TSTP Solution File: NUM390+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : NUM390+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 17:59:19 EDT 2022
% Result : Theorem 0.15s 0.48s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 12 unt; 0 def)
% Number of atoms : 180 ( 10 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 187 ( 61 ~; 48 |; 56 &)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 82 ( 64 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f241,plain,
$false,
inference(subsumption_resolution,[],[f223,f194]) ).
fof(f194,plain,
~ in(sK2,sK1),
inference(resolution,[],[f131,f168]) ).
fof(f168,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
~ ( in(X1,X0)
& subset(X0,X1) ),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X1,X0] :
~ ( in(X0,X1)
& subset(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
fof(f131,plain,
subset(sK1,sK2),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
( ~ in(sK1,sK3)
& subset(sK1,sK2)
& ordinal(sK3)
& in(sK2,sK3)
& ordinal(sK2)
& epsilon_transitive(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f61,f86,f85,f84]) ).
fof(f84,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X0,X2)
& subset(X0,X1)
& ordinal(X2)
& in(X1,X2) )
& ordinal(X1) )
& epsilon_transitive(X0) )
=> ( ? [X1] :
( ? [X2] :
( ~ in(sK1,X2)
& subset(sK1,X1)
& ordinal(X2)
& in(X1,X2) )
& ordinal(X1) )
& epsilon_transitive(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
( ? [X1] :
( ? [X2] :
( ~ in(sK1,X2)
& subset(sK1,X1)
& ordinal(X2)
& in(X1,X2) )
& ordinal(X1) )
=> ( ? [X2] :
( ~ in(sK1,X2)
& subset(sK1,sK2)
& ordinal(X2)
& in(sK2,X2) )
& ordinal(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
( ? [X2] :
( ~ in(sK1,X2)
& subset(sK1,sK2)
& ordinal(X2)
& in(sK2,X2) )
=> ( ~ in(sK1,sK3)
& subset(sK1,sK2)
& ordinal(sK3)
& in(sK2,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X0,X2)
& subset(X0,X1)
& ordinal(X2)
& in(X1,X2) )
& ordinal(X1) )
& epsilon_transitive(X0) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X0,X2)
& subset(X0,X1)
& in(X1,X2)
& ordinal(X2) )
& ordinal(X1) )
& epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( ( subset(X0,X1)
& in(X1,X2) )
=> in(X0,X2) ) ) ) ),
inference(negated_conjecture,[],[f30]) ).
fof(f30,conjecture,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( ( subset(X0,X1)
& in(X1,X2) )
=> in(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_ordinal1) ).
fof(f223,plain,
in(sK2,sK1),
inference(backward_demodulation,[],[f129,f220]) ).
fof(f220,plain,
sK3 = sK1,
inference(subsumption_resolution,[],[f219,f132]) ).
fof(f132,plain,
~ in(sK1,sK3),
inference(cnf_transformation,[],[f87]) ).
fof(f219,plain,
( in(sK1,sK3)
| sK3 = sK1 ),
inference(subsumption_resolution,[],[f218,f127]) ).
fof(f127,plain,
epsilon_transitive(sK1),
inference(cnf_transformation,[],[f87]) ).
fof(f218,plain,
( ~ epsilon_transitive(sK1)
| in(sK1,sK3)
| sK3 = sK1 ),
inference(subsumption_resolution,[],[f216,f130]) ).
fof(f130,plain,
ordinal(sK3),
inference(cnf_transformation,[],[f87]) ).
fof(f216,plain,
( sK3 = sK1
| ~ ordinal(sK3)
| ~ epsilon_transitive(sK1)
| in(sK1,sK3) ),
inference(resolution,[],[f206,f151]) ).
fof(f151,plain,
! [X0,X1] :
( ~ proper_subset(X0,X1)
| ~ ordinal(X1)
| ~ epsilon_transitive(X0)
| in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ~ proper_subset(X0,X1)
| ~ ordinal(X1)
| in(X0,X1) )
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ( proper_subset(X0,X1)
=> in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(f206,plain,
( proper_subset(sK1,sK3)
| sK3 = sK1 ),
inference(resolution,[],[f204,f142]) ).
fof(f142,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| X0 = X1
| proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| proper_subset(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f68]) ).
fof(f68,plain,
! [X1,X0] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,plain,
! [X1,X0] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f9,axiom,
! [X1,X0] :
( ( X0 != X1
& subset(X0,X1) )
<=> proper_subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f204,plain,
subset(sK1,sK3),
inference(resolution,[],[f193,f196]) ).
fof(f196,plain,
subset(sK2,sK3),
inference(subsumption_resolution,[],[f187,f184]) ).
fof(f184,plain,
epsilon_transitive(sK3),
inference(resolution,[],[f130,f166]) ).
fof(f166,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ~ ordinal(X0)
| ( epsilon_transitive(X0)
& epsilon_connected(X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_transitive(X0)
& epsilon_connected(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f187,plain,
( subset(sK2,sK3)
| ~ epsilon_transitive(sK3) ),
inference(resolution,[],[f129,f133]) ).
fof(f133,plain,
! [X2,X0] :
( ~ in(X2,X0)
| subset(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK4(X0),X0)
& in(sK4(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f89,f90]) ).
fof(f90,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) )
=> ( ~ subset(sK4(X0),X0)
& in(sK4(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f193,plain,
! [X0] :
( ~ subset(sK2,X0)
| subset(sK1,X0) ),
inference(resolution,[],[f131,f138]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X2)
| subset(X1,X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ subset(X1,X0)
| subset(X1,X2)
| ~ subset(X0,X2) ),
inference(rectify,[],[f73]) ).
fof(f73,plain,
! [X1,X0,X2] :
( ~ subset(X0,X1)
| subset(X0,X2)
| ~ subset(X1,X2) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0,X2,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X2,X1] :
( ( subset(X0,X1)
& subset(X1,X2) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f129,plain,
in(sK2,sK3),
inference(cnf_transformation,[],[f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.10 % Problem : NUM390+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.10/0.30 % Computer : n007.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Aug 30 06:21:45 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.15/0.46 % (15338)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.15/0.47 % (15330)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.47 % (15320)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.15/0.47 % (15338)First to succeed.
% 0.15/0.47 % (15320)Refutation not found, incomplete strategy% (15320)------------------------------
% 0.15/0.47 % (15320)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.48 % (15337)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.15/0.48 % (15320)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.48 % (15320)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.48
% 0.15/0.48 % (15320)Memory used [KB]: 1535
% 0.15/0.48 % (15320)Time elapsed: 0.113 s
% 0.15/0.48 % (15320)Instructions burned: 6 (million)
% 0.15/0.48 % (15320)------------------------------
% 0.15/0.48 % (15320)------------------------------
% 0.15/0.48 % (15322)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.15/0.48 % (15338)Refutation found. Thanks to Tanya!
% 0.15/0.48 % SZS status Theorem for theBenchmark
% 0.15/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48 % (15338)------------------------------
% 0.15/0.48 % (15338)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.48 % (15338)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.48 % (15338)Termination reason: Refutation
% 0.15/0.48
% 0.15/0.48 % (15338)Memory used [KB]: 1535
% 0.15/0.48 % (15338)Time elapsed: 0.064 s
% 0.15/0.48 % (15338)Instructions burned: 5 (million)
% 0.15/0.48 % (15338)------------------------------
% 0.15/0.48 % (15338)------------------------------
% 0.15/0.48 % (15314)Success in time 0.17 s
%------------------------------------------------------------------------------