%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET890+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 : n001.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 12:44:56 PM UTC 2026
% Result : Theorem 0.12s 0.46s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 140 ( 58 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 167 ( 61 ~; 77 |; 25 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 75 ( 65 !; 10 ?)
% 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(f5,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X2,X3)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f10,conjecture,
! [X0] : union(singleton(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0] : union(singleton(X0)) = X0,
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f16,plain,
? [X0] : union(singleton(X0)) != X0,
inference(ennf_transformation,[],[f11]) ).
fof(f19,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(f20,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,[],[f19]) ).
fof(f21,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))],[f20]) ).
fof(f25,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) ) )
& ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) ) )
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X2,X4)
& in(X4,X0) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ? [X7] :
( in(X5,X7)
& in(X7,X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(rectify,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ( ( ! [X3] :
( ~ in(sK2(X0,X1),X3)
| ~ in(X3,X0) )
| ~ in(sK2(X0,X1),X1) )
& ( ( in(sK2(X0,X1),sK3(X0,X1))
& in(sK3(X0,X1),X0) )
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ( in(X5,sK4(X0,X5))
& in(sK4(X0,X5),X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X2,sK2(X0,X1)),skolemize(X4,sK3(X0,X1)),skolemize(X7,sK4(X0,X5))],[f26]) ).
fof(f30,plain,
sK7 != union(singleton(sK7)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f16]) ).
fof(f35,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f45,plain,
! [X0,X1] :
( in(sK3(X0,X1),X0)
| in(sK2(X0,X1),X1)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
! [X0,X1] :
( in(sK2(X0,X1),sK3(X0,X1))
| union(X0) = X1
| in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X3,X0,X1] :
( ~ in(sK2(X0,X1),X3)
| union(X0) = X1
| ~ in(X3,X0)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f52,plain,
sK7 != union(singleton(sK7)),
inference(cnf_transformation,[],[f30]) ).
fof(f55,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f36]) ).
fof(f56,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f55]) ).
fof(f57,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f35]) ).
fof(f102,plain,
! [X0,X1] :
( union(X0) = X1
| ~ in(X1,X0)
| ~ in(sK2(X0,X1),X1)
| in(sK3(X0,X1),X0)
| union(X0) = X1 ),
inference(resolution,[],[f47,f45]) ).
fof(f108,plain,
! [X0,X1] :
( union(X0) = X1
| ~ in(X1,X0)
| ~ in(sK2(X0,X1),X1)
| in(sK3(X0,X1),X0) ),
inference(duplicate_literal_removal,[],[f102]) ).
fof(f109,plain,
! [X0,X1] :
( in(sK3(X0,X1),X0)
| ~ in(X1,X0)
| union(X0) = X1 ),
inference(forward_subsumption_resolution,[],[f108,f45]) ).
fof(f143,plain,
! [X0,X1] :
( ~ in(X0,singleton(X1))
| union(singleton(X1)) = X0
| sK3(singleton(X1),X0) = X1 ),
inference(resolution,[],[f109,f57]) ).
fof(f448,plain,
! [X0] :
( sK3(singleton(X0),X0) = X0
| union(singleton(X0)) = X0 ),
inference(resolution,[],[f143,f56]) ).
fof(f459,plain,
! [X0] :
( in(sK2(singleton(X0),X0),X0)
| union(singleton(X0)) = X0
| in(sK2(singleton(X0),X0),X0)
| union(singleton(X0)) = X0 ),
inference(superposition,[],[f46,f448]) ).
fof(f472,plain,
! [X0] :
( in(sK2(singleton(X0),X0),X0)
| union(singleton(X0)) = X0 ),
inference(duplicate_literal_removal,[],[f459]) ).
fof(f525,plain,
! [X0] :
( union(singleton(X0)) = X0
| union(singleton(X0)) = X0
| ~ in(X0,singleton(X0))
| ~ in(sK2(singleton(X0),X0),X0) ),
inference(resolution,[],[f472,f47]) ).
fof(f543,plain,
! [X0] :
( union(singleton(X0)) = X0
| ~ in(X0,singleton(X0))
| ~ in(sK2(singleton(X0),X0),X0) ),
inference(duplicate_literal_removal,[],[f525]) ).
fof(f544,plain,
! [X0] :
( union(singleton(X0)) = X0
| ~ in(X0,singleton(X0)) ),
inference(forward_subsumption_resolution,[],[f543,f472]) ).
fof(f545,plain,
! [X0] : union(singleton(X0)) = X0,
inference(forward_subsumption_resolution,[],[f544,f56]) ).
fof(f588,plain,
sK7 != sK7,
inference(superposition,[],[f52,f545]) ).
fof(f599,plain,
$false,
inference(trivial_inequality_removal,[],[f588]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET890+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n001.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 03:13:02 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 Running first-order model finding
% 0.12/0.39 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
% 0.12/0.46 % (4174800)Will run a generic schedule for satisfiability detection.
% 0.12/0.46 % (4174807)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1092124983:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.46 % (4174806)% WARNING: option uhcvi not known.
% 0.12/0.46 % (4174805)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1198041010_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.46 % (4174808)dis+10_1_sil=32000:sp=arity:random_seed=97963542:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.46 % (4174811)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3937567651:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.46 % (4174809)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2815389916:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.46 % (4174810)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1291668237:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.46 % (4174806)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1954245529:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.46 % TRYING [1]
% 0.12/0.46 % TRYING [2]
% 0.12/0.46 % TRYING [3]
% 0.12/0.46 % TRYING [4]
% 0.12/0.46 % TRYING [5]
% 0.12/0.46 % TRYING [6]
% 0.12/0.46 % (4174808) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4174800-4174808"...
% 0.12/0.46 % (4174808)...printing done.
% 0.12/0.46 % (4174808)Refutation found. Thanks to Tanya!
% 0.12/0.46 % SZS status Theorem for theBenchmark
% 0.12/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.46 % (4174808)------------------------------
% 0.12/0.46 % (4174808)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (4174808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (4174808)CaDiCaL version: 2.1.3
% 0.12/0.46 % (4174808)Termination reason: Refutation
% 0.12/0.46 % (4174808)Time elapsed: 0.021 s
% 0.12/0.46 % (4174808)Peak memory usage: 11 MB
% 0.12/0.46 % (4174808)Instructions burned: 31 (million)
% 0.12/0.46 % (4174800)Success in time 0.055 s
% 0.12/0.46 % Vampire exiting
%------------------------------------------------------------------------------