%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET188-6 : 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 : n017.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 12:40:27 PM UTC 2026
% Result : Unsatisfiable 3.08s 1.33s
% Output : Refutation 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 79 ( 17 unt; 7 def)
% Number of atoms : 172 ( 11 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 179 ( 86 ~; 86 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 36 !; 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(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f5,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass1) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
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(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f122,negated_conjecture,
intersection(complement(y),x) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subclass_property6_1) ).
fof(f123,plain,
null_class = intersection(complement(y),x),
inference(reorient_equations,[],[f122]) ).
fof(f124,negated_conjecture,
~ subclass(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subclass_property6_2) ).
fof(f125,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f5]) ).
fof(f136,plain,
! [X2,X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),intersection(X1,X2)) ),
inference(resolution,[],[f21,f3]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,X1),X2)
| ~ subclass(X2,X1)
| subclass(X0,X1) ),
inference(resolution,[],[f1,f3]) ).
fof(f282,plain,
! [X0] :
( member(X0,null_class)
| ~ member(X0,x)
| ~ member(X0,complement(y)) ),
inference(superposition,[],[f23,f123]) ).
fof(f595,plain,
! [X0] : ~ member(not_subclass_element(x,y),intersection(y,X0)),
inference(resolution,[],[f136,f124]) ).
fof(f701,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X1,X0),x)
| subclass(X1,X0)
| ~ subclass(null_class,X0)
| ~ member(not_subclass_element(X1,X0),complement(y)) ),
inference(resolution,[],[f144,f282]) ).
fof(f938,definition,
( spl0_44
<=> null_class = y ),
introduced(definition,[new_symbols(definition,[spl0_44])],[avatar_definition]) ).
fof(f939,plain,
( null_class != y
| spl0_44 ),
inference(avatar_component_clause,[],[f938]) ).
fof(f940,plain,
( null_class = y
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f938]) ).
fof(f1099,plain,
( ~ subclass(x,null_class)
| ~ spl0_44 ),
inference(superposition,[],[f124,f940]) ).
fof(f1123,definition,
( spl0_54
<=> member(not_subclass_element(x,null_class),x) ),
introduced(definition,[new_symbols(definition,[spl0_54])],[avatar_definition]) ).
fof(f1124,plain,
( member(not_subclass_element(x,null_class),x)
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f1123]) ).
fof(f1127,definition,
( spl0_55
<=> member(not_subclass_element(x,null_class),complement(null_class)) ),
introduced(definition,[new_symbols(definition,[spl0_55])],[avatar_definition]) ).
fof(f1644,plain,
! [X0] :
( ~ member(not_subclass_element(x,y),X0)
| ~ member(not_subclass_element(x,y),y) ),
inference(resolution,[],[f595,f23]) ).
fof(f1648,plain,
( ~ member(not_subclass_element(x,y),null_class)
| null_class = y ),
inference(superposition,[],[f595,f70]) ).
fof(f1650,plain,
( ~ member(not_subclass_element(x,y),null_class)
| spl0_44 ),
inference(forward_subsumption_resolution,[],[f1648,f939]) ).
fof(f1652,definition,
( spl0_77
<=> member(not_subclass_element(x,y),y) ),
introduced(definition,[new_symbols(definition,[spl0_77])],[avatar_definition]) ).
fof(f1654,plain,
( ~ member(not_subclass_element(x,y),y)
| spl0_77 ),
inference(avatar_component_clause,[],[f1652]) ).
fof(f1656,definition,
( spl0_78
<=> ! [X0] : ~ member(not_subclass_element(x,y),X0) ),
introduced(definition,[new_symbols(definition,[spl0_78])],[avatar_definition]) ).
fof(f1657,plain,
( ! [X0] : ~ member(not_subclass_element(x,y),X0)
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1656]) ).
fof(f1658,plain,
( ~ spl0_77
| spl0_78 ),
inference(avatar_split_clause,[],[f1644,f1656,f1652]) ).
fof(f1663,plain,
( ~ member(not_subclass_element(x,y),x)
| ~ member(not_subclass_element(x,y),complement(y))
| spl0_44 ),
inference(resolution,[],[f1650,f282]) ).
fof(f1668,definition,
( spl0_79
<=> member(not_subclass_element(x,y),complement(y)) ),
introduced(definition,[new_symbols(definition,[spl0_79])],[avatar_definition]) ).
fof(f1669,plain,
( member(not_subclass_element(x,y),complement(y))
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f1668]) ).
fof(f1670,plain,
( ~ member(not_subclass_element(x,y),complement(y))
| spl0_79 ),
inference(avatar_component_clause,[],[f1668]) ).
fof(f1672,definition,
( spl0_80
<=> member(not_subclass_element(x,y),x) ),
introduced(definition,[new_symbols(definition,[spl0_80])],[avatar_definition]) ).
fof(f1673,plain,
( member(not_subclass_element(x,y),x)
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f1672]) ).
fof(f1674,plain,
( ~ member(not_subclass_element(x,y),x)
| spl0_80 ),
inference(avatar_component_clause,[],[f1672]) ).
fof(f1675,plain,
( ~ spl0_79
| ~ spl0_80
| spl0_44 ),
inference(avatar_split_clause,[],[f1663,f938,f1672,f1668]) ).
fof(f1681,plain,
( ~ member(not_subclass_element(x,y),universal_class)
| member(not_subclass_element(x,y),y)
| spl0_79 ),
inference(resolution,[],[f1670,f25]) ).
fof(f1685,plain,
( ~ member(not_subclass_element(x,y),universal_class)
| spl0_77
| spl0_79 ),
inference(forward_subsumption_resolution,[],[f1681,f1654]) ).
fof(f1691,plain,
( ! [X0] :
( ~ member(not_subclass_element(x,y),X0)
| ~ subclass(X0,universal_class) )
| spl0_77
| spl0_79 ),
inference(resolution,[],[f1685,f1]) ).
fof(f1694,plain,
( ! [X0] : ~ member(not_subclass_element(x,y),X0)
| spl0_77
| spl0_79 ),
inference(forward_subsumption_resolution,[],[f1691,f4]) ).
fof(f1695,plain,
( spl0_78
| spl0_77
| spl0_79 ),
inference(avatar_split_clause,[],[f1694,f1668,f1652,f1656]) ).
fof(f1701,plain,
( subclass(x,y)
| ~ spl0_78 ),
inference(resolution,[],[f1657,f2]) ).
fof(f1716,plain,
( $false
| ~ spl0_78 ),
inference(forward_subsumption_resolution,[],[f1701,f124]) ).
fof(f1717,plain,
~ spl0_78,
inference(avatar_contradiction_clause,[],[f1716]) ).
fof(f1725,plain,
( subclass(x,y)
| spl0_80 ),
inference(resolution,[],[f1674,f2]) ).
fof(f1729,plain,
( $false
| spl0_80 ),
inference(forward_subsumption_resolution,[],[f1725,f124]) ).
fof(f1730,plain,
spl0_80,
inference(avatar_contradiction_clause,[],[f1729]) ).
fof(f1918,plain,
( member(not_subclass_element(x,null_class),x)
| ~ spl0_44
| ~ spl0_80 ),
inference(forward_demodulation,[],[f1673,f940]) ).
fof(f1919,plain,
( spl0_54
| ~ spl0_44
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f1918,f1672,f938,f1123]) ).
fof(f1962,plain,
( subclass(x,null_class)
| ~ subclass(null_class,null_class)
| ~ member(not_subclass_element(x,null_class),complement(y))
| ~ spl0_54 ),
inference(resolution,[],[f1124,f701]) ).
fof(f1964,plain,
( ~ subclass(null_class,null_class)
| ~ member(not_subclass_element(x,null_class),complement(y))
| ~ spl0_44
| ~ spl0_54 ),
inference(forward_subsumption_resolution,[],[f1962,f1099]) ).
fof(f1965,plain,
( ~ member(not_subclass_element(x,null_class),complement(y))
| ~ spl0_44
| ~ spl0_54 ),
inference(forward_subsumption_resolution,[],[f1964,f125]) ).
fof(f1966,plain,
( ~ member(not_subclass_element(x,null_class),complement(null_class))
| ~ spl0_44
| ~ spl0_54 ),
inference(forward_demodulation,[],[f1965,f940]) ).
fof(f1967,plain,
( ~ spl0_55
| ~ spl0_44
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f1966,f1123,f938,f1127]) ).
fof(f2184,plain,
( member(not_subclass_element(x,null_class),complement(null_class))
| ~ spl0_44
| ~ spl0_79 ),
inference(forward_demodulation,[],[f1669,f940]) ).
fof(f2185,plain,
( spl0_55
| ~ spl0_44
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f2184,f1668,f938,f1127]) ).
cnf(s53,plain,
( ~ spl0_77
| spl0_78 ),
inference(sat_conversion,[],[f1658]) ).
cnf(s54,plain,
( spl0_44
| ~ spl0_79
| ~ spl0_80 ),
inference(sat_conversion,[],[f1675]) ).
cnf(s55,plain,
( spl0_77
| spl0_78
| spl0_79 ),
inference(sat_conversion,[],[f1695]) ).
cnf(s56,plain,
~ spl0_78,
inference(sat_conversion,[],[f1717]) ).
cnf(s57,plain,
spl0_80,
inference(sat_conversion,[],[f1730]) ).
cnf(s77,plain,
( ~ spl0_44
| spl0_54
| ~ spl0_80 ),
inference(sat_conversion,[],[f1919]) ).
cnf(s79,plain,
( ~ spl0_44
| ~ spl0_54
| ~ spl0_55 ),
inference(sat_conversion,[],[f1967]) ).
cnf(s87,plain,
( ~ spl0_44
| spl0_55
| ~ spl0_79 ),
inference(sat_conversion,[],[f2185]) ).
cnf(s88,plain,
( spl0_77
| spl0_79 ),
inference(rat,[],[s55,s56]) ).
cnf(s89,plain,
( spl0_44
| ~ spl0_79 ),
inference(rat,[],[s54,s57]) ).
cnf(s90,plain,
~ spl0_77,
inference(rat,[],[s53,s56]) ).
cnf(s91,plain,
spl0_79,
inference(rat,[],[s88,s90]) ).
cnf(s92,plain,
spl0_44,
inference(rat,[],[s89,s91]) ).
cnf(s93,plain,
spl0_55,
inference(rat,[],[s87,s91,s92]) ).
cnf(s94,plain,
~ spl0_54,
inference(rat,[],[s79,s93,s92]) ).
cnf(s95,plain,
$false,
inference(rat,[],[s77,s57,s94,s92]) ).
fof(f2186,plain,
$false,
inference(avatar_sat_refutation,[],[s95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET188-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 00:58:20 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 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
% 3.08/1.33 % (3124949)Input is clausal, will run a generic CNF schedule.
% 3.08/1.33 % (3124957)lrs+10_1_sil=8000:sp=occurrence:random_seed=167878927:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.08/1.33 % (3124957)Refutation not found, incomplete strategy
% 3.08/1.33 % (3124957)------------------------------
% 3.08/1.33 % (3124957)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.08/1.33 % (3124957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.08/1.33 % (3124957)CaDiCaL version: 2.1.3
% 3.08/1.33 % (3124957)Termination reason: Refutation not found, incomplete strategy
% 3.08/1.33 % (3124957)Time elapsed: 0.001 s
% 3.08/1.33 % (3124957)Peak memory usage: 88 MB
% 3.08/1.33 % (3124957)Instructions burned: 2 (million)
% 3.08/1.33 % (3124956)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=593652510:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.08/1.33 % (3124960)dis-21_1_sil=8000:lcm=predicate:random_seed=1855744249: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)
% 3.08/1.33 % (3124958)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3953834440:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.08/1.33 % (3124955)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2614252838:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.08/1.33 % (3124954)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=1379473389:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.08/1.33 % (3124959)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=348015580:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.08/1.33 % (3124959)First to succeed.
% 3.08/1.33 % (3124959)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3124949"
% 3.08/1.33 % (3124958)Instruction limit reached!
% 3.08/1.33 % (3124958)------------------------------
% 3.08/1.33 % (3124958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.08/1.33 % (3124958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.08/1.33 % (3124958)CaDiCaL version: 2.1.3
% 3.08/1.33 % (3124958)Termination reason: Instruction limit
% 3.08/1.33 % (3124958)Termination phase: Saturation
% 3.08/1.33 % (3124958)Time elapsed: 0.068 s
% 3.08/1.33 % (3124958)Peak memory usage: 89 MB
% 3.08/1.33 % (3124958)Instructions burned: 115 (million)
% 3.08/1.33 % (3124960)Instruction limit reached!
% 3.08/1.33 % (3124960)------------------------------
% 3.08/1.33 % (3124960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.08/1.33 % (3124960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.08/1.33 % (3124960)CaDiCaL version: 2.1.3
% 3.08/1.33 % (3124960)Termination reason: Instruction limit
% 3.08/1.33 % (3124960)Termination phase: Saturation
% 3.08/1.33 % (3124960)Time elapsed: 0.071 s
% 3.08/1.33 % (3124960)Peak memory usage: 89 MB
% 3.08/1.33 % (3124960)Instructions burned: 117 (million)
% 3.08/1.33 % (3124957)------------------------------
% 3.08/1.33 % (3124957)------------------------------
% 3.08/1.33 % (3124969)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2253681922:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.08/1.33 % (3124968)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=2241676696:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.08/1.33 % (3124970)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3336347276:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.08/1.33 % (3124969)Also succeeded, but the first one will report.
% 3.08/1.33 % (3124959)Refutation found. Thanks to Tanya!
% 3.08/1.33 % SZS status Unsatisfiable for theBenchmark
% 3.08/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 4.10/1.52 % (3124959)------------------------------
% 4.10/1.52 % (3124959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.10/1.52 % (3124959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.10/1.52 % (3124959)CaDiCaL version: 2.1.3
% 4.10/1.52 % (3124959)Termination reason: Refutation
% 4.10/1.52 % (3124959)Time elapsed: 0.065 s
% 4.10/1.52 % (3124959)Peak memory usage: 91 MB
% 4.10/1.52 % (3124959)Instructions burned: 80 (million)
% 4.10/1.52 % (3124959)------------------------------
% 4.10/1.52 % (3124959)------------------------------
% 4.10/1.52 % (3124949)Success in time 0.495 s
% 4.10/1.52 % Vampire exiting
%------------------------------------------------------------------------------