TSTP Solution File: DAT049_1 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : DAT049_1 : TPTP v8.1.0. Released v5.0.0.
% 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 16:04:01 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of formulae : 65 ( 14 unt; 9 typ; 0 def)
% Number of atoms : 112 ( 34 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 105 ( 49 ~; 37 |; 6 &)
% ( 12 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 84 ( 0 atm; 31 fun; 24 num; 29 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 11 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 56 ( 52 !; 4 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
collection: $tType ).
tff(func_def_0,type,
empty: collection ).
tff(func_def_1,type,
add: ( $int * collection ) > collection ).
tff(func_def_2,type,
remove: ( $int * collection ) > collection ).
tff(func_def_3,type,
count: collection > $int ).
tff(func_def_9,type,
sK0: collection ).
tff(func_def_10,type,
sK1: $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(pred_def_4,type,
sP2: $int > $o ).
tff(f130,plain,
$false,
inference(avatar_sat_refutation,[],[f99,f115,f117,f129]) ).
tff(f129,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f128]) ).
tff(f128,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(subsumption_resolution,[],[f127,f97]) ).
tff(f97,plain,
( ~ in(sK1,sK0)
| spl3_2 ),
inference(avatar_component_clause,[],[f96]) ).
tff(f96,plain,
( spl3_2
<=> in(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
tff(f127,plain,
( in(sK1,sK0)
| ~ spl3_1 ),
inference(subsumption_resolution,[],[f110,f94]) ).
tff(f94,plain,
( sP2(count(sK0))
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f92]) ).
tff(f92,plain,
( spl3_1
<=> sP2(count(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
tff(f110,plain,
( ~ sP2(count(sK0))
| in(sK1,sK0) ),
inference(evaluation,[],[f108]) ).
tff(f108,plain,
( in(sK1,sK0)
| ~ sP2($sum(-1,$sum(count(sK0),1))) ),
inference(superposition,[],[f103,f58]) ).
tff(f58,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tff(f43,plain,
! [X0: $int,X1: collection] :
( ( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) )
& ( ~ in(X0,X1)
| ( count(add(X0,X1)) != $sum(count(X1),1) ) ) ),
inference(rectify,[],[f42]) ).
tff(f42,plain,
! [X1: $int,X0: collection] :
( ( ( count(add(X1,X0)) = $sum(count(X0),1) )
| in(X1,X0) )
& ( ~ in(X1,X0)
| ( count(add(X1,X0)) != $sum(count(X0),1) ) ) ),
inference(nnf_transformation,[],[f36]) ).
tff(f36,plain,
! [X1: $int,X0: collection] :
( ( count(add(X1,X0)) = $sum(count(X0),1) )
<=> ~ in(X1,X0) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X14: collection,X13: $int] :
( ( count(add(X13,X14)) = $sum(count(X14),1) )
<=> ~ in(X13,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(f103,plain,
~ sP2($sum(-1,count(add(sK1,sK0)))),
inference(superposition,[],[f90,f17]) ).
tff(f17,plain,
! [X0: $int,X1: $int] : ( $sum(X1,X0) = $sum(X0,X1) ),
introduced(theory_axiom_140,[]) ).
tff(f90,plain,
~ sP2($sum(count(add(sK1,sK0)),-1)),
inference(subsumption_resolution,[],[f88,f74]) ).
tff(f74,plain,
! [X0: collection,X1: $int] : in(X1,add(X1,X0)),
inference(cnf_transformation,[],[f34]) ).
tff(f34,plain,
! [X0: collection,X1: $int] : in(X1,add(X1,X0)),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X2: collection,X1: $int] : in(X1,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
tff(f88,plain,
( ~ in(sK1,add(sK1,sK0))
| ~ sP2($sum(count(add(sK1,sK0)),-1)) ),
inference(superposition,[],[f79,f85]) ).
tff(f85,plain,
! [X0: $int,X1: collection] :
( ( $sum(count(X1),-1) = count(remove(X0,X1)) )
| ~ in(X0,X1) ),
inference(evaluation,[],[f72]) ).
tff(f72,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
| ( $sum(count(X1),$uminus(1)) = count(remove(X0,X1)) ) ),
inference(cnf_transformation,[],[f53]) ).
tff(f53,plain,
! [X0: $int,X1: collection] :
( ( ( $sum(count(X1),$uminus(1)) = count(remove(X0,X1)) )
| ~ in(X0,X1) )
& ( in(X0,X1)
| ( $sum(count(X1),$uminus(1)) != count(remove(X0,X1)) ) ) ),
inference(nnf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: $int,X1: collection] :
( ( $sum(count(X1),$uminus(1)) = count(remove(X0,X1)) )
<=> in(X0,X1) ),
inference(rectify,[],[f15]) ).
tff(f15,plain,
! [X17: $int,X18: collection] :
( in(X17,X18)
<=> ( count(remove(X17,X18)) = $sum(count(X18),$uminus(1)) ) ),
inference(theory_normalization,[],[f10]) ).
tff(f10,axiom,
! [X17: $int,X18: collection] :
( in(X17,X18)
<=> ( count(remove(X17,X18)) = $difference(count(X18),1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
tff(f79,plain,
~ sP2(count(remove(sK1,add(sK1,sK0)))),
introduced(inequality_splitting_name_introduction,[new_symbols(naming,[sP2])]) ).
tff(f117,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f116]) ).
tff(f116,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(subsumption_resolution,[],[f114,f105]) ).
tff(f105,plain,
( ~ sP2($sum(count(sK0),-1))
| ~ spl3_2 ),
inference(subsumption_resolution,[],[f101,f98]) ).
tff(f98,plain,
( in(sK1,sK0)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f96]) ).
tff(f101,plain,
( ~ in(sK1,sK0)
| ~ sP2($sum(count(sK0),-1)) ),
inference(superposition,[],[f90,f70]) ).
tff(f70,plain,
! [X0: collection,X1: $int] :
( ( count(add(X1,X0)) = count(X0) )
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f52]) ).
tff(f52,plain,
! [X0: collection,X1: $int] :
( ( ( count(add(X1,X0)) = count(X0) )
| ~ in(X1,X0) )
& ( in(X1,X0)
| ( count(add(X1,X0)) != count(X0) ) ) ),
inference(rectify,[],[f51]) ).
tff(f51,plain,
! [X1: collection,X0: $int] :
( ( ( count(add(X0,X1)) = count(X1) )
| ~ in(X0,X1) )
& ( in(X0,X1)
| ( count(add(X0,X1)) != count(X1) ) ) ),
inference(nnf_transformation,[],[f37]) ).
tff(f37,plain,
! [X1: collection,X0: $int] :
( ( count(add(X0,X1)) = count(X1) )
<=> in(X0,X1) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X15: $int,X16: collection] :
( in(X15,X16)
<=> ( count(add(X15,X16)) = count(X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
tff(f114,plain,
( sP2($sum(count(sK0),-1))
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f112]) ).
tff(f112,plain,
( spl3_3
<=> sP2($sum(count(sK0),-1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
tff(f115,plain,
( ~ spl3_2
| spl3_3 ),
inference(avatar_split_clause,[],[f86,f112,f96]) ).
tff(f86,plain,
( sP2($sum(count(sK0),-1))
| ~ in(sK1,sK0) ),
inference(superposition,[],[f80,f85]) ).
tff(f80,plain,
sP2(count(remove(sK1,sK0))),
inference(inequality_splitting,[],[f78,f79]) ).
tff(f78,plain,
count(remove(sK1,add(sK1,sK0))) != count(remove(sK1,sK0)),
inference(cnf_transformation,[],[f56]) ).
tff(f56,plain,
count(remove(sK1,add(sK1,sK0))) != count(remove(sK1,sK0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f41,f55]) ).
tff(f55,plain,
( ? [X0: collection,X1: $int] : ( count(remove(X1,add(X1,X0))) != count(remove(X1,X0)) )
=> ( count(remove(sK1,add(sK1,sK0))) != count(remove(sK1,sK0)) ) ),
introduced(choice_axiom,[]) ).
tff(f41,plain,
? [X0: collection,X1: $int] : ( count(remove(X1,add(X1,X0))) != count(remove(X1,X0)) ),
inference(ennf_transformation,[],[f14]) ).
tff(f14,negated_conjecture,
~ ! [X1: $int,X0: collection] : ( count(remove(X1,add(X1,X0))) = count(remove(X1,X0)) ),
inference(negated_conjecture,[],[f13]) ).
tff(f13,conjecture,
! [X1: $int,X0: collection] : ( count(remove(X1,add(X1,X0))) = count(remove(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f99,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f87,f96,f92]) ).
tff(f87,plain,
( in(sK1,sK0)
| sP2(count(sK0)) ),
inference(superposition,[],[f80,f75]) ).
tff(f75,plain,
! [X0: $int,X1: collection] :
( ( count(X1) = count(remove(X0,X1)) )
| in(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tff(f54,plain,
! [X0: $int,X1: collection] :
( ( ~ in(X0,X1)
| ( count(X1) != count(remove(X0,X1)) ) )
& ( ( count(X1) = count(remove(X0,X1)) )
| in(X0,X1) ) ),
inference(nnf_transformation,[],[f29]) ).
tff(f29,plain,
! [X0: $int,X1: collection] :
( ~ in(X0,X1)
<=> ( count(X1) = count(remove(X0,X1)) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X19: $int,X20: collection] :
( ( count(remove(X19,X20)) = count(X20) )
<=> ~ in(X19,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT049=1 : TPTP v8.1.0. Released v5.0.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 29 20:03:15 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.51 % (18782)dis+1011_1:64_drc=off:flr=on:nwc=2.0:sac=on:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.20/0.51 % (18803)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.51 % (18783)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.51 % (18783)Instruction limit reached!
% 0.20/0.51 % (18783)------------------------------
% 0.20/0.51 % (18783)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (18783)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (18783)Termination reason: Unknown
% 0.20/0.51 % (18783)Termination phase: Unused predicate definition removal
% 0.20/0.51
% 0.20/0.51 % (18783)Memory used [KB]: 895
% 0.20/0.51 % (18783)Time elapsed: 0.002 s
% 0.20/0.51 % (18783)Instructions burned: 2 (million)
% 0.20/0.51 % (18783)------------------------------
% 0.20/0.51 % (18783)------------------------------
% 0.20/0.52 % (18795)dis+20_1:12_aac=none:acc=model:awrs=converge:fd=preordered:fsr=off:nicw=on:nwc=3.0:s2a=on:s2agt=16:spb=goal:to=lpo:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.52 % (18795)Instruction limit reached!
% 0.20/0.52 % (18795)------------------------------
% 0.20/0.52 % (18795)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (18795)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (18795)Termination reason: Unknown
% 0.20/0.52 % (18795)Termination phase: Saturation
% 0.20/0.52
% 0.20/0.52 % (18795)Memory used [KB]: 1023
% 0.20/0.52 % (18795)Time elapsed: 0.005 s
% 0.20/0.52 % (18795)Instructions burned: 3 (million)
% 0.20/0.52 % (18795)------------------------------
% 0.20/0.52 % (18795)------------------------------
% 0.20/0.52 % (18803)Refutation not found, incomplete strategy% (18803)------------------------------
% 0.20/0.52 % (18803)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (18803)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (18803)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.52
% 0.20/0.52 % (18803)Memory used [KB]: 5500
% 0.20/0.52 % (18803)Time elapsed: 0.071 s
% 0.20/0.52 % (18803)Instructions burned: 3 (million)
% 0.20/0.52 % (18803)------------------------------
% 0.20/0.52 % (18803)------------------------------
% 0.20/0.52 % (18787)lrs+1010_1:1_bd=off:fd=off:fde=none:ins=3:sac=on:sos=on:spb=goal:to=lpo:i=36:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/36Mi)
% 0.20/0.52 % (18787)First to succeed.
% 0.20/0.52 % (18787)Refutation found. Thanks to Tanya!
% 0.20/0.52 % SZS status Theorem for theBenchmark
% 0.20/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53 % (18787)------------------------------
% 0.20/0.53 % (18787)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (18787)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (18787)Termination reason: Refutation
% 0.20/0.53
% 0.20/0.53 % (18787)Memory used [KB]: 5500
% 0.20/0.53 % (18787)Time elapsed: 0.074 s
% 0.20/0.53 % (18787)Instructions burned: 3 (million)
% 0.20/0.53 % (18787)------------------------------
% 0.20/0.53 % (18787)------------------------------
% 0.20/0.53 % (18779)Success in time 0.171 s
%------------------------------------------------------------------------------