%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET442-6 : 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 : 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 12:40:58 PM UTC 2026
% Result : Unsatisfiable 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 50 ( 14 unt; 5 def)
% Number of atoms : 94 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 83 ( 39 ~; 39 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f29,axiom,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction2) ).
fof(f63,axiom,
! [X0] :
( ~ function(X0)
| subclass(X0,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).
fof(f122,negated_conjecture,
function(xf),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_restrict_a_function_1) ).
fof(f123,negated_conjecture,
restrict(xf,universal_class,universal_class) != xf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_restrict_a_function_2) ).
fof(f124,plain,
xf != restrict(xf,universal_class,universal_class),
inference(reorient_equations,[],[f123]) ).
fof(f138,plain,
xf != intersection(cross_product(universal_class,universal_class),xf),
inference(definition_unfolding,[],[f124,f29]) ).
fof(f182,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f183,plain,
~ sQ0_eqProxy(xf,intersection(cross_product(universal_class,universal_class),xf)),
inference(equality_proxy_replacement,[],[f138,f182]) ).
fof(f186,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(equality_proxy_replacement,[],[f7,f182]) ).
fof(f210,plain,
subclass(xf,cross_product(universal_class,universal_class)),
inference(resolution,[],[f63,f122]) ).
fof(f221,plain,
! [X0] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,xf) ),
inference(resolution,[],[f1,f210]) ).
fof(f222,plain,
( ~ subclass(intersection(cross_product(universal_class,universal_class),xf),xf)
| ~ subclass(xf,intersection(cross_product(universal_class,universal_class),xf)) ),
inference(resolution,[],[f186,f183]) ).
fof(f225,definition,
( spl1_1
<=> subclass(intersection(cross_product(universal_class,universal_class),xf),xf) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f226,plain,
( ~ subclass(intersection(cross_product(universal_class,universal_class),xf),xf)
| spl1_1 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f228,definition,
( spl1_2
<=> subclass(xf,intersection(cross_product(universal_class,universal_class),xf)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f229,plain,
( ~ subclass(xf,intersection(cross_product(universal_class,universal_class),xf))
| spl1_2 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f231,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f222,f225,f228]) ).
fof(f232,plain,
( ~ member(not_subclass_element(intersection(cross_product(universal_class,universal_class),xf),xf),xf)
| spl1_1 ),
inference(resolution,[],[f226,f3]) ).
fof(f233,plain,
( member(not_subclass_element(intersection(cross_product(universal_class,universal_class),xf),xf),intersection(cross_product(universal_class,universal_class),xf))
| spl1_1 ),
inference(resolution,[],[f226,f2]) ).
fof(f234,plain,
( member(not_subclass_element(intersection(cross_product(universal_class,universal_class),xf),xf),xf)
| spl1_1 ),
inference(resolution,[],[f233,f22]) ).
fof(f236,plain,
( $false
| spl1_1 ),
inference(resolution,[],[f234,f232]) ).
fof(f237,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f236]) ).
fof(f238,plain,
( ~ member(not_subclass_element(xf,intersection(cross_product(universal_class,universal_class),xf)),intersection(cross_product(universal_class,universal_class),xf))
| spl1_2 ),
inference(resolution,[],[f229,f3]) ).
fof(f239,plain,
( member(not_subclass_element(xf,intersection(cross_product(universal_class,universal_class),xf)),xf)
| spl1_2 ),
inference(resolution,[],[f229,f2]) ).
fof(f245,plain,
( ~ member(not_subclass_element(xf,intersection(cross_product(universal_class,universal_class),xf)),xf)
| ~ member(not_subclass_element(xf,intersection(cross_product(universal_class,universal_class),xf)),cross_product(universal_class,universal_class))
| spl1_2 ),
inference(resolution,[],[f23,f238]) ).
fof(f247,definition,
( spl1_3
<=> member(not_subclass_element(xf,intersection(cross_product(universal_class,universal_class),xf)),cross_product(universal_class,universal_class)) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f248,plain,
( ~ member(not_subclass_element(xf,intersection(cross_product(universal_class,universal_class),xf)),cross_product(universal_class,universal_class))
| spl1_3 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f250,definition,
( spl1_4
<=> member(not_subclass_element(xf,intersection(cross_product(universal_class,universal_class),xf)),xf) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f251,plain,
( ~ member(not_subclass_element(xf,intersection(cross_product(universal_class,universal_class),xf)),xf)
| spl1_4 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f252,plain,
( ~ spl1_3
| ~ spl1_4
| spl1_2 ),
inference(avatar_split_clause,[],[f245,f228,f250,f247]) ).
fof(f256,plain,
( ~ member(not_subclass_element(xf,intersection(cross_product(universal_class,universal_class),xf)),xf)
| spl1_3 ),
inference(resolution,[],[f248,f221]) ).
fof(f257,plain,
( ~ spl1_4
| spl1_3 ),
inference(avatar_split_clause,[],[f256,f247,f250]) ).
fof(f258,plain,
( $false
| spl1_2
| spl1_4 ),
inference(resolution,[],[f251,f239]) ).
fof(f259,plain,
( spl1_2
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f258]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f231]) ).
cnf(s3,plain,
spl1_1,
inference(sat_conversion,[],[f237]) ).
cnf(s4,plain,
( spl1_2
| ~ spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f252]) ).
cnf(s5,plain,
( spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f257]) ).
cnf(s6,plain,
( spl1_2
| spl1_4 ),
inference(sat_conversion,[],[f259]) ).
cnf(s7,plain,
~ spl1_2,
inference(rat,[],[s2,s3]) ).
cnf(s8,plain,
spl1_4,
inference(rat,[],[s6,s7]) ).
cnf(s9,plain,
~ spl1_3,
inference(rat,[],[s4,s8,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s5,s8,s9]) ).
fof(f260,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET442-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.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 01:50:09 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.17/1.50 % (1796065)Input is clausal, will run a generic CNF schedule.
% 0.17/1.50 % (1796074)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2041722743:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.17/1.50 % (1796074)Instruction limit reached!
% 0.17/1.50 % (1796074)------------------------------
% 0.17/1.50 % (1796074)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (1796074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (1796074)CaDiCaL version: 2.1.3
% 0.17/1.50 % (1796074)Termination reason: Instruction limit
% 0.17/1.50 % (1796074)Termination phase: Saturation
% 0.17/1.50 % (1796074)Time elapsed: 0.036 s
% 0.17/1.50 % (1796074)Peak memory usage: 88 MB
% 0.17/1.50 % (1796074)Instructions burned: 118 (million)
% 0.17/1.50 % (1796075)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1518161815:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.17/1.50 % (1796073)lrs+10_1_sil=8000:sp=occurrence:random_seed=3093271950:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.17/1.50 % (1796076)dis-21_1_sil=8000:lcm=predicate:random_seed=3488468960: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)
% 0.17/1.50 % (1796071)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=590173956:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.17/1.50 % (1796072)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1786685788:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.17/1.50 % (1796070)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=1172703750:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.17/1.50 % (1796073)Refutation not found, incomplete strategy
% 0.17/1.50 % (1796073)------------------------------
% 0.17/1.50 % (1796073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (1796073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (1796073)CaDiCaL version: 2.1.3
% 0.17/1.50 % (1796073)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (1796073)Time elapsed: 0.003 s
% 0.17/1.50 % (1796073)Peak memory usage: 88 MB
% 0.17/1.50 % (1796073)Instructions burned: 2 (million)
% 0.17/1.50 % (1796076)First to succeed.
% 0.17/1.50 % (1796076)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1796065"
% 0.17/1.50 % (1796078)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=4145084902:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 0.17/1.50 % (1796075)Instruction limit reached!
% 0.17/1.50 % (1796075)------------------------------
% 0.17/1.50 % (1796075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (1796075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (1796075)CaDiCaL version: 2.1.3
% 0.17/1.50 % (1796075)Termination reason: Instruction limit
% 0.17/1.50 % (1796075)Termination phase: Saturation
% 0.17/1.50 % (1796075)Time elapsed: 0.135 s
% 0.17/1.50 % (1796075)Peak memory usage: 90 MB
% 0.17/1.50 % (1796075)Instructions burned: 181 (million)
% 0.17/1.50 % (1796078)Refutation not found, incomplete strategy
% 0.17/1.50 % (1796078)------------------------------
% 0.17/1.50 % (1796078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (1796078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (1796078)CaDiCaL version: 2.1.3
% 0.17/1.50 % (1796078)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (1796078)Time elapsed: 0.002 s
% 0.17/1.50 % (1796078)Peak memory usage: 88 MB
% 0.17/1.50 % (1796078)Instructions burned: 4 (million)
% 0.17/1.50 % (1796073)------------------------------
% 0.17/1.50 % (1796073)------------------------------
% 0.17/1.50 % (1796076)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (1796076)------------------------------
% 0.17/1.50 % (1796076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (1796076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (1796076)CaDiCaL version: 2.1.3
% 0.17/1.50 % (1796076)Termination reason: Refutation
% 0.17/1.50 % (1796076)Time elapsed: 0.006 s
% 0.17/1.50 % (1796076)Peak memory usage: 89 MB
% 0.17/1.50 % (1796076)Instructions burned: 8 (million)
% 0.17/1.50 % (1796076)------------------------------
% 0.17/1.50 % (1796076)------------------------------
% 0.17/1.50 % (1796065)Success in time 0.443 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------