TSTP Solution File: LCL525+1 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : LCL525+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : n009.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 17:48:37 EDT 2022
% Result : Theorem 0.14s 0.48s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 68 ( 15 unt; 0 def)
% Number of atoms : 178 ( 6 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 179 ( 69 ~; 68 |; 17 &)
% ( 14 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 15 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 41 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f520,plain,
$false,
inference(avatar_sat_refutation,[],[f284,f289,f348,f386,f404,f410,f427,f469,f479,f483,f519]) ).
fof(f519,plain,
( ~ spl2_10
| ~ spl2_11
| ~ spl2_32
| spl2_38
| ~ spl2_42
| ~ spl2_51 ),
inference(avatar_contradiction_clause,[],[f518]) ).
fof(f518,plain,
( $false
| ~ spl2_10
| ~ spl2_11
| ~ spl2_32
| spl2_38
| ~ spl2_42
| ~ spl2_51 ),
inference(subsumption_resolution,[],[f517,f409]) ).
fof(f409,plain,
( ~ is_a_theorem(sK1)
| spl2_38 ),
inference(avatar_component_clause,[],[f407]) ).
fof(f407,plain,
( spl2_38
<=> is_a_theorem(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_38])]) ).
fof(f517,plain,
( is_a_theorem(sK1)
| ~ spl2_10
| ~ spl2_11
| ~ spl2_32
| ~ spl2_42
| ~ spl2_51 ),
inference(subsumption_resolution,[],[f516,f288]) ).
fof(f288,plain,
( is_a_theorem(sK0)
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f286,plain,
( spl2_11
<=> is_a_theorem(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
fof(f516,plain,
( ~ is_a_theorem(sK0)
| is_a_theorem(sK1)
| ~ spl2_10
| ~ spl2_32
| ~ spl2_42
| ~ spl2_51 ),
inference(resolution,[],[f514,f426]) ).
fof(f426,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) )
| ~ spl2_42 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f425,plain,
( spl2_42
<=> ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_42])]) ).
fof(f514,plain,
( is_a_theorem(implies(sK0,sK1))
| ~ spl2_10
| ~ spl2_32
| ~ spl2_42
| ~ spl2_51 ),
inference(resolution,[],[f505,f283]) ).
fof(f283,plain,
( is_a_theorem(strict_implies(sK0,sK1))
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f281,plain,
( spl2_10
<=> is_a_theorem(strict_implies(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
fof(f505,plain,
( ! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) )
| ~ spl2_32
| ~ spl2_42
| ~ spl2_51 ),
inference(superposition,[],[f502,f381]) ).
fof(f381,plain,
( ! [X0,X1] : strict_implies(X1,X0) = necessarily(implies(X1,X0))
| ~ spl2_32 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f380,plain,
( spl2_32
<=> ! [X0,X1] : strict_implies(X1,X0) = necessarily(implies(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_32])]) ).
fof(f502,plain,
( ! [X14] :
( ~ is_a_theorem(necessarily(X14))
| is_a_theorem(X14) )
| ~ spl2_42
| ~ spl2_51 ),
inference(resolution,[],[f426,f464]) ).
fof(f464,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ spl2_51 ),
inference(avatar_component_clause,[],[f463]) ).
fof(f463,plain,
( spl2_51
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_51])]) ).
fof(f483,plain,
spl2_52,
inference(avatar_split_clause,[],[f211,f466]) ).
fof(f466,plain,
( spl2_52
<=> axiom_M ),
introduced(avatar_definition,[new_symbols(naming,[spl2_52])]) ).
fof(f211,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_M) ).
fof(f479,plain,
spl2_41,
inference(avatar_split_clause,[],[f201,f421]) ).
fof(f421,plain,
( spl2_41
<=> modus_ponens ),
introduced(avatar_definition,[new_symbols(naming,[spl2_41])]) ).
fof(f201,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f469,plain,
( spl2_51
| ~ spl2_52 ),
inference(avatar_split_clause,[],[f208,f466,f463]) ).
fof(f208,plain,
! [X0] :
( ~ axiom_M
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
( ~ axiom_M
| ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(ennf_transformation,[],[f123]) ).
fof(f123,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_M) ).
fof(f427,plain,
( ~ spl2_41
| spl2_42 ),
inference(avatar_split_clause,[],[f240,f425,f421]) ).
fof(f240,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| ~ modus_ponens
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f167]) ).
fof(f167,plain,
( ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f166]) ).
fof(f166,plain,
( ! [X1,X0] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f141]) ).
fof(f141,plain,
( modus_ponens
=> ! [X1,X0] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f1,axiom,
( ! [X1,X0] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) )
<=> modus_ponens ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
fof(f410,plain,
( ~ spl2_38
| spl2_9 ),
inference(avatar_split_clause,[],[f191,f277,f407]) ).
fof(f277,plain,
( spl2_9
<=> modus_ponens_strict_implies ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
fof(f191,plain,
( modus_ponens_strict_implies
| ~ is_a_theorem(sK1) ),
inference(cnf_transformation,[],[f177]) ).
fof(f177,plain,
( modus_ponens_strict_implies
| ( is_a_theorem(sK0)
& ~ is_a_theorem(sK1)
& is_a_theorem(strict_implies(sK0,sK1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f175,f176]) ).
fof(f176,plain,
( ? [X0,X1] :
( is_a_theorem(X0)
& ~ is_a_theorem(X1)
& is_a_theorem(strict_implies(X0,X1)) )
=> ( is_a_theorem(sK0)
& ~ is_a_theorem(sK1)
& is_a_theorem(strict_implies(sK0,sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f175,plain,
( modus_ponens_strict_implies
| ? [X0,X1] :
( is_a_theorem(X0)
& ~ is_a_theorem(X1)
& is_a_theorem(strict_implies(X0,X1)) ) ),
inference(rectify,[],[f148]) ).
fof(f148,plain,
( modus_ponens_strict_implies
| ? [X1,X0] :
( is_a_theorem(X1)
& ~ is_a_theorem(X0)
& is_a_theorem(strict_implies(X1,X0)) ) ),
inference(flattening,[],[f147]) ).
fof(f147,plain,
( modus_ponens_strict_implies
| ? [X0,X1] :
( ~ is_a_theorem(X0)
& is_a_theorem(X1)
& is_a_theorem(strict_implies(X1,X0)) ) ),
inference(ennf_transformation,[],[f125]) ).
fof(f125,plain,
( ! [X0,X1] :
( ( is_a_theorem(X1)
& is_a_theorem(strict_implies(X1,X0)) )
=> is_a_theorem(X0) )
=> modus_ponens_strict_implies ),
inference(unused_predicate_definition_removal,[],[f108]) ).
fof(f108,plain,
( ! [X0,X1] :
( ( is_a_theorem(X1)
& is_a_theorem(strict_implies(X1,X0)) )
=> is_a_theorem(X0) )
<=> modus_ponens_strict_implies ),
inference(rectify,[],[f51]) ).
fof(f51,axiom,
( modus_ponens_strict_implies
<=> ! [X1,X0] :
( ( is_a_theorem(strict_implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens_strict_implies) ).
fof(f404,plain,
spl2_33,
inference(avatar_split_clause,[],[f243,f383]) ).
fof(f383,plain,
( spl2_33
<=> op_strict_implies ),
introduced(avatar_definition,[new_symbols(naming,[spl2_33])]) ).
fof(f243,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f386,plain,
( spl2_32
| ~ spl2_33 ),
inference(avatar_split_clause,[],[f232,f383,f380]) ).
fof(f232,plain,
! [X0,X1] :
( ~ op_strict_implies
| strict_implies(X1,X0) = necessarily(implies(X1,X0)) ),
inference(cnf_transformation,[],[f159]) ).
fof(f159,plain,
( ~ op_strict_implies
| ! [X0,X1] : strict_implies(X1,X0) = necessarily(implies(X1,X0)) ),
inference(ennf_transformation,[],[f103]) ).
fof(f103,plain,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X1,X0) = necessarily(implies(X1,X0)) ),
inference(rectify,[],[f75]) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X1,X0] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f348,plain,
~ spl2_9,
inference(avatar_split_clause,[],[f224,f277]) ).
fof(f224,plain,
~ modus_ponens_strict_implies,
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
~ modus_ponens_strict_implies,
inference(flattening,[],[f89]) ).
fof(f89,negated_conjecture,
~ modus_ponens_strict_implies,
inference(negated_conjecture,[],[f88]) ).
fof(f88,conjecture,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
fof(f289,plain,
( spl2_11
| spl2_9 ),
inference(avatar_split_clause,[],[f192,f277,f286]) ).
fof(f192,plain,
( modus_ponens_strict_implies
| is_a_theorem(sK0) ),
inference(cnf_transformation,[],[f177]) ).
fof(f284,plain,
( spl2_9
| spl2_10 ),
inference(avatar_split_clause,[],[f190,f281,f277]) ).
fof(f190,plain,
( is_a_theorem(strict_implies(sK0,sK1))
| modus_ponens_strict_implies ),
inference(cnf_transformation,[],[f177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : LCL525+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.09/0.30 % Computer : n009.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue Aug 30 02:04:05 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.14/0.46 % (26590)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.46 % (26599)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.14/0.47 % (26591)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.47 % (26606)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.14/0.47 % (26591)Instruction limit reached!
% 0.14/0.47 % (26591)------------------------------
% 0.14/0.47 % (26591)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.48 % (26591)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.48 % (26591)Termination reason: Unknown
% 0.14/0.48 % (26591)Termination phase: shuffling
% 0.14/0.48
% 0.14/0.48 % (26591)Memory used [KB]: 1023
% 0.14/0.48 % (26591)Time elapsed: 0.005 s
% 0.14/0.48 % (26591)Instructions burned: 2 (million)
% 0.14/0.48 % (26591)------------------------------
% 0.14/0.48 % (26591)------------------------------
% 0.14/0.48 % (26599)First to succeed.
% 0.14/0.48 % (26590)Instruction limit reached!
% 0.14/0.48 % (26590)------------------------------
% 0.14/0.48 % (26590)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.48 % (26599)Refutation found. Thanks to Tanya!
% 0.14/0.48 % SZS status Theorem for theBenchmark
% 0.14/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.48 % (26599)------------------------------
% 0.14/0.48 % (26599)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.14/0.48 % (26599)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.14/0.48 % (26599)Termination reason: Refutation
% 0.14/0.48
% 0.14/0.48 % (26599)Memory used [KB]: 5756
% 0.14/0.48 % (26599)Time elapsed: 0.098 s
% 0.14/0.48 % (26599)Instructions burned: 6 (million)
% 0.14/0.48 % (26599)------------------------------
% 0.14/0.48 % (26599)------------------------------
% 0.14/0.48 % (26582)Success in time 0.174 s
%------------------------------------------------------------------------------