%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET082-6 : 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 : n007.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 12:40:00 PM UTC 2026
% Result : Unsatisfiable 2.68s 1.33s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 32 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f101,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_is_null_class_1) ).
fof(f102,negated_conjecture,
singleton(x) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_is_null_class_2) ).
fof(f103,plain,
null_class != singleton(x),
inference(reorient_equations,[],[f102]) ).
fof(f140,plain,
! [X0] :
( ~ member(x,X0)
| ~ subclass(X0,universal_class) ),
inference(resolution,[],[f1,f101]) ).
fof(f141,plain,
! [X0] : ~ member(x,X0),
inference(forward_subsumption_resolution,[],[f140,f4]) ).
fof(f285,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f8,f12]) ).
fof(f286,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f285]) ).
fof(f328,plain,
! [X0] :
( regular(singleton(X0)) = X0
| singleton(X0) = null_class ),
inference(resolution,[],[f286,f68]) ).
fof(f470,plain,
! [X0] :
( member(X0,singleton(X0))
| singleton(X0) = null_class
| singleton(X0) = null_class ),
inference(superposition,[],[f68,f328]) ).
fof(f471,plain,
! [X0] :
( member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(duplicate_literal_removal,[],[f470]) ).
fof(f779,plain,
null_class = singleton(x),
inference(resolution,[],[f471,f141]) ).
fof(f781,plain,
$false,
inference(forward_subsumption_resolution,[],[f779,f103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET082-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 00:32:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.68/1.33 % (1924988)Input is clausal, will run a generic CNF schedule.
% 2.68/1.33 % (1924998)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3248643022:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.68/1.33 % (1924998)First to succeed.
% 2.68/1.33 % (1924998)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1924988"
% 2.68/1.33 % (1924996)lrs+10_1_sil=8000:sp=occurrence:random_seed=473965581:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.68/1.33 % (1924997)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4240266296:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.68/1.33 % (1924993)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=2569947524:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.68/1.33 % (1924999)dis-21_1_sil=8000:lcm=predicate:random_seed=1511859310: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)
% 2.68/1.33 % (1924995)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3002373233:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.68/1.33 % (1924994)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1360111190:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.68/1.33 % (1924996)Refutation not found, incomplete strategy
% 2.68/1.33 % (1924996)------------------------------
% 2.68/1.33 % (1924996)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.33 % (1924996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.33 % (1924996)CaDiCaL version: 2.1.3
% 2.68/1.33 % (1924996)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.33 % (1924996)Time elapsed: 0.001 s
% 2.68/1.33 % (1924996)Peak memory usage: 87 MB
% 2.68/1.33 % (1924999)Instruction limit reached!
% 2.68/1.33 % (1924999)------------------------------
% 2.68/1.33 % (1924999)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.33 % (1924999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.33 % (1924999)CaDiCaL version: 2.1.3
% 2.68/1.33 % (1924999)Termination reason: Instruction limit
% 2.68/1.33 % (1924999)Termination phase: Saturation
% 2.68/1.33 % (1924999)Time elapsed: 0.065 s
% 2.68/1.33 % (1924999)Peak memory usage: 89 MB
% 2.68/1.33 % (1924999)Instructions burned: 121 (million)
% 2.68/1.33 % (1924997)Instruction limit reached!
% 2.68/1.33 % (1924997)------------------------------
% 2.68/1.33 % (1924997)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.33 % (1924997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.33 % (1924997)CaDiCaL version: 2.1.3
% 2.68/1.33 % (1924997)Termination reason: Instruction limit
% 2.68/1.33 % (1924997)Termination phase: Saturation
% 2.68/1.33 % (1924997)Time elapsed: 0.067 s
% 2.68/1.33 % (1924997)Peak memory usage: 89 MB
% 2.68/1.33 % (1924997)Instructions burned: 114 (million)
% 2.68/1.33 % (1924998)Refutation found. Thanks to Tanya!
% 2.68/1.33 % SZS status Unsatisfiable for theBenchmark
% 2.68/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.33 % (1924998)------------------------------
% 2.68/1.33 % (1924998)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.33 % (1924998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.33 % (1924998)CaDiCaL version: 2.1.3
% 2.68/1.33 % (1924998)Termination reason: Refutation
% 2.68/1.33 % (1924998)Time elapsed: 0.014 s
% 2.68/1.33 % (1924998)Peak memory usage: 89 MB
% 2.68/1.33 % (1924998)Instructions burned: 31 (million)
% 2.68/1.33 % (1924998)------------------------------
% 2.68/1.33 % (1924998)------------------------------
% 2.68/1.33 % (1924988)Success in time 0.295 s
% 2.68/1.33 % Vampire exiting
%------------------------------------------------------------------------------