%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET244-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:40:36 PM UTC 2026
% Result : Unsatisfiable 3.50s 1.38s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 48 ( 12 unt; 5 def)
% Number of atoms : 93 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 79 ( 34 ~; 40 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 26 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
fof(f29,axiom,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).
fof(f122,negated_conjecture,
restrict(universal_class,x,y) != cross_product(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_restriction_with_universal_class_1) ).
fof(f136,plain,
cross_product(x,y) != intersection(cross_product(x,y),universal_class),
inference(definition_unfolding,[],[f122,f29]) ).
fof(f180,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f181,plain,
~ sQ0_eqProxy(cross_product(x,y),intersection(cross_product(x,y),universal_class)),
inference(equality_proxy_replacement,[],[f136,f180]) ).
fof(f182,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(equality_proxy_replacement,[],[f7,f180]) ).
fof(f209,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f1,f4]) ).
fof(f218,plain,
( ~ subclass(intersection(cross_product(x,y),universal_class),cross_product(x,y))
| ~ subclass(cross_product(x,y),intersection(cross_product(x,y),universal_class)) ),
inference(resolution,[],[f182,f181]) ).
fof(f221,definition,
( spl1_1
<=> subclass(intersection(cross_product(x,y),universal_class),cross_product(x,y)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f222,plain,
( ~ subclass(intersection(cross_product(x,y),universal_class),cross_product(x,y))
| spl1_1 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f224,definition,
( spl1_2
<=> subclass(cross_product(x,y),intersection(cross_product(x,y),universal_class)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f225,plain,
( ~ subclass(cross_product(x,y),intersection(cross_product(x,y),universal_class))
| spl1_2 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f227,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f218,f221,f224]) ).
fof(f228,plain,
( ~ member(not_subclass_element(intersection(cross_product(x,y),universal_class),cross_product(x,y)),cross_product(x,y))
| spl1_1 ),
inference(resolution,[],[f222,f3]) ).
fof(f229,plain,
( member(not_subclass_element(intersection(cross_product(x,y),universal_class),cross_product(x,y)),intersection(cross_product(x,y),universal_class))
| spl1_1 ),
inference(resolution,[],[f222,f2]) ).
fof(f231,plain,
( member(not_subclass_element(intersection(cross_product(x,y),universal_class),cross_product(x,y)),cross_product(x,y))
| spl1_1 ),
inference(resolution,[],[f229,f21]) ).
fof(f232,plain,
( $false
| spl1_1 ),
inference(resolution,[],[f231,f228]) ).
fof(f233,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f232]) ).
fof(f234,plain,
( ~ member(not_subclass_element(cross_product(x,y),intersection(cross_product(x,y),universal_class)),intersection(cross_product(x,y),universal_class))
| spl1_2 ),
inference(resolution,[],[f225,f3]) ).
fof(f235,plain,
( member(not_subclass_element(cross_product(x,y),intersection(cross_product(x,y),universal_class)),cross_product(x,y))
| spl1_2 ),
inference(resolution,[],[f225,f2]) ).
fof(f241,plain,
( ~ member(not_subclass_element(cross_product(x,y),intersection(cross_product(x,y),universal_class)),universal_class)
| ~ member(not_subclass_element(cross_product(x,y),intersection(cross_product(x,y),universal_class)),cross_product(x,y))
| spl1_2 ),
inference(resolution,[],[f23,f234]) ).
fof(f243,definition,
( spl1_3
<=> member(not_subclass_element(cross_product(x,y),intersection(cross_product(x,y),universal_class)),cross_product(x,y)) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f244,plain,
( ~ member(not_subclass_element(cross_product(x,y),intersection(cross_product(x,y),universal_class)),cross_product(x,y))
| spl1_3 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f246,definition,
( spl1_4
<=> member(not_subclass_element(cross_product(x,y),intersection(cross_product(x,y),universal_class)),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f247,plain,
( ~ member(not_subclass_element(cross_product(x,y),intersection(cross_product(x,y),universal_class)),universal_class)
| spl1_4 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f248,plain,
( ~ spl1_3
| ~ spl1_4
| spl1_2 ),
inference(avatar_split_clause,[],[f241,f224,f246,f243]) ).
fof(f249,plain,
( $false
| spl1_2
| spl1_3 ),
inference(resolution,[],[f244,f235]) ).
fof(f250,plain,
( spl1_2
| spl1_3 ),
inference(avatar_contradiction_clause,[],[f249]) ).
fof(f251,plain,
( ! [X0] : ~ member(not_subclass_element(cross_product(x,y),intersection(cross_product(x,y),universal_class)),X0)
| spl1_4 ),
inference(resolution,[],[f247,f209]) ).
fof(f252,plain,
( $false
| spl1_2
| spl1_4 ),
inference(resolution,[],[f251,f235]) ).
fof(f261,plain,
( spl1_2
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f252]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f227]) ).
cnf(s3,plain,
spl1_1,
inference(sat_conversion,[],[f233]) ).
cnf(s4,plain,
( spl1_2
| ~ spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f248]) ).
cnf(s5,plain,
( spl1_2
| spl1_3 ),
inference(sat_conversion,[],[f250]) ).
cnf(s6,plain,
( spl1_2
| spl1_4 ),
inference(sat_conversion,[],[f261]) ).
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,[],[s5,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s4,s8,s9,s7]) ).
fof(f262,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET244-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 01:12:22 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.50/1.38 % (4057329)Input is clausal, will run a generic CNF schedule.
% 3.50/1.38 % (4057336)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2036315072:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.50/1.38 % (4057337)lrs+10_1_sil=8000:sp=occurrence:random_seed=601568988:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.50/1.38 % (4057338)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3965552657:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.50/1.38 % (4057334)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=3090988272:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.50/1.38 % (4057335)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2199974055:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.50/1.38 % (4057340)dis-21_1_sil=8000:lcm=predicate:random_seed=1179149606: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)
% 3.50/1.38 % (4057339)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2373470978:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.50/1.38 % (4057337)Refutation not found, incomplete strategy
% 3.50/1.38 % (4057337)------------------------------
% 3.50/1.38 % (4057337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (4057337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (4057337)CaDiCaL version: 2.1.3
% 3.50/1.38 % (4057337)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.38 % (4057337)Time elapsed: 0.002 s
% 3.50/1.38 % (4057337)Peak memory usage: 88 MB
% 3.50/1.38 % (4057337)Instructions burned: 1 (million)
% 3.50/1.38 % (4057340)First to succeed.
% 3.50/1.38 % (4057340)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4057329"
% 3.50/1.38 % (4057338)Instruction limit reached!
% 3.50/1.38 % (4057338)------------------------------
% 3.50/1.38 % (4057338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (4057338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (4057338)CaDiCaL version: 2.1.3
% 3.50/1.38 % (4057338)Termination reason: Instruction limit
% 3.50/1.38 % (4057338)Termination phase: Saturation
% 3.50/1.38 % (4057338)Time elapsed: 0.067 s
% 3.50/1.38 % (4057338)Peak memory usage: 88 MB
% 3.50/1.38 % (4057338)Instructions burned: 114 (million)
% 3.50/1.38 % (4057339)Instruction limit reached!
% 3.50/1.38 % (4057339)------------------------------
% 3.50/1.38 % (4057339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (4057339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (4057339)CaDiCaL version: 2.1.3
% 3.50/1.38 % (4057339)Termination reason: Instruction limit
% 3.50/1.38 % (4057339)Termination phase: Saturation
% 3.50/1.38 % (4057339)Time elapsed: 0.135 s
% 3.50/1.38 % (4057339)Peak memory usage: 91 MB
% 3.50/1.38 % (4057339)Instructions burned: 181 (million)
% 3.50/1.38 % (4057348)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=663394921:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.50/1.38 % (4057348)Refutation not found, incomplete strategy
% 3.50/1.38 % (4057348)------------------------------
% 3.50/1.38 % (4057348)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (4057348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (4057348)CaDiCaL version: 2.1.3
% 3.50/1.38 % (4057348)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.38 % (4057348)Time elapsed: 0.002 s
% 3.50/1.38 % (4057348)Peak memory usage: 88 MB
% 3.50/1.38 % (4057348)Instructions burned: 2 (million)
% 3.50/1.38 % (4057337)------------------------------
% 3.50/1.38 % (4057337)------------------------------
% 3.50/1.38 % (4057340)Refutation found. Thanks to Tanya!
% 3.50/1.38 % SZS status Unsatisfiable for theBenchmark
% 3.50/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.38 % (4057340)------------------------------
% 3.50/1.38 % (4057340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.38 % (4057340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.38 % (4057340)CaDiCaL version: 2.1.3
% 3.50/1.38 % (4057340)Termination reason: Refutation
% 3.50/1.38 % (4057340)Time elapsed: 0.006 s
% 3.50/1.38 % (4057340)Peak memory usage: 89 MB
% 3.50/1.38 % (4057340)Instructions burned: 8 (million)
% 3.50/1.38 % (4057340)------------------------------
% 3.50/1.38 % (4057340)------------------------------
% 3.50/1.38 % (4057329)Success in time 0.433 s
% 3.50/1.38 % Vampire exiting
%------------------------------------------------------------------------------