TSTP Solution File: DAT103_1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : DAT103_1 : TPTP v8.1.0. Released v6.1.0.
% 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 16:04:11 EDT 2022
% Result : Theorem 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 50 ( 22 unt; 10 typ; 0 def)
% Number of atoms : 127 ( 44 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 134 ( 47 ~; 33 |; 49 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 169 ( 48 atm; 44 fun; 34 num; 43 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 72 ( 48 !; 24 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
list: $tType ).
tff(func_def_0,type,
nil: list ).
tff(func_def_1,type,
cons: ( $int * list ) > list ).
tff(func_def_2,type,
head: list > $int ).
tff(func_def_3,type,
tail: list > list ).
tff(func_def_9,type,
sK0: ( list * $int ) > $int ).
tff(func_def_10,type,
sK1: ( list * $int ) > list ).
tff(func_def_11,type,
sK2: $int ).
tff(func_def_12,type,
sK3: list ).
tff(pred_def_1,type,
inRange: ( $int * list ) > $o ).
tff(f138,plain,
$false,
inference(subsumption_resolution,[],[f137,f100]) ).
tff(f100,plain,
~ $less(sK2,$sum(1,head(sK3))),
inference(backward_demodulation,[],[f69,f89]) ).
tff(f89,plain,
sK0(sK3,sK2) = head(sK3),
inference(superposition,[],[f42,f51]) ).
tff(f51,plain,
sK3 = cons(sK0(sK3,sK2),sK1(sK3,sK2)),
inference(unit_resulting_resolution,[],[f43,f45,f40]) ).
tff(f40,plain,
! [X0: list,X1: $int] :
( ~ inRange(X1,X0)
| ( nil = X0 )
| ( cons(sK0(X0,X1),sK1(X0,X1)) = X0 ) ),
inference(cnf_transformation,[],[f31]) ).
tff(f31,plain,
! [X0: list,X1: $int] :
( ( ( inRange(X1,sK1(X0,X1))
& ( cons(sK0(X0,X1),sK1(X0,X1)) = X0 )
& $less(sK0(X0,X1),X1)
& ~ $less(sK0(X0,X1),0) )
| ( nil = X0 )
| ~ inRange(X1,X0) )
& ( inRange(X1,X0)
| ( ! [X4: $int,X5: list] :
( ~ inRange(X1,X5)
| ( cons(X4,X5) != X0 )
| ~ $less(X4,X1)
| $less(X4,0) )
& ( nil != X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f29,f30]) ).
tff(f30,plain,
! [X0: list,X1: $int] :
( ? [X2: $int,X3: list] :
( inRange(X1,X3)
& ( cons(X2,X3) = X0 )
& $less(X2,X1)
& ~ $less(X2,0) )
=> ( inRange(X1,sK1(X0,X1))
& ( cons(sK0(X0,X1),sK1(X0,X1)) = X0 )
& $less(sK0(X0,X1),X1)
& ~ $less(sK0(X0,X1),0) ) ),
introduced(choice_axiom,[]) ).
tff(f29,plain,
! [X0: list,X1: $int] :
( ( ? [X2: $int,X3: list] :
( inRange(X1,X3)
& ( cons(X2,X3) = X0 )
& $less(X2,X1)
& ~ $less(X2,0) )
| ( nil = X0 )
| ~ inRange(X1,X0) )
& ( inRange(X1,X0)
| ( ! [X4: $int,X5: list] :
( ~ inRange(X1,X5)
| ( cons(X4,X5) != X0 )
| ~ $less(X4,X1)
| $less(X4,0) )
& ( nil != X0 ) ) ) ),
inference(rectify,[],[f28]) ).
tff(f28,plain,
! [X0: list,X1: $int] :
( ( ? [X2: $int,X3: list] :
( inRange(X1,X3)
& ( cons(X2,X3) = X0 )
& $less(X2,X1)
& ~ $less(X2,0) )
| ( nil = X0 )
| ~ inRange(X1,X0) )
& ( inRange(X1,X0)
| ( ! [X2: $int,X3: list] :
( ~ inRange(X1,X3)
| ( cons(X2,X3) != X0 )
| ~ $less(X2,X1)
| $less(X2,0) )
& ( nil != X0 ) ) ) ),
inference(flattening,[],[f27]) ).
tff(f27,plain,
! [X0: list,X1: $int] :
( ( ? [X2: $int,X3: list] :
( inRange(X1,X3)
& ( cons(X2,X3) = X0 )
& $less(X2,X1)
& ~ $less(X2,0) )
| ( nil = X0 )
| ~ inRange(X1,X0) )
& ( inRange(X1,X0)
| ( ! [X2: $int,X3: list] :
( ~ inRange(X1,X3)
| ( cons(X2,X3) != X0 )
| ~ $less(X2,X1)
| $less(X2,0) )
& ( nil != X0 ) ) ) ),
inference(nnf_transformation,[],[f23]) ).
tff(f23,plain,
! [X0: list,X1: $int] :
( ( ? [X2: $int,X3: list] :
( inRange(X1,X3)
& ( cons(X2,X3) = X0 )
& $less(X2,X1)
& ~ $less(X2,0) )
| ( nil = X0 ) )
<=> inRange(X1,X0) ),
inference(rectify,[],[f8]) ).
tff(f8,plain,
! [X1: list,X2: $int] :
( inRange(X2,X1)
<=> ( ? [X0: $int,X3: list] :
( inRange(X2,X3)
& ( cons(X0,X3) = X1 )
& ~ $less(X0,0)
& $less(X0,X2) )
| ( nil = X1 ) ) ),
inference(theory_normalization,[],[f5]) ).
tff(f5,axiom,
! [X1: list,X2: $int] :
( inRange(X2,X1)
<=> ( ? [X0: $int,X3: list] :
( inRange(X2,X3)
& ( cons(X0,X3) = X1 )
& $lesseq(0,X0)
& $less(X0,X2) )
| ( nil = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inRange) ).
tff(f45,plain,
inRange(sK2,sK3),
inference(cnf_transformation,[],[f34]) ).
tff(f34,plain,
( inRange(sK2,sK3)
& $less($sum(sK2,$uminus(head(sK3))),1)
& ( nil != sK3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f22,f33]) ).
tff(f33,plain,
( ? [X0: $int,X1: list] :
( inRange(X0,X1)
& $less($sum(X0,$uminus(head(X1))),1)
& ( nil != X1 ) )
=> ( inRange(sK2,sK3)
& $less($sum(sK2,$uminus(head(sK3))),1)
& ( nil != sK3 ) ) ),
introduced(choice_axiom,[]) ).
tff(f22,plain,
? [X0: $int,X1: list] :
( inRange(X0,X1)
& $less($sum(X0,$uminus(head(X1))),1)
& ( nil != X1 ) ),
inference(rectify,[],[f9]) ).
tff(f9,plain,
? [X2: $int,X1: list] :
( $less($sum(X2,$uminus(head(X1))),1)
& ( nil != X1 )
& inRange(X2,X1) ),
inference(theory_normalization,[],[f7]) ).
tff(f7,negated_conjecture,
~ ~ ? [X2: $int,X1: list] :
( $less($difference(X2,head(X1)),1)
& ( nil != X1 )
& inRange(X2,X1) ),
inference(negated_conjecture,[],[f6]) ).
tff(f6,conjecture,
~ ? [X2: $int,X1: list] :
( $less($difference(X2,head(X1)),1)
& ( nil != X1 )
& inRange(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f43,plain,
nil != sK3,
inference(cnf_transformation,[],[f34]) ).
tff(f42,plain,
! [X0: list,X1: $int] : ( head(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: list,X1: $int] : ( head(cons(X1,X0)) = X1 ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X1: list,X0: $int] : ( head(cons(X0,X1)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
tff(f69,plain,
~ $less(sK2,$sum(1,sK0(sK3,sK2))),
inference(forward_demodulation,[],[f66,f10]) ).
tff(f10,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_140,[]) ).
tff(f66,plain,
~ $less(sK2,$sum(sK0(sK3,sK2),1)),
inference(unit_resulting_resolution,[],[f52,f21]) ).
tff(f21,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(theory_axiom_166,[]) ).
tff(f52,plain,
$less(sK0(sK3,sK2),sK2),
inference(unit_resulting_resolution,[],[f43,f45,f39]) ).
tff(f39,plain,
! [X0: list,X1: $int] :
( ~ inRange(X1,X0)
| $less(sK0(X0,X1),X1)
| ( nil = X0 ) ),
inference(cnf_transformation,[],[f31]) ).
tff(f137,plain,
$less(sK2,$sum(1,head(sK3))),
inference(forward_demodulation,[],[f129,f12]) ).
tff(f12,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_142,[]) ).
tff(f129,plain,
$less($sum(sK2,0),$sum(1,head(sK3))),
inference(evaluation,[],[f123]) ).
tff(f123,plain,
$less($sum(sK2,0),$sum(1,$uminus($uminus(head(sK3))))),
inference(superposition,[],[f58,f14]) ).
tff(f14,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_145,[]) ).
tff(f58,plain,
! [X0: $int] : $less($sum(sK2,$sum($uminus(head(sK3)),X0)),$sum(1,X0)),
inference(forward_demodulation,[],[f56,f11]) ).
tff(f11,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum($sum(X0,X1),X2) = $sum(X0,$sum(X1,X2)) ),
introduced(theory_axiom_141,[]) ).
tff(f56,plain,
! [X0: $int] : $less($sum($sum(sK2,$uminus(head(sK3))),X0),$sum(1,X0)),
inference(unit_resulting_resolution,[],[f44,f18]) ).
tff(f18,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(theory_axiom_150,[]) ).
tff(f44,plain,
$less($sum(sK2,$uminus(head(sK3))),1),
inference(cnf_transformation,[],[f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT103=1 : TPTP v8.1.0. Released v6.1.0.
% 0.00/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 29 20:34:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.45 % (7894)dis+1011_1:1_bd=off:canc=force:ev=cautious:nwc=5.0:i=21:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.18/0.46 % (7886)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)
% 0.18/0.46 % (7878)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)
% 0.18/0.46 % (7878)Instruction limit reached!
% 0.18/0.46 % (7878)------------------------------
% 0.18/0.46 % (7878)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.46 % (7878)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.46 % (7878)Termination reason: Unknown
% 0.18/0.46 % (7878)Termination phase: Equality proxy
% 0.18/0.46
% 0.18/0.46 % (7878)Memory used [KB]: 895
% 0.18/0.46 % (7878)Time elapsed: 0.004 s
% 0.18/0.46 % (7878)Instructions burned: 2 (million)
% 0.18/0.46 % (7878)------------------------------
% 0.18/0.46 % (7878)------------------------------
% 0.18/0.50 % (7886)Instruction limit reached!
% 0.18/0.50 % (7886)------------------------------
% 0.18/0.50 % (7886)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50 % (7886)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50 % (7886)Termination reason: Unknown
% 0.18/0.50 % (7886)Termination phase: Saturation
% 0.18/0.50
% 0.18/0.50 % (7886)Memory used [KB]: 1151
% 0.18/0.50 % (7886)Time elapsed: 0.097 s
% 0.18/0.50 % (7886)Instructions burned: 16 (million)
% 0.18/0.50 % (7886)------------------------------
% 0.18/0.50 % (7886)------------------------------
% 0.18/0.50 % (7894)Instruction limit reached!
% 0.18/0.50 % (7894)------------------------------
% 0.18/0.50 % (7894)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50 % (7894)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50 % (7894)Termination reason: Unknown
% 0.18/0.50 % (7894)Termination phase: Saturation
% 0.18/0.50
% 0.18/0.50 % (7894)Memory used [KB]: 5756
% 0.18/0.50 % (7894)Time elapsed: 0.102 s
% 0.18/0.50 % (7894)Instructions burned: 21 (million)
% 0.18/0.50 % (7894)------------------------------
% 0.18/0.50 % (7894)------------------------------
% 0.18/0.50 % (7889)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)
% 0.18/0.50 % (7880)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)
% 0.18/0.50 % (7879)dis+10_1:64_nwc=1.4:tha=off:i=21:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.18/0.50 % (7872)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)
% 0.18/0.50 % (7888)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)
% 0.18/0.51 % (7866)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 % (7869)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 % (7869)Instruction limit reached!
% 0.18/0.51 % (7869)------------------------------
% 0.18/0.51 % (7869)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51 % (7869)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51 % (7869)Termination reason: Unknown
% 0.18/0.51 % (7869)Termination phase: Saturation
% 0.18/0.51
% 0.18/0.51 % (7869)Memory used [KB]: 5500
% 0.18/0.51 % (7869)Time elapsed: 0.003 s
% 0.18/0.51 % (7869)Instructions burned: 3 (million)
% 0.18/0.51 % (7869)------------------------------
% 0.18/0.51 % (7869)------------------------------
% 0.18/0.51 % (7873)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)
% 0.18/0.51 % (7876)lrs+10_1:1_canc=force:tha=some:to=lpo:i=35:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/35Mi)
% 0.18/0.51 % (7868)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)
% 0.18/0.51 % (7872)First to succeed.
% 0.18/0.51 % (7872)Refutation found. Thanks to Tanya!
% 0.18/0.51 % SZS status Theorem for theBenchmark
% 0.18/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.51 % (7872)------------------------------
% 0.18/0.51 % (7872)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51 % (7872)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51 % (7872)Termination reason: Refutation
% 0.18/0.51
% 0.18/0.51 % (7872)Memory used [KB]: 5628
% 0.18/0.51 % (7872)Time elapsed: 0.075 s
% 0.18/0.51 % (7872)Instructions burned: 7 (million)
% 0.18/0.51 % (7872)------------------------------
% 0.18/0.51 % (7872)------------------------------
% 0.18/0.51 % (7865)Success in time 0.175 s
%------------------------------------------------------------------------------