%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET884+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 12:44:55 PM UTC 2026
% Result : Theorem 0.07s 0.35s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 7 unt; 0 def)
% Number of atoms : 140 ( 85 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 177 ( 67 ~; 65 |; 37 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 71 ( 63 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,conjecture,
! [X0,X1,X2] :
~ ( subset(singleton(X0),unordered_pair(X1,X2))
& X0 != X1
& X0 != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( subset(singleton(X0),unordered_pair(X1,X2))
& X0 != X1
& X0 != X2 ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f14,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f15,plain,
? [X0,X1,X2] :
( subset(singleton(X0),unordered_pair(X1,X2))
& X0 != X1
& X0 != X2 ),
inference(ennf_transformation,[],[f10]) ).
fof(f16,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK1(X0,X1,X2) != X0
& sK1(X0,X1,X2) != X1 )
| ~ in(sK1(X0,X1,X2),X2) )
& ( sK1(X0,X1,X2) = X0
| sK1(X0,X1,X2) = X1
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f21]) ).
fof(f25,plain,
( subset(singleton(sK4),unordered_pair(sK5,sK6))
& sK4 != sK5
& sK4 != sK6 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f15]) ).
fof(f29,plain,
! [X3,X0,X1] :
( X0 != X3
| in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X2)
| X1 = X4
| X0 = X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f42,plain,
sK4 != sK6,
inference(cnf_transformation,[],[f25]) ).
fof(f43,plain,
sK4 != sK5,
inference(cnf_transformation,[],[f25]) ).
fof(f44,plain,
subset(singleton(sK4),unordered_pair(sK5,sK6)),
inference(cnf_transformation,[],[f25]) ).
fof(f45,plain,
! [X0] :
( ~ in(X0,singleton(sK4))
| in(X0,unordered_pair(sK5,sK6)) ),
inference(resolution,[],[f38,f44]) ).
fof(f47,plain,
! [X0,X1] :
( singleton(X0) != X1
| in(X0,X1) ),
inference(equality_resolution,[],[f29]) ).
fof(f48,plain,
! [X0] : in(X0,singleton(X0)),
inference(equality_resolution,[],[f47]) ).
fof(f50,plain,
in(sK4,unordered_pair(sK5,sK6)),
inference(resolution,[],[f48,f45]) ).
fof(f62,plain,
! [X0,X1] :
( unordered_pair(X1,X0) != unordered_pair(sK5,sK6)
| sK4 = X1
| sK4 = X0 ),
inference(resolution,[],[f32,f50]) ).
fof(f66,plain,
( sK4 = sK5
| sK4 = sK6 ),
inference(equality_resolution,[],[f62]) ).
fof(f67,plain,
sK4 = sK6,
inference(forward_subsumption_resolution,[],[f66,f43]) ).
fof(f68,plain,
$false,
inference(forward_subsumption_resolution,[],[f67,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET884+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Mon Sep 28 03:05:49 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.05/0.32 Running first-order model finding
% 0.05/0.32 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
% 0.07/0.35 % (2979566)Will run a generic schedule for satisfiability detection.
% 0.07/0.35 % (2979572)% WARNING: option uhcvi not known.
% 0.07/0.35 % (2979573)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3548933259:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.35 % (2979571)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1004082020_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.35 % (2979572)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3119490287:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.35 % (2979574)dis+10_1_sil=32000:sp=arity:random_seed=2784232185:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.35 % (2979575)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=195088567:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.35 % (2979576)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2002040911:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.35 % (2979577)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2626368738:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.35 % TRYING [1]
% 0.07/0.35 % TRYING [2]
% 0.07/0.35 % TRYING [3]
% 0.07/0.35 % TRYING [4]
% 0.07/0.35 % (2979576) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2979566-2979576"...
% 0.07/0.35 % (2979575) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2979566-2979575"...
% 0.07/0.35 % (2979574) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2979566-2979574"...
% 0.07/0.35 % (2979577) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2979566-2979577"...
% 0.07/0.35 % (2979573) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2979566-2979573"...
% 0.07/0.35 % (2979576)...printing done.
% 0.07/0.35 % (2979575)...printing done.
% 0.07/0.35 % (2979574)...printing done.
% 0.07/0.35 % TRYING [5]
% 0.07/0.35 % (2979573)...printing done.
% 0.07/0.35 % (2979577)...printing done.
% 0.07/0.35 % (2979576)Refutation found. Thanks to Tanya!
% 0.07/0.35 % SZS status Theorem for theBenchmark
% 0.07/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.35 % (2979576)------------------------------
% 0.07/0.35 % (2979576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.35 % (2979576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.35 % (2979576)CaDiCaL version: 2.1.3
% 0.07/0.35 % (2979576)Termination reason: Refutation
% 0.07/0.35 % (2979576)Time elapsed: 0.001 s
% 0.07/0.35 % (2979576)Peak memory usage: 11 MB
% 0.07/0.35 % (2979576)Instructions burned: 3 (million)
% 0.07/0.35 % (2979566)Success in time 0.026 s
% 0.07/0.35 % Vampire exiting
%------------------------------------------------------------------------------