%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET083-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:40:01 PM UTC 2026
% Result : Unsatisfiable 2.29s 0.99s
% Output : Refutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 10 unt; 2 def)
% Number of atoms : 45 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 15 ~; 16 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 5 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f113,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f134,axiom,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_in_its_singleton) ).
fof(f137,axiom,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f138,axiom,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f139,negated_conjecture,
singleton(x) = singleton(y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_identified_by_element1_1) ).
fof(f140,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_identified_by_element1_2) ).
fof(f141,negated_conjecture,
x != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_identified_by_element1_3) ).
fof(f188,plain,
( member(y,singleton(x))
| ~ member(y,universal_class) ),
inference(superposition,[],[f134,f139]) ).
fof(f190,definition,
( spl0_3
<=> member(y,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f192,plain,
( ~ member(y,universal_class)
| spl0_3 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f194,definition,
( spl0_4
<=> member(y,singleton(x)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f196,plain,
( member(y,singleton(x))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f197,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f188,f194,f190]) ).
fof(f204,plain,
( null_class = singleton(y)
| spl0_3 ),
inference(resolution,[],[f138,f192]) ).
fof(f205,plain,
( null_class = singleton(x)
| spl0_3 ),
inference(superposition,[],[f204,f139]) ).
fof(f226,plain,
( member(x,null_class)
| ~ member(x,universal_class)
| spl0_3 ),
inference(superposition,[],[f134,f205]) ).
fof(f233,plain,
( ~ member(x,universal_class)
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f226,f113]) ).
fof(f234,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f233,f140]) ).
fof(f235,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f234]) ).
fof(f245,plain,
( x = y
| ~ spl0_4 ),
inference(resolution,[],[f196,f137]) ).
fof(f246,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f245,f141]) ).
fof(f247,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f246]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f197]) ).
cnf(s4,plain,
spl0_3,
inference(sat_conversion,[],[f235]) ).
cnf(s6,plain,
~ spl0_4,
inference(sat_conversion,[],[f247]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s2,s6,s4]) ).
fof(f248,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET083-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.36 % Computer : n003.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 28 00:36:12 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.29/0.99 % (1082835)Input is clausal, will run a generic CNF schedule.
% 2.29/0.99 % (1082845)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2355586383:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.29/0.99 % (1082845)First to succeed.
% 2.29/0.99 % (1082845)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1082835"
% 2.29/0.99 % (1082846)dis-21_1_sil=8000:lcm=predicate:random_seed=1366930808:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.29/0.99 % (1082843)lrs+10_1_sil=8000:sp=occurrence:random_seed=1471350611:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.29/0.99 % (1082841)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1990318180:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.29/0.99 % (1082842)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1254061305:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.29/0.99 % (1082840)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3309618699:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.29/0.99 % (1082844)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4097237557:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.29/0.99 % (1082843)Also succeeded, but the first one will report.
% 2.29/0.99 % (1082844)Also succeeded, but the first one will report.
% 2.29/0.99 % (1082846)Instruction limit reached!
% 2.29/0.99 % (1082846)------------------------------
% 2.29/0.99 % (1082846)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.29/0.99 % (1082846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.29/0.99 % (1082846)CaDiCaL version: 2.1.3
% 2.29/0.99 % (1082846)Termination reason: Instruction limit
% 2.29/0.99 % (1082846)Termination phase: Saturation
% 2.29/0.99 % (1082846)Time elapsed: 0.077 s
% 2.29/0.99 % (1082846)Peak memory usage: 88 MB
% 2.29/0.99 % (1082846)Instructions burned: 118 (million)
% 2.29/0.99 % (1082845)Refutation found. Thanks to Tanya!
% 2.29/0.99 % SZS status Unsatisfiable for theBenchmark
% 2.29/0.99 % SZS output start Proof for theBenchmark
% See solution above
% 2.29/0.99 % (1082845)------------------------------
% 2.29/0.99 % (1082845)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.29/0.99 % (1082845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.29/0.99 % (1082845)CaDiCaL version: 2.1.3
% 2.29/0.99 % (1082845)Termination reason: Refutation
% 2.29/0.99 % (1082845)Time elapsed: 0.004 s
% 2.29/0.99 % (1082845)Peak memory usage: 90 MB
% 2.29/0.99 % (1082845)Instructions burned: 8 (million)
% 2.29/0.99 % (1082845)------------------------------
% 2.29/0.99 % (1082845)------------------------------
% 2.29/0.99 % (1082835)Success in time 0.289 s
% 2.29/0.99 % Vampire exiting
%------------------------------------------------------------------------------