TSTP Solution File: DAT025_1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : DAT025_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 : n026.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 1.31s 0.58s
% Output : Refutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 60 ( 12 unt; 7 typ; 0 def)
% Number of atoms : 158 ( 17 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 174 ( 69 ~; 48 |; 35 &)
% ( 11 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 179 ( 38 atm; 7 fun; 84 num; 50 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 9 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 66 ( 56 !; 10 ?; 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_8,type,
sK0: collection ).
tff(func_def_9,type,
sK1: $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f247,plain,
$false,
inference(avatar_sat_refutation,[],[f80,f96,f154,f190,f246]) ).
tff(f246,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f241]) ).
tff(f241,plain,
( $false
| ~ spl2_1 ),
inference(resolution,[],[f235,f44]) ).
tff(f44,plain,
! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)),
inference(cnf_transformation,[],[f22]) ).
tff(f22,plain,
! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X3: $int,X4: collection] : ~ in(X3,remove(X3,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f235,plain,
( in(1,remove(1,sK0))
| ~ spl2_1 ),
inference(resolution,[],[f204,f47]) ).
tff(f47,plain,
! [X2: $int,X0: $int,X1: collection] :
( ~ in(X0,remove(X2,X1))
| in(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tff(f34,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( in(X0,remove(X2,X1))
| ~ in(X0,X1)
| ( X0 = X2 ) )
& ( ( in(X0,X1)
& ( X0 != X2 ) )
| ~ in(X0,remove(X2,X1)) ) ),
inference(rectify,[],[f33]) ).
tff(f33,plain,
! [X2: $int,X0: collection,X1: $int] :
( ( in(X2,remove(X1,X0))
| ~ in(X2,X0)
| ( X1 = X2 ) )
& ( ( in(X2,X0)
& ( X1 != X2 ) )
| ~ in(X2,remove(X1,X0)) ) ),
inference(flattening,[],[f32]) ).
tff(f32,plain,
! [X2: $int,X0: collection,X1: $int] :
( ( in(X2,remove(X1,X0))
| ~ in(X2,X0)
| ( X1 = X2 ) )
& ( ( in(X2,X0)
& ( X1 != X2 ) )
| ~ in(X2,remove(X1,X0)) ) ),
inference(nnf_transformation,[],[f21]) ).
tff(f21,plain,
! [X2: $int,X0: collection,X1: $int] :
( in(X2,remove(X1,X0))
<=> ( in(X2,X0)
& ( X1 != X2 ) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X9: collection,X10: $int,X8: $int] :
( ( ( X8 != X10 )
& in(X8,X9) )
<=> in(X8,remove(X10,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
tff(f204,plain,
( in(1,remove(0,remove(1,sK0)))
| ~ spl2_1 ),
inference(backward_demodulation,[],[f161,f73]) ).
tff(f73,plain,
( ( 1 = sK1 )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f71]) ).
tff(f71,plain,
( spl2_1
<=> ( 1 = sK1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
tff(f161,plain,
in(sK1,remove(0,remove(1,sK0))),
inference(resolution,[],[f39,f41]) ).
tff(f41,plain,
! [X2: $int] :
( ~ in(X2,sK0)
| in(X2,remove(0,remove(1,sK0))) ),
inference(cnf_transformation,[],[f30]) ).
tff(f30,plain,
( ! [X1: $int] :
( ~ in(X1,sK0)
| ~ $less(X1,0) )
& ! [X2: $int] :
( ( in(X2,remove(0,remove(1,sK0)))
| ~ in(X2,sK0) )
& ( in(X2,sK0)
| ~ in(X2,remove(0,remove(1,sK0))) ) )
& in(sK1,sK0)
& $less(sK1,2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f27,f29,f28]) ).
tff(f28,plain,
( ? [X0: collection] :
( ! [X1: $int] :
( ~ in(X1,X0)
| ~ $less(X1,0) )
& ! [X2: $int] :
( ( in(X2,remove(0,remove(1,X0)))
| ~ in(X2,X0) )
& ( in(X2,X0)
| ~ in(X2,remove(0,remove(1,X0))) ) )
& ? [X3: $int] :
( in(X3,X0)
& $less(X3,2) ) )
=> ( ! [X1: $int] :
( ~ in(X1,sK0)
| ~ $less(X1,0) )
& ! [X2: $int] :
( ( in(X2,remove(0,remove(1,sK0)))
| ~ in(X2,sK0) )
& ( in(X2,sK0)
| ~ in(X2,remove(0,remove(1,sK0))) ) )
& ? [X3: $int] :
( in(X3,sK0)
& $less(X3,2) ) ) ),
introduced(choice_axiom,[]) ).
tff(f29,plain,
( ? [X3: $int] :
( in(X3,sK0)
& $less(X3,2) )
=> ( in(sK1,sK0)
& $less(sK1,2) ) ),
introduced(choice_axiom,[]) ).
tff(f27,plain,
? [X0: collection] :
( ! [X1: $int] :
( ~ in(X1,X0)
| ~ $less(X1,0) )
& ! [X2: $int] :
( ( in(X2,remove(0,remove(1,X0)))
| ~ in(X2,X0) )
& ( in(X2,X0)
| ~ in(X2,remove(0,remove(1,X0))) ) )
& ? [X3: $int] :
( in(X3,X0)
& $less(X3,2) ) ),
inference(nnf_transformation,[],[f26]) ).
tff(f26,plain,
? [X0: collection] :
( ! [X1: $int] :
( ~ in(X1,X0)
| ~ $less(X1,0) )
& ! [X2: $int] :
( in(X2,remove(0,remove(1,X0)))
<=> in(X2,X0) )
& ? [X3: $int] :
( in(X3,X0)
& $less(X3,2) ) ),
inference(flattening,[],[f25]) ).
tff(f25,plain,
? [X0: collection] :
( ? [X3: $int] :
( in(X3,X0)
& $less(X3,2) )
& ! [X2: $int] :
( in(X2,remove(0,remove(1,X0)))
<=> in(X2,X0) )
& ! [X1: $int] :
( ~ in(X1,X0)
| ~ $less(X1,0) ) ),
inference(ennf_transformation,[],[f8]) ).
tff(f8,plain,
~ ! [X0: collection] :
( ( ! [X2: $int] :
( in(X2,remove(0,remove(1,X0)))
<=> in(X2,X0) )
& ! [X1: $int] :
( in(X1,X0)
=> ~ $less(X1,0) ) )
=> ! [X3: $int] :
( in(X3,X0)
=> ~ $less(X3,2) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f7,negated_conjecture,
~ ! [X0: collection] :
( ( ! [X1: $int] :
( in(X1,X0)
=> $greatereq(X1,0) )
& ! [X2: $int] :
( in(X2,remove(0,remove(1,X0)))
<=> in(X2,X0) ) )
=> ! [X3: $int] :
( in(X3,X0)
=> $greatereq(X3,2) ) ),
inference(negated_conjecture,[],[f6]) ).
tff(f6,conjecture,
! [X0: collection] :
( ( ! [X1: $int] :
( in(X1,X0)
=> $greatereq(X1,0) )
& ! [X2: $int] :
( in(X2,remove(0,remove(1,X0)))
<=> in(X2,X0) ) )
=> ! [X3: $int] :
( in(X3,X0)
=> $greatereq(X3,2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f39,plain,
in(sK1,sK0),
inference(cnf_transformation,[],[f30]) ).
tff(f190,plain,
( ~ spl2_4
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f186,f75,f92]) ).
tff(f92,plain,
( spl2_4
<=> $less(0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
tff(f75,plain,
( spl2_2
<=> $less(sK1,1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
tff(f186,plain,
( ~ $less(0,sK1)
| ~ spl2_2 ),
inference(evaluation,[],[f185]) ).
tff(f185,plain,
( ~ $less($sum(1,$uminus(1)),sK1)
| ~ spl2_2 ),
inference(gaussian_variable_elimination,[],[f181]) ).
tff(f181,plain,
( ! [X0: $int] :
( ( 1 != $sum(X0,1) )
| ~ $less(X0,sK1) )
| ~ spl2_2 ),
inference(constrained_resolution,[],[f77,f20]) ).
tff(f20,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(theory_axiom_166,[]) ).
tff(f77,plain,
( $less(sK1,1)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f75]) ).
tff(f154,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f149]) ).
tff(f149,plain,
( $false
| ~ spl2_3 ),
inference(resolution,[],[f113,f44]) ).
tff(f113,plain,
( in(0,remove(0,remove(1,sK0)))
| ~ spl2_3 ),
inference(resolution,[],[f41,f98]) ).
tff(f98,plain,
( in(0,sK0)
| ~ spl2_3 ),
inference(backward_demodulation,[],[f39,f90]) ).
tff(f90,plain,
( ( 0 = sK1 )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f88]) ).
tff(f88,plain,
( spl2_3
<=> ( 0 = sK1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
tff(f96,plain,
( spl2_4
| spl2_3 ),
inference(avatar_split_clause,[],[f83,f88,f92]) ).
tff(f83,plain,
( ( 0 = sK1 )
| $less(0,sK1) ),
inference(resolution,[],[f63,f16]) ).
tff(f16,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_149,[]) ).
tff(f63,plain,
~ $less(sK1,0),
inference(resolution,[],[f42,f39]) ).
tff(f42,plain,
! [X1: $int] :
( ~ in(X1,sK0)
| ~ $less(X1,0) ),
inference(cnf_transformation,[],[f30]) ).
tff(f80,plain,
( spl2_2
| spl2_1 ),
inference(avatar_split_clause,[],[f67,f71,f75]) ).
tff(f67,plain,
( ( 1 = sK1 )
| $less(sK1,1) ),
inference(resolution,[],[f59,f16]) ).
tff(f59,plain,
~ $less(1,sK1),
inference(evaluation,[],[f58]) ).
tff(f58,plain,
~ $less($sum(2,$uminus(1)),sK1),
inference(gaussian_variable_elimination,[],[f54]) ).
tff(f54,plain,
! [X0: $int] :
( ~ $less(X0,sK1)
| ( 2 != $sum(X0,1) ) ),
inference(constrained_resolution,[],[f38,f20]) ).
tff(f38,plain,
$less(sK1,2),
inference(cnf_transformation,[],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT025=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
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 29 20:31:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.55 % (10056)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)
% 0.21/0.56 % (10072)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)
% 1.31/0.56 % (10057)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)
% 1.31/0.56 % (10061)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)
% 1.31/0.57 % (10064)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)
% 1.31/0.57 % (10053)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)
% 1.31/0.57 % (10065)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)
% 1.31/0.57 % (10053)Instruction limit reached!
% 1.31/0.57 % (10053)------------------------------
% 1.31/0.57 % (10053)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.31/0.57 % (10053)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.31/0.57 % (10053)Termination reason: Unknown
% 1.31/0.57 % (10053)Termination phase: Saturation
% 1.31/0.57
% 1.31/0.57 % (10053)Memory used [KB]: 1023
% 1.31/0.57 % (10053)Time elapsed: 0.002 s
% 1.31/0.57 % (10053)Instructions burned: 2 (million)
% 1.31/0.57 % (10053)------------------------------
% 1.31/0.57 % (10053)------------------------------
% 1.31/0.57 % (10069)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)
% 1.31/0.58 % (10058)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)
% 1.31/0.58 % (10070)dis+1002_1:5_av=off:nwc=2.0:sos=all:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 1.31/0.58 % (10077)dis+10_1:64_nwc=1.4:tha=off:i=21:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 1.31/0.58 % (10064)First to succeed.
% 1.31/0.58 % (10064)Refutation found. Thanks to Tanya!
% 1.31/0.58 % SZS status Theorem for theBenchmark
% 1.31/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.31/0.58 % (10064)------------------------------
% 1.31/0.58 % (10064)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.31/0.58 % (10064)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.31/0.58 % (10064)Termination reason: Refutation
% 1.31/0.58
% 1.31/0.58 % (10064)Memory used [KB]: 5628
% 1.31/0.58 % (10064)Time elapsed: 0.132 s
% 1.31/0.58 % (10064)Instructions burned: 7 (million)
% 1.31/0.58 % (10064)------------------------------
% 1.31/0.58 % (10064)------------------------------
% 1.31/0.58 % (10049)Success in time 0.217 s
%------------------------------------------------------------------------------