TSTP Solution File: DAT028_1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT028_1 : TPTP v8.2.0. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -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 : Mon May 20 19:51:04 EDT 2024
% Result : Theorem 0.22s 0.39s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 30
% Syntax : Number of formulae : 149 ( 44 unt; 9 typ; 0 def)
% Number of atoms : 342 ( 48 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 327 ( 125 ~; 133 |; 46 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 626 ( 198 atm; 60 fun; 180 num; 188 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 5 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 226 ( 202 !; 24 ?; 226 :)
% 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(f218,plain,
$false,
inference(global_subsumption,[],[f17,f12,f10,f51,f45,f50,f52,f40,f41,f14,f42,f37,f11,f19,f43,f44,f38,f39,f13,f54,f53,f56,f55,f9,f18,f70,f68,f74,f73,f72,f20,f87,f46,f89,f48,f69,f97,f98,f106,f86,f111,f112,f113,f120,f123,f118,f85,f127,f128,f91,f132,f133,f15,f135,f136,f137,f138,f139,f140,f142,f143,f145,f144,f149,f148,f146,f150,f151,f154,f158,f153,f159,f161,f163,f162,f141,f168,f169,f172,f16,f174,f175,f176,f177,f178,f180,f201,f184,f185,f187,f188,f189,f190,f191,f202,f193,f203,f197,f198,f200,f204,f206,f207,f208]) ).
tff(f208,plain,
~ $less(sK3(1),1),
inference(superposition,[],[f118,f200]) ).
tff(f207,plain,
$less(0,sK3(1)),
inference(superposition,[],[f56,f200]) ).
tff(f206,plain,
$less(sK3(1),1),
inference(superposition,[],[f54,f200]) ).
tff(f204,plain,
in(1,sK0),
inference(superposition,[],[f40,f200]) ).
tff(f200,plain,
1 = sK2,
inference(subsumption_resolution,[],[f179,f150]) ).
tff(f179,plain,
( $less(sK2,1)
| ( 1 = sK2 ) ),
inference(resolution,[],[f16,f41]) ).
tff(f198,plain,
! [X0: $int] :
( $less(X0,-1)
| ( -1 = X0 )
| ~ $less(X0,0) ),
inference(resolution,[],[f16,f89]) ).
tff(f197,plain,
( $less(1,sK3(sK2))
| ( 1 = sK3(sK2) ) ),
inference(resolution,[],[f16,f118]) ).
tff(f203,plain,
1 = sK2,
inference(subsumption_resolution,[],[f194,f41]) ).
tff(f194,plain,
( $less(1,sK2)
| ( 1 = sK2 ) ),
inference(resolution,[],[f16,f150]) ).
tff(f193,plain,
! [X0: $int] :
( $less(0,$sum(X0,1))
| ( 0 = $sum(X0,1) )
| $less(X0,-1) ),
inference(resolution,[],[f16,f91]) ).
tff(f202,plain,
1 = sK2,
inference(subsumption_resolution,[],[f192,f150]) ).
tff(f192,plain,
( $less(sK2,1)
| ( 1 = sK2 ) ),
inference(resolution,[],[f16,f41]) ).
tff(f191,plain,
! [X0: $int] :
( $less(X0,0)
| ( 0 = X0 )
| ~ $less(X0,1) ),
inference(resolution,[],[f16,f113]) ).
tff(f190,plain,
! [X0: $int] :
( $less(sK3(sK2),X0)
| ( sK3(sK2) = X0 )
| $less(X0,sK2) ),
inference(resolution,[],[f16,f144]) ).
tff(f189,plain,
! [X0: $int,X1: $int] :
( $less($sum(1,X0),X1)
| ( $sum(1,X0) = X1 )
| ~ $less(X0,X1) ),
inference(resolution,[],[f16,f86]) ).
tff(f188,plain,
! [X0: $int,X1: $int] :
( $less($sum(X0,1),X1)
| ( $sum(X0,1) = X1 )
| ~ $less(X0,X1) ),
inference(resolution,[],[f16,f20]) ).
tff(f187,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X1)
| ( X0 = X1 )
| ~ $less(X2,X1)
| $less(X2,X0) ),
inference(resolution,[],[f16,f15]) ).
tff(f185,plain,
! [X0: $int] :
( $less(X0,-1)
| ( -1 = X0 )
| ~ $less(X0,0) ),
inference(resolution,[],[f16,f89]) ).
tff(f184,plain,
( $less(1,sK3(sK2))
| ( 1 = sK3(sK2) ) ),
inference(resolution,[],[f16,f118]) ).
tff(f201,plain,
1 = sK2,
inference(subsumption_resolution,[],[f181,f41]) ).
tff(f181,plain,
( $less(1,sK2)
| ( 1 = sK2 ) ),
inference(resolution,[],[f16,f150]) ).
tff(f180,plain,
! [X0: $int] :
( $less(0,$sum(X0,1))
| ( 0 = $sum(X0,1) )
| $less(X0,-1) ),
inference(resolution,[],[f16,f91]) ).
tff(f178,plain,
! [X0: $int] :
( $less(X0,0)
| ( 0 = X0 )
| ~ $less(X0,1) ),
inference(resolution,[],[f16,f113]) ).
tff(f177,plain,
! [X0: $int] :
( $less(sK3(sK2),X0)
| ( sK3(sK2) = X0 )
| $less(X0,sK2) ),
inference(resolution,[],[f16,f144]) ).
tff(f176,plain,
! [X0: $int,X1: $int] :
( $less($sum(1,X0),X1)
| ( $sum(1,X0) = X1 )
| ~ $less(X0,X1) ),
inference(resolution,[],[f16,f86]) ).
tff(f175,plain,
! [X0: $int,X1: $int] :
( $less($sum(X0,1),X1)
| ( $sum(X0,1) = X1 )
| ~ $less(X0,X1) ),
inference(resolution,[],[f16,f20]) ).
tff(f174,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X1)
| ( X0 = X1 )
| ~ $less(X2,X1)
| $less(X2,X0) ),
inference(resolution,[],[f16,f15]) ).
tff(f16,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f172,plain,
~ $less(sK3(sK2),0),
inference(evaluation,[],[f171]) ).
tff(f171,plain,
( ~ $less(-1,0)
| ~ $less(sK3(sK2),0) ),
inference(resolution,[],[f141,f89]) ).
tff(f169,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,0)
| ~ $less(X1,X0)
| $less(X1,sK3(sK2)) ),
inference(resolution,[],[f141,f15]) ).
tff(f168,plain,
~ $less(sK3(sK2),0),
inference(resolution,[],[f141,f14]) ).
tff(f141,plain,
! [X0: $int] :
( $less(X0,sK3(sK2))
| ~ $less(X0,0) ),
inference(resolution,[],[f15,f56]) ).
tff(f162,plain,
~ $less(sK2,-1),
inference(resolution,[],[f161,f14]) ).
tff(f163,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,-1)
| ~ $less(X1,X0)
| $less(X1,sK2) ),
inference(resolution,[],[f161,f15]) ).
tff(f161,plain,
! [X0: $int] :
( $less(X0,sK2)
| ~ $less(X0,-1) ),
inference(resolution,[],[f159,f15]) ).
tff(f159,plain,
$less(-1,sK2),
inference(resolution,[],[f153,f72]) ).
tff(f153,plain,
~ $less(sK2,0),
inference(resolution,[],[f151,f14]) ).
tff(f158,plain,
~ $less(sK2,0),
inference(evaluation,[],[f157]) ).
tff(f157,plain,
( ~ $less(-1,0)
| ~ $less(sK2,0) ),
inference(resolution,[],[f151,f89]) ).
tff(f154,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,0)
| ~ $less(X1,X0)
| $less(X1,sK2) ),
inference(resolution,[],[f151,f15]) ).
tff(f151,plain,
! [X0: $int] :
( $less(X0,sK2)
| ~ $less(X0,0) ),
inference(resolution,[],[f146,f15]) ).
tff(f150,plain,
~ $less(sK2,1),
inference(resolution,[],[f146,f113]) ).
tff(f146,plain,
$less(0,sK2),
inference(resolution,[],[f144,f56]) ).
tff(f148,plain,
( $less(-1,sK2)
| $less(sK3(sK2),0) ),
inference(resolution,[],[f144,f72]) ).
tff(f149,plain,
$less(0,sK2),
inference(subsumption_resolution,[],[f147,f118]) ).
tff(f147,plain,
( $less(0,sK2)
| $less(sK3(sK2),1) ),
inference(resolution,[],[f144,f98]) ).
tff(f144,plain,
! [X0: $int] :
( ~ $less(X0,sK3(sK2))
| $less(X0,sK2) ),
inference(resolution,[],[f15,f54]) ).
tff(f145,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,-1)
| $less(X0,X1)
| $less(X1,0) ),
inference(resolution,[],[f15,f72]) ).
tff(f143,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,$sum(X1,1))
| $less(X0,0)
| ~ $less(X1,-1) ),
inference(resolution,[],[f15,f85]) ).
tff(f142,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,0)
| $less(X0,X1)
| $less(X1,1) ),
inference(resolution,[],[f15,f98]) ).
tff(f140,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,1)
| $less(0,X1) ),
inference(resolution,[],[f15,f98]) ).
tff(f139,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,0)
| $less(-1,X1) ),
inference(resolution,[],[f15,f72]) ).
tff(f138,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(1,X2))
| $less(X2,X1) ),
inference(resolution,[],[f15,f69]) ).
tff(f137,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(1,X1)) ),
inference(resolution,[],[f15,f73]) ).
tff(f136,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X1,1)) ),
inference(resolution,[],[f15,f68]) ).
tff(f135,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) ),
inference(resolution,[],[f15,f18]) ).
tff(f15,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f133,plain,
! [X0: $int] :
( ~ $less($sum(1,X0),0)
| $less(X0,-1) ),
inference(superposition,[],[f91,f9]) ).
tff(f132,plain,
! [X0: $int] :
( ~ $less($sum(1,X0),0)
| $less(X0,-1) ),
inference(superposition,[],[f91,f9]) ).
tff(f91,plain,
! [X0: $int] :
( ~ $less($sum(X0,1),0)
| $less(X0,-1) ),
inference(resolution,[],[f89,f18]) ).
tff(f128,plain,
! [X0: $int] :
( $less($sum(1,X0),0)
| ~ $less(X0,-1) ),
inference(superposition,[],[f85,f9]) ).
tff(f127,plain,
! [X0: $int] :
( $less($sum(1,X0),0)
| ~ $less(X0,-1) ),
inference(superposition,[],[f85,f9]) ).
tff(f85,plain,
! [X0: $int] :
( $less($sum(X0,1),0)
| ~ $less(X0,-1) ),
inference(resolution,[],[f20,f72]) ).
tff(f118,plain,
~ $less(sK3(sK2),1),
inference(resolution,[],[f113,f56]) ).
tff(f123,plain,
! [X0: $int] :
( ~ $less($sum(1,X0),1)
| $less(X0,0) ),
inference(resolution,[],[f113,f69]) ).
tff(f120,plain,
! [X0: $int] :
( ~ $less($sum(X0,1),1)
| $less(X0,0) ),
inference(resolution,[],[f113,f18]) ).
tff(f113,plain,
! [X0: $int] :
( ~ $less(0,X0)
| ~ $less(X0,1) ),
inference(superposition,[],[f86,f11]) ).
tff(f112,plain,
! [X0: $int] :
( ~ $less(X0,-1)
| $less($sum(1,X0),0) ),
inference(resolution,[],[f86,f72]) ).
tff(f111,plain,
! [X0: $int] :
( ~ $less(X0,0)
| $less($sum(1,X0),1) ),
inference(resolution,[],[f86,f98]) ).
tff(f86,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ),
inference(superposition,[],[f20,f9]) ).
tff(f106,plain,
! [X0: $int] :
( $less($sum(X0,1),1)
| ~ $less(X0,0) ),
inference(resolution,[],[f98,f20]) ).
tff(f98,plain,
! [X0: $int] :
( $less(X0,1)
| $less(0,X0) ),
inference(superposition,[],[f69,f11]) ).
tff(f97,plain,
! [X0: $int] :
( $less(X0,-1)
| ~ $less($sum(1,X0),0) ),
inference(resolution,[],[f69,f89]) ).
tff(f69,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ),
inference(superposition,[],[f18,f9]) ).
tff(f48,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tff(f36,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ( X0 != X2 )
& ~ in(X0,X1) ) ) ),
inference(flattening,[],[f35]) ).
tff(f35,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) )
& ( in(X0,add(X2,X1))
| ( ( X0 != X2 )
& ~ in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f25]) ).
tff(f25,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 = X2 )
| in(X0,X1) )
<=> in(X0,add(X2,X1)) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X5: $int,X6: collection,X7: $int] :
( ( ( X5 = X7 )
| in(X5,X6) )
<=> in(X5,add(X7,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
tff(f89,plain,
! [X0: $int] :
( ~ $less(-1,X0)
| ~ $less(X0,0) ),
inference(evaluation,[],[f88]) ).
tff(f88,plain,
! [X0: $int] :
( ~ $less(X0,0)
| ~ $less($uminus(1),X0) ),
inference(superposition,[],[f20,f55]) ).
tff(f46,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] :
( ( ( ( X0 != X2 )
& in(X0,X1) )
| ~ in(X0,remove(X2,X1)) )
& ( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
inference(flattening,[],[f33]) ).
tff(f33,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( ( X0 != X2 )
& in(X0,X1) )
| ~ in(X0,remove(X2,X1)) )
& ( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f24]) ).
tff(f24,plain,
! [X0: $int,X1: collection,X2: $int] :
( ( ( X0 != X2 )
& in(X0,X1) )
<=> in(X0,remove(X2,X1)) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X8: $int,X9: collection,X10: $int] :
( ( ( X8 != X10 )
& in(X8,X9) )
<=> in(X8,remove(X10,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
tff(f87,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ),
inference(superposition,[],[f20,f9]) ).
tff(f20,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(theory_axiom_161,[]) ).
tff(f72,plain,
! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) ),
inference(evaluation,[],[f71]) ).
tff(f71,plain,
! [X0: $int] :
( $less(X0,0)
| $less($uminus(1),X0) ),
inference(superposition,[],[f18,f55]) ).
tff(f73,plain,
! [X0: $int] : $less(X0,$sum(1,X0)),
inference(superposition,[],[f68,f9]) ).
tff(f74,plain,
! [X0: $int] : $less(X0,$sum(1,X0)),
inference(superposition,[],[f68,f9]) ).
tff(f68,plain,
! [X0: $int] : $less(X0,$sum(X0,1)),
inference(resolution,[],[f18,f14]) ).
tff(f70,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ),
inference(superposition,[],[f18,f9]) ).
tff(f18,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(theory_axiom_147,[]) ).
tff(f9,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f55,plain,
! [X0: $int] : ( 0 = $sum($uminus(X0),X0) ),
inference(superposition,[],[f13,f19]) ).
tff(f56,plain,
$less(0,sK3(sK2)),
inference(resolution,[],[f53,f40]) ).
tff(f53,plain,
! [X0: $int] :
( ~ in(X0,sK0)
| $less(0,sK3(X0)) ),
inference(resolution,[],[f38,f37]) ).
tff(f54,plain,
$less(sK3(sK2),sK2),
inference(resolution,[],[f39,f40]) ).
tff(f13,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f39,plain,
! [X3: $int] :
( ~ in(X3,sK0)
| $less(sK3(X3),X3) ),
inference(cnf_transformation,[],[f32]) ).
tff(f32,plain,
( ~ $less(1,sK2)
& in(sK2,sK0)
& ! [X3: $int] :
( ( $less(sK3(X3),X3)
& in(sK3(X3),sK1) )
| ~ in(X3,sK0) )
& ! [X5: $int] :
( $less(0,X5)
| ~ in(X5,sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f28,f31,f30,f29]) ).
tff(f29,plain,
( ? [X0: collection,X1: collection] :
( ? [X2: $int] :
( ~ $less(1,X2)
& in(X2,X0) )
& ! [X3: $int] :
( ? [X4: $int] :
( $less(X4,X3)
& in(X4,X1) )
| ~ in(X3,X0) )
& ! [X5: $int] :
( $less(0,X5)
| ~ in(X5,X1) ) )
=> ( ? [X2: $int] :
( ~ $less(1,X2)
& in(X2,sK0) )
& ! [X3: $int] :
( ? [X4: $int] :
( $less(X4,X3)
& in(X4,sK1) )
| ~ in(X3,sK0) )
& ! [X5: $int] :
( $less(0,X5)
| ~ in(X5,sK1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f30,plain,
( ? [X2: $int] :
( ~ $less(1,X2)
& in(X2,sK0) )
=> ( ~ $less(1,sK2)
& in(sK2,sK0) ) ),
introduced(choice_axiom,[]) ).
tff(f31,plain,
! [X3: $int] :
( ? [X4: $int] :
( $less(X4,X3)
& in(X4,sK1) )
=> ( $less(sK3(X3),X3)
& in(sK3(X3),sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f28,plain,
? [X0: collection,X1: collection] :
( ? [X2: $int] :
( ~ $less(1,X2)
& in(X2,X0) )
& ! [X3: $int] :
( ? [X4: $int] :
( $less(X4,X3)
& in(X4,X1) )
| ~ in(X3,X0) )
& ! [X5: $int] :
( $less(0,X5)
| ~ in(X5,X1) ) ),
inference(rectify,[],[f27]) ).
tff(f27,plain,
? [X0: collection,X1: collection] :
( ? [X5: $int] :
( ~ $less(1,X5)
& in(X5,X0) )
& ! [X2: $int] :
( ? [X3: $int] :
( $less(X3,X2)
& in(X3,X1) )
| ~ in(X2,X0) )
& ! [X4: $int] :
( $less(0,X4)
| ~ in(X4,X1) ) ),
inference(flattening,[],[f26]) ).
tff(f26,plain,
? [X0: collection,X1: collection] :
( ? [X5: $int] :
( ~ $less(1,X5)
& in(X5,X0) )
& ! [X2: $int] :
( ? [X3: $int] :
( $less(X3,X2)
& in(X3,X1) )
| ~ in(X2,X0) )
& ! [X4: $int] :
( $less(0,X4)
| ~ in(X4,X1) ) ),
inference(ennf_transformation,[],[f21]) ).
tff(f21,plain,
~ ! [X0: collection,X1: collection] :
( ( ! [X2: $int] :
( in(X2,X0)
=> ? [X3: $int] :
( $less(X3,X2)
& in(X3,X1) ) )
& ! [X4: $int] :
( in(X4,X1)
=> $less(0,X4) ) )
=> ! [X5: $int] :
( in(X5,X0)
=> $less(1,X5) ) ),
inference(rectify,[],[f8]) ).
tff(f8,plain,
~ ! [X0: collection,X1: 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,
~ ! [X0: collection,X1: 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,
! [X0: collection,X1: 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/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f38,plain,
! [X3: $int] :
( in(sK3(X3),sK1)
| ~ in(X3,sK0) ),
inference(cnf_transformation,[],[f32]) ).
tff(f44,plain,
! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
inference(cnf_transformation,[],[f23]) ).
tff(f23,plain,
! [X0: $int,X1: collection] : in(X0,add(X0,X1)),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X1: $int,X2: collection] : in(X1,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
tff(f43,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/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(f19,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f11,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f37,plain,
! [X5: $int] :
( ~ in(X5,sK1)
| $less(0,X5) ),
inference(cnf_transformation,[],[f32]) ).
tff(f42,plain,
! [X0: $int] : ~ in(X0,empty),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: $int] : ~ in(X0,empty),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
tff(f14,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f41,plain,
~ $less(1,sK2),
inference(cnf_transformation,[],[f32]) ).
tff(f40,plain,
in(sK2,sK0),
inference(cnf_transformation,[],[f32]) ).
tff(f52,plain,
! [X2: $int,X1: collection] : in(X2,add(X2,X1)),
inference(equality_resolution,[],[f49]) ).
tff(f49,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,add(X2,X1))
| ( X0 != X2 ) ),
inference(cnf_transformation,[],[f36]) ).
tff(f50,plain,
! [X2: $int,X0: $int,X1: collection] :
( ( X0 = X2 )
| in(X0,X1)
| ~ in(X0,add(X2,X1)) ),
inference(cnf_transformation,[],[f36]) ).
tff(f45,plain,
! [X2: $int,X0: $int,X1: collection] :
( in(X0,remove(X2,X1))
| ( X0 = X2 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tff(f51,plain,
! [X2: $int,X1: collection] : ~ in(X2,remove(X2,X1)),
inference(equality_resolution,[],[f47]) ).
tff(f47,plain,
! [X2: $int,X0: $int,X1: collection] :
( ( X0 != X2 )
| ~ in(X0,remove(X2,X1)) ),
inference(cnf_transformation,[],[f34]) ).
tff(f10,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f12,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f17,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : DAT028_1 : TPTP v8.2.0. Released v5.0.0.
% 0.15/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 23:43:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % (19453)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.37 % (19454)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (19454)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.38 % (19454)Terminated due to inappropriate strategy.
% 0.22/0.38 % (19454)------------------------------
% 0.22/0.38 % (19454)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.38 % (19454)Termination reason: Inappropriate
% 0.22/0.38
% 0.22/0.38 % (19454)Memory used [KB]: 746
% 0.22/0.38 % (19454)Time elapsed: 0.002 s
% 0.22/0.38 % (19454)Instructions burned: 2 (million)
% 0.22/0.38 % (19454)------------------------------
% 0.22/0.38 % (19454)------------------------------
% 0.22/0.38 % (19456)WARNING: value z3 for option sas not known
% 0.22/0.38 % (19457)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (19456)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.38 % (19460)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.38 % (19459)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.38 % (19457)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.38 % (19457)Terminated due to inappropriate strategy.
% 0.22/0.38 % (19457)------------------------------
% 0.22/0.38 % (19457)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.38 % (19457)Termination reason: Inappropriate
% 0.22/0.38
% 0.22/0.38 % (19457)Memory used [KB]: 746
% 0.22/0.38 % (19457)Time elapsed: 0.002 s
% 0.22/0.38 % (19457)Instructions burned: 2 (million)
% 0.22/0.38 % (19457)------------------------------
% 0.22/0.38 % (19457)------------------------------
% 0.22/0.38 % (19455)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (19455)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.38 % (19455)Terminated due to inappropriate strategy.
% 0.22/0.38 % (19455)------------------------------
% 0.22/0.38 % (19455)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.38 % (19455)Termination reason: Inappropriate
% 0.22/0.38
% 0.22/0.38 % (19455)Memory used [KB]: 747
% 0.22/0.38 % (19455)Time elapsed: 0.002 s
% 0.22/0.38 % (19455)Instructions burned: 2 (million)
% 0.22/0.38 % (19455)------------------------------
% 0.22/0.38 % (19455)------------------------------
% 0.22/0.38 % (19461)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.38 % (19461)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.38 % (19461)Terminated due to inappropriate strategy.
% 0.22/0.38 % (19461)------------------------------
% 0.22/0.38 % (19461)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.38 % (19461)Termination reason: Inappropriate
% 0.22/0.38
% 0.22/0.38 % (19461)Memory used [KB]: 746
% 0.22/0.38 % (19461)Time elapsed: 0.001 s
% 0.22/0.38 % (19461)Instructions burned: 2 (million)
% 0.22/0.38 % (19458)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.39 % (19461)------------------------------
% 0.22/0.39 % (19461)------------------------------
% 0.22/0.39 % (19456)First to succeed.
% 0.22/0.39 % (19459)Also succeeded, but the first one will report.
% 0.22/0.39 % (19456)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19453"
% 0.22/0.39 % (19456)Refutation found. Thanks to Tanya!
% 0.22/0.39 % SZS status Theorem for theBenchmark
% 0.22/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.39 % (19456)------------------------------
% 0.22/0.39 % (19456)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.39 % (19456)Termination reason: Refutation
% 0.22/0.39
% 0.22/0.39 % (19456)Memory used [KB]: 897
% 0.22/0.39 % (19456)Time elapsed: 0.009 s
% 0.22/0.39 % (19456)Instructions burned: 13 (million)
% 0.22/0.39 % (19453)Success in time 0.021 s
%------------------------------------------------------------------------------