TSTP Solution File: LCL544+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : LCL544+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 : n025.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 17:48:41 EDT 2022
% Result : Theorem 1.35s 0.55s
% Output : Refutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of formulae : 77 ( 21 unt; 0 def)
% Number of atoms : 166 ( 6 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 152 ( 63 ~; 58 |; 2 &)
% ( 17 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 17 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 69 ( 67 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f639,plain,
$false,
inference(avatar_sat_refutation,[],[f270,f286,f295,f304,f313,f314,f315,f330,f333,f348,f637]) ).
fof(f637,plain,
( ~ spl1_6
| ~ spl1_10
| ~ spl1_11
| ~ spl1_15
| spl1_18 ),
inference(avatar_contradiction_clause,[],[f633]) ).
fof(f633,plain,
( $false
| ~ spl1_6
| ~ spl1_10
| ~ spl1_11
| ~ spl1_15
| spl1_18 ),
inference(resolution,[],[f552,f408]) ).
fof(f408,plain,
( ~ is_a_theorem(implies(sK0,and(sK0,sK0)))
| ~ spl1_6
| ~ spl1_11
| spl1_18 ),
inference(resolution,[],[f358,f329]) ).
fof(f329,plain,
( ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0)))
| spl1_18 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f327,plain,
( spl1_18
<=> is_a_theorem(strict_implies(sK0,and(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
fof(f358,plain,
( ! [X4,X5] :
( is_a_theorem(strict_implies(X4,X5))
| ~ is_a_theorem(implies(X4,X5)) )
| ~ spl1_6
| ~ spl1_11 ),
inference(superposition,[],[f290,f269]) ).
fof(f269,plain,
( ! [X0,X1] : strict_implies(X1,X0) = necessarily(implies(X1,X0))
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f268,plain,
( spl1_6
<=> ! [X0,X1] : strict_implies(X1,X0) = necessarily(implies(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
fof(f290,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f289,plain,
( spl1_11
<=> ! [X0] :
( ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
fof(f552,plain,
( ! [X1] : is_a_theorem(implies(X1,and(X1,X1)))
| ~ spl1_10
| ~ spl1_15 ),
inference(resolution,[],[f414,f308]) ).
fof(f308,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,implies(X0,and(X1,X0))))
| ~ spl1_15 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f307,plain,
( spl1_15
<=> ! [X0,X1] : is_a_theorem(implies(X1,implies(X0,and(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
fof(f414,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) )
| ~ spl1_10 ),
inference(resolution,[],[f346,f285]) ).
fof(f285,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f284,plain,
( spl1_10
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
fof(f346,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(subsumption_resolution,[],[f230,f193]) ).
fof(f193,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f230,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f185]) ).
fof(f185,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(rectify,[],[f171]) ).
fof(f171,plain,
( ! [X1,X0] : is_a_theorem(implies(implies(X1,implies(X1,X0)),implies(X1,X0)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f138]) ).
fof(f138,plain,
( implies_2
=> ! [X1,X0] : is_a_theorem(implies(implies(X1,implies(X1,X0)),implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f108]) ).
fof(f108,plain,
( implies_2
<=> ! [X1,X0] : is_a_theorem(implies(implies(X1,implies(X1,X0)),implies(X1,X0))) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
( ! [X1,X0] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
<=> implies_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_2) ).
fof(f348,plain,
~ spl1_17,
inference(avatar_split_clause,[],[f192,f323]) ).
fof(f323,plain,
( spl1_17
<=> axiom_m4 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
fof(f192,plain,
~ axiom_m4,
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
~ axiom_m4,
inference(flattening,[],[f90]) ).
fof(f90,negated_conjecture,
~ axiom_m4,
inference(negated_conjecture,[],[f89]) ).
fof(f89,conjecture,
axiom_m4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
fof(f333,plain,
spl1_12,
inference(avatar_split_clause,[],[f234,f292]) ).
fof(f292,plain,
( spl1_12
<=> necessitation ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
fof(f234,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km4b_necessitation) ).
fof(f330,plain,
( spl1_17
| ~ spl1_18 ),
inference(avatar_split_clause,[],[f205,f327,f323]) ).
fof(f205,plain,
( ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0)))
| axiom_m4 ),
inference(cnf_transformation,[],[f178]) ).
fof(f178,plain,
( axiom_m4
| ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f147,f177]) ).
fof(f177,plain,
( ? [X0] : ~ is_a_theorem(strict_implies(X0,and(X0,X0)))
=> ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))) ),
introduced(choice_axiom,[]) ).
fof(f147,plain,
( axiom_m4
| ? [X0] : ~ is_a_theorem(strict_implies(X0,and(X0,X0))) ),
inference(ennf_transformation,[],[f122]) ).
fof(f122,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
=> axiom_m4 ),
inference(unused_predicate_definition_removal,[],[f66]) ).
fof(f66,axiom,
( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
<=> axiom_m4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m4) ).
fof(f315,plain,
spl1_9,
inference(avatar_split_clause,[],[f200,f280]) ).
fof(f280,plain,
( spl1_9
<=> modus_ponens ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
fof(f200,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f314,plain,
spl1_16,
inference(avatar_split_clause,[],[f206,f310]) ).
fof(f310,plain,
( spl1_16
<=> and_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
fof(f206,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f313,plain,
( spl1_15
| ~ spl1_16 ),
inference(avatar_split_clause,[],[f190,f310,f307]) ).
fof(f190,plain,
! [X0,X1] :
( ~ and_3
| is_a_theorem(implies(X1,implies(X0,and(X1,X0)))) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
( ~ and_3
| ! [X0,X1] : is_a_theorem(implies(X1,implies(X0,and(X1,X0)))) ),
inference(ennf_transformation,[],[f134]) ).
fof(f134,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X1,implies(X0,and(X1,X0)))) ),
inference(unused_predicate_definition_removal,[],[f119]) ).
fof(f119,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,implies(X0,and(X1,X0))))
<=> and_3 ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
( and_3
<=> ! [X1,X0] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_3) ).
fof(f304,plain,
spl1_5,
inference(avatar_split_clause,[],[f214,f264]) ).
fof(f264,plain,
( spl1_5
<=> op_strict_implies ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
fof(f214,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f295,plain,
( spl1_11
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f245,f292,f289]) ).
fof(f245,plain,
! [X0] :
( ~ necessitation
| ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
( ~ necessitation
| ! [X0] :
( ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ) ),
inference(ennf_transformation,[],[f127]) ).
fof(f127,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',necessitation) ).
fof(f286,plain,
( ~ spl1_9
| spl1_10 ),
inference(avatar_split_clause,[],[f242,f284,f280]) ).
fof(f242,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ modus_ponens
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
( ~ modus_ponens
| ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ) ),
inference(flattening,[],[f151]) ).
fof(f151,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f142]) ).
fof(f142,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f270,plain,
( ~ spl1_5
| spl1_6 ),
inference(avatar_split_clause,[],[f237,f268,f264]) ).
fof(f237,plain,
! [X0,X1] :
( strict_implies(X1,X0) = necessarily(implies(X1,X0))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
( ~ op_strict_implies
| ! [X0,X1] : strict_implies(X1,X0) = necessarily(implies(X1,X0)) ),
inference(ennf_transformation,[],[f100]) ).
fof(f100,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/sandbox/benchmark/theBenchmark.p',op_strict_implies) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL544+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % 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 : n025.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 02:16:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50 % (5215)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50 % (5224)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.51 % (5231)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.19/0.51 % (5222)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.52 % (5240)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)
% 0.19/0.52 % (5232)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.53 % (5214)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53 % (5216)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.53 % (5212)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.53 % (5233)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.53 % (5219)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.54 % (5219)Instruction limit reached!
% 0.19/0.54 % (5219)------------------------------
% 0.19/0.54 % (5219)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54 % (5219)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54 % (5219)Termination reason: Unknown
% 0.19/0.54 % (5219)Termination phase: Preprocessing 3
% 0.19/0.54
% 0.19/0.54 % (5219)Memory used [KB]: 1023
% 0.19/0.54 % (5219)Time elapsed: 0.002 s
% 0.19/0.54 % (5219)Instructions burned: 2 (million)
% 0.19/0.54 % (5219)------------------------------
% 0.19/0.54 % (5219)------------------------------
% 0.19/0.54 % (5225)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.54 % (5218)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.54 % (5230)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.35/0.54 % (5220)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)
% 1.35/0.54 % (5232)First to succeed.
% 1.35/0.54 % (5229)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.35/0.54 % (5221)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.35/0.54 % (5235)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.35/0.54 % (5239)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.35/0.54 % (5223)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.35/0.55 % (5232)Refutation found. Thanks to Tanya!
% 1.35/0.55 % SZS status Theorem for theBenchmark
% 1.35/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 1.35/0.55 % (5232)------------------------------
% 1.35/0.55 % (5232)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.35/0.55 % (5232)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.35/0.55 % (5232)Termination reason: Refutation
% 1.35/0.55
% 1.35/0.55 % (5232)Memory used [KB]: 6012
% 1.35/0.55 % (5232)Time elapsed: 0.118 s
% 1.35/0.55 % (5232)Instructions burned: 18 (million)
% 1.35/0.55 % (5232)------------------------------
% 1.35/0.55 % (5232)------------------------------
% 1.35/0.55 % (5210)Success in time 0.194 s
%------------------------------------------------------------------------------