(sK0,sK2)
| ~ in(sK1,sK2)
| set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| X0 = X1
| in(X1,X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| in(X0,X2)
| X0 != X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| in(X0,X2)
| ~ in(X1,X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,definition,
~ sP3(set_difference(unordered_pair(sK0,sK1),sK2)),
introduced(definition,[new_symbols(definition,[sP3])],[inequality_splitting_name_introduction]) ).
fof(f26,plain,
( in(sK0,sK2)
| ~ in(sK1,sK2)
| sP3(singleton(sK0)) ),
inference(inequality_splitting,[],[f18,f25]) ).
fof(f27,definition,
~ sP4(sK0),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f28,definition,
~ sP5(set_difference(unordered_pair(sK0,sK1),sK2)),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
fof(f29,plain,
( in(sK0,sK2)
| sP4(sK1)
| sP5(singleton(sK0)) ),
inference(inequality_splitting,[],[f17,f28,f27]) ).
fof(f30,plain,
! [X2,X1] :
( set_difference(unordered_pair(X1,X1),X2) = singleton(X1)
| in(X1,X2) ),
inference(equality_resolution,[],[f23]) ).
fof(f31,plain,
( in(sK1,sK2)
| sK0 = sK1 ),
inference(forward_subsumption_resolution,[],[f15,f21]) ).
fof(f32,plain,
~ in(sK0,sK2),
inference(forward_subsumption_resolution,[],[f16,f22]) ).
fof(f34,definition,
( spl6_1
<=> sP5(singleton(sK0)) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f36,plain,
( sP5(singleton(sK0))
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f38,definition,
( spl6_2
<=> sP4(sK1) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f40,plain,
( sP4(sK1)
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f42,definition,
( spl6_3
<=> in(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f43,plain,
( ~ in(sK0,sK2)
| spl6_3 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f45,plain,
( spl6_1
| spl6_2
| spl6_3 ),
inference(avatar_split_clause,[],[f29,f42,f38,f34]) ).
fof(f47,definition,
( spl6_4
<=> sP3(singleton(sK0)) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f49,plain,
( sP3(singleton(sK0))
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f51,definition,
( spl6_5
<=> in(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
fof(f52,plain,
( in(sK1,sK2)
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,plain,
( spl6_4
| ~ spl6_5
| spl6_3 ),
inference(avatar_split_clause,[],[f26,f42,f51,f47]) ).
fof(f56,definition,
( spl6_6
<=> sK0 = sK1 ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
fof(f58,plain,
( sK0 = sK1
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f59,plain,
( spl6_6
| spl6_5 ),
inference(avatar_split_clause,[],[f31,f51,f56]) ).
fof(f60,plain,
~ spl6_3,
inference(avatar_split_clause,[],[f32,f42]) ).
fof(f62,plain,
( ~ sP3(singleton(sK0))
| in(sK0,sK2)
| ~ in(sK1,sK2) ),
inference(superposition,[],[f25,f24]) ).
fof(f63,plain,
( in(sK0,sK2)
| ~ in(sK1,sK2)
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f62,f49]) ).
fof(f64,plain,
( ~ in(sK1,sK2)
| spl6_3
| ~ spl6_4 ),
inference(forward_subsumption_resolution,[],[f63,f43]) ).
fof(f65,plain,
( $false
| spl6_3
| ~ spl6_4
| ~ spl6_5 ),
inference(forward_subsumption_resolution,[],[f64,f52]) ).
fof(f66,plain,
( spl6_3
| ~ spl6_4
| ~ spl6_5 ),
inference(avatar_contradiction_clause,[],[f65]) ).
fof(f69,plain,
( sP4(sK0)
| ~ spl6_2
| ~ spl6_6 ),
inference(superposition,[],[f40,f58]) ).
fof(f70,plain,
( $false
| ~ spl6_2
| ~ spl6_6 ),
inference(forward_subsumption_resolution,[],[f69,f27]) ).
fof(f71,plain,
( ~ spl6_2
| ~ spl6_6 ),
inference(avatar_contradiction_clause,[],[f70]) ).
fof(f73,plain,
( ~ sP5(set_difference(unordered_pair(sK0,sK0),sK2))
| ~ spl6_6 ),
inference(superposition,[],[f28,f58]) ).
fof(f81,plain,
( ~ sP5(singleton(sK0))
| in(sK0,sK2)
| ~ spl6_6 ),
inference(superposition,[],[f73,f30]) ).
fof(f82,plain,
( in(sK0,sK2)
| ~ spl6_1
| ~ spl6_6 ),
inference(forward_subsumption_resolution,[],[f81,f36]) ).
fof(f83,plain,
( $false
| ~ spl6_1
| spl6_3
| ~ spl6_6 ),
inference(forward_subsumption_resolution,[],[f82,f43]) ).
fof(f84,plain,
( ~ spl6_1
| spl6_3
| ~ spl6_6 ),
inference(avatar_contradiction_clause,[],[f83]) ).
cnf(s1,plain,
( spl6_1
| spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f45]) ).
cnf(s2,plain,
( spl6_3
| spl6_4
| ~ spl6_5 ),
inference(sat_conversion,[],[f54]) ).
cnf(s3,plain,
( spl6_5
| spl6_6 ),
inference(sat_conversion,[],[f59]) ).
cnf(s4,plain,
~ spl6_3,
inference(sat_conversion,[],[f60]) ).
cnf(s5,plain,
( spl6_3
| ~ spl6_4
| ~ spl6_5 ),
inference(sat_conversion,[],[f66]) ).
cnf(s6,plain,
( ~ spl6_2
| ~ spl6_6 ),
inference(sat_conversion,[],[f71]) ).
cnf(s8,plain,
( ~ spl6_1
| spl6_3
| ~ spl6_6 ),
inference(sat_conversion,[],[f84]) ).
cnf(s9,plain,
( spl6_4
| ~ spl6_5 ),
inference(rat,[],[s2,s4]) ).
cnf(s10,plain,
( spl6_1
| spl6_2 ),
inference(rat,[],[s1,s4]) ).
cnf(s11,plain,
~ spl6_5,
inference(rat,[],[s9,s5,s4]) ).
cnf(s12,plain,
spl6_6,
inference(rat,[],[s3,s11]) ).
cnf(s13,plain,
~ spl6_2,
inference(rat,[],[s6,s12]) ).
cnf(s14,plain,
~ spl6_1,
inference(rat,[],[s8,s4,s12]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s10,s13,s14]) ).
fof(f85,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET927+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n015.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
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:14:31 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.37/1.23 % (2224831)Detected formulas, will run a generic FOF schedule.
% 3.37/1.23 % (2224841)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=999570880:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.37/1.23 % (2224839)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2030451707:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.37/1.23 % (2224840)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=648608512:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.37/1.23 % (2224842)dis-21_1_sil=8000:lcm=predicate:random_seed=454702248: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)
% 3.37/1.23 % (2224836)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=3432318235:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.37/1.23 % (2224838)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=480354133:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.37/1.23 % (2224837)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=2399192779:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.37/1.23 % (2224842)Refutation not found, incomplete strategy
% 3.37/1.23 % (2224842)------------------------------
% 3.37/1.23 % (2224842)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.23 % (2224842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.23 % (2224842)CaDiCaL version: 2.1.3
% 3.37/1.23 % (2224842)Termination reason: Refutation not found, incomplete strategy
% 3.37/1.23 % (2224842)Time elapsed: 0.002 s
% 3.37/1.23 % (2224842)Peak memory usage: 88 MB
% 3.37/1.23 % (2224842)Instructions burned: 1 (million)
% 3.37/1.23 % (2224840)Also succeeded, but the first one will report.
% 3.37/1.23 % (2224839)First to succeed.
% 3.37/1.23 % (2224841)Also succeeded, but the first one will report.
% 3.37/1.23 % (2224839)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2224831"
% 3.37/1.23 % (2224842)------------------------------
% 3.37/1.23 % (2224842)------------------------------
% 3.37/1.23 % (2224839)Refutation found. Thanks to Tanya!
% 3.37/1.23 % SZS status Theorem for theBenchmark
% 3.37/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 3.37/1.23 % (2224839)------------------------------
% 3.37/1.23 % (2224839)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.23 % (2224839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.23 % (2224839)CaDiCaL version: 2.1.3
% 3.37/1.23 % (2224839)Termination reason: Refutation
% 3.37/1.23 % (2224839)Time elapsed: 0.004 s
% 3.37/1.23 % (2224839)Peak memory usage: 89 MB
% 3.37/1.23 % (2224839)Instructions burned: 3 (million)
% 3.37/1.23 % (2224839)------------------------------
% 3.37/1.23 % (2224839)------------------------------
% 3.37/1.23 % (2224831)Success in time 0.421 s
% 3.37/1.23 % Vampire exiting
%------------------------------------------------------------------------------