%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET587+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 12:44:01 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 61 ( 7 unt; 2 def)
% Number of atoms : 164 ( 20 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 173 ( 70 ~; 75 |; 18 &)
% ( 8 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 70 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f9,conjecture,
! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_difference_empty_set) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f13,plain,
? [X0,X1] :
( difference(X0,X1) = empty_set
<~> subset(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f21]) ).
fof(f26,plain,
? [X0,X1] :
( ( ~ subset(X0,X1)
| difference(X0,X1) != empty_set )
& ( subset(X0,X1)
| difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f27,plain,
( ( ~ subset(sK3,sK4)
| empty_set != difference(sK3,sK4) )
& ( subset(sK3,sK4)
| empty_set = difference(sK3,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f26]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
( subset(sK3,sK4)
| empty_set = difference(sK3,sK4) ),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
( ~ subset(sK3,sK4)
| empty_set != difference(sK3,sK4) ),
inference(cnf_transformation,[],[f27]) ).
fof(f52,definition,
( spl5_1
<=> empty_set = difference(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f53,plain,
( empty_set != difference(sK3,sK4)
| spl5_1 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f54,plain,
( empty_set = difference(sK3,sK4)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f56,definition,
( spl5_2
<=> subset(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f57,plain,
( ~ subset(sK3,sK4)
| spl5_2 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f58,plain,
( subset(sK3,sK4)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f59,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f45,f56,f52]) ).
fof(f60,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f46,f56,f52]) ).
fof(f61,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[],[f35,f33]) ).
fof(f62,plain,
! [X2,X0,X1] :
( member(sK1(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[],[f35,f31]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ member(sK1(difference(X0,X1),X2),X1)
| subset(difference(X0,X1),X2) ),
inference(resolution,[],[f35,f30]) ).
fof(f72,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(resolution,[],[f39,f61]) ).
fof(f104,plain,
( ! [X0] :
( member(X0,empty_set)
| ~ member(X0,sK3)
| member(X0,sK4) )
| ~ spl5_1 ),
inference(superposition,[],[f32,f54]) ).
fof(f107,plain,
( ! [X0] :
( ~ member(X0,sK3)
| member(X0,sK4) )
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f104,f33]) ).
fof(f111,plain,
( ! [X0] :
( member(sK1(sK3,X0),sK4)
| subset(sK3,X0) )
| ~ spl5_1 ),
inference(resolution,[],[f107,f35]) ).
fof(f123,plain,
( subset(sK3,sK4)
| subset(sK3,sK4)
| ~ spl5_1 ),
inference(resolution,[],[f111,f36]) ).
fof(f124,plain,
( subset(sK3,sK4)
| ~ spl5_1 ),
inference(duplicate_literal_removal,[],[f123]) ).
fof(f125,plain,
( $false
| ~ spl5_1
| spl5_2 ),
inference(forward_subsumption_resolution,[],[f124,f57]) ).
fof(f126,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_contradiction_clause,[],[f125]) ).
fof(f128,plain,
( ! [X0] :
( ~ member(X0,sK3)
| member(X0,sK4) )
| ~ spl5_2 ),
inference(resolution,[],[f58,f34]) ).
fof(f188,plain,
( ! [X0,X1] :
( member(sK1(difference(sK3,X0),X1),sK4)
| subset(difference(sK3,X0),X1) )
| ~ spl5_2 ),
inference(resolution,[],[f62,f128]) ).
fof(f360,plain,
( ! [X0] :
( subset(difference(sK3,sK4),X0)
| subset(difference(sK3,sK4),X0) )
| ~ spl5_2 ),
inference(resolution,[],[f188,f63]) ).
fof(f365,plain,
( ! [X0] : subset(difference(sK3,sK4),X0)
| ~ spl5_2 ),
inference(duplicate_literal_removal,[],[f360]) ).
fof(f689,plain,
( empty_set = difference(sK3,sK4)
| ~ spl5_2 ),
inference(resolution,[],[f72,f365]) ).
fof(f694,plain,
( $false
| spl5_1
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f689,f53]) ).
fof(f695,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f694]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f59]) ).
cnf(s2,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f60]) ).
cnf(s5,plain,
( ~ spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f126]) ).
cnf(s23,plain,
( spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f695]) ).
cnf(s24,plain,
spl5_1,
inference(rat,[],[s1,s23]) ).
cnf(s25,plain,
spl5_2,
inference(rat,[],[s5,s24]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s2,s25,s24]) ).
fof(f696,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET587+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n003.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 02:15:11 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.16/0.41 Running first-order model finding
% 0.16/0.41 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
% 0.16/0.46 % (1123247)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (1123255)dis+10_1_sil=32000:sp=arity:random_seed=2328458823:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (1123253)% WARNING: option uhcvi not known.
% 0.16/0.46 % (1123256)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4151690736:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % (1123253)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1519841631:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.46 % (1123254)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1062911219:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.46 % (1123258)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1712570541:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % (1123257)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3313085587:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % (1123252)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3600515903_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % (1123255) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1123247-1123255"...
% 0.16/0.46 % (1123255)...printing done.
% 0.16/0.46 % TRYING [1]
% 0.16/0.46 % TRYING [2]
% 0.16/0.46 % (1123255)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (1123255)------------------------------
% 0.16/0.46 % (1123255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (1123255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (1123255)CaDiCaL version: 2.1.3
% 0.16/0.46 % (1123255)Termination reason: Refutation
% 0.16/0.46 % (1123255)Time elapsed: 0.010 s
% 0.16/0.46 % (1123255)Peak memory usage: 12 MB
% 0.16/0.46 % (1123255)Instructions burned: 25 (million)
% 0.16/0.46 % (1123247)Success in time 0.036 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------