TSTP Solution File: SET985+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET985+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 : n028.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 18:22:57 EDT 2022
% Result : Theorem 0.19s 0.56s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 68 ( 13 unt; 0 def)
% Number of atoms : 185 ( 51 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 181 ( 64 ~; 77 |; 23 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 78 ( 60 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f401,plain,
$false,
inference(avatar_sat_refutation,[],[f57,f94,f248,f260,f268,f273,f400]) ).
fof(f400,plain,
( ~ spl10_1
| spl10_9 ),
inference(avatar_contradiction_clause,[],[f399]) ).
fof(f399,plain,
( $false
| ~ spl10_1
| spl10_9 ),
inference(subsumption_resolution,[],[f398,f39]) ).
fof(f39,plain,
~ subset(sK3,sK2),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
( ~ subset(sK3,sK2)
& ( subset(cartesian_product2(sK0,sK3),cartesian_product2(sK1,sK2))
| subset(cartesian_product2(sK3,sK0),cartesian_product2(sK2,sK1)) )
& ~ empty(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f21,f23,f22]) ).
fof(f22,plain,
( ? [X0] :
( ? [X1,X2,X3] :
( ~ subset(X3,X2)
& ( subset(cartesian_product2(X0,X3),cartesian_product2(X1,X2))
| subset(cartesian_product2(X3,X0),cartesian_product2(X2,X1)) ) )
& ~ empty(X0) )
=> ( ? [X3,X2,X1] :
( ~ subset(X3,X2)
& ( subset(cartesian_product2(sK0,X3),cartesian_product2(X1,X2))
| subset(cartesian_product2(X3,sK0),cartesian_product2(X2,X1)) ) )
& ~ empty(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
( ? [X3,X2,X1] :
( ~ subset(X3,X2)
& ( subset(cartesian_product2(sK0,X3),cartesian_product2(X1,X2))
| subset(cartesian_product2(X3,sK0),cartesian_product2(X2,X1)) ) )
=> ( ~ subset(sK3,sK2)
& ( subset(cartesian_product2(sK0,sK3),cartesian_product2(sK1,sK2))
| subset(cartesian_product2(sK3,sK0),cartesian_product2(sK2,sK1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
? [X0] :
( ? [X1,X2,X3] :
( ~ subset(X3,X2)
& ( subset(cartesian_product2(X0,X3),cartesian_product2(X1,X2))
| subset(cartesian_product2(X3,X0),cartesian_product2(X2,X1)) ) )
& ~ empty(X0) ),
inference(rectify,[],[f13]) ).
fof(f13,plain,
? [X0] :
( ? [X3,X1,X2] :
( ~ subset(X2,X1)
& ( subset(cartesian_product2(X0,X2),cartesian_product2(X3,X1))
| subset(cartesian_product2(X2,X0),cartesian_product2(X1,X3)) ) )
& ~ empty(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,plain,
~ ! [X0] :
( ~ empty(X0)
=> ! [X3,X2,X1] :
( ( subset(cartesian_product2(X0,X2),cartesian_product2(X3,X1))
| subset(cartesian_product2(X2,X0),cartesian_product2(X1,X3)) )
=> subset(X2,X1) ) ),
inference(rectify,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ! [X3,X1,X2] :
( ( subset(cartesian_product2(X1,X0),cartesian_product2(X3,X2))
| subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) )
=> subset(X1,X3) ) ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X0] :
( ~ empty(X0)
=> ! [X3,X1,X2] :
( ( subset(cartesian_product2(X1,X0),cartesian_product2(X3,X2))
| subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) )
=> subset(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
fof(f398,plain,
( subset(sK3,sK2)
| ~ spl10_1
| spl10_9 ),
inference(subsumption_resolution,[],[f396,f52]) ).
fof(f52,plain,
( subset(sF8,sF9)
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f50,plain,
( spl10_1
<=> subset(sF8,sF9) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_1])]) ).
fof(f396,plain,
( ~ subset(sF8,sF9)
| subset(sK3,sK2)
| spl10_9 ),
inference(superposition,[],[f383,f47]) ).
fof(f47,plain,
sF9 = cartesian_product2(sK2,sK1),
introduced(function_definition,[]) ).
fof(f383,plain,
( ! [X12,X13] :
( ~ subset(sF8,cartesian_product2(X12,X13))
| subset(sK3,X12) )
| spl10_9 ),
inference(subsumption_resolution,[],[f375,f93]) ).
fof(f93,plain,
( empty_set != sF8
| spl10_9 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f91,plain,
( spl10_9
<=> empty_set = sF8 ),
introduced(avatar_definition,[new_symbols(naming,[spl10_9])]) ).
fof(f375,plain,
! [X12,X13] :
( ~ subset(sF8,cartesian_product2(X12,X13))
| empty_set = sF8
| subset(sK3,X12) ),
inference(superposition,[],[f32,f46]) ).
fof(f46,plain,
cartesian_product2(sK3,sK0) = sF8,
introduced(function_definition,[]) ).
fof(f32,plain,
! [X2,X3,X0,X1] :
( ~ subset(cartesian_product2(X1,X2),cartesian_product2(X3,X0))
| subset(X1,X3)
| empty_set = cartesian_product2(X1,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( ( subset(X1,X3)
& subset(X2,X0) )
| ~ subset(cartesian_product2(X1,X2),cartesian_product2(X3,X0))
| empty_set = cartesian_product2(X1,X2) ),
inference(rectify,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X3,X2] :
( ( subset(X1,X2)
& subset(X3,X0) )
| ~ subset(cartesian_product2(X1,X3),cartesian_product2(X2,X0))
| empty_set = cartesian_product2(X1,X3) ),
inference(flattening,[],[f14]) ).
fof(f14,plain,
! [X2,X3,X1,X0] :
( empty_set = cartesian_product2(X1,X3)
| ( subset(X1,X2)
& subset(X3,X0) )
| ~ subset(cartesian_product2(X1,X3),cartesian_product2(X2,X0)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
! [X2,X3,X1,X0] :
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X0))
=> ( empty_set = cartesian_product2(X1,X3)
| ( subset(X1,X2)
& subset(X3,X0) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X3,X0,X2,X1] :
( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
=> ( ( subset(X0,X2)
& subset(X1,X3) )
| empty_set = cartesian_product2(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
fof(f273,plain,
~ spl10_8,
inference(avatar_contradiction_clause,[],[f272]) ).
fof(f272,plain,
( $false
| ~ spl10_8 ),
inference(subsumption_resolution,[],[f271,f30]) ).
fof(f30,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f271,plain,
( ~ subset(empty_set,sK2)
| ~ spl10_8 ),
inference(backward_demodulation,[],[f39,f89]) ).
fof(f89,plain,
( empty_set = sK3
| ~ spl10_8 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f87,plain,
( spl10_8
<=> empty_set = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl10_8])]) ).
fof(f268,plain,
( spl10_8
| ~ spl10_10
| spl10_7 ),
inference(avatar_split_clause,[],[f267,f83,f96,f87]) ).
fof(f96,plain,
( spl10_10
<=> empty_set = sF6 ),
introduced(avatar_definition,[new_symbols(naming,[spl10_10])]) ).
fof(f83,plain,
( spl10_7
<=> empty_set = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl10_7])]) ).
fof(f267,plain,
( empty_set = sK0
| empty_set != sF6
| empty_set = sK3 ),
inference(superposition,[],[f36,f44]) ).
fof(f44,plain,
sF6 = cartesian_product2(sK0,sK3),
introduced(function_definition,[]) ).
fof(f36,plain,
! [X0,X1] :
( empty_set != cartesian_product2(X1,X0)
| empty_set = X1
| empty_set = X0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( empty_set = X0
| empty_set = X1
| empty_set != cartesian_product2(X1,X0) )
& ( empty_set = cartesian_product2(X1,X0)
| ( empty_set != X0
& empty_set != X1 ) ) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X1,X0] :
( ( empty_set = X1
| empty_set = X0
| empty_set != cartesian_product2(X0,X1) )
& ( empty_set = cartesian_product2(X0,X1)
| ( empty_set != X1
& empty_set != X0 ) ) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
! [X1,X0] :
( ( empty_set = X1
| empty_set = X0
| empty_set != cartesian_product2(X0,X1) )
& ( empty_set = cartesian_product2(X0,X1)
| ( empty_set != X1
& empty_set != X0 ) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( ( empty_set = X1
| empty_set = X0 )
<=> empty_set = cartesian_product2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(f260,plain,
~ spl10_7,
inference(avatar_contradiction_clause,[],[f259]) ).
fof(f259,plain,
( $false
| ~ spl10_7 ),
inference(subsumption_resolution,[],[f255,f29]) ).
fof(f29,plain,
empty(empty_set),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f255,plain,
( ~ empty(empty_set)
| ~ spl10_7 ),
inference(backward_demodulation,[],[f37,f85]) ).
fof(f85,plain,
( empty_set = sK0
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f37,plain,
~ empty(sK0),
inference(cnf_transformation,[],[f24]) ).
fof(f248,plain,
( ~ spl10_2
| spl10_10 ),
inference(avatar_contradiction_clause,[],[f247]) ).
fof(f247,plain,
( $false
| ~ spl10_2
| spl10_10 ),
inference(subsumption_resolution,[],[f246,f39]) ).
fof(f246,plain,
( subset(sK3,sK2)
| ~ spl10_2
| spl10_10 ),
inference(subsumption_resolution,[],[f212,f56]) ).
fof(f56,plain,
( subset(sF6,sF7)
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f54,plain,
( spl10_2
<=> subset(sF6,sF7) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_2])]) ).
fof(f212,plain,
( ~ subset(sF6,sF7)
| subset(sK3,sK2)
| spl10_10 ),
inference(superposition,[],[f115,f45]) ).
fof(f45,plain,
cartesian_product2(sK1,sK2) = sF7,
introduced(function_definition,[]) ).
fof(f115,plain,
( ! [X6,X7] :
( ~ subset(sF6,cartesian_product2(X6,X7))
| subset(sK3,X7) )
| spl10_10 ),
inference(subsumption_resolution,[],[f103,f98]) ).
fof(f98,plain,
( empty_set != sF6
| spl10_10 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f103,plain,
! [X6,X7] :
( subset(sK3,X7)
| empty_set = sF6
| ~ subset(sF6,cartesian_product2(X6,X7)) ),
inference(superposition,[],[f31,f44]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( ~ subset(cartesian_product2(X1,X2),cartesian_product2(X3,X0))
| subset(X2,X0)
| empty_set = cartesian_product2(X1,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f94,plain,
( spl10_7
| spl10_8
| ~ spl10_9 ),
inference(avatar_split_clause,[],[f63,f91,f87,f83]) ).
fof(f63,plain,
( empty_set != sF8
| empty_set = sK3
| empty_set = sK0 ),
inference(superposition,[],[f36,f46]) ).
fof(f57,plain,
( spl10_1
| spl10_2 ),
inference(avatar_split_clause,[],[f48,f54,f50]) ).
fof(f48,plain,
( subset(sF6,sF7)
| subset(sF8,sF9) ),
inference(definition_folding,[],[f38,f47,f46,f45,f44]) ).
fof(f38,plain,
( subset(cartesian_product2(sK0,sK3),cartesian_product2(sK1,sK2))
| subset(cartesian_product2(sK3,sK0),cartesian_product2(sK2,sK1)) ),
inference(cnf_transformation,[],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET985+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 14:42:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.54 % (3348)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.54 % (3330)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.54 % (3330)Refutation not found, incomplete strategy% (3330)------------------------------
% 0.19/0.54 % (3330)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54 % (3330)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54 % (3330)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.54
% 0.19/0.54 % (3330)Memory used [KB]: 5884
% 0.19/0.54 % (3330)Time elapsed: 0.126 s
% 0.19/0.54 % (3330)Instructions burned: 2 (million)
% 0.19/0.54 % (3330)------------------------------
% 0.19/0.54 % (3330)------------------------------
% 0.19/0.54 % (3332)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.55 % (3324)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.55 % (3346)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)
% 0.19/0.55 % (3338)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.55 % (3338)Instruction limit reached!
% 0.19/0.55 % (3338)------------------------------
% 0.19/0.55 % (3338)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55 % (3324)First to succeed.
% 0.19/0.55 % (3338)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.55 % (3338)Termination reason: Unknown
% 0.19/0.55 % (3338)Termination phase: Saturation
% 0.19/0.55
% 0.19/0.55 % (3338)Memory used [KB]: 5884
% 0.19/0.55 % (3338)Time elapsed: 0.140 s
% 0.19/0.55 % (3338)Instructions burned: 3 (million)
% 0.19/0.55 % (3338)------------------------------
% 0.19/0.55 % (3338)------------------------------
% 0.19/0.55 % (3346)Also succeeded, but the first one will report.
% 0.19/0.55 % (3340)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.56 % (3324)Refutation found. Thanks to Tanya!
% 0.19/0.56 % SZS status Theorem for theBenchmark
% 0.19/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.56 % (3324)------------------------------
% 0.19/0.56 % (3324)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.56 % (3324)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.56 % (3324)Termination reason: Refutation
% 0.19/0.56
% 0.19/0.56 % (3324)Memory used [KB]: 6140
% 0.19/0.56 % (3324)Time elapsed: 0.145 s
% 0.19/0.56 % (3324)Instructions burned: 7 (million)
% 0.19/0.56 % (3324)------------------------------
% 0.19/0.56 % (3324)------------------------------
% 0.19/0.56 % (3323)Success in time 0.204 s
%------------------------------------------------------------------------------