TSTP Solution File: DAT101_1 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : DAT101_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 : n005.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 16:04:10 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 49 ( 23 unt; 8 typ; 0 def)
% Number of atoms : 120 ( 42 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 123 ( 44 ~; 36 |; 35 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number arithmetic : 187 ( 40 atm; 2 fun; 106 num; 39 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 6 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 6 usr; 7 con; 0-2 aty)
% Number of variables : 69 ( 55 !; 14 ?; 69 :)
% 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_11,type,
sK0: ( $int * list ) > $int ).
tff(func_def_12,type,
sK1: ( $int * list ) > list ).
tff(pred_def_1,type,
inRange: ( $int * list ) > $o ).
tff(f154,plain,
$false,
inference(evaluation,[],[f145]) ).
tff(f145,plain,
~ $less(3,5),
inference(backward_demodulation,[],[f111,f141]) ).
tff(f141,plain,
5 = sK0(4,cons(5,cons(2,nil))),
inference(forward_demodulation,[],[f131,f34]) ).
tff(f34,plain,
! [X0: list,X1: $int] : ( head(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f26]) ).
tff(f26,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(f131,plain,
head(cons(5,cons(2,nil))) = sK0(4,cons(5,cons(2,nil))),
inference(superposition,[],[f34,f87]) ).
tff(f87,plain,
cons(5,cons(2,nil)) = cons(sK0(4,cons(5,cons(2,nil))),sK1(4,cons(5,cons(2,nil)))),
inference(unit_resulting_resolution,[],[f36,f82,f40]) ).
tff(f40,plain,
! [X0: $int,X1: list] :
( ( cons(sK0(X0,X1),sK1(X0,X1)) = X1 )
| ( nil = X1 )
| ~ inRange(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tff(f32,plain,
! [X0: $int,X1: list] :
( ( ( ~ $less(sK0(X0,X1),0)
& $less(sK0(X0,X1),X0)
& inRange(X0,sK1(X0,X1))
& ( cons(sK0(X0,X1),sK1(X0,X1)) = X1 ) )
| ( nil = X1 )
| ~ inRange(X0,X1) )
& ( inRange(X0,X1)
| ( ! [X4: $int,X5: list] :
( $less(X4,0)
| ~ $less(X4,X0)
| ~ inRange(X0,X5)
| ( cons(X4,X5) != X1 ) )
& ( nil != X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f30,f31]) ).
tff(f31,plain,
! [X0: $int,X1: list] :
( ? [X2: $int,X3: list] :
( ~ $less(X2,0)
& $less(X2,X0)
& inRange(X0,X3)
& ( cons(X2,X3) = X1 ) )
=> ( ~ $less(sK0(X0,X1),0)
& $less(sK0(X0,X1),X0)
& inRange(X0,sK1(X0,X1))
& ( cons(sK0(X0,X1),sK1(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f30,plain,
! [X0: $int,X1: list] :
( ( ? [X2: $int,X3: list] :
( ~ $less(X2,0)
& $less(X2,X0)
& inRange(X0,X3)
& ( cons(X2,X3) = X1 ) )
| ( nil = X1 )
| ~ inRange(X0,X1) )
& ( inRange(X0,X1)
| ( ! [X4: $int,X5: list] :
( $less(X4,0)
| ~ $less(X4,X0)
| ~ inRange(X0,X5)
| ( cons(X4,X5) != X1 ) )
& ( nil != X1 ) ) ) ),
inference(rectify,[],[f29]) ).
tff(f29,plain,
! [X1: $int,X0: list] :
( ( ? [X3: $int,X2: list] :
( ~ $less(X3,0)
& $less(X3,X1)
& inRange(X1,X2)
& ( cons(X3,X2) = X0 ) )
| ( nil = X0 )
| ~ inRange(X1,X0) )
& ( inRange(X1,X0)
| ( ! [X3: $int,X2: list] :
( $less(X3,0)
| ~ $less(X3,X1)
| ~ inRange(X1,X2)
| ( cons(X3,X2) != X0 ) )
& ( nil != X0 ) ) ) ),
inference(flattening,[],[f28]) ).
tff(f28,plain,
! [X1: $int,X0: list] :
( ( ? [X3: $int,X2: list] :
( ~ $less(X3,0)
& $less(X3,X1)
& inRange(X1,X2)
& ( cons(X3,X2) = X0 ) )
| ( nil = X0 )
| ~ inRange(X1,X0) )
& ( inRange(X1,X0)
| ( ! [X3: $int,X2: list] :
( $less(X3,0)
| ~ $less(X3,X1)
| ~ inRange(X1,X2)
| ( cons(X3,X2) != X0 ) )
& ( nil != X0 ) ) ) ),
inference(nnf_transformation,[],[f22]) ).
tff(f22,plain,
! [X1: $int,X0: list] :
( ( ? [X3: $int,X2: list] :
( ~ $less(X3,0)
& $less(X3,X1)
& inRange(X1,X2)
& ( cons(X3,X2) = X0 ) )
| ( nil = X0 ) )
<=> inRange(X1,X0) ),
inference(rectify,[],[f8]) ).
tff(f8,plain,
! [X1: list,X2: $int] :
( ( ( nil = X1 )
| ? [X3: list,X0: $int] :
( $less(X0,X2)
& inRange(X2,X3)
& ~ $less(X0,0)
& ( cons(X0,X3) = X1 ) ) )
<=> inRange(X2,X1) ),
inference(theory_normalization,[],[f5]) ).
tff(f5,axiom,
! [X1: list,X2: $int] :
( ( ( nil = X1 )
| ? [X3: list,X0: $int] :
( $less(X0,X2)
& inRange(X2,X3)
& $lesseq(0,X0)
& ( cons(X0,X3) = X1 ) ) )
<=> inRange(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inRange) ).
tff(f82,plain,
inRange(4,cons(5,cons(2,nil))),
inference(backward_demodulation,[],[f48,f80]) ).
tff(f80,plain,
cons(5,cons(2,nil)) = sK1(4,cons(1,cons(5,cons(2,nil)))),
inference(forward_demodulation,[],[f66,f37]) ).
tff(f37,plain,
! [X0: list,X1: $int] : ( tail(cons(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f27]) ).
tff(f27,plain,
! [X0: list,X1: $int] : ( tail(cons(X1,X0)) = X0 ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X1: list,X0: $int] : ( tail(cons(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2) ).
tff(f66,plain,
tail(cons(1,cons(5,cons(2,nil)))) = sK1(4,cons(1,cons(5,cons(2,nil)))),
inference(superposition,[],[f37,f47]) ).
tff(f47,plain,
cons(1,cons(5,cons(2,nil))) = cons(sK0(4,cons(1,cons(5,cons(2,nil)))),sK1(4,cons(1,cons(5,cons(2,nil))))),
inference(unit_resulting_resolution,[],[f36,f46,f40]) ).
tff(f46,plain,
inRange(4,cons(1,cons(5,cons(2,nil)))),
inference(unit_resulting_resolution,[],[f15,f33]) ).
tff(f33,plain,
! [X0: $int] :
( inRange(X0,cons(1,cons(5,cons(2,nil))))
| $less(X0,4) ),
inference(cnf_transformation,[],[f25]) ).
tff(f25,plain,
! [X0: $int] :
( inRange(X0,cons(1,cons(5,cons(2,nil))))
| $less(X0,4) ),
inference(ennf_transformation,[],[f24]) ).
tff(f24,plain,
! [X0: $int] :
( ~ $less(X0,4)
=> inRange(X0,cons(1,cons(5,cons(2,nil)))) ),
inference(rectify,[],[f9]) ).
tff(f9,plain,
! [X2: $int] :
( ~ $less(X2,4)
=> inRange(X2,cons(1,cons(5,cons(2,nil)))) ),
inference(theory_normalization,[],[f7]) ).
tff(f7,negated_conjecture,
~ ~ ! [X2: $int] :
( $greatereq(X2,4)
=> inRange(X2,cons(1,cons(5,cons(2,nil)))) ),
inference(negated_conjecture,[],[f6]) ).
tff(f6,conjecture,
~ ! [X2: $int] :
( $greatereq(X2,4)
=> inRange(X2,cons(1,cons(5,cons(2,nil)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(f15,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_147,[]) ).
tff(f48,plain,
inRange(4,sK1(4,cons(1,cons(5,cons(2,nil))))),
inference(unit_resulting_resolution,[],[f36,f46,f41]) ).
tff(f41,plain,
! [X0: $int,X1: list] :
( inRange(X0,sK1(X0,X1))
| ~ inRange(X0,X1)
| ( nil = X1 ) ),
inference(cnf_transformation,[],[f32]) ).
tff(f36,plain,
! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
inference(cnf_transformation,[],[f4]) ).
tff(f4,axiom,
! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).
tff(f111,plain,
~ $less(3,sK0(4,cons(5,cons(2,nil)))),
inference(cancellation,[],[f109]) ).
tff(f109,plain,
~ $less(4,$sum(sK0(4,cons(5,cons(2,nil))),1)),
inference(unit_resulting_resolution,[],[f89,f21]) ).
tff(f21,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(theory_axiom_166,[]) ).
tff(f89,plain,
$less(sK0(4,cons(5,cons(2,nil))),4),
inference(unit_resulting_resolution,[],[f36,f82,f42]) ).
tff(f42,plain,
! [X0: $int,X1: list] :
( $less(sK0(X0,X1),X0)
| ( nil = X1 )
| ~ inRange(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : DAT101=1 : TPTP v8.1.0. Released v6.1.0.
% 0.06/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 20:21:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.48 % (1324)lrs+10_1:1_canc=force:tha=some:to=lpo:i=35:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/35Mi)
% 0.20/0.50 % (1325)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)
% 0.20/0.50 % (1340)lrs+1002_1:1_br=off:canc=force:drc=off:s2a=on:sos=on:sp=reverse_frequency:urr=on:i=42:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/42Mi)
% 0.20/0.51 % (1340)First to succeed.
% 0.20/0.51 % (1325)Instruction limit reached!
% 0.20/0.51 % (1325)------------------------------
% 0.20/0.51 % (1325)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (1325)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (1325)Termination reason: Unknown
% 0.20/0.51 % (1325)Termination phase: Saturation
% 0.20/0.51
% 0.20/0.51 % (1325)Memory used [KB]: 5500
% 0.20/0.51 % (1325)Time elapsed: 0.111 s
% 0.20/0.51 % (1325)Instructions burned: 6 (million)
% 0.20/0.51 % (1325)------------------------------
% 0.20/0.51 % (1325)------------------------------
% 0.20/0.51 % (1331)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.20/0.51 % (1336)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)
% 0.20/0.51 % (1317)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 % (1323)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)
% 0.20/0.51 % (1330)lrs+10_1:1_ev=force:gve=cautious:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.51 % (1330)Instruction limit reached!
% 0.20/0.51 % (1330)------------------------------
% 0.20/0.51 % (1330)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (1330)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (1330)Termination reason: Unknown
% 0.20/0.51 % (1330)Termination phase: Saturation
% 0.20/0.51
% 0.20/0.51 % (1330)Memory used [KB]: 895
% 0.20/0.51 % (1330)Time elapsed: 0.003 s
% 0.20/0.51 % (1330)Instructions burned: 2 (million)
% 0.20/0.51 % (1330)------------------------------
% 0.20/0.51 % (1330)------------------------------
% 0.20/0.51 % (1323)Instruction limit reached!
% 0.20/0.51 % (1323)------------------------------
% 0.20/0.51 % (1323)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (1323)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (1323)Termination reason: Unknown
% 0.20/0.51 % (1323)Termination phase: Property scanning
% 0.20/0.51
% 0.20/0.51 % (1323)Memory used [KB]: 895
% 0.20/0.51 % (1323)Time elapsed: 0.004 s
% 0.20/0.51 % (1323)Instructions burned: 2 (million)
% 0.20/0.51 % (1323)------------------------------
% 0.20/0.51 % (1323)------------------------------
% 0.20/0.51 % (1341)lrs+1_3:1_ep=RSTC:sos=on:urr=on:i=43:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/43Mi)
% 0.20/0.52 % (1338)lrs+1_1:10_av=off:drc=off:nwc=2.0:sp=reverse_frequency:thsq=on:thsqc=64:thsql=off:i=47:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/47Mi)
% 0.20/0.52 % (1344)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=41:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/41Mi)
% 0.20/0.52 % (1333)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)
% 0.20/0.52 % (1340)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
% 0.20/0.52 % (1340)------------------------------
% 0.20/0.52 % (1340)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (1340)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (1340)Termination reason: Refutation
% 0.20/0.52
% 0.20/0.52 % (1340)Memory used [KB]: 5628
% 0.20/0.52 % (1340)Time elapsed: 0.118 s
% 0.20/0.52 % (1340)Instructions burned: 8 (million)
% 0.20/0.52 % (1340)------------------------------
% 0.20/0.52 % (1340)------------------------------
% 0.20/0.52 % (1313)Success in time 0.168 s
%------------------------------------------------------------------------------