%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET632+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 12:44:15 PM UTC 2026
% Result : Theorem 0.06s 0.35s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 15 unt; 1 def)
% Number of atoms : 139 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 141 ( 53 ~; 47 |; 31 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 72 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_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(f9,conjecture,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X0,X2)
& disjoint(X1,X2) )
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th114) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X0,X2)
& disjoint(X1,X2) )
=> X0 = empty_set ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( disjoint(X0,X1)
=> ~ intersect(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f13,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f15,plain,
? [X0,X1,X2] :
( empty_set != X0
& subset(X0,X1)
& subset(X0,X2)
& disjoint(X1,X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f16,plain,
? [X0,X1,X2] :
( empty_set != X0
& subset(X0,X1)
& subset(X0,X2)
& disjoint(X1,X2) ),
inference(flattening,[],[f15]) ).
fof(f17,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(f18,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,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f18]) ).
fof(f20,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(f21,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,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ( member(sK1(X0,X1),X0)
& member(sK1(X0,X1),X1) )
| ~ intersect(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f21]) ).
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,
( empty_set != sK2
& subset(sK2,sK3)
& subset(sK2,sK4)
& disjoint(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f16]) ).
fof(f26,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| intersect(X0,X1)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f32,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f36,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
disjoint(sK3,sK4),
inference(cnf_transformation,[],[f25]) ).
fof(f40,plain,
subset(sK2,sK4),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
empty_set != sK2,
inference(cnf_transformation,[],[f25]) ).
fof(f43,plain,
~ intersect(sK3,sK4),
inference(resolution,[],[f33,f39]) ).
fof(f45,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[],[f27,f32]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ subset(X0,X2)
| member(sK0(X0,X1),X2)
| subset(X0,X1) ),
inference(resolution,[],[f26,f27]) ).
fof(f53,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(resolution,[],[f36,f45]) ).
fof(f74,plain,
! [X0] :
( member(sK0(sK2,X0),sK4)
| subset(sK2,X0) ),
inference(resolution,[],[f48,f40]) ).
fof(f75,plain,
! [X0] :
( member(sK0(sK2,X0),sK3)
| subset(sK2,X0) ),
inference(resolution,[],[f48,f41]) ).
fof(f87,definition,
( spl5_5
<=> ! [X0] : subset(sK2,X0) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f88,plain,
( ! [X0] : subset(sK2,X0)
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f96,plain,
( empty_set = sK2
| ~ spl5_5 ),
inference(resolution,[],[f88,f53]) ).
fof(f97,plain,
( $false
| ~ spl5_5 ),
inference(forward_subsumption_resolution,[],[f96,f42]) ).
fof(f98,plain,
~ spl5_5,
inference(avatar_contradiction_clause,[],[f97]) ).
fof(f101,plain,
! [X0,X1] :
( ~ member(sK0(sK2,X0),X1)
| intersect(sK3,X1)
| subset(sK2,X0) ),
inference(resolution,[],[f75,f31]) ).
fof(f143,plain,
! [X0] :
( intersect(sK3,sK4)
| subset(sK2,X0)
| subset(sK2,X0) ),
inference(resolution,[],[f101,f74]) ).
fof(f146,plain,
! [X0] :
( intersect(sK3,sK4)
| subset(sK2,X0) ),
inference(duplicate_literal_removal,[],[f143]) ).
fof(f153,plain,
! [X0] : subset(sK2,X0),
inference(forward_subsumption_resolution,[],[f146,f43]) ).
fof(f154,plain,
spl5_5,
inference(avatar_split_clause,[],[f153,f87]) ).
cnf(s4,plain,
~ spl5_5,
inference(sat_conversion,[],[f98]) ).
cnf(s9,plain,
spl5_5,
inference(sat_conversion,[],[f154]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s4,s9]) ).
fof(f155,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET632+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 02:22:19 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
% 0.06/0.35 % (2951149)Will run a generic schedule for satisfiability detection.
% 0.06/0.35 % (2951155)% WARNING: option uhcvi not known.
% 0.06/0.35 % (2951157)dis+10_1_sil=32000:sp=arity:random_seed=286603933:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.06/0.35 % (2951160)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1589128262:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.35 % (2951159)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=534216117:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.06/0.35 % (2951154)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3709686705_2999 on theBenchmark for (2999ds/0Mi)
% 0.06/0.35 % (2951155)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1175369538:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.06/0.35 % (2951156)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=962255890:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.06/0.35 % (2951158)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2657490020:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.06/0.35 % TRYING [1]
% 0.06/0.35 % TRYING [2]
% 0.06/0.35 % TRYING [3]
% 0.06/0.35 % TRYING [4]
% 0.06/0.35 % (2951159) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2951149-2951159"...
% 0.06/0.35 % TRYING [5]
% 0.06/0.35 % (2951160) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2951149-2951160"...
% 0.06/0.35 % (2951159)...printing done.
% 0.06/0.35 % TRYING [6]
% 0.06/0.35 % (2951159)Refutation found. Thanks to Tanya!
% 0.06/0.35 % SZS status Theorem for theBenchmark
% 0.06/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.35 % (2951159)------------------------------
% 0.06/0.35 % (2951159)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.35 % (2951159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.35 % (2951159)CaDiCaL version: 2.1.3
% 0.06/0.35 % (2951159)Termination reason: Refutation
% 0.06/0.35 % (2951159)Time elapsed: 0.002 s
% 0.06/0.35 % (2951159)Peak memory usage: 12 MB
% 0.06/0.35 % (2951159)Instructions burned: 3 (million)
% 0.06/0.35 % (2951149)Success in time 0.027 s
% 0.06/0.35 % Vampire exiting
%------------------------------------------------------------------------------