TSTP Solution File: DAT028_1 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : DAT028_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 : n006.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 16:03:56 EDT 2022
% Result : Theorem 0.20s 0.54s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 51 ( 10 unt; 9 typ; 0 def)
% Number of atoms : 133 ( 4 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 140 ( 49 ~; 34 |; 36 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 160 ( 58 atm; 3 fun; 47 num; 52 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 7 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 68 ( 44 !; 24 ?; 68 :)
% 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_7,type,
sK0: collection ).
tff(func_def_8,type,
sK1: collection ).
tff(func_def_9,type,
sK2: $int ).
tff(func_def_10,type,
sK3: $int > $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f113,plain,
$false,
inference(avatar_sat_refutation,[],[f45,f64,f112]) ).
tff(f112,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f111]) ).
tff(f111,plain,
( $false
| ~ spl4_1 ),
inference(subsumption_resolution,[],[f110,f77]) ).
tff(f77,plain,
~ $less(sK3(sK2),1),
inference(evaluation,[],[f76]) ).
tff(f76,plain,
~ $less(sK3(sK2),$sum(0,1)),
inference(resolution,[],[f73,f20]) ).
tff(f20,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_166,[]) ).
tff(f73,plain,
$less(0,sK3(sK2)),
inference(resolution,[],[f51,f29]) ).
tff(f29,plain,
! [X5: $int] :
( ~ in(X5,sK0)
| $less(0,X5) ),
inference(cnf_transformation,[],[f28]) ).
tff(f28,plain,
( in(sK2,sK1)
& ~ $less(1,sK2)
& ! [X3: $int] :
( ~ in(X3,sK1)
| ( in(sK3(X3),sK0)
& $less(sK3(X3),X3) ) )
& ! [X5: $int] :
( ~ in(X5,sK0)
| $less(0,X5) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f24,f27,f26,f25]) ).
tff(f25,plain,
( ? [X0: collection,X1: collection] :
( ? [X2: $int] :
( in(X2,X1)
& ~ $less(1,X2) )
& ! [X3: $int] :
( ~ in(X3,X1)
| ? [X4: $int] :
( in(X4,X0)
& $less(X4,X3) ) )
& ! [X5: $int] :
( ~ in(X5,X0)
| $less(0,X5) ) )
=> ( ? [X2: $int] :
( in(X2,sK1)
& ~ $less(1,X2) )
& ! [X3: $int] :
( ~ in(X3,sK1)
| ? [X4: $int] :
( in(X4,sK0)
& $less(X4,X3) ) )
& ! [X5: $int] :
( ~ in(X5,sK0)
| $less(0,X5) ) ) ),
introduced(choice_axiom,[]) ).
tff(f26,plain,
( ? [X2: $int] :
( in(X2,sK1)
& ~ $less(1,X2) )
=> ( in(sK2,sK1)
& ~ $less(1,sK2) ) ),
introduced(choice_axiom,[]) ).
tff(f27,plain,
! [X3: $int] :
( ? [X4: $int] :
( in(X4,sK0)
& $less(X4,X3) )
=> ( in(sK3(X3),sK0)
& $less(sK3(X3),X3) ) ),
introduced(choice_axiom,[]) ).
tff(f24,plain,
? [X0: collection,X1: collection] :
( ? [X2: $int] :
( in(X2,X1)
& ~ $less(1,X2) )
& ! [X3: $int] :
( ~ in(X3,X1)
| ? [X4: $int] :
( in(X4,X0)
& $less(X4,X3) ) )
& ! [X5: $int] :
( ~ in(X5,X0)
| $less(0,X5) ) ),
inference(rectify,[],[f23]) ).
tff(f23,plain,
? [X0: collection,X1: collection] :
( ? [X5: $int] :
( in(X5,X1)
& ~ $less(1,X5) )
& ! [X2: $int] :
( ~ in(X2,X1)
| ? [X3: $int] :
( in(X3,X0)
& $less(X3,X2) ) )
& ! [X4: $int] :
( ~ in(X4,X0)
| $less(0,X4) ) ),
inference(flattening,[],[f22]) ).
tff(f22,plain,
? [X0: collection,X1: collection] :
( ? [X5: $int] :
( in(X5,X1)
& ~ $less(1,X5) )
& ! [X2: $int] :
( ~ in(X2,X1)
| ? [X3: $int] :
( in(X3,X0)
& $less(X3,X2) ) )
& ! [X4: $int] :
( ~ in(X4,X0)
| $less(0,X4) ) ),
inference(ennf_transformation,[],[f21]) ).
tff(f21,plain,
~ ! [X0: collection,X1: collection] :
( ( ! [X2: $int] :
( in(X2,X1)
=> ? [X3: $int] :
( in(X3,X0)
& $less(X3,X2) ) )
& ! [X4: $int] :
( in(X4,X0)
=> $less(0,X4) ) )
=> ! [X5: $int] :
( in(X5,X1)
=> $less(1,X5) ) ),
inference(rectify,[],[f8]) ).
tff(f8,plain,
~ ! [X1: collection,X0: collection] :
( ( ! [X3: $int] :
( in(X3,X0)
=> ? [X4: $int] :
( $less(X4,X3)
& in(X4,X1) ) )
& ! [X2: $int] :
( in(X2,X1)
=> $less(0,X2) ) )
=> ! [X5: $int] :
( in(X5,X0)
=> $less(1,X5) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f7,negated_conjecture,
~ ! [X1: collection,X0: collection] :
( ( ! [X3: $int] :
( in(X3,X0)
=> ? [X4: $int] :
( $greater(X3,X4)
& in(X4,X1) ) )
& ! [X2: $int] :
( in(X2,X1)
=> $greater(X2,0) ) )
=> ! [X5: $int] :
( in(X5,X0)
=> $greater(X5,1) ) ),
inference(negated_conjecture,[],[f6]) ).
tff(f6,conjecture,
! [X1: collection,X0: collection] :
( ( ! [X3: $int] :
( in(X3,X0)
=> ? [X4: $int] :
( $greater(X3,X4)
& in(X4,X1) ) )
& ! [X2: $int] :
( in(X2,X1)
=> $greater(X2,0) ) )
=> ! [X5: $int] :
( in(X5,X0)
=> $greater(X5,1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f51,plain,
in(sK3(sK2),sK0),
inference(resolution,[],[f31,f33]) ).
tff(f33,plain,
in(sK2,sK1),
inference(cnf_transformation,[],[f28]) ).
tff(f31,plain,
! [X3: $int] :
( ~ in(X3,sK1)
| in(sK3(X3),sK0) ),
inference(cnf_transformation,[],[f28]) ).
tff(f110,plain,
( $less(sK3(sK2),1)
| ~ spl4_1 ),
inference(resolution,[],[f66,f48]) ).
tff(f48,plain,
$less(sK3(sK2),sK2),
inference(resolution,[],[f30,f33]) ).
tff(f30,plain,
! [X3: $int] :
( ~ in(X3,sK1)
| $less(sK3(X3),X3) ),
inference(cnf_transformation,[],[f28]) ).
tff(f66,plain,
( ! [X1: $int] :
( ~ $less(X1,sK2)
| $less(X1,1) )
| ~ spl4_1 ),
inference(resolution,[],[f39,f15]) ).
tff(f15,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) ),
introduced(theory_axiom_148,[]) ).
tff(f39,plain,
( $less(sK2,1)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f37]) ).
tff(f37,plain,
( spl4_1
<=> $less(sK2,1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
tff(f64,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f63]) ).
tff(f63,plain,
( $false
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f62,f50]) ).
tff(f50,plain,
( $less(sK3(1),1)
| ~ spl4_2 ),
inference(forward_demodulation,[],[f48,f43]) ).
tff(f43,plain,
( ( 1 = sK2 )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f41]) ).
tff(f41,plain,
( spl4_2
<=> ( 1 = sK2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
tff(f62,plain,
( ~ $less(sK3(1),1)
| ~ spl4_2 ),
inference(evaluation,[],[f61]) ).
tff(f61,plain,
( ~ $less(sK3(1),$sum(0,1))
| ~ spl4_2 ),
inference(resolution,[],[f58,f20]) ).
tff(f58,plain,
( $less(0,sK3(1))
| ~ spl4_2 ),
inference(resolution,[],[f53,f29]) ).
tff(f53,plain,
( in(sK3(1),sK0)
| ~ spl4_2 ),
inference(forward_demodulation,[],[f51,f43]) ).
tff(f45,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f35,f37,f41]) ).
tff(f35,plain,
( $less(sK2,1)
| ( 1 = sK2 ) ),
inference(resolution,[],[f32,f16]) ).
tff(f16,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_149,[]) ).
tff(f32,plain,
~ $less(1,sK2),
inference(cnf_transformation,[],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT028=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 : n006.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 20:15:40 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.51 % (1235)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=4:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.53 % (1230)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)
% 0.20/0.53 % (1243)lrs+10_1:1_sd=10:sos=all:ss=axioms:st=5.0:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.53 % (1231)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)
% 0.20/0.53 % (1246)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)
% 0.20/0.54 % (1238)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)
% 0.20/0.54 % (1235)First to succeed.
% 0.20/0.54 % (1247)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)
% 0.20/0.54 % (1240)lrs+10_1:1_ev=force:gve=cautious:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.54 % (1235)Refutation found. Thanks to Tanya!
% 0.20/0.54 % SZS status Theorem for theBenchmark
% 0.20/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.54 % (1235)------------------------------
% 0.20/0.54 % (1235)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (1235)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (1235)Termination reason: Refutation
% 0.20/0.54
% 0.20/0.54 % (1235)Memory used [KB]: 5500
% 0.20/0.54 % (1235)Time elapsed: 0.126 s
% 0.20/0.54 % (1235)Instructions burned: 3 (million)
% 0.20/0.54 % (1235)------------------------------
% 0.20/0.54 % (1235)------------------------------
% 0.20/0.54 % (1223)Success in time 0.188 s
%------------------------------------------------------------------------------