%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET144-6 : 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 : n014.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 12:40:17 PM UTC 2026
% Result : Unsatisfiable 0.18s 1.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 57 ( 8 unt; 7 def)
% Number of atoms : 119 ( 3 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 100 ( 38 ~; 55 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
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(f122,negated_conjecture,
intersection(x,y) != intersection(y,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity_of_intersection_1) ).
fof(f168,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f169,plain,
~ sQ0_eqProxy(intersection(x,y),intersection(y,x)),
inference(equality_proxy_replacement,[],[f122,f168]) ).
fof(f170,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(equality_proxy_replacement,[],[f7,f168]) ).
fof(f196,plain,
( ~ subclass(intersection(y,x),intersection(x,y))
| ~ subclass(intersection(x,y),intersection(y,x)) ),
inference(resolution,[],[f170,f169]) ).
fof(f199,definition,
( spl1_1
<=> subclass(intersection(y,x),intersection(x,y)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f200,plain,
( ~ subclass(intersection(y,x),intersection(x,y))
| spl1_1 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f202,definition,
( spl1_2
<=> subclass(intersection(x,y),intersection(y,x)) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f203,plain,
( ~ subclass(intersection(x,y),intersection(y,x))
| spl1_2 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f205,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f196,f199,f202]) ).
fof(f206,plain,
( ~ member(not_subclass_element(intersection(y,x),intersection(x,y)),intersection(x,y))
| spl1_1 ),
inference(resolution,[],[f200,f3]) ).
fof(f207,plain,
( member(not_subclass_element(intersection(y,x),intersection(x,y)),intersection(y,x))
| spl1_1 ),
inference(resolution,[],[f200,f2]) ).
fof(f208,plain,
( member(not_subclass_element(intersection(y,x),intersection(x,y)),x)
| spl1_1 ),
inference(resolution,[],[f207,f22]) ).
fof(f209,plain,
( member(not_subclass_element(intersection(y,x),intersection(x,y)),y)
| spl1_1 ),
inference(resolution,[],[f207,f21]) ).
fof(f214,plain,
( ~ member(not_subclass_element(intersection(y,x),intersection(x,y)),y)
| ~ member(not_subclass_element(intersection(y,x),intersection(x,y)),x)
| spl1_1 ),
inference(resolution,[],[f23,f206]) ).
fof(f216,definition,
( spl1_3
<=> member(not_subclass_element(intersection(y,x),intersection(x,y)),x) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f217,plain,
( ~ member(not_subclass_element(intersection(y,x),intersection(x,y)),x)
| spl1_3 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f219,definition,
( spl1_4
<=> member(not_subclass_element(intersection(y,x),intersection(x,y)),y) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f220,plain,
( ~ member(not_subclass_element(intersection(y,x),intersection(x,y)),y)
| spl1_4 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f221,plain,
( ~ spl1_3
| ~ spl1_4
| spl1_1 ),
inference(avatar_split_clause,[],[f214,f199,f219,f216]) ).
fof(f222,plain,
( $false
| spl1_1
| spl1_3 ),
inference(resolution,[],[f217,f208]) ).
fof(f223,plain,
( spl1_1
| spl1_3 ),
inference(avatar_contradiction_clause,[],[f222]) ).
fof(f224,plain,
( $false
| spl1_1
| spl1_4 ),
inference(resolution,[],[f220,f209]) ).
fof(f225,plain,
( spl1_1
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f224]) ).
fof(f226,plain,
( ~ member(not_subclass_element(intersection(x,y),intersection(y,x)),intersection(y,x))
| spl1_2 ),
inference(resolution,[],[f203,f3]) ).
fof(f227,plain,
( member(not_subclass_element(intersection(x,y),intersection(y,x)),intersection(x,y))
| spl1_2 ),
inference(resolution,[],[f203,f2]) ).
fof(f228,plain,
( ~ member(not_subclass_element(intersection(x,y),intersection(y,x)),x)
| ~ member(not_subclass_element(intersection(x,y),intersection(y,x)),y)
| spl1_2 ),
inference(resolution,[],[f226,f23]) ).
fof(f230,definition,
( spl1_5
<=> member(not_subclass_element(intersection(x,y),intersection(y,x)),y) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f231,plain,
( ~ member(not_subclass_element(intersection(x,y),intersection(y,x)),y)
| spl1_5 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f233,definition,
( spl1_6
<=> member(not_subclass_element(intersection(x,y),intersection(y,x)),x) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f234,plain,
( ~ member(not_subclass_element(intersection(x,y),intersection(y,x)),x)
| spl1_6 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f235,plain,
( ~ spl1_5
| ~ spl1_6
| spl1_2 ),
inference(avatar_split_clause,[],[f228,f202,f233,f230]) ).
fof(f236,plain,
( member(not_subclass_element(intersection(x,y),intersection(y,x)),y)
| spl1_2 ),
inference(resolution,[],[f227,f22]) ).
fof(f237,plain,
( member(not_subclass_element(intersection(x,y),intersection(y,x)),x)
| spl1_2 ),
inference(resolution,[],[f227,f21]) ).
fof(f238,plain,
( $false
| spl1_2
| spl1_5 ),
inference(resolution,[],[f236,f231]) ).
fof(f239,plain,
( spl1_2
| spl1_5 ),
inference(avatar_contradiction_clause,[],[f238]) ).
fof(f240,plain,
( $false
| spl1_2
| spl1_6 ),
inference(resolution,[],[f237,f234]) ).
fof(f241,plain,
( spl1_2
| spl1_6 ),
inference(avatar_contradiction_clause,[],[f240]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f205]) ).
cnf(s3,plain,
( spl1_1
| ~ spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f221]) ).
cnf(s4,plain,
( spl1_1
| spl1_3 ),
inference(sat_conversion,[],[f223]) ).
cnf(s5,plain,
( spl1_1
| spl1_4 ),
inference(sat_conversion,[],[f225]) ).
cnf(s6,plain,
( spl1_2
| ~ spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f235]) ).
cnf(s7,plain,
( spl1_2
| spl1_5 ),
inference(sat_conversion,[],[f239]) ).
cnf(s8,plain,
( spl1_2
| spl1_6 ),
inference(sat_conversion,[],[f241]) ).
cnf(s9,plain,
spl1_1,
inference(rat,[],[s3,s4,s5]) ).
cnf(s10,plain,
~ spl1_2,
inference(rat,[],[s2,s9]) ).
cnf(s11,plain,
spl1_6,
inference(rat,[],[s8,s10]) ).
cnf(s12,plain,
spl1_5,
inference(rat,[],[s7,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s6,s11,s12,s10]) ).
fof(f242,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET144-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n014.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 00:54:01 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.18/1.51 % (1330519)Input is clausal, will run a generic CNF schedule.
% 0.18/1.51 % (1330614)lrs+10_1_sil=8000:sp=occurrence:random_seed=3293899815:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.18/1.51 % (1330614)Refutation not found, incomplete strategy
% 0.18/1.51 % (1330614)------------------------------
% 0.18/1.51 % (1330614)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (1330614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (1330614)CaDiCaL version: 2.1.3
% 0.18/1.51 % (1330614)Termination reason: Refutation not found, incomplete strategy
% 0.18/1.51 % (1330614)Time elapsed: 0.001 s
% 0.18/1.51 % (1330614)Peak memory usage: 88 MB
% 0.18/1.51 % (1330613)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4163834636:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.18/1.51 % (1330612)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3191914647:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.18/1.51 % (1330611)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=1836720601:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.18/1.51 % (1330615)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1341449084:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.18/1.51 % (1330617)dis-21_1_sil=8000:lcm=predicate:random_seed=133690558: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)
% 0.18/1.51 % (1330615)Refutation not found, incomplete strategy
% 0.18/1.51 % (1330615)------------------------------
% 0.18/1.51 % (1330615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (1330615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (1330615)CaDiCaL version: 2.1.3
% 0.18/1.51 % (1330615)Termination reason: Refutation not found, incomplete strategy
% 0.18/1.51 % (1330615)Time elapsed: 0.002 s
% 0.18/1.51 % (1330615)Peak memory usage: 87 MB
% 0.18/1.51 % (1330617)First to succeed.
% 0.18/1.51 % (1330617)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1330519"
% 0.18/1.51 % (1330616)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3469056814:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.18/1.51 % (1330614)------------------------------
% 0.18/1.51 % (1330614)------------------------------
% 0.18/1.51 % (1330616)Instruction limit reached!
% 0.18/1.51 % (1330616)------------------------------
% 0.18/1.51 % (1330616)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (1330616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (1330616)CaDiCaL version: 2.1.3
% 0.18/1.51 % (1330616)Termination reason: Instruction limit
% 0.18/1.51 % (1330616)Termination phase: Saturation
% 0.18/1.51 % (1330616)Time elapsed: 0.135 s
% 0.18/1.51 % (1330616)Peak memory usage: 90 MB
% 0.18/1.51 % (1330616)Instructions burned: 181 (million)
% 0.18/1.51 % (1330690)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=1314828922:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.18/1.51 % (1330690)Refutation not found, incomplete strategy
% 0.18/1.51 % (1330690)------------------------------
% 0.18/1.51 % (1330690)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (1330690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (1330690)CaDiCaL version: 2.1.3
% 0.18/1.51 % (1330690)Termination reason: Refutation not found, incomplete strategy
% 0.18/1.51 % (1330690)Time elapsed: 0.002 s
% 0.18/1.51 % (1330690)Peak memory usage: 88 MB
% 0.18/1.51 % (1330690)Instructions burned: 2 (million)
% 0.18/1.51 % (1330615)------------------------------
% 0.18/1.51 % (1330615)------------------------------
% 0.18/1.51 % (1330617)Refutation found. Thanks to Tanya!
% 0.18/1.51 % SZS status Unsatisfiable for theBenchmark
% 0.18/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.51 % (1330617)------------------------------
% 0.18/1.51 % (1330617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (1330617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (1330617)CaDiCaL version: 2.1.3
% 0.18/1.51 % (1330617)Termination reason: Refutation
% 0.18/1.51 % (1330617)Time elapsed: 0.005 s
% 0.18/1.51 % (1330617)Peak memory usage: 89 MB
% 0.18/1.51 % (1330617)Instructions burned: 7 (million)
% 0.18/1.51 % (1330617)------------------------------
% 0.18/1.51 % (1330617)------------------------------
% 0.18/1.51 % (1330519)Success in time 0.443 s
% 0.18/1.51 % Vampire exiting
%------------------------------------------------------------------------------