%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET964+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:45:06 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 70 ( 14 unt; 4 def)
% Number of atoms : 185 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 206 ( 91 ~; 84 |; 22 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn 108 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f13,conjecture,
! [X0,X1,X2] :
~ ( X0 != empty_set
& ( subset(cartesian_product2(X1,X0),cartesian_product2(X2,X0))
| subset(cartesian_product2(X0,X1),cartesian_product2(X0,X2)) )
& ~ subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_zfmisc_1) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( X0 != empty_set
& ( subset(cartesian_product2(X1,X0),cartesian_product2(X2,X0))
| subset(cartesian_product2(X0,X1),cartesian_product2(X0,X2)) )
& ~ subset(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f18,plain,
? [X0,X1,X2] :
( X0 != empty_set
& ( subset(cartesian_product2(X1,X0),cartesian_product2(X2,X0))
| subset(cartesian_product2(X0,X1),cartesian_product2(X0,X2)) )
& ~ subset(X1,X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f19,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f20,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0] :
( ( X0 = empty_set
| in(sK0(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f20]) ).
fof(f25,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f26,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f26]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f28]) ).
fof(f32,plain,
( empty_set != sK9
& ( subset(cartesian_product2(sK10,sK9),cartesian_product2(sK11,sK9))
| subset(cartesian_product2(sK9,sK10),cartesian_product2(sK9,sK11)) )
& ~ subset(sK10,sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11)],[f18]) ).
fof(f34,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f36,plain,
! [X0] :
( in(sK0(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f21]) ).
fof(f45,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
! [X0,X1] :
( in(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f29]) ).
fof(f57,plain,
~ subset(sK10,sK11),
inference(cnf_transformation,[],[f32]) ).
fof(f58,plain,
( subset(cartesian_product2(sK10,sK9),cartesian_product2(sK11,sK9))
| subset(cartesian_product2(sK9,sK10),cartesian_product2(sK9,sK11)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f59,plain,
empty_set != sK9,
inference(cnf_transformation,[],[f32]) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f53,f48]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f52,f48]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f51,f48]) ).
fof(f75,definition,
( spl12_1
<=> subset(cartesian_product2(sK9,sK10),cartesian_product2(sK9,sK11)) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f77,plain,
( subset(cartesian_product2(sK9,sK10),cartesian_product2(sK9,sK11))
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl12_2
<=> subset(cartesian_product2(sK10,sK9),cartesian_product2(sK11,sK9)) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f81,plain,
( subset(cartesian_product2(sK10,sK9),cartesian_product2(sK11,sK9))
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f58,f79,f75]) ).
fof(f92,plain,
( ! [X0] :
( ~ in(X0,cartesian_product2(sK10,sK9))
| in(X0,cartesian_product2(sK11,sK9)) )
| ~ spl12_2 ),
inference(resolution,[],[f45,f81]) ).
fof(f117,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(forward_demodulation,[],[f66,f34]) ).
fof(f118,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(forward_demodulation,[],[f67,f34]) ).
fof(f130,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(forward_demodulation,[],[f65,f34]) ).
fof(f138,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK11,sK9))
| ~ in(X1,sK9)
| ~ in(X0,sK10) )
| ~ spl12_2 ),
inference(resolution,[],[f130,f92]) ).
fof(f146,definition,
( spl12_5
<=> ! [X1] : ~ in(X1,sK9) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f147,plain,
( ! [X1] : ~ in(X1,sK9)
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f183,plain,
( ! [X0,X1] :
( ~ in(X0,sK9)
| ~ in(X1,sK10)
| in(X1,sK11) )
| ~ spl12_2 ),
inference(resolution,[],[f138,f117]) ).
fof(f189,definition,
( spl12_7
<=> ! [X1] :
( ~ in(X1,sK10)
| in(X1,sK11) ) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
fof(f190,plain,
( ! [X1] :
( ~ in(X1,sK10)
| in(X1,sK11) )
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f191,plain,
( spl12_7
| spl12_5
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f183,f79,f146,f189]) ).
fof(f193,plain,
( empty_set = sK9
| ~ spl12_5 ),
inference(resolution,[],[f147,f36]) ).
fof(f199,plain,
( $false
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f193,f59]) ).
fof(f200,plain,
~ spl12_5,
inference(avatar_contradiction_clause,[],[f199]) ).
fof(f274,plain,
( ! [X0] :
( in(sK6(sK10,X0),sK11)
| subset(sK10,X0) )
| ~ spl12_7 ),
inference(resolution,[],[f190,f46]) ).
fof(f280,plain,
( subset(sK10,sK11)
| subset(sK10,sK11)
| ~ spl12_7 ),
inference(resolution,[],[f274,f47]) ).
fof(f282,plain,
( subset(sK10,sK11)
| ~ spl12_7 ),
inference(duplicate_literal_removal,[],[f280]) ).
fof(f283,plain,
( $false
| ~ spl12_7 ),
inference(forward_subsumption_resolution,[],[f282,f57]) ).
fof(f284,plain,
~ spl12_7,
inference(avatar_contradiction_clause,[],[f283]) ).
fof(f285,plain,
( ! [X0] :
( ~ in(X0,cartesian_product2(sK9,sK10))
| in(X0,cartesian_product2(sK9,sK11)) )
| ~ spl12_1 ),
inference(resolution,[],[f77,f45]) ).
fof(f302,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK9,sK11))
| ~ in(X0,sK9)
| ~ in(X1,sK10) )
| ~ spl12_1 ),
inference(resolution,[],[f285,f130]) ).
fof(f325,plain,
( ! [X0,X1] :
( ~ in(X0,sK9)
| ~ in(X1,sK10)
| in(X1,sK11) )
| ~ spl12_1 ),
inference(resolution,[],[f302,f118]) ).
fof(f331,plain,
( spl12_7
| spl12_5
| ~ spl12_1 ),
inference(avatar_split_clause,[],[f325,f75,f146,f189]) ).
cnf(s1,plain,
( spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f82]) ).
cnf(s4,plain,
( ~ spl12_2
| spl12_5
| spl12_7 ),
inference(sat_conversion,[],[f191]) ).
cnf(s5,plain,
~ spl12_5,
inference(sat_conversion,[],[f200]) ).
cnf(s9,plain,
~ spl12_7,
inference(sat_conversion,[],[f284]) ).
cnf(s13,plain,
( ~ spl12_1
| spl12_5
| spl12_7 ),
inference(sat_conversion,[],[f331]) ).
cnf(s15,plain,
~ spl12_1,
inference(rat,[],[s13,s9,s5]) ).
cnf(s17,plain,
~ spl12_2,
inference(rat,[],[s4,s9,s5]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s17,s15]) ).
fof(f332,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET964+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n004.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 03:16:22 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.17/0.47 % (4116329)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (4116338)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2963659710:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (4116335)% WARNING: option uhcvi not known.
% 0.17/0.47 % (4116334)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1339561128_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (4116335)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2615281127:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (4116336)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4116548279:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (4116337)dis+10_1_sil=32000:sp=arity:random_seed=2153362774:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (4116340)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3286330354:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (4116339)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4014222072:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % (4116337) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4116329-4116337"...
% 0.17/0.47 % (4116337)...printing done.
% 0.17/0.47 % (4116337)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (4116337)------------------------------
% 0.17/0.47 % (4116337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (4116337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (4116337)CaDiCaL version: 2.1.3
% 0.17/0.47 % (4116337)Termination reason: Refutation
% 0.17/0.47 % (4116337)Time elapsed: 0.012 s
% 0.17/0.47 % (4116337)Peak memory usage: 12 MB
% 0.17/0.47 % (4116337)Instructions burned: 15 (million)
% 0.17/0.47 % (4116329)Success in time 0.044 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------