TSTP Solution File: DAT044_1 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : DAT044_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 : n003.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 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of formulae : 59 ( 7 unt; 8 typ; 0 def)
% Number of atoms : 121 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 127 ( 57 ~; 49 |; 7 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 116 ( 46 atm; 15 fun; 13 num; 42 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 8 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 57 ( 51 !; 6 ?; 57 :)
% 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(func_def_9,type,
sK0: $int ).
tff(func_def_10,type,
sK1: collection ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f231,plain,
$false,
inference(avatar_sat_refutation,[],[f106,f120,f123,f230]) ).
tff(f230,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[],[f229]) ).
tff(f229,plain,
( $false
| ~ spl2_4 ),
inference(subsumption_resolution,[],[f228,f23]) ).
tff(f23,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_147,[]) ).
tff(f228,plain,
( $less(count(sK1),count(sK1))
| ~ spl2_4 ),
inference(evaluation,[],[f226]) ).
tff(f226,plain,
( $less(count(sK1),count(sK1))
| ~ $less(0,1)
| ~ spl2_4 ),
inference(superposition,[],[f163,f20]) ).
tff(f20,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_142,[]) ).
tff(f163,plain,
( ! [X2: $int] :
( $less($sum(count(sK1),X2),count(sK1))
| ~ $less(X2,1) )
| ~ spl2_4 ),
inference(superposition,[],[f148,f18]) ).
tff(f18,plain,
! [X0: $int,X1: $int] : ( $sum(X1,X0) = $sum(X0,X1) ),
introduced(theory_axiom_140,[]) ).
tff(f148,plain,
( ! [X1: $int] :
( $less($sum(X1,count(sK1)),count(sK1))
| ~ $less(X1,1) )
| ~ spl2_4 ),
inference(resolution,[],[f137,f26]) ).
tff(f26,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(theory_axiom_150,[]) ).
tff(f137,plain,
( ! [X0: $int] :
( ~ $less(X0,$sum(1,count(sK1)))
| $less(X0,count(sK1)) )
| ~ spl2_4 ),
inference(forward_demodulation,[],[f136,f18]) ).
tff(f136,plain,
( ! [X0: $int] :
( $less(X0,count(sK1))
| ~ $less(X0,$sum(count(sK1),1)) )
| ~ spl2_4 ),
inference(subsumption_resolution,[],[f134,f132]) ).
tff(f132,plain,
( ~ in(sK0,sK1)
| ~ spl2_4 ),
inference(subsumption_resolution,[],[f130,f23]) ).
tff(f130,plain,
( $less(count(sK1),count(sK1))
| ~ in(sK0,sK1)
| ~ spl2_4 ),
inference(superposition,[],[f105,f61]) ).
tff(f61,plain,
! [X0: collection,X1: $int] :
( ( count(add(X1,X0)) = count(X0) )
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f43]) ).
tff(f43,plain,
! [X0: collection,X1: $int] :
( ( ( count(add(X1,X0)) = count(X0) )
| ~ in(X1,X0) )
& ( in(X1,X0)
| ( count(add(X1,X0)) != count(X0) ) ) ),
inference(nnf_transformation,[],[f31]) ).
tff(f31,plain,
! [X0: collection,X1: $int] :
( ( count(add(X1,X0)) = count(X0) )
<=> in(X1,X0) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X16: collection,X15: $int] :
( ( count(add(X15,X16)) = count(X16) )
<=> in(X15,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
tff(f105,plain,
( $less(count(add(sK0,sK1)),count(sK1))
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f104]) ).
tff(f104,plain,
( spl2_4
<=> $less(count(add(sK0,sK1)),count(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
tff(f134,plain,
( ! [X0: $int] :
( in(sK0,sK1)
| $less(X0,count(sK1))
| ~ $less(X0,$sum(count(sK1),1)) )
| ~ spl2_4 ),
inference(superposition,[],[f128,f73]) ).
tff(f73,plain,
! [X0: collection,X1: $int] :
( ( count(add(X1,X0)) = $sum(count(X0),1) )
| in(X1,X0) ),
inference(cnf_transformation,[],[f52]) ).
tff(f52,plain,
! [X0: collection,X1: $int] :
( ( ( count(add(X1,X0)) = $sum(count(X0),1) )
| in(X1,X0) )
& ( ~ in(X1,X0)
| ( count(add(X1,X0)) != $sum(count(X0),1) ) ) ),
inference(nnf_transformation,[],[f39]) ).
tff(f39,plain,
! [X0: collection,X1: $int] :
( ( count(add(X1,X0)) = $sum(count(X0),1) )
<=> ~ in(X1,X0) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X14: collection,X13: $int] :
( ( count(add(X13,X14)) = $sum(count(X14),1) )
<=> ~ in(X13,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(f128,plain,
( ! [X0: $int] :
( ~ $less(X0,count(add(sK0,sK1)))
| $less(X0,count(sK1)) )
| ~ spl2_4 ),
inference(resolution,[],[f105,f24]) ).
tff(f24,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) ),
introduced(theory_axiom_148,[]) ).
tff(f123,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f122]) ).
tff(f122,plain,
( $false
| ~ spl2_2 ),
inference(subsumption_resolution,[],[f121,f23]) ).
tff(f121,plain,
( $less(sK0,sK0)
| ~ spl2_2 ),
inference(resolution,[],[f97,f78]) ).
tff(f78,plain,
! [X2: $int] :
( ~ in(X2,sK1)
| $less(X2,sK0) ),
inference(cnf_transformation,[],[f56]) ).
tff(f56,plain,
( ! [X2: $int] :
( $less(X2,sK0)
| ~ in(X2,sK1) )
& ~ $less(count(sK1),count(add(sK0,sK1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f54,f55]) ).
tff(f55,plain,
( ? [X0: $int,X1: collection] :
( ! [X2: $int] :
( $less(X2,X0)
| ~ in(X2,X1) )
& ~ $less(count(X1),count(add(X0,X1))) )
=> ( ! [X2: $int] :
( $less(X2,sK0)
| ~ in(X2,sK1) )
& ~ $less(count(sK1),count(add(sK0,sK1))) ) ),
introduced(choice_axiom,[]) ).
tff(f54,plain,
? [X0: $int,X1: collection] :
( ! [X2: $int] :
( $less(X2,X0)
| ~ in(X2,X1) )
& ~ $less(count(X1),count(add(X0,X1))) ),
inference(rectify,[],[f42]) ).
tff(f42,plain,
? [X1: $int,X0: collection] :
( ! [X2: $int] :
( $less(X2,X1)
| ~ in(X2,X0) )
& ~ $less(count(X0),count(add(X1,X0))) ),
inference(ennf_transformation,[],[f16]) ).
tff(f16,plain,
~ ! [X0: collection,X1: $int] :
( ! [X2: $int] :
( in(X2,X0)
=> $less(X2,X1) )
=> $less(count(X0),count(add(X1,X0))) ),
inference(theory_normalization,[],[f14]) ).
tff(f14,negated_conjecture,
~ ! [X0: collection,X1: $int] :
( ! [X2: $int] :
( in(X2,X0)
=> $greater(X1,X2) )
=> $greater(count(add(X1,X0)),count(X0)) ),
inference(negated_conjecture,[],[f13]) ).
tff(f13,conjecture,
! [X0: collection,X1: $int] :
( ! [X2: $int] :
( in(X2,X0)
=> $greater(X1,X2) )
=> $greater(count(add(X1,X0)),count(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f97,plain,
( in(sK0,sK1)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f96]) ).
tff(f96,plain,
( spl2_2
<=> in(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
tff(f120,plain,
( spl2_2
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f114,f101,f96]) ).
tff(f101,plain,
( spl2_3
<=> ( count(add(sK0,sK1)) = count(sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
tff(f114,plain,
( in(sK0,sK1)
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f109]) ).
tff(f109,plain,
( in(sK0,sK1)
| ( count(sK1) != count(sK1) )
| ~ spl2_3 ),
inference(superposition,[],[f60,f102]) ).
tff(f102,plain,
( ( count(add(sK0,sK1)) = count(sK1) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f101]) ).
tff(f60,plain,
! [X0: collection,X1: $int] :
( ( count(add(X1,X0)) != count(X0) )
| in(X1,X0) ),
inference(cnf_transformation,[],[f43]) ).
tff(f106,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f88,f104,f101]) ).
tff(f88,plain,
( $less(count(add(sK0,sK1)),count(sK1))
| ( count(add(sK0,sK1)) = count(sK1) ) ),
inference(resolution,[],[f77,f25]) ).
tff(f25,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(theory_axiom_149,[]) ).
tff(f77,plain,
~ $less(count(sK1),count(add(sK0,sK1))),
inference(cnf_transformation,[],[f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : DAT044=1 : TPTP v8.1.0. Released v5.0.0.
% 0.04/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n003.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 20:18:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.49 % (18319)lrs+10_1:1_ss=axioms:st=5.0:tha=off:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.49 % (18302)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)
% 0.20/0.49 % (18301)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)
% 0.20/0.50 % (18308)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)
% 0.20/0.50 % (18310)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)
% 0.20/0.50 % (18302)First to succeed.
% 0.20/0.50 % (18318)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)
% 0.20/0.50 % (18326)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)
% 0.20/0.50 % (18324)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)
% 0.20/0.50 % (18311)lrs+10_1:1_canc=force:tha=some:to=lpo:i=35:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/35Mi)
% 0.20/0.51 % (18302)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Theorem for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51 % (18302)------------------------------
% 0.20/0.51 % (18302)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (18302)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (18302)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (18302)Memory used [KB]: 5628
% 0.20/0.51 % (18302)Time elapsed: 0.099 s
% 0.20/0.51 % (18302)Instructions burned: 9 (million)
% 0.20/0.51 % (18302)------------------------------
% 0.20/0.51 % (18302)------------------------------
% 0.20/0.51 % (18300)Success in time 0.163 s
%------------------------------------------------------------------------------