%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET927+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 12:45:01 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 9 unt; 2 def)
% Number of atoms : 101 ( 44 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 112 ( 44 ~; 43 |; 19 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 27 !; 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/sandbox/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/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f9,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(f12,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,[],[f9]) ).
fof(f13,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,[],[f12]) ).
fof(f14,plain,
( ( in(sK2,sK4)
| ( ~ in(sK3,sK4)
& sK2 != sK3 )
| set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2) )
& ( ( ~ in(sK2,sK4)
& ( in(sK3,sK4)
| sK2 = sK3 ) )
| set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f13]) ).
fof(f15,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(f16,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,[],[f15]) ).
fof(f21,plain,
( in(sK3,sK4)
| sK2 = sK3
| set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
( ~ in(sK2,sK4)
| set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
( in(sK2,sK4)
| sK2 != sK3
| set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
( in(sK2,sK4)
| ~ in(sK3,sK4)
| set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X2,X0,X1] :
( in(X1,X2)
| X0 = X1
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| in(X0,X2)
| X0 != X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| in(X0,X2)
| ~ in(X1,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
( in(sK3,sK4)
| sK2 = sK3 ),
inference(forward_subsumption_resolution,[],[f21,f25]) ).
fof(f30,plain,
~ in(sK2,sK4),
inference(forward_subsumption_resolution,[],[f22,f26]) ).
fof(f31,plain,
( in(sK2,sK4)
| sK2 != sK3 ),
inference(forward_subsumption_resolution,[],[f23,f27]) ).
fof(f32,plain,
( in(sK2,sK4)
| ~ in(sK3,sK4) ),
inference(forward_subsumption_resolution,[],[f24,f28]) ).
fof(f34,definition,
( spl5_1
<=> sK2 = sK3 ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f38,definition,
( spl5_2
<=> in(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f41,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f29,f38,f34]) ).
fof(f42,plain,
sK2 != sK3,
inference(forward_subsumption_resolution,[],[f31,f30]) ).
fof(f43,plain,
~ in(sK3,sK4),
inference(forward_subsumption_resolution,[],[f32,f30]) ).
fof(f44,plain,
~ spl5_1,
inference(avatar_split_clause,[],[f42,f34]) ).
fof(f45,plain,
~ spl5_2,
inference(avatar_split_clause,[],[f43,f38]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f41]) ).
cnf(s2,plain,
~ spl5_1,
inference(sat_conversion,[],[f44]) ).
cnf(s3,plain,
~ spl5_2,
inference(sat_conversion,[],[f45]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f46,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET927+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n011.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 03:11:15 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.17/0.47 % (2980866)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (2980871)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1180008359_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % TRYING [4]
% 0.17/0.47 % (2980872)% WARNING: option uhcvi not known.
% 0.17/0.47 % TRYING [5]
% 0.17/0.47 % (2980872)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3957302702:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (2980873)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3278075744:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (2980874)dis+10_1_sil=32000:sp=arity:random_seed=3890174436:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % TRYING [6]
% 0.17/0.47 % (2980876)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3471945698:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (2980875)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=504765303:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (2980877)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1695730862:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (2980876) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2980866-2980876"...
% 0.17/0.47 % (2980875) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2980866-2980875"...
% 0.17/0.47 % (2980874) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2980866-2980874"...
% 0.17/0.47 % (2980876)...printing done.
% 0.17/0.47 % (2980872) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2980866-2980872"...
% 0.17/0.47 % (2980875)...printing done.
% 0.17/0.47 % (2980877) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2980866-2980877"...
% 0.17/0.47 % (2980876)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (2980876)------------------------------
% 0.17/0.47 % (2980876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (2980876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (2980876)CaDiCaL version: 2.1.3
% 0.17/0.47 % (2980876)Termination reason: Refutation
% 0.17/0.47 % (2980876)Time elapsed: 0.002 s
% 0.17/0.47 % (2980876)Peak memory usage: 12 MB
% 0.17/0.47 % (2980876)Instructions burned: 1 (million)
% 0.17/0.47 % (2980866)Success in time 0.047 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------