%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET090-7 : 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 : n008.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 12:40:03 PM UTC 2026
% Result : Unsatisfiable 3.33s 1.39s
% Output : Refutation 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 10 unt; 2 def)
% Number of atoms : 42 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 33 ( 17 ~; 14 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 6 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f143,axiom,
! [X0] :
( member(member_of(singleton(X0)),universal_class)
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_exists1) ).
fof(f144,axiom,
! [X0] :
( ~ member(X0,universal_class)
| singleton(member_of(singleton(X0))) = singleton(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_exists2) ).
fof(f145,plain,
! [X0] :
( ~ member(X0,universal_class)
| singleton(X0) = singleton(member_of(singleton(X0))) ),
inference(reorient_equations,[],[f144]) ).
fof(f148,negated_conjecture,
member(u,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_member_of_singleton_is_unique_1) ).
fof(f149,negated_conjecture,
member_of(singleton(u)) != u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_member_of_singleton_is_unique_2) ).
fof(f150,plain,
u != member_of(singleton(u)),
inference(reorient_equations,[],[f149]) ).
fof(f161,plain,
singleton(u) = singleton(member_of(singleton(u))),
inference(resolution,[],[f145,f148]) ).
fof(f164,plain,
( member(member_of(singleton(u)),singleton(u))
| ~ member(member_of(singleton(u)),universal_class) ),
inference(superposition,[],[f134,f161]) ).
fof(f167,definition,
( spl0_1
<=> member(member_of(singleton(u)),universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f169,plain,
( ~ member(member_of(singleton(u)),universal_class)
| spl0_1 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f171,definition,
( spl0_2
<=> member(member_of(singleton(u)),singleton(u)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f173,plain,
( member(member_of(singleton(u)),singleton(u))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f174,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f164,f171,f167]) ).
fof(f181,plain,
( ~ member(u,universal_class)
| spl0_1 ),
inference(resolution,[],[f169,f143]) ).
fof(f184,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f181,f148]) ).
fof(f185,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f184]) ).
fof(f200,plain,
( u = member_of(singleton(u))
| ~ spl0_2 ),
inference(resolution,[],[f173,f137]) ).
fof(f201,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f200,f150]) ).
fof(f202,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f201]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f174]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f185]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f202]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f203,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET090-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 % Computer : n008.cluster.edu
% 0.11/0.41 % Model : x86_64 x86_64
% 0.11/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.41 % Memory : 8046.5625MB
% 0.11/0.41 % OS : Linux 6.8.0-71-generic
% 0.11/0.41 % CPULimit : 300
% 0.11/0.41 % WCLimit : 300
% 0.11/0.41 % DateTime : Mon Sep 28 00:38:41 UTC 2026
% 0.11/0.42 % CPUTime :
% 0.11/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 3.33/1.39 % (1761786)Input is clausal, will run a generic CNF schedule.
% 3.33/1.39 % (1761792)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3157521807:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.33/1.39 % (1761793)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3289384447:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.33/1.39 % (1761796)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1767671502:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.33/1.39 % (1761791)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=1232485813:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.33/1.39 % (1761794)lrs+10_1_sil=8000:sp=occurrence:random_seed=3350437264:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.33/1.39 % (1761795)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2545440589:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.33/1.39 % (1761794)First to succeed.
% 3.33/1.39 % (1761794)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1761786"
% 3.33/1.39 % (1761797)dis-21_1_sil=8000:lcm=predicate:random_seed=238872125: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)
% 3.33/1.39 % (1761796)Also succeeded, but the first one will report.
% 3.33/1.39 % (1761795)Also succeeded, but the first one will report.
% 3.33/1.39 % (1761797)Instruction limit reached!
% 3.33/1.39 % (1761797)------------------------------
% 3.33/1.39 % (1761797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.39 % (1761797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.39 % (1761797)CaDiCaL version: 2.1.3
% 3.33/1.39 % (1761797)Termination reason: Instruction limit
% 3.33/1.39 % (1761797)Termination phase: Saturation
% 3.33/1.39 % (1761797)Time elapsed: 0.077 s
% 3.33/1.39 % (1761797)Peak memory usage: 89 MB
% 3.33/1.39 % (1761797)Instructions burned: 117 (million)
% 3.33/1.39 % (1761805)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3690642284:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.33/1.39 % (1761805)Refutation not found, incomplete strategy
% 3.33/1.39 % (1761805)------------------------------
% 3.33/1.39 % (1761805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.39 % (1761805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.39 % (1761805)CaDiCaL version: 2.1.3
% 3.33/1.39 % (1761805)Termination reason: Refutation not found, incomplete strategy
% 3.33/1.39 % (1761805)Time elapsed: 0.001 s
% 3.33/1.39 % (1761805)Peak memory usage: 87 MB
% 3.33/1.39 % (1761805)Instructions burned: 1 (million)
% 3.33/1.39 % (1761794)Refutation found. Thanks to Tanya!
% 3.33/1.39 % SZS status Unsatisfiable for theBenchmark
% 3.33/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.33/1.39 % (1761794)------------------------------
% 3.33/1.39 % (1761794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.39 % (1761794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.39 % (1761794)CaDiCaL version: 2.1.3
% 3.33/1.39 % (1761794)Termination reason: Refutation
% 3.33/1.39 % (1761794)Time elapsed: 0.004 s
% 3.33/1.39 % (1761794)Peak memory usage: 89 MB
% 3.33/1.39 % (1761794)Instructions burned: 3 (million)
% 3.33/1.39 % (1761794)------------------------------
% 3.33/1.39 % (1761794)------------------------------
% 3.33/1.39 % (1761786)Success in time 0.41 s
% 3.33/1.39 % Vampire exiting
%------------------------------------------------------------------------------