TSTP Solution File: SET517-6 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET517-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n027.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 18:24:51 EDT 2022
% Result : Unsatisfiable 1.33s 0.53s
% Output : Refutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 66 ( 18 unt; 0 def)
% Number of atoms : 135 ( 35 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 122 ( 53 ~; 64 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f948,plain,
$false,
inference(avatar_sat_refutation,[],[f390,f862,f881,f904,f943,f947]) ).
fof(f947,plain,
~ spl2_31,
inference(avatar_contradiction_clause,[],[f946]) ).
fof(f946,plain,
( $false
| ~ spl2_31 ),
inference(resolution,[],[f389,f50]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f389,plain,
( ! [X0] : ~ inductive(X0)
| ~ spl2_31 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f388,plain,
( spl2_31
<=> ! [X0] : ~ inductive(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_31])]) ).
fof(f943,plain,
( spl2_80
| ~ spl2_81 ),
inference(avatar_contradiction_clause,[],[f942]) ).
fof(f942,plain,
( $false
| spl2_80
| ~ spl2_81 ),
inference(subsumption_resolution,[],[f937,f189]) ).
fof(f189,plain,
member(x,universal_class),
inference(superposition,[],[f11,f187]) ).
fof(f187,plain,
x = unordered_pair(x,x),
inference(forward_demodulation,[],[f186,f184]) ).
fof(f184,plain,
x = sF1,
inference(definition_folding,[],[f133,f183,f182,f182]) ).
fof(f182,plain,
member_of(x) = sF0,
introduced(function_definition,[]) ).
fof(f183,plain,
sF1 = unordered_pair(sF0,sF0),
introduced(function_definition,[]) ).
fof(f133,plain,
x = unordered_pair(member_of(x),member_of(x)),
inference(definition_unfolding,[],[f113,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f113,axiom,
x = singleton(member_of(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_not_singleton_of_set_1) ).
fof(f186,plain,
sF1 = unordered_pair(x,x),
inference(forward_demodulation,[],[f183,f185]) ).
fof(f185,plain,
x = sF0,
inference(definition_folding,[],[f114,f182]) ).
fof(f114,axiom,
x = member_of(x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_not_singleton_of_set_2) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f937,plain,
( ~ member(x,universal_class)
| spl2_80
| ~ spl2_81 ),
inference(resolution,[],[f935,f652]) ).
fof(f652,plain,
! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(superposition,[],[f24,f640]) ).
fof(f640,plain,
null_class = complement(universal_class),
inference(resolution,[],[f637,f4]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f637,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class ),
inference(duplicate_literal_removal,[],[f627]) ).
fof(f627,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class
| complement(X0) = null_class ),
inference(resolution,[],[f205,f191]) ).
fof(f191,plain,
! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(resolution,[],[f66,f24]) ).
fof(f66,axiom,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f205,plain,
! [X2,X3] :
( member(regular(X2),X3)
| null_class = X2
| ~ subclass(X2,X3) ),
inference(resolution,[],[f1,f66]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f935,plain,
( member(x,null_class)
| spl2_80
| ~ spl2_81 ),
inference(forward_demodulation,[],[f934,f861]) ).
fof(f861,plain,
( x = regular(x)
| ~ spl2_81 ),
inference(avatar_component_clause,[],[f859]) ).
fof(f859,plain,
( spl2_81
<=> x = regular(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_81])]) ).
fof(f934,plain,
( member(regular(x),null_class)
| spl2_80
| ~ spl2_81 ),
inference(subsumption_resolution,[],[f930,f855]) ).
fof(f855,plain,
( null_class != x
| spl2_80 ),
inference(avatar_component_clause,[],[f854]) ).
fof(f854,plain,
( spl2_80
<=> null_class = x ),
introduced(avatar_definition,[new_symbols(naming,[spl2_80])]) ).
fof(f930,plain,
( member(regular(x),null_class)
| null_class = x
| spl2_80
| ~ spl2_81 ),
inference(resolution,[],[f921,f66]) ).
fof(f921,plain,
( ! [X2] :
( ~ member(X2,x)
| member(X2,null_class) )
| spl2_80
| ~ spl2_81 ),
inference(duplicate_literal_removal,[],[f916]) ).
fof(f916,plain,
( ! [X2] :
( ~ member(X2,x)
| ~ member(X2,x)
| member(X2,null_class) )
| spl2_80
| ~ spl2_81 ),
inference(superposition,[],[f23,f913]) ).
fof(f913,plain,
( null_class = intersection(x,x)
| spl2_80
| ~ spl2_81 ),
inference(subsumption_resolution,[],[f909,f855]) ).
fof(f909,plain,
( null_class = x
| null_class = intersection(x,x)
| ~ spl2_81 ),
inference(superposition,[],[f67,f861]) ).
fof(f67,axiom,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f23,axiom,
! [X0,X1,X4] :
( member(X4,intersection(X0,X1))
| ~ member(X4,X0)
| ~ member(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f904,plain,
( ~ spl2_30
| ~ spl2_66 ),
inference(avatar_contradiction_clause,[],[f903]) ).
fof(f903,plain,
( $false
| ~ spl2_30
| ~ spl2_66 ),
inference(subsumption_resolution,[],[f897,f386]) ).
fof(f386,plain,
( member(null_class,universal_class)
| ~ spl2_30 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f384,plain,
( spl2_30
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).
fof(f897,plain,
( ~ member(null_class,universal_class)
| ~ spl2_66 ),
inference(resolution,[],[f731,f652]) ).
fof(f731,plain,
( member(null_class,null_class)
| ~ spl2_66 ),
inference(avatar_component_clause,[],[f730]) ).
fof(f730,plain,
( spl2_66
<=> member(null_class,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_66])]) ).
fof(f881,plain,
( spl2_66
| ~ spl2_80 ),
inference(avatar_split_clause,[],[f874,f854,f730]) ).
fof(f874,plain,
( member(null_class,null_class)
| ~ spl2_80 ),
inference(superposition,[],[f196,f856]) ).
fof(f856,plain,
( null_class = x
| ~ spl2_80 ),
inference(avatar_component_clause,[],[f854]) ).
fof(f196,plain,
member(x,x),
inference(subsumption_resolution,[],[f195,f189]) ).
fof(f195,plain,
( member(x,x)
| ~ member(x,universal_class) ),
inference(superposition,[],[f9,f187]) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f862,plain,
( spl2_81
| spl2_80 ),
inference(avatar_split_clause,[],[f845,f854,f859]) ).
fof(f845,plain,
( null_class = x
| x = regular(x) ),
inference(resolution,[],[f842,f66]) ).
fof(f842,plain,
! [X0] :
( ~ member(X0,x)
| x = X0 ),
inference(duplicate_literal_removal,[],[f841]) ).
fof(f841,plain,
! [X0] :
( x = X0
| x = X0
| ~ member(X0,x) ),
inference(superposition,[],[f8,f187]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| X1 = X2
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f390,plain,
( spl2_30
| spl2_31 ),
inference(avatar_split_clause,[],[f317,f388,f384]) ).
fof(f317,plain,
! [X0] :
( ~ inductive(X0)
| member(null_class,universal_class) ),
inference(resolution,[],[f204,f4]) ).
fof(f204,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| member(null_class,X1)
| ~ inductive(X0) ),
inference(resolution,[],[f1,f47]) ).
fof(f47,axiom,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET517-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n027.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 14:14:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.47 % (2663)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.48 % (2682)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.20/0.52 % (2663)First to succeed.
% 0.20/0.52 % (2659)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.52 % (2659)Instruction limit reached!
% 0.20/0.52 % (2659)------------------------------
% 0.20/0.52 % (2659)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (2659)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (2659)Termination reason: Unknown
% 0.20/0.52 % (2659)Termination phase: Function definition elimination
% 0.20/0.52
% 0.20/0.52 % (2659)Memory used [KB]: 1023
% 0.20/0.52 % (2659)Time elapsed: 0.002 s
% 0.20/0.52 % (2659)Instructions burned: 2 (million)
% 0.20/0.52 % (2659)------------------------------
% 0.20/0.52 % (2659)------------------------------
% 0.20/0.52 % (2653)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.33/0.53 % (2660)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.33/0.53 % (2658)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.33/0.53 % (2663)Refutation found. Thanks to Tanya!
% 1.33/0.53 % SZS status Unsatisfiable for theBenchmark
% 1.33/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 1.33/0.53 % (2663)------------------------------
% 1.33/0.53 % (2663)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.33/0.53 % (2663)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.33/0.53 % (2663)Termination reason: Refutation
% 1.33/0.53
% 1.33/0.53 % (2663)Memory used [KB]: 6268
% 1.33/0.53 % (2663)Time elapsed: 0.092 s
% 1.33/0.53 % (2663)Instructions burned: 30 (million)
% 1.33/0.53 % (2663)------------------------------
% 1.33/0.53 % (2663)------------------------------
% 1.33/0.53 % (2650)Success in time 0.174 s
%------------------------------------------------------------------------------