%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET611+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 : 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 12:44:08 PM UTC 2026
% Result : Theorem 0.09s 0.46s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 77 ( 10 unt; 2 def)
% Number of atoms : 205 ( 36 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 215 ( 87 ~; 94 |; 23 &)
% ( 9 <=>; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 104 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,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(f3,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f4,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f6,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f11,conjecture,
! [X0,X1] :
( intersection(X0,X1) = empty_set
<=> difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th84) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( intersection(X0,X1) = empty_set
<=> difference(X0,X1) = X0 ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f15,plain,
? [X0,X1] :
( intersection(X0,X1) = empty_set
<~> difference(X0,X1) = X0 ),
inference(ennf_transformation,[],[f12]) ).
fof(f18,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,[],[f2]) ).
fof(f19,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,[],[f18]) ).
fof(f20,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,[],[f3]) ).
fof(f21,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,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f23,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f22]) ).
fof(f27,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,[],[f14]) ).
fof(f28,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,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f28]) ).
fof(f30,plain,
? [X0,X1] :
( ( difference(X0,X1) != X0
| intersection(X0,X1) != empty_set )
& ( difference(X0,X1) = X0
| intersection(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f31,plain,
( ( sK3 != difference(sK3,sK4)
| empty_set != intersection(sK3,sK4) )
& ( sK3 = difference(sK3,sK4)
| empty_set = intersection(sK3,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f30]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f40,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f4]) ).
fof(f43,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f50,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f51,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
( sK3 = difference(sK3,sK4)
| empty_set = intersection(sK3,sK4) ),
inference(cnf_transformation,[],[f31]) ).
fof(f54,plain,
( sK3 != difference(sK3,sK4)
| empty_set != intersection(sK3,sK4) ),
inference(cnf_transformation,[],[f31]) ).
fof(f60,definition,
( spl5_1
<=> empty_set = intersection(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f61,plain,
( empty_set != intersection(sK3,sK4)
| spl5_1 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f62,plain,
( empty_set = intersection(sK3,sK4)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f64,definition,
( spl5_2
<=> sK3 = difference(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f65,plain,
( sK3 != difference(sK3,sK4)
| spl5_2 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f66,plain,
( sK3 = difference(sK3,sK4)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f67,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f53,f64,f60]) ).
fof(f68,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f54,f64,f60]) ).
fof(f73,plain,
( ! [X0] :
( ~ member(X0,sK4)
| ~ member(X0,sK3) )
| ~ spl5_2 ),
inference(superposition,[],[f37,f66]) ).
fof(f75,plain,
! [X2,X0,X1] :
( member(sK2(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[],[f50,f35]) ).
fof(f76,plain,
! [X2,X0,X1] :
( member(sK2(intersection(X0,X1),X2),X1)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[],[f50,f34]) ).
fof(f77,plain,
! [X2,X0,X1] :
( member(sK2(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[],[f50,f38]) ).
fof(f79,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[],[f50,f40]) ).
fof(f84,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(resolution,[],[f79,f43]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ member(sK2(X0,difference(X1,X2)),X1)
| member(sK2(X0,difference(X1,X2)),X2)
| subset(X0,difference(X1,X2)) ),
inference(resolution,[],[f39,f51]) ).
fof(f194,plain,
( ! [X0,X1] :
( ~ member(sK2(intersection(sK4,X0),X1),sK3)
| subset(intersection(sK4,X0),X1) )
| ~ spl5_2 ),
inference(resolution,[],[f75,f73]) ).
fof(f201,plain,
( ! [X0] :
( subset(intersection(sK4,sK3),X0)
| subset(intersection(sK4,sK3),X0) )
| ~ spl5_2 ),
inference(resolution,[],[f76,f194]) ).
fof(f210,plain,
( ! [X0] : subset(intersection(sK4,sK3),X0)
| ~ spl5_2 ),
inference(duplicate_literal_removal,[],[f201]) ).
fof(f212,plain,
( ! [X0] : subset(intersection(sK3,sK4),X0)
| ~ spl5_2 ),
inference(forward_demodulation,[],[f210,f44]) ).
fof(f215,plain,
( empty_set = intersection(sK3,sK4)
| ~ spl5_2 ),
inference(resolution,[],[f212,f84]) ).
fof(f216,plain,
( $false
| spl5_1
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f215,f61]) ).
fof(f217,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f216]) ).
fof(f220,plain,
( ! [X0] :
( member(X0,empty_set)
| ~ member(X0,sK3)
| ~ member(X0,sK4) )
| ~ spl5_1 ),
inference(superposition,[],[f36,f62]) ).
fof(f223,plain,
( ! [X0] :
( ~ member(X0,sK4)
| ~ member(X0,sK3) )
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f220,f40]) ).
fof(f235,plain,
! [X0,X1] :
( subset(difference(X0,X1),X0)
| subset(difference(X0,X1),X0) ),
inference(resolution,[],[f77,f51]) ).
fof(f242,plain,
! [X0,X1] : subset(difference(X0,X1),X0),
inference(duplicate_literal_removal,[],[f235]) ).
fof(f272,plain,
! [X0,X1] :
( member(sK2(X0,difference(X0,X1)),X1)
| subset(X0,difference(X0,X1))
| subset(X0,difference(X0,X1)) ),
inference(resolution,[],[f96,f50]) ).
fof(f281,plain,
! [X0,X1] :
( member(sK2(X0,difference(X0,X1)),X1)
| subset(X0,difference(X0,X1)) ),
inference(duplicate_literal_removal,[],[f272]) ).
fof(f977,plain,
( ! [X0] :
( ~ member(sK2(X0,difference(X0,sK4)),sK3)
| subset(X0,difference(X0,sK4)) )
| ~ spl5_1 ),
inference(resolution,[],[f281,f223]) ).
fof(f1547,plain,
( subset(sK3,difference(sK3,sK4))
| subset(sK3,difference(sK3,sK4))
| ~ spl5_1 ),
inference(resolution,[],[f977,f50]) ).
fof(f1554,plain,
( subset(sK3,difference(sK3,sK4))
| ~ spl5_1 ),
inference(duplicate_literal_removal,[],[f1547]) ).
fof(f1571,plain,
( ~ subset(difference(sK3,sK4),sK3)
| sK3 = difference(sK3,sK4)
| ~ spl5_1 ),
inference(resolution,[],[f1554,f43]) ).
fof(f1572,plain,
( sK3 = difference(sK3,sK4)
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f1571,f242]) ).
fof(f1573,plain,
( $false
| ~ spl5_1
| spl5_2 ),
inference(forward_subsumption_resolution,[],[f1572,f65]) ).
fof(f1574,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_contradiction_clause,[],[f1573]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f67]) ).
cnf(s2,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f68]) ).
cnf(s7,plain,
( spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f217]) ).
cnf(s8,plain,
( ~ spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f1574]) ).
cnf(s9,plain,
spl5_1,
inference(rat,[],[s1,s7]) ).
cnf(s10,plain,
spl5_2,
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s2,s10,s9]) ).
fof(f1575,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET611+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 02:20:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 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
% 0.09/0.46 % (1125252)Will run a generic schedule for satisfiability detection.
% 0.09/0.46 % (1125260)dis+10_1_sil=32000:sp=arity:random_seed=1050314705:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.46 % (1125258)% WARNING: option uhcvi not known.
% 0.09/0.46 % (1125257)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1620874258_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.46 % (1125261)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4104554682:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.46 % (1125259)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3712596355:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.46 % (1125262)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=167961227:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.46 % (1125263)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=611329179:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.46 % (1125258)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3041967213:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.46 % TRYING [1]
% 0.09/0.46 % TRYING [2]
% 0.09/0.46 % TRYING [3]
% 0.09/0.46 % TRYING [4]
% 0.09/0.46 % (1125260) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1125252-1125260"...
% 0.09/0.46 % TRYING [5]
% 0.09/0.46 % (1125260)...printing done.
% 0.09/0.46 % (1125260)Refutation found. Thanks to Tanya!
% 0.09/0.46 % SZS status Theorem for theBenchmark
% 0.09/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.46 % (1125260)------------------------------
% 0.09/0.46 % (1125260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.46 % (1125260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.46 % (1125260)CaDiCaL version: 2.1.3
% 0.09/0.46 % (1125260)Termination reason: Refutation
% 0.09/0.46 % (1125260)Time elapsed: 0.024 s
% 0.09/0.46 % (1125260)Peak memory usage: 13 MB
% 0.09/0.46 % (1125260)Instructions burned: 68 (million)
% 0.09/0.46 % (1125252)Success in time 0.05 s
% 0.09/0.46 % Vampire exiting
%------------------------------------------------------------------------------