%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET637+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:44:16 PM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 6 unt; 2 def)
% Number of atoms : 192 ( 24 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 201 ( 75 ~; 92 |; 24 &)
% ( 9 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn 81 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f2,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f5,axiom,
! [X0,X1] :
( not_equal(X0,X1)
<=> X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
fof(f9,conjecture,
! [X0,X1] :
( intersect(X0,X1)
<=> not_equal(intersection(X0,X1),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th119) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( intersect(X0,X1)
<=> not_equal(intersection(X0,X1),empty_set) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
? [X0,X1] :
( intersect(X0,X1)
<~> not_equal(intersection(X0,X1),empty_set) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& member(X2,X1) )
| ~ intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ? [X3] :
( member(X3,X0)
& member(X3,X1) )
| ~ intersect(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& member(sK0(X0,X1),X1) )
| ~ intersect(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( not_equal(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ not_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f22,plain,
? [X0,X1] :
( ( ~ not_equal(intersection(X0,X1),empty_set)
| ~ intersect(X0,X1) )
& ( not_equal(intersection(X0,X1),empty_set)
| intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f23,plain,
( ( ~ not_equal(intersection(sK2,sK3),empty_set)
| ~ intersect(sK2,sK3) )
& ( not_equal(intersection(sK2,sK3),empty_set)
| intersect(sK2,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f22]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,intersection(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| intersect(X0,X1)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0,X1] :
( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
! [X0,X1] :
( ~ not_equal(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
( not_equal(intersection(sK2,sK3),empty_set)
| intersect(sK2,sK3) ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
( ~ not_equal(intersection(sK2,sK3),empty_set)
| ~ intersect(sK2,sK3) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,definition,
( spl4_1
<=> intersect(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f43,plain,
( ~ intersect(sK2,sK3)
| spl4_1 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f44,plain,
( intersect(sK2,sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f46,definition,
( spl4_2
<=> not_equal(intersection(sK2,sK3),empty_set) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f47,plain,
( ~ not_equal(intersection(sK2,sK3),empty_set)
| spl4_2 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f48,plain,
( not_equal(intersection(sK2,sK3),empty_set)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f49,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f39,f46,f42]) ).
fof(f50,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f40,f46,f42]) ).
fof(f51,plain,
( empty_set != intersection(sK2,sK3)
| ~ spl4_2 ),
inference(resolution,[],[f35,f48]) ).
fof(f58,plain,
! [X2,X0,X1] :
( member(sK1(X0,intersection(X1,X2)),X0)
| member(sK1(X0,intersection(X1,X2)),X1)
| intersection(X1,X2) = X0 ),
inference(resolution,[],[f33,f25]) ).
fof(f63,plain,
! [X0] :
( member(sK1(empty_set,X0),X0)
| empty_set = X0 ),
inference(resolution,[],[f33,f30]) ).
fof(f83,plain,
! [X0,X1] :
( member(sK1(empty_set,intersection(X0,X1)),X1)
| intersection(X0,X1) = empty_set ),
inference(resolution,[],[f63,f24]) ).
fof(f141,plain,
! [X2,X3,X0,X1] :
( ~ member(sK1(X0,intersection(X1,X2)),X3)
| intersection(X1,X2) = X0
| intersect(X1,X3)
| member(sK1(X0,intersection(X1,X2)),X0) ),
inference(resolution,[],[f58,f29]) ).
fof(f1556,plain,
! [X0,X1] :
( intersection(X0,X1) = empty_set
| intersect(X0,X1)
| member(sK1(empty_set,intersection(X0,X1)),empty_set)
| intersection(X0,X1) = empty_set ),
inference(resolution,[],[f141,f83]) ).
fof(f1592,plain,
! [X0,X1] :
( intersection(X0,X1) = empty_set
| intersect(X0,X1)
| member(sK1(empty_set,intersection(X0,X1)),empty_set) ),
inference(duplicate_literal_removal,[],[f1556]) ).
fof(f1616,plain,
! [X0,X1] :
( intersect(X0,X1)
| intersection(X0,X1) = empty_set ),
inference(forward_subsumption_resolution,[],[f1592,f30]) ).
fof(f1624,plain,
( empty_set = intersection(sK2,sK3)
| spl4_1 ),
inference(resolution,[],[f1616,f43]) ).
fof(f1628,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f1624,f51]) ).
fof(f1629,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f1628]) ).
fof(f1630,plain,
( member(sK0(sK2,sK3),sK2)
| ~ spl4_1 ),
inference(resolution,[],[f44,f28]) ).
fof(f1631,plain,
( member(sK0(sK2,sK3),sK3)
| ~ spl4_1 ),
inference(resolution,[],[f44,f27]) ).
fof(f1636,plain,
( empty_set = intersection(sK2,sK3)
| spl4_2 ),
inference(resolution,[],[f47,f36]) ).
fof(f1637,plain,
( ! [X0] :
( ~ member(sK0(sK2,sK3),X0)
| member(sK0(sK2,sK3),intersection(sK2,X0)) )
| ~ spl4_1 ),
inference(resolution,[],[f1630,f26]) ).
fof(f1696,plain,
( member(sK0(sK2,sK3),intersection(sK2,sK3))
| ~ spl4_1 ),
inference(resolution,[],[f1637,f1631]) ).
fof(f1697,plain,
( member(sK0(sK2,sK3),empty_set)
| ~ spl4_1
| spl4_2 ),
inference(forward_demodulation,[],[f1696,f1636]) ).
fof(f1699,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f1697,f30]) ).
fof(f1700,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f1699]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f49]) ).
cnf(s2,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f50]) ).
cnf(s3,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f1629]) ).
cnf(s4,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f1700]) ).
cnf(s5,plain,
spl4_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl4_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f1701,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET637+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n011.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 02:23:30 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.16/0.47 % (2959227)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (2959237)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=123126006:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (2959233)% WARNING: option uhcvi not known.
% 0.16/0.47 % (2959232)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=147720049_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (2959234)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3990218678:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (2959233)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=703135920:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (2959235)dis+10_1_sil=32000:sp=arity:random_seed=1604068079:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (2959236)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1087205074:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (2959238)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3351789090:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % TRYING [4]
% 0.16/0.47 % TRYING [5]
% 0.16/0.47 % (2959237) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2959227-2959237"...
% 0.16/0.47 % (2959234) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2959227-2959234"...
% 0.16/0.47 % (2959237)...printing done.
% 0.16/0.47 % (2959237)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (2959237)------------------------------
% 0.16/0.47 % (2959237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (2959237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (2959237)CaDiCaL version: 2.1.3
% 0.16/0.47 % (2959237)Termination reason: Refutation
% 0.16/0.47 % (2959237)Time elapsed: 0.021 s
% 0.16/0.47 % (2959237)Peak memory usage: 12 MB
% 0.16/0.47 % (2959237)Instructions burned: 58 (million)
% 0.16/0.47 % (2959227)Success in time 0.053 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------