%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET934+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 : n018.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 12:45:02 PM UTC 2026
% Result : Theorem 0.14s 0.53s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 18 unt; 2 def)
% Number of atoms : 112 ( 7 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 104 ( 48 ~; 45 |; 1 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 78 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X1,X2) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f13,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f14,conjecture,
! [X0,X1] : subset(set_union2(powerset(X0),powerset(X1)),powerset(set_union2(X0,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t81_zfmisc_1) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] : subset(set_union2(powerset(X0),powerset(X1)),powerset(set_union2(X0,X1))),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(ennf_transformation,[],[f12]) ).
fof(f23,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
? [X0,X1] : ~ subset(set_union2(powerset(X0),powerset(X1)),powerset(set_union2(X0,X1))),
inference(ennf_transformation,[],[f15]) ).
fof(f26,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ subset(X2,X0)
| in(X2,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f3]) ).
fof(f28,plain,
! [X2,X0,X1] :
( subset(X2,X0)
| ~ in(X2,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f4]) ).
fof(f38,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f39,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f47,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f13]) ).
fof(f48,plain,
~ subset(set_union2(powerset(sK5),powerset(sK6)),powerset(set_union2(sK5,sK6))),
inference(cnf_transformation,[],[f24]) ).
fof(f49,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,powerset(X0)) ),
inference(equality_resolution,[],[f28]) ).
fof(f50,plain,
! [X2,X0] :
( ~ subset(X2,X0)
| in(X2,powerset(X0)) ),
inference(equality_resolution,[],[f27]) ).
fof(f53,plain,
! [X3,X0,X1] :
( ~ in(X3,set_union2(X0,X1))
| in(X3,X0)
| in(X3,X1) ),
inference(equality_resolution,[],[f34]) ).
fof(f56,plain,
! [X2,X0] :
( ~ in(X2,powerset(X0))
| ~ subset(X2,X0) ),
inference(consistent_polarity_flipping,[],[f49]) ).
fof(f57,plain,
! [X2,X0] :
( in(X2,powerset(X0))
| subset(X2,X0) ),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f58,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| ~ subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f39]) ).
fof(f59,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(consistent_polarity_flipping,[],[f38]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ subset(X0,X2)
| subset(X0,X1)
| subset(X1,X2) ),
inference(consistent_polarity_flipping,[],[f46]) ).
fof(f63,plain,
! [X0,X1] : ~ subset(X0,set_union2(X0,X1)),
inference(consistent_polarity_flipping,[],[f47]) ).
fof(f64,plain,
subset(set_union2(powerset(sK5),powerset(sK6)),powerset(set_union2(sK5,sK6))),
inference(consistent_polarity_flipping,[],[f48]) ).
fof(f70,plain,
! [X0,X1] : ~ subset(X1,set_union2(X0,X1)),
inference(superposition,[],[f63,f26]) ).
fof(f82,plain,
! [X0,X1] :
( subset(sK2(X0,powerset(X1)),X1)
| ~ subset(X0,powerset(X1)) ),
inference(resolution,[],[f58,f57]) ).
fof(f83,plain,
in(sK2(set_union2(powerset(sK5),powerset(sK6)),powerset(set_union2(sK5,sK6))),set_union2(powerset(sK5),powerset(sK6))),
inference(resolution,[],[f59,f64]) ).
fof(f142,plain,
( in(sK2(set_union2(powerset(sK5),powerset(sK6)),powerset(set_union2(sK5,sK6))),powerset(sK5))
| in(sK2(set_union2(powerset(sK5),powerset(sK6)),powerset(set_union2(sK5,sK6))),powerset(sK6)) ),
inference(resolution,[],[f83,f53]) ).
fof(f148,definition,
( spl7_1
<=> in(sK2(set_union2(powerset(sK5),powerset(sK6)),powerset(set_union2(sK5,sK6))),powerset(sK6)) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
fof(f150,plain,
( in(sK2(set_union2(powerset(sK5),powerset(sK6)),powerset(set_union2(sK5,sK6))),powerset(sK6))
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f152,definition,
( spl7_2
<=> in(sK2(set_union2(powerset(sK5),powerset(sK6)),powerset(set_union2(sK5,sK6))),powerset(sK5)) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
fof(f154,plain,
( in(sK2(set_union2(powerset(sK5),powerset(sK6)),powerset(set_union2(sK5,sK6))),powerset(sK5))
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f155,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f142,f152,f148]) ).
fof(f156,plain,
( ~ subset(sK2(set_union2(powerset(sK5),powerset(sK6)),powerset(set_union2(sK5,sK6))),sK5)
| ~ spl7_2 ),
inference(resolution,[],[f154,f56]) ).
fof(f187,plain,
! [X2,X0,X1] :
( subset(sK2(X0,powerset(X1)),X2)
| ~ subset(X0,powerset(X1))
| subset(X2,X1) ),
inference(resolution,[],[f82,f62]) ).
fof(f1500,plain,
( ~ subset(set_union2(powerset(sK5),powerset(sK6)),powerset(set_union2(sK5,sK6)))
| subset(sK5,set_union2(sK5,sK6))
| ~ spl7_2 ),
inference(resolution,[],[f187,f156]) ).
fof(f1509,plain,
( subset(sK5,set_union2(sK5,sK6))
| ~ spl7_2 ),
inference(forward_subsumption_resolution,[],[f1500,f64]) ).
fof(f1512,plain,
( $false
| ~ spl7_2 ),
inference(forward_subsumption_resolution,[],[f1509,f63]) ).
fof(f1513,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[],[f1512]) ).
fof(f1514,plain,
( ~ subset(sK2(set_union2(powerset(sK5),powerset(sK6)),powerset(set_union2(sK5,sK6))),sK6)
| ~ spl7_1 ),
inference(resolution,[],[f150,f56]) ).
fof(f1520,plain,
( ~ subset(set_union2(powerset(sK5),powerset(sK6)),powerset(set_union2(sK5,sK6)))
| subset(sK6,set_union2(sK5,sK6))
| ~ spl7_1 ),
inference(resolution,[],[f1514,f187]) ).
fof(f1526,plain,
( subset(sK6,set_union2(sK5,sK6))
| ~ spl7_1 ),
inference(forward_subsumption_resolution,[],[f1520,f64]) ).
fof(f1527,plain,
( $false
| ~ spl7_1 ),
inference(forward_subsumption_resolution,[],[f1526,f70]) ).
fof(f1528,plain,
~ spl7_1,
inference(avatar_contradiction_clause,[],[f1527]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f155]) ).
cnf(s5,plain,
~ spl7_2,
inference(sat_conversion,[],[f1513]) ).
cnf(s6,plain,
~ spl7_1,
inference(sat_conversion,[],[f1528]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s5,s6]) ).
fof(f1529,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET934+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Mon Sep 28 03:17:52 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 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
% 0.14/0.53 % (2962975)Will run a generic schedule for satisfiability detection.
% 0.14/0.53 % (2962991)dis+10_1_sil=32000:sp=arity:random_seed=729090719:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.53 % (2962989)% WARNING: option uhcvi not known.
% 0.14/0.53 % (2962990)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=13798326:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.53 % (2962988)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3280609396_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.53 % (2962989)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=980956104:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.53 % (2962992)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1721552274:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.53 % (2962993)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1968565830:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.53 % (2962994)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1708150538:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.53 % TRYING [1]
% 0.14/0.53 % TRYING [2]
% 0.14/0.53 % TRYING [3]
% 0.14/0.53 % TRYING [4]
% 0.14/0.53 % TRYING [5]
% 0.14/0.53 % TRYING [6]
% 0.14/0.53 % (2962991)Instruction limit reached!
% 0.14/0.53 % (2962991)------------------------------
% 0.14/0.53 % (2962991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.53 % (2962991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.53 % (2962991)CaDiCaL version: 2.1.3
% 0.14/0.53 % (2962991)Termination reason: Instruction limit
% 0.14/0.53 % (2962991)Termination phase: Saturation
% 0.14/0.53 % (2962991)Time elapsed: 0.035 s
% 0.14/0.53 % (2962991)Peak memory usage: 12 MB
% 0.14/0.53 % (2962991)Instructions burned: 106 (million)
% 0.14/0.53 % (2963017)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1620213631:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.14/0.53 % TRYING [1]
% 0.14/0.53 % TRYING [2]
% 0.14/0.53 % TRYING [3]
% 0.14/0.53 % TRYING [4]
% 0.14/0.53 % TRYING [5]
% 0.14/0.53 % (2962989) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2962975-2962989"...
% 0.14/0.53 % (2962989)...printing done.
% 0.14/0.53 % (2962989)Refutation found. Thanks to Tanya!
% 0.14/0.53 % SZS status Theorem for theBenchmark
% 0.14/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.53 % (2962989)------------------------------
% 0.14/0.53 % (2962989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.53 % (2962989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.53 % (2962989)CaDiCaL version: 2.1.3
% 0.14/0.53 % (2962989)Termination reason: Refutation
% 0.14/0.53 % (2962989)Time elapsed: 0.051 s
% 0.14/0.53 % (2962989)Peak memory usage: 13 MB
% 0.14/0.53 % (2962989)Instructions burned: 84 (million)
% 0.14/0.53 % (2962975)Success in time 0.093 s
% 0.14/0.53 % Vampire exiting
%------------------------------------------------------------------------------