%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET636+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 : n012.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 0.07s 0.36s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 79 ( 9 unt; 2 def)
% Number of atoms : 214 ( 24 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 230 ( 95 ~; 97 |; 26 &)
% ( 10 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 122 ( 0 sgn 113 !; 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] :
( disjoint(X0,X1)
<=> ~ intersect(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_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(f12,conjecture,
! [X0,X1] :
( disjoint(X0,X1)
<=> intersection(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th118) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
( disjoint(X0,X1)
<=> intersection(X0,X1) = empty_set ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f16,plain,
? [X0,X1] :
( disjoint(X0,X1)
<~> intersection(X0,X1) = empty_set ),
inference(ennf_transformation,[],[f13]) ).
fof(f17,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(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(flattening,[],[f17]) ).
fof(f19,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(f20,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,[],[f19]) ).
fof(f21,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))],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| intersect(X0,X1) )
& ( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f23,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f24,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f23]) ).
fof(f25,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,[],[f15]) ).
fof(f26,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,[],[f25]) ).
fof(f27,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))],[f26]) ).
fof(f31,plain,
? [X0,X1] :
( ( intersection(X0,X1) != empty_set
| ~ disjoint(X0,X1) )
& ( intersection(X0,X1) = empty_set
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f32,plain,
( ( empty_set != intersection(sK3,sK4)
| ~ disjoint(sK3,sK4) )
& ( empty_set = intersection(sK3,sK4)
| disjoint(sK3,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f31]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f36,plain,
! [X0,X1] :
( member(sK0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f37,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f40,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X0,X1] :
( disjoint(X0,X1)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f48,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f55,plain,
( empty_set = intersection(sK3,sK4)
| disjoint(sK3,sK4) ),
inference(cnf_transformation,[],[f32]) ).
fof(f56,plain,
( empty_set != intersection(sK3,sK4)
| ~ disjoint(sK3,sK4) ),
inference(cnf_transformation,[],[f32]) ).
fof(f62,definition,
( spl5_1
<=> disjoint(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f63,plain,
( ~ disjoint(sK3,sK4)
| spl5_1 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f64,plain,
( disjoint(sK3,sK4)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f66,definition,
( spl5_2
<=> empty_set = intersection(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f67,plain,
( empty_set != intersection(sK3,sK4)
| spl5_2 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f68,plain,
( empty_set = intersection(sK3,sK4)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f69,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f55,f66,f62]) ).
fof(f70,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f56,f66,f62]) ).
fof(f71,plain,
( intersect(sK3,sK4)
| spl5_1 ),
inference(resolution,[],[f41,f63]) ).
fof(f83,plain,
! [X2,X0,X1] :
( member(sK0(X0,intersection(X1,X2)),X2)
| ~ intersect(X0,intersection(X1,X2)) ),
inference(resolution,[],[f36,f33]) ).
fof(f87,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[],[f48,f39]) ).
fof(f88,plain,
! [X2,X0,X1] :
( member(sK1(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[],[f48,f34]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ member(sK0(X0,X1),X2)
| intersect(X2,X0)
| ~ intersect(X0,X1) ),
inference(resolution,[],[f38,f37]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ member(sK1(X0,X1),X2)
| intersect(X2,X0)
| subset(X0,X1) ),
inference(resolution,[],[f38,f48]) ).
fof(f96,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(resolution,[],[f44,f87]) ).
fof(f105,plain,
( ! [X0] :
( member(X0,empty_set)
| ~ member(X0,sK3)
| ~ member(X0,sK4) )
| ~ spl5_2 ),
inference(superposition,[],[f35,f68]) ).
fof(f108,plain,
( ! [X0] :
( ~ member(X0,sK4)
| ~ member(X0,sK3) )
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f105,f39]) ).
fof(f109,plain,
( ! [X0] :
( ~ member(sK0(X0,sK4),sK3)
| ~ intersect(X0,sK4) )
| ~ spl5_2 ),
inference(resolution,[],[f108,f36]) ).
fof(f123,plain,
( ~ intersect(sK3,sK4)
| ~ intersect(sK3,sK4)
| ~ spl5_2 ),
inference(resolution,[],[f109,f37]) ).
fof(f124,plain,
( ~ intersect(sK3,sK4)
| ~ spl5_2 ),
inference(duplicate_literal_removal,[],[f123]) ).
fof(f125,plain,
( $false
| spl5_1
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f124,f71]) ).
fof(f126,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f125]) ).
fof(f127,plain,
( ~ intersect(sK3,sK4)
| ~ spl5_1 ),
inference(resolution,[],[f64,f40]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ intersect(X0,intersection(X1,X2))
| intersect(X2,X0)
| ~ intersect(X0,intersection(X1,X2)) ),
inference(resolution,[],[f83,f93]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ~ intersect(X0,intersection(X1,X2))
| intersect(X2,X0) ),
inference(duplicate_literal_removal,[],[f175]) ).
fof(f215,plain,
! [X2,X0,X1] :
( subset(intersection(X0,X1),X2)
| intersect(X0,intersection(X0,X1))
| subset(intersection(X0,X1),X2) ),
inference(resolution,[],[f88,f94]) ).
fof(f222,plain,
! [X2,X0,X1] :
( subset(intersection(X0,X1),X2)
| intersect(X0,intersection(X0,X1)) ),
inference(duplicate_literal_removal,[],[f215]) ).
fof(f535,plain,
! [X2,X0,X1] :
( subset(intersection(X0,X1),X2)
| intersect(X1,X0) ),
inference(resolution,[],[f222,f184]) ).
fof(f776,plain,
! [X0,X1] :
( intersect(X0,X1)
| empty_set = intersection(X1,X0) ),
inference(resolution,[],[f535,f96]) ).
fof(f963,plain,
( empty_set = intersection(sK4,sK3)
| ~ spl5_1 ),
inference(resolution,[],[f776,f127]) ).
fof(f964,plain,
( empty_set = intersection(sK3,sK4)
| ~ spl5_1 ),
inference(forward_demodulation,[],[f963,f45]) ).
fof(f969,plain,
( $false
| ~ spl5_1
| spl5_2 ),
inference(forward_subsumption_resolution,[],[f964,f67]) ).
fof(f970,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_contradiction_clause,[],[f969]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f69]) ).
cnf(s2,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f70]) ).
cnf(s3,plain,
( spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f126]) ).
cnf(s4,plain,
( ~ spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f970]) ).
cnf(s5,plain,
spl5_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl5_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f971,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET636+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 28 02:23:04 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.32 Running first-order model finding
% 0.03/0.32 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
% 0.07/0.36 % (2952416)Will run a generic schedule for satisfiability detection.
% 0.07/0.36 % (2952422)% WARNING: option uhcvi not known.
% 0.07/0.36 % (2952423)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1500799816:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.36 % (2952426)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2271259414:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.36 % (2952421)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=617706644_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.36 % (2952422)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2153157720:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.36 % (2952424)dis+10_1_sil=32000:sp=arity:random_seed=260502724:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.36 % (2952425)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2698396845:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.36 % (2952427)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1979081884:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.36 % TRYING [1]
% 0.07/0.36 % TRYING [2]
% 0.07/0.36 % TRYING [3]
% 0.07/0.36 % TRYING [4]
% 0.07/0.36 % TRYING [5]
% 0.07/0.36 % (2952424) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2952416-2952424"...
% 0.07/0.36 % (2952424)...printing done.
% 0.07/0.36 % (2952424)Refutation found. Thanks to Tanya!
% 0.07/0.36 % SZS status Theorem for theBenchmark
% 0.07/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.36 % (2952424)------------------------------
% 0.07/0.36 % (2952424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.36 % (2952424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.36 % (2952424)CaDiCaL version: 2.1.3
% 0.07/0.36 % (2952424)Termination reason: Refutation
% 0.07/0.36 % (2952424)Time elapsed: 0.011 s
% 0.07/0.36 % (2952424)Peak memory usage: 12 MB
% 0.07/0.36 % (2952424)Instructions burned: 31 (million)
% 0.07/0.36 % (2952416)Success in time 0.037 s
% 0.07/0.36 % Vampire exiting
%------------------------------------------------------------------------------