%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM045-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:17:52 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.51s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 55 ( 17 unt; 3 def)
% Number of atoms : 104 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 96 ( 47 ~; 46 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
fof(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f124,axiom,
! [X0,X1] :
( ~ subclass(restrict(X0,X1,X1),complement(identity_relation))
| irreflexive(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',irreflexive2) ).
fof(f176,negated_conjecture,
restrict(intersection(x,identity_relation),y,y) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_irreflexive_class_property7_1) ).
fof(f177,plain,
null_class = restrict(intersection(x,identity_relation),y,y),
inference(reorient_equations,[],[f176]) ).
fof(f178,negated_conjecture,
~ irreflexive(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_irreflexive_class_property7_2) ).
fof(f246,plain,
! [X0,X1] :
( irreflexive(X0,X1)
| ~ subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation)) ),
inference(definition_unfolding,[],[f124,f28]) ).
fof(f269,plain,
null_class = intersection(intersection(x,identity_relation),cross_product(y,y)),
inference(definition_unfolding,[],[f177,f28]) ).
fof(f303,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f1,f4]) ).
fof(f350,plain,
! [X0,X1] :
( ~ member(X0,null_class)
| member(X0,X1)
| null_class = X1 ),
inference(superposition,[],[f21,f70]) ).
fof(f391,plain,
! [X0] :
( ~ member(X0,intersection(x,identity_relation))
| ~ member(X0,cross_product(y,y))
| member(X0,null_class) ),
inference(superposition,[],[f23,f269]) ).
fof(f398,plain,
! [X0] :
( ~ member(X0,cross_product(y,y))
| member(X0,null_class)
| ~ member(X0,identity_relation)
| ~ member(X0,x) ),
inference(resolution,[],[f391,f23]) ).
fof(f452,plain,
~ subclass(intersection(x,cross_product(y,y)),complement(identity_relation)),
inference(resolution,[],[f246,f178]) ).
fof(f456,plain,
~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),complement(identity_relation)),
inference(resolution,[],[f452,f3]) ).
fof(f457,plain,
member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),intersection(x,cross_product(y,y))),
inference(resolution,[],[f452,f2]) ).
fof(f459,plain,
( ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),universal_class)
| member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),identity_relation) ),
inference(resolution,[],[f456,f25]) ).
fof(f461,definition,
( spl0_14
<=> member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),identity_relation) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f463,plain,
( member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),identity_relation)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f465,definition,
( spl0_15
<=> member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f467,plain,
( ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),universal_class)
| spl0_15 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f468,plain,
( spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f459,f465,f461]) ).
fof(f470,plain,
( ! [X0] : ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),X0)
| spl0_15 ),
inference(resolution,[],[f467,f303]) ).
fof(f485,plain,
member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),cross_product(y,y)),
inference(resolution,[],[f457,f22]) ).
fof(f486,plain,
member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),x),
inference(resolution,[],[f457,f21]) ).
fof(f493,plain,
( $false
| spl0_15 ),
inference(forward_subsumption_resolution,[],[f485,f470]) ).
fof(f494,plain,
spl0_15,
inference(avatar_contradiction_clause,[],[f493]) ).
fof(f499,plain,
( member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),null_class)
| ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),identity_relation)
| ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),x) ),
inference(resolution,[],[f485,f398]) ).
fof(f501,plain,
( member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),null_class)
| ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),x)
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f499,f463]) ).
fof(f502,plain,
( member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),null_class)
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f501,f486]) ).
fof(f1280,definition,
( spl0_69
<=> null_class = complement(identity_relation) ),
introduced(definition,[new_symbols(definition,[spl0_69])],[avatar_definition]) ).
fof(f1282,plain,
( null_class = complement(identity_relation)
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f1280]) ).
fof(f1486,plain,
( ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),null_class)
| null_class = complement(identity_relation) ),
inference(resolution,[],[f350,f456]) ).
fof(f1622,plain,
( null_class = complement(identity_relation)
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f1486,f502]) ).
fof(f1671,plain,
( spl0_69
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f1622,f461,f1280]) ).
fof(f1811,plain,
( ~ member(not_subclass_element(intersection(x,cross_product(y,y)),null_class),null_class)
| ~ spl0_69 ),
inference(superposition,[],[f456,f1282]) ).
fof(f1817,plain,
( member(not_subclass_element(intersection(x,cross_product(y,y)),null_class),null_class)
| ~ spl0_14
| ~ spl0_69 ),
inference(superposition,[],[f502,f1282]) ).
fof(f1852,plain,
( $false
| ~ spl0_14
| ~ spl0_69 ),
inference(forward_subsumption_resolution,[],[f1811,f1817]) ).
fof(f1853,plain,
( ~ spl0_14
| ~ spl0_69 ),
inference(avatar_contradiction_clause,[],[f1852]) ).
cnf(s8,plain,
( spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f468]) ).
cnf(s12,plain,
spl0_15,
inference(sat_conversion,[],[f494]) ).
cnf(s80,plain,
( ~ spl0_14
| spl0_69 ),
inference(sat_conversion,[],[f1671]) ).
cnf(s109,plain,
( ~ spl0_14
| ~ spl0_69 ),
inference(sat_conversion,[],[f1853]) ).
cnf(s116,plain,
spl0_14,
inference(rat,[],[s8,s12]) ).
cnf(s117,plain,
~ spl0_69,
inference(rat,[],[s109,s116]) ).
cnf(s118,plain,
$false,
inference(rat,[],[s80,s117,s116]) ).
fof(f1872,plain,
$false,
inference(avatar_sat_refutation,[],[s118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM045-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 % Computer : n008.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 18:42:54 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.51 % (1528561)Will run a generic schedule for satisfiability detection.
% 0.17/0.51 % (1528570)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3083667008:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.51 % (1528567)% WARNING: option uhcvi not known.
% 0.17/0.51 % (1528566)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3486428636_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.51 % (1528567)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=467891839:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.51 % (1528568)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1203613345:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.51 % (1528569)dis+10_1_sil=32000:sp=arity:random_seed=121146231:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.51 % (1528571)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3754445968:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.51 % (1528572)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2381682441:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.51 % (1528570) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1528561-1528570"...
% 0.17/0.51 % (1528570)...printing done.
% 0.17/0.51 % (1528570)Refutation found. Thanks to Tanya!
% 0.17/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.51 % (1528570)------------------------------
% 0.17/0.51 % (1528570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.51 % (1528570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.51 % (1528570)CaDiCaL version: 2.1.3
% 0.17/0.51 % (1528570)Termination reason: Refutation
% 0.17/0.51 % (1528570)Time elapsed: 0.036 s
% 0.17/0.51 % (1528570)Peak memory usage: 14 MB
% 0.17/0.51 % (1528570)Instructions burned: 110 (million)
% 0.17/0.51 % (1528561)Success in time 0.07 s
% 0.17/0.51 % Vampire exiting
%------------------------------------------------------------------------------