%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET902+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 12:44:57 PM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 20 unt; 4 def)
% Number of atoms : 132 ( 73 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 134 ( 61 ~; 46 |; 22 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 1 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f5,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f6,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1,X2] :
~ ( singleton(X0) = set_union2(X1,X2)
& ~ ( X1 = singleton(X0)
& X2 = singleton(X0) )
& ~ ( X1 = empty_set
& X2 = singleton(X0) )
& ~ ( X1 = singleton(X0)
& X2 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( singleton(X0) = set_union2(X1,X2)
& ~ ( X1 = singleton(X0)
& X2 = singleton(X0) )
& ~ ( X1 = empty_set
& X2 = singleton(X0) )
& ~ ( X1 = singleton(X0)
& X2 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f14,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f5]) ).
fof(f18,plain,
? [X0,X1,X2] :
( singleton(X0) = set_union2(X1,X2)
& ( singleton(X0) != X1
| singleton(X0) != X2 )
& ( empty_set != X1
| singleton(X0) != X2 )
& ( singleton(X0) != X1
| empty_set != X2 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( X0 = empty_set
| X0 = singleton(X1)
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( X0 = empty_set
| X0 = singleton(X1)
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f19]) ).
fof(f23,plain,
( singleton(sK2) = set_union2(sK3,sK4)
& ( sK3 != singleton(sK2)
| sK4 != singleton(sK2) )
& ( empty_set != sK3
| sK4 != singleton(sK2) )
& ( sK3 != singleton(sK2)
| empty_set != sK4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f18]) ).
fof(f24,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X0] : empty_set != singleton(X0),
inference(cnf_transformation,[],[f6]) ).
fof(f30,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
( sK3 != singleton(sK2)
| empty_set != sK4 ),
inference(cnf_transformation,[],[f23]) ).
fof(f37,plain,
( empty_set != sK3
| sK4 != singleton(sK2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f38,plain,
( sK3 != singleton(sK2)
| sK4 != singleton(sK2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
singleton(sK2) = set_union2(sK3,sK4),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f13]) ).
fof(f44,definition,
( spl5_1
<=> empty_set = sK4 ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f45,plain,
( empty_set = sK4
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f46,plain,
( empty_set != sK4
| spl5_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f48,definition,
( spl5_2
<=> sK3 = singleton(sK2) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f50,plain,
( sK3 != singleton(sK2)
| spl5_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f36,f48,f44]) ).
fof(f53,definition,
( spl5_3
<=> sK4 = singleton(sK2) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f54,plain,
( sK4 = singleton(sK2)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f55,plain,
( sK4 != singleton(sK2)
| spl5_3 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f57,definition,
( spl5_4
<=> empty_set = sK3 ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f58,plain,
( empty_set = sK3
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f61,plain,
subset(sK3,singleton(sK2)),
inference(superposition,[],[f40,f39]) ).
fof(f98,plain,
! [X0,X1] : subset(X1,set_union2(X0,X1)),
inference(superposition,[],[f40,f24]) ).
fof(f102,plain,
subset(sK4,singleton(sK2)),
inference(superposition,[],[f98,f39]) ).
fof(f117,plain,
( sK3 = singleton(sK2)
| empty_set = sK3 ),
inference(resolution,[],[f30,f61]) ).
fof(f118,plain,
( sK4 = singleton(sK2)
| empty_set = sK4 ),
inference(resolution,[],[f30,f102]) ).
fof(f119,plain,
( empty_set = sK4
| spl5_3 ),
inference(forward_subsumption_resolution,[],[f118,f55]) ).
fof(f120,plain,
( $false
| spl5_1
| spl5_3 ),
inference(forward_subsumption_resolution,[],[f119,f46]) ).
fof(f121,plain,
( spl5_1
| spl5_3 ),
inference(avatar_contradiction_clause,[],[f120]) ).
fof(f137,plain,
( empty_set = sK3
| spl5_2 ),
inference(forward_subsumption_resolution,[],[f117,f50]) ).
fof(f138,plain,
( spl5_4
| spl5_2 ),
inference(avatar_split_clause,[],[f137,f48,f57]) ).
fof(f142,plain,
( singleton(sK2) = set_union2(empty_set,sK4)
| ~ spl5_4 ),
inference(superposition,[],[f39,f58]) ).
fof(f143,plain,
( singleton(sK2) = set_union2(empty_set,empty_set)
| ~ spl5_1
| ~ spl5_4 ),
inference(forward_demodulation,[],[f142,f45]) ).
fof(f145,plain,
( empty_set = singleton(sK2)
| ~ spl5_1
| ~ spl5_4 ),
inference(forward_demodulation,[],[f143,f28]) ).
fof(f148,plain,
( $false
| ~ spl5_1
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f145,f29]) ).
fof(f149,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f148]) ).
fof(f150,plain,
( $false
| ~ spl5_3 ),
inference(global_subsumption,[],[f54,f117,f37,f38]) ).
fof(f151,plain,
~ spl5_3,
inference(avatar_contradiction_clause,[],[f150]) ).
cnf(s19,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f51]) ).
cnf(s68,plain,
( spl5_1
| spl5_3 ),
inference(sat_conversion,[],[f121]) ).
cnf(s86,plain,
( spl5_2
| spl5_4 ),
inference(sat_conversion,[],[f138]) ).
cnf(s90,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(sat_conversion,[],[f149]) ).
cnf(s94,plain,
~ spl5_3,
inference(sat_conversion,[],[f151]) ).
cnf(s102,plain,
spl5_1,
inference(rat,[],[s68,s94]) ).
cnf(s103,plain,
~ spl5_4,
inference(rat,[],[s90,s102]) ).
cnf(s104,plain,
spl5_2,
inference(rat,[],[s86,s103]) ).
cnf(s105,plain,
$false,
inference(rat,[],[s19,s104,s102]) ).
fof(f155,plain,
$false,
inference(avatar_sat_refutation,[],[s105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET902+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n004.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 03:07:52 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 Running first-order model finding
% 0.13/0.39 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
% 0.13/0.44 % (4113777)Will run a generic schedule for satisfiability detection.
% 0.13/0.44 % (4113784)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=183277597_3000 on theBenchmark for (3000ds/0Mi)
% 0.13/0.44 % TRYING [1]
% 0.13/0.44 % TRYING [2]
% 0.13/0.44 % TRYING [3]
% 0.13/0.44 % TRYING [4]
% 0.13/0.44 % (4113785)% WARNING: option uhcvi not known.
% 0.13/0.44 % TRYING [5]
% 0.13/0.44 % (4113786)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1132293439:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.13/0.44 % (4113785)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2241667249:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.13/0.44 % (4113788)dis+10_1_sil=32000:sp=arity:random_seed=1213407005:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.13/0.44 % (4113791)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3722311515:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.13/0.44 % (4113786) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4113777-4113786"...
% 0.13/0.44 % (4113791) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4113777-4113791"...
% 0.13/0.44 % (4113785) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4113777-4113785"...
% 0.13/0.44 % TRYING [6]
% 0.13/0.44 % (4113786)...printing done.
% 0.13/0.44 % (4113791)...printing done.
% 0.13/0.44 % (4113789)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1871075119:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.13/0.44 % (4113785)...printing done.
% 0.13/0.44 % (4113786)Refutation found. Thanks to Tanya!
% 0.13/0.44 % SZS status Theorem for theBenchmark
% 0.13/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.44 % (4113786)------------------------------
% 0.13/0.44 % (4113786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.44 % (4113786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.44 % (4113786)CaDiCaL version: 2.1.3
% 0.13/0.44 % (4113786)Termination reason: Refutation
% 0.13/0.44 % (4113786)Time elapsed: 0.008 s
% 0.13/0.44 % (4113786)Peak memory usage: 12 MB
% 0.13/0.44 % (4113786)Instructions burned: 5 (million)
% 0.13/0.44 % (4113777)Success in time 0.04 s
% 0.13/0.44 % Vampire exiting
%------------------------------------------------------------------------------