%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU145+1 : 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 : 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 12:52:05 PM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 60 ( 13 unt; 4 def)
% Number of atoms : 209 ( 34 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 242 ( 93 ~; 94 |; 42 &)
% ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 86 ( 0 sgn 73 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f4,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(f7,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( in(X2,X0)
| subset(X0,set_difference(X1,singleton(X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> ( in(X2,X0)
| subset(X0,set_difference(X1,singleton(X2))) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f13,plain,
? [X0,X1,X2] :
( ~ in(X2,X0)
& ~ subset(X0,set_difference(X1,singleton(X2)))
& subset(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f14,plain,
? [X0,X1,X2] :
( ~ in(X2,X0)
& ~ subset(X0,set_difference(X1,singleton(X2)))
& subset(X0,X1) ),
inference(flattening,[],[f13]) ).
fof(f15,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,[],[f2]) ).
fof(f16,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,[],[f15]) ).
fof(f17,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))],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ( ( ~ in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X2) )
& ( ( in(sK2(X0,X1,X2),X0)
& ~ in(sK2(X0,X1,X2),X1) )
| in(sK2(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f23]) ).
fof(f25,plain,
( ~ in(sK5,sK3)
& ~ subset(sK3,set_difference(sK4,singleton(sK5)))
& subset(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f14]) ).
fof(f27,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X0,X1] :
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f24]) ).
fof(f40,plain,
subset(sK3,sK4),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
~ subset(sK3,set_difference(sK4,singleton(sK5))),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
~ in(sK5,sK3),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f27]) ).
fof(f47,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| ~ in(X4,X0)
| in(X4,X1) ),
inference(equality_resolution,[],[f36]) ).
fof(f55,plain,
~ in(sK1(sK3,set_difference(sK4,singleton(sK5))),set_difference(sK4,singleton(sK5))),
inference(resolution,[],[f33,f41]) ).
fof(f59,plain,
! [X0] :
( in(X0,sK4)
| ~ in(X0,sK3) ),
inference(resolution,[],[f31,f40]) ).
fof(f71,plain,
( ~ in(sK1(sK3,set_difference(sK4,singleton(sK5))),sK4)
| in(sK1(sK3,set_difference(sK4,singleton(sK5))),singleton(sK5)) ),
inference(resolution,[],[f47,f55]) ).
fof(f73,definition,
( spl6_1
<=> in(sK1(sK3,set_difference(sK4,singleton(sK5))),singleton(sK5)) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f75,plain,
( in(sK1(sK3,set_difference(sK4,singleton(sK5))),singleton(sK5))
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f77,definition,
( spl6_2
<=> in(sK1(sK3,set_difference(sK4,singleton(sK5))),sK4) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f79,plain,
( ~ in(sK1(sK3,set_difference(sK4,singleton(sK5))),sK4)
| spl6_2 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f71,f77,f73]) ).
fof(f86,plain,
( ~ in(sK1(sK3,set_difference(sK4,singleton(sK5))),sK3)
| spl6_2 ),
inference(resolution,[],[f79,f59]) ).
fof(f87,plain,
( subset(sK3,set_difference(sK4,singleton(sK5)))
| spl6_2 ),
inference(resolution,[],[f86,f32]) ).
fof(f88,plain,
( $false
| spl6_2 ),
inference(resolution,[],[f87,f41]) ).
fof(f90,plain,
spl6_2,
inference(avatar_contradiction_clause,[],[f88]) ).
fof(f93,plain,
( sK5 = sK1(sK3,set_difference(sK4,singleton(sK5)))
| ~ spl6_1 ),
inference(resolution,[],[f75,f46]) ).
fof(f101,plain,
( in(sK5,sK3)
| subset(sK3,set_difference(sK4,singleton(sK5)))
| ~ spl6_1 ),
inference(superposition,[],[f32,f93]) ).
fof(f103,definition,
( spl6_3
<=> subset(sK3,set_difference(sK4,singleton(sK5))) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f105,plain,
( subset(sK3,set_difference(sK4,singleton(sK5)))
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f107,definition,
( spl6_4
<=> in(sK5,sK3) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f109,plain,
( in(sK5,sK3)
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,plain,
( spl6_3
| spl6_4
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f101,f73,f107,f103]) ).
fof(f111,plain,
( $false
| ~ spl6_4 ),
inference(resolution,[],[f109,f42]) ).
fof(f115,plain,
~ spl6_4,
inference(avatar_contradiction_clause,[],[f111]) ).
fof(f119,plain,
( $false
| ~ spl6_3 ),
inference(resolution,[],[f105,f41]) ).
fof(f121,plain,
~ spl6_3,
inference(avatar_contradiction_clause,[],[f119]) ).
cnf(s1,plain,
( spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f80]) ).
cnf(s2,plain,
spl6_2,
inference(sat_conversion,[],[f90]) ).
cnf(s3,plain,
( ~ spl6_1
| spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f110]) ).
cnf(s4,plain,
~ spl6_4,
inference(sat_conversion,[],[f115]) ).
cnf(s5,plain,
~ spl6_3,
inference(sat_conversion,[],[f121]) ).
cnf(s6,plain,
~ spl6_1,
inference(rat,[],[s3,s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s2,s6]) ).
fof(f122,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU145+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:47:01 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.17/0.46 % (2237718)Will run a generic schedule for satisfiability detection.
% 0.17/0.46 % (2237726)dis+10_1_sil=32000:sp=arity:random_seed=234501491:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.46 % (2237724)% WARNING: option uhcvi not known.
% 0.17/0.46 % (2237723)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1251556653_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.46 % (2237725)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=209409495:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.46 % (2237724)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1306470107:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.46 % (2237727)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1113475248:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.46 % (2237728)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4110377934:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.46 % (2237729)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3808120827:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.46 % TRYING [1]
% 0.17/0.46 % TRYING [2]
% 0.17/0.46 % TRYING [3]
% 0.17/0.46 % (2237729) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2237718-2237729"...
% 0.17/0.46 % TRYING [4]
% 0.17/0.46 % (2237729)...printing done.
% 0.17/0.46 % (2237729)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.46 % (2237729)------------------------------
% 0.17/0.46 % (2237729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.46 % (2237729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.46 % (2237729)CaDiCaL version: 2.1.3
% 0.17/0.46 % (2237729)Termination reason: Refutation
% 0.17/0.46 % (2237729)Time elapsed: 0.004 s
% 0.17/0.46 % (2237729)Peak memory usage: 12 MB
% 0.17/0.46 % (2237729)Instructions burned: 4 (million)
% 0.17/0.46 % (2237718)Success in time 0.041 s
% 0.17/0.46 % Vampire exiting
%------------------------------------------------------------------------------