%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET083-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 12:43:02 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 13 unt; 2 def)
% Number of atoms : 54 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 18 ~; 19 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f113,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f137,axiom,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f138,axiom,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f139,negated_conjecture,
singleton(x) = singleton(y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_identified_by_element1_1) ).
fof(f140,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_identified_by_element1_2) ).
fof(f141,negated_conjecture,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_identified_by_element1_3) ).
fof(f206,plain,
! [X0,X1] :
( ~ member(X0,unordered_pair(X1,X1))
| X0 = X1 ),
inference(definition_unfolding,[],[f137,f12]) ).
fof(f207,plain,
! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ),
inference(definition_unfolding,[],[f138,f12]) ).
fof(f208,plain,
unordered_pair(x,x) = unordered_pair(y,y),
inference(definition_unfolding,[],[f139,f12,f12]) ).
fof(f250,definition,
( spl0_1
<=> member(y,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f252,plain,
( ~ member(y,universal_class)
| spl0_1 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f254,definition,
( spl0_2
<=> member(y,unordered_pair(x,x)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f256,plain,
( member(y,unordered_pair(x,x))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f258,plain,
( member(y,unordered_pair(x,x))
| ~ member(y,universal_class) ),
inference(superposition,[],[f10,f208]) ).
fof(f292,plain,
( null_class = unordered_pair(y,y)
| spl0_1 ),
inference(resolution,[],[f207,f252]) ).
fof(f293,plain,
( null_class = unordered_pair(x,x)
| spl0_1 ),
inference(superposition,[],[f292,f208]) ).
fof(f323,plain,
( member(x,null_class)
| ~ member(x,universal_class)
| spl0_1 ),
inference(superposition,[],[f9,f293]) ).
fof(f340,plain,
( ~ member(x,universal_class)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f323,f113]) ).
fof(f343,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f340,f140]) ).
fof(f344,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f343]) ).
fof(f345,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f258,f254,f250]) ).
fof(f389,plain,
( x = y
| ~ spl0_2 ),
inference(resolution,[],[f256,f206]) ).
fof(f391,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f389,f141]) ).
fof(f392,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f391]) ).
cnf(s5,plain,
spl0_1,
inference(sat_conversion,[],[f344]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f345]) ).
cnf(s11,plain,
~ spl0_2,
inference(sat_conversion,[],[f392]) ).
cnf(s12,plain,
~ spl0_1,
inference(rat,[],[s6,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s5,s12]) ).
fof(f393,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET083-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n020.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 00:36:20 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.18/0.47 % (3921220)Will run a generic schedule for satisfiability detection.
% 0.18/0.47 % (3921225)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3696098943_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.47 % (3921226)% WARNING: option uhcvi not known.
% 0.18/0.47 % (3921226)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2105575868:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.47 % (3921227)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3951419799:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.47 % (3921228)dis+10_1_sil=32000:sp=arity:random_seed=4050441641:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.47 % (3921230)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1654227352:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.47 % (3921229)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4225831256:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.47 % (3921231)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2641397338:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.47 % (3921228) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3921220-3921228"...
% 0.18/0.47 % (3921226) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3921220-3921226"...
% 0.18/0.47 % (3921230) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3921220-3921230"...
% 0.18/0.47 % (3921229) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3921220-3921229"...
% 0.18/0.47 % (3921226)...printing done.
% 0.18/0.47 % (3921228)...printing done.
% 0.18/0.47 % (3921230)...printing done.
% 0.18/0.47 % (3921228)Refutation found. Thanks to Tanya!
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.47 % (3921228)------------------------------
% 0.18/0.47 % (3921228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.47 % (3921228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.47 % (3921228)CaDiCaL version: 2.1.3
% 0.18/0.47 % (3921228)Termination reason: Refutation
% 0.18/0.47 % (3921228)Time elapsed: 0.008 s
% 0.18/0.47 % (3921228)Peak memory usage: 12 MB
% 0.18/0.47 % (3921228)Instructions burned: 11 (million)
% 0.18/0.47 % (3921220)Success in time 0.044 s
% 0.18/0.47 % Vampire exiting
%------------------------------------------------------------------------------