TSTP Solution File: DAT047_1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : DAT047_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 : n002.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 16:04:00 EDT 2022
% Result : Theorem 0.18s 0.52s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 65 ( 13 unt; 7 typ; 0 def)
% Number of atoms : 140 ( 46 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 139 ( 57 ~; 53 |; 16 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 144 ( 0 atm; 27 fun; 79 num; 38 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 4 usr; 6 con; 0-2 aty)
% Number of variables : 66 ( 66 !; 0 ?; 66 :)
% 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(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(pred_def_4,type,
sP0: $int > $o ).
tff(f139,plain,
$false,
inference(avatar_sat_refutation,[],[f102,f127,f138]) ).
tff(f138,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f137]) ).
tff(f137,plain,
( $false
| ~ spl1_2 ),
inference(subsumption_resolution,[],[f136,f55]) ).
tff(f55,plain,
! [X0: $int] : ~ in(X0,empty),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: $int] : ~ in(X0,empty),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
tff(f136,plain,
( in(5,empty)
| ~ spl1_2 ),
inference(evaluation,[],[f135]) ).
tff(f135,plain,
( ( 5 = 3 )
| in(5,empty)
| ~ spl1_2 ),
inference(resolution,[],[f128,f65]) ).
tff(f65,plain,
! [X2: collection,X0: $int,X1: $int] :
( ~ in(X1,add(X0,X2))
| ( X0 = X1 )
| in(X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
tff(f46,plain,
! [X0: $int,X1: $int,X2: collection] :
( ( in(X1,add(X0,X2))
| ( ( X0 != X1 )
& ~ in(X1,X2) ) )
& ( ( X0 = X1 )
| in(X1,X2)
| ~ in(X1,add(X0,X2)) ) ),
inference(flattening,[],[f45]) ).
tff(f45,plain,
! [X0: $int,X1: $int,X2: collection] :
( ( in(X1,add(X0,X2))
| ( ( X0 != X1 )
& ~ in(X1,X2) ) )
& ( ( X0 = X1 )
| in(X1,X2)
| ~ in(X1,add(X0,X2)) ) ),
inference(nnf_transformation,[],[f29]) ).
tff(f29,plain,
! [X0: $int,X1: $int,X2: collection] :
( in(X1,add(X0,X2))
<=> ( ( X0 = X1 )
| in(X1,X2) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X7: $int,X5: $int,X6: collection] :
( ( ( X5 = X7 )
| in(X5,X6) )
<=> in(X5,add(X7,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
tff(f128,plain,
( in(5,add(3,empty))
| ~ spl1_2 ),
inference(resolution,[],[f92,f75]) ).
tff(f75,plain,
! [X2: collection,X0: $int,X1: $int] :
( ~ in(X0,remove(X1,X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f54]) ).
tff(f54,plain,
! [X0: $int,X1: $int,X2: collection] :
( ( in(X0,remove(X1,X2))
| ~ in(X0,X2)
| ( X0 = X1 ) )
& ( ( in(X0,X2)
& ( X0 != X1 ) )
| ~ in(X0,remove(X1,X2)) ) ),
inference(rectify,[],[f53]) ).
tff(f53,plain,
! [X1: $int,X2: $int,X0: collection] :
( ( in(X1,remove(X2,X0))
| ~ in(X1,X0)
| ( X1 = X2 ) )
& ( ( in(X1,X0)
& ( X1 != X2 ) )
| ~ in(X1,remove(X2,X0)) ) ),
inference(flattening,[],[f52]) ).
tff(f52,plain,
! [X1: $int,X2: $int,X0: collection] :
( ( in(X1,remove(X2,X0))
| ~ in(X1,X0)
| ( X1 = X2 ) )
& ( ( in(X1,X0)
& ( X1 != X2 ) )
| ~ in(X1,remove(X2,X0)) ) ),
inference(nnf_transformation,[],[f38]) ).
tff(f38,plain,
! [X1: $int,X2: $int,X0: collection] :
( in(X1,remove(X2,X0))
<=> ( in(X1,X0)
& ( X1 != X2 ) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X9: collection,X8: $int,X10: $int] :
( ( in(X8,X9)
& ( X8 != X10 ) )
<=> in(X8,remove(X10,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
tff(f92,plain,
( in(5,remove(3,add(3,empty)))
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f91]) ).
tff(f91,plain,
( spl1_2
<=> in(5,remove(3,add(3,empty))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
tff(f127,plain,
spl1_3,
inference(avatar_contradiction_clause,[],[f126]) ).
tff(f126,plain,
( $false
| spl1_3 ),
inference(subsumption_resolution,[],[f125,f78]) ).
tff(f78,plain,
sP0(1),
inference(inequality_splitting,[],[f57,f77]) ).
tff(f77,plain,
~ sP0(count(add(5,remove(3,add(3,empty))))),
introduced(inequality_splitting_name_introduction,[new_symbols(naming,[sP0])]) ).
tff(f57,plain,
1 != count(add(5,remove(3,add(3,empty)))),
inference(cnf_transformation,[],[f36]) ).
tff(f36,plain,
1 != count(add(5,remove(3,add(3,empty)))),
inference(flattening,[],[f14]) ).
tff(f14,negated_conjecture,
( ( ~ 1 )
= count(add(5,remove(3,add(3,empty)))) ),
inference(negated_conjecture,[],[f13]) ).
tff(f13,conjecture,
1 = count(add(5,remove(3,add(3,empty)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f125,plain,
( ~ sP0(1)
| spl1_3 ),
inference(evaluation,[],[f122]) ).
tff(f122,plain,
( ~ sP0($sum(0,1))
| spl1_3 ),
inference(superposition,[],[f117,f79]) ).
tff(f79,plain,
0 = count(empty),
inference(equality_resolution,[],[f64]) ).
tff(f64,plain,
! [X0: collection] :
( ( 0 = count(X0) )
| ( empty != X0 ) ),
inference(cnf_transformation,[],[f44]) ).
tff(f44,plain,
! [X0: collection] :
( ( ( 0 = count(X0) )
| ( empty != X0 ) )
& ( ( empty = X0 )
| ( 0 != count(X0) ) ) ),
inference(nnf_transformation,[],[f30]) ).
tff(f30,plain,
! [X0: collection] :
( ( 0 = count(X0) )
<=> ( empty = X0 ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X12: collection] :
( ( 0 = count(X12) )
<=> ( empty = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
tff(f117,plain,
( ~ sP0($sum(count(empty),1))
| spl1_3 ),
inference(subsumption_resolution,[],[f116,f55]) ).
tff(f116,plain,
( ~ sP0($sum(count(empty),1))
| in(3,empty)
| spl1_3 ),
inference(superposition,[],[f114,f69]) ).
tff(f69,plain,
! [X0: collection,X1: $int] :
( ( $sum(count(X0),1) = count(add(X1,X0)) )
| in(X1,X0) ),
inference(cnf_transformation,[],[f49]) ).
tff(f49,plain,
! [X0: collection,X1: $int] :
( ( ~ in(X1,X0)
| ( $sum(count(X0),1) != count(add(X1,X0)) ) )
& ( ( $sum(count(X0),1) = count(add(X1,X0)) )
| in(X1,X0) ) ),
inference(rectify,[],[f48]) ).
tff(f48,plain,
! [X1: collection,X0: $int] :
( ( ~ in(X0,X1)
| ( count(add(X0,X1)) != $sum(count(X1),1) ) )
& ( ( count(add(X0,X1)) = $sum(count(X1),1) )
| in(X0,X1) ) ),
inference(nnf_transformation,[],[f31]) ).
tff(f31,plain,
! [X1: collection,X0: $int] :
( ~ in(X0,X1)
<=> ( count(add(X0,X1)) = $sum(count(X1),1) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X13: $int,X14: collection] :
( ~ in(X13,X14)
<=> ( count(add(X13,X14)) = $sum(count(X14),1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(f114,plain,
( ~ sP0(count(add(3,empty)))
| spl1_3 ),
inference(subsumption_resolution,[],[f113,f80]) ).
tff(f80,plain,
! [X2: collection,X1: $int] : in(X1,add(X1,X2)),
inference(equality_resolution,[],[f67]) ).
tff(f67,plain,
! [X2: collection,X0: $int,X1: $int] :
( in(X1,add(X0,X2))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f46]) ).
tff(f113,plain,
( ~ sP0(count(add(3,empty)))
| ~ in(3,add(3,empty))
| spl1_3 ),
inference(evaluation,[],[f109]) ).
tff(f109,plain,
( ~ sP0($sum($sum(count(add(3,empty)),-1),1))
| ~ in(3,add(3,empty))
| spl1_3 ),
inference(superposition,[],[f101,f83]) ).
tff(f83,plain,
! [X0: $int,X1: collection] :
( ( count(remove(X0,X1)) = $sum(count(X1),-1) )
| ~ in(X0,X1) ),
inference(evaluation,[],[f62]) ).
tff(f62,plain,
! [X0: $int,X1: collection] :
( ( $sum(count(X1),$uminus(1)) = count(remove(X0,X1)) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tff(f43,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,[],[f33]) ).
tff(f33,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)) = $difference(count(X18),1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
tff(f101,plain,
( ~ sP0($sum(count(remove(3,add(3,empty))),1))
| spl1_3 ),
inference(avatar_component_clause,[],[f99]) ).
tff(f99,plain,
( spl1_3
<=> sP0($sum(count(remove(3,add(3,empty))),1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
tff(f102,plain,
( ~ spl1_3
| spl1_2 ),
inference(avatar_split_clause,[],[f85,f91,f99]) ).
tff(f85,plain,
( in(5,remove(3,add(3,empty)))
| ~ sP0($sum(count(remove(3,add(3,empty))),1)) ),
inference(superposition,[],[f77,f69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT047=1 : TPTP v8.1.0. Released v5.0.0.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.33 % Computer : n002.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 20:30:13 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.18/0.49 % (24427)dis+2_1:1_av=off:bsr=on:erd=off:s2pl=on:sgt=16:sos=on:sp=frequency:ss=axioms:i=46:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/46Mi)
% 0.18/0.49 % (24419)lrs+22_1:1_amm=sco:fsr=off:gve=force:sos=on:uwa=all:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.49 % (24427)Refutation not found, incomplete strategy% (24427)------------------------------
% 0.18/0.49 % (24427)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.49 % (24419)Refutation not found, incomplete strategy% (24419)------------------------------
% 0.18/0.49 % (24419)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.49 % (24427)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.49 % (24427)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.49
% 0.18/0.49 % (24427)Memory used [KB]: 1023
% 0.18/0.49 % (24427)Time elapsed: 0.055 s
% 0.18/0.49 % (24427)Instructions burned: 3 (million)
% 0.18/0.49 % (24427)------------------------------
% 0.18/0.49 % (24427)------------------------------
% 0.18/0.49 % (24411)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/32Mi)
% 0.18/0.49 % (24419)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.49 % (24419)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.49
% 0.18/0.49 % (24419)Memory used [KB]: 5628
% 0.18/0.49 % (24419)Time elapsed: 0.054 s
% 0.18/0.49 % (24419)Instructions burned: 3 (million)
% 0.18/0.49 % (24419)------------------------------
% 0.18/0.49 % (24419)------------------------------
% 0.18/0.50 % (24414)lrs+10_1:8_ep=R:erd=off:fs=off:fsr=off:gve=force:nwc=2.0:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.50 % (24412)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)
% 0.18/0.50 % (24408)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)
% 0.18/0.51 % (24413)lrs+1010_1:1_ep=RST:s2a=on:s2at=5.0:sos=all:i=26:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/26Mi)
% 0.18/0.51 % (24405)dis+1010_1:4_aac=none:abs=on:atotf=0.5:avsq=on:avsqc=2:avsqr=215,247:awrs=converge:awrsf=128:bsd=on:erd=off:fde=none:gve=cautious:newcnf=on:nwc=5.0:rnwc=on:sac=on:sas=z3:sp=const_min:tgt=ground:thsq=on:thsqc=64:thsqr=1,4:i=59848:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59848Mi)
% 0.18/0.51 % (24412)First to succeed.
% 0.18/0.51 % (24407)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)
% 0.18/0.52 % (24406)lrs+1010_1:1_aac=none:bce=on:nicw=on:nm=0:plsq=on:plsql=on:sac=on:sos=on:sp=frequency:spb=units:to=lpo:i=34:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/34Mi)
% 0.18/0.52 % (24417)lrs+10_1:1_ep=R:gve=force:plsq=on:plsqr=32,1:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.52 % (24412)Refutation found. Thanks to Tanya!
% 0.18/0.52 % SZS status Theorem for theBenchmark
% 0.18/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.52 % (24412)------------------------------
% 0.18/0.52 % (24412)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52 % (24412)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.52 % (24412)Termination reason: Refutation
% 0.18/0.52
% 0.18/0.52 % (24412)Memory used [KB]: 5500
% 0.18/0.52 % (24412)Time elapsed: 0.119 s
% 0.18/0.52 % (24412)Instructions burned: 3 (million)
% 0.18/0.52 % (24412)------------------------------
% 0.18/0.52 % (24412)------------------------------
% 0.18/0.52 % (24404)Success in time 0.173 s
%------------------------------------------------------------------------------