TSTP Solution File: SWV492+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SWV492+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n009.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 : Thu Aug 31 23:25:11 EDT 2023
% Result : Theorem 1.47s 0.57s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 25
% Syntax : Number of formulae : 132 ( 5 unt; 0 def)
% Number of atoms : 534 ( 96 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 681 ( 279 ~; 268 |; 96 &)
% ( 16 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 15 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 145 (; 121 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f407,plain,
$false,
inference(avatar_sat_refutation,[],[f82,f86,f90,f94,f101,f116,f187,f200,f225,f309,f374,f379,f385,f406]) ).
fof(f406,plain,
( ~ spl7_3
| ~ spl7_4
| ~ spl7_5
| ~ spl7_13 ),
inference(avatar_contradiction_clause,[],[f405]) ).
fof(f405,plain,
( $false
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5
| ~ spl7_13 ),
inference(subsumption_resolution,[],[f404,f102]) ).
fof(f102,plain,
( int_leq(sK3,n)
| ~ spl7_3
| ~ spl7_4 ),
inference(backward_demodulation,[],[f89,f85]) ).
fof(f85,plain,
( sK3 = sK4
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f84,plain,
( spl7_3
<=> sK3 = sK4 ),
introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).
fof(f89,plain,
( int_leq(sK4,n)
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f88,plain,
( spl7_4
<=> int_leq(sK4,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).
fof(f404,plain,
( ~ int_leq(sK3,n)
| ~ spl7_5
| ~ spl7_13 ),
inference(subsumption_resolution,[],[f401,f93]) ).
fof(f93,plain,
( int_leq(int_one,sK3)
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f92,plain,
( spl7_5
<=> int_leq(int_one,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).
fof(f401,plain,
( ~ int_leq(int_one,sK3)
| ~ int_leq(sK3,n)
| ~ spl7_13 ),
inference(resolution,[],[f222,f73]) ).
fof(f73,plain,
! [X1] : int_leq(X1,X1),
inference(equality_resolution,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( int_leq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( ( int_leq(X0,X1)
| ( X0 != X1
& ~ int_less(X0,X1) ) )
& ( X0 = X1
| int_less(X0,X1)
| ~ int_leq(X0,X1) ) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( ( int_leq(X0,X1)
| ( X0 != X1
& ~ int_less(X0,X1) ) )
& ( X0 = X1
| int_less(X0,X1)
| ~ int_leq(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( int_leq(X0,X1)
<=> ( X0 = X1
| int_less(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.QPKnhshnLL/Vampire---4.8_25743',int_leq) ).
fof(f222,plain,
( ! [X0] :
( ~ int_leq(sK3,X0)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) )
| ~ spl7_13 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f221,plain,
( spl7_13
<=> ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(sK3,X0)
| ~ int_leq(X0,n) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_13])]) ).
fof(f385,plain,
( ~ spl7_1
| spl7_11 ),
inference(avatar_split_clause,[],[f44,f182,f77]) ).
fof(f77,plain,
( spl7_1
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
fof(f182,plain,
( spl7_11
<=> int_leq(sK2,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_11])]) ).
fof(f44,plain,
( int_leq(sK2,n)
| ~ sP0 ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
( ( real_zero != a(sK1,sK2)
& int_leq(sK2,n)
& int_less(sK1,sK2)
& int_leq(int_one,sK1) )
| ~ sP0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f30,f31]) ).
fof(f31,plain,
( ? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) )
=> ( real_zero != a(sK1,sK2)
& int_leq(sK2,n)
& int_less(sK1,sK2)
& int_leq(int_one,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
( ? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) )
| ~ sP0 ),
inference(rectify,[],[f29]) ).
fof(f29,plain,
( ? [X2,X3] :
( real_zero != a(X2,X3)
& int_leq(X3,n)
& int_less(X2,X3)
& int_leq(int_one,X2) )
| ~ sP0 ),
inference(nnf_transformation,[],[f27]) ).
fof(f27,plain,
( ? [X2,X3] :
( real_zero != a(X2,X3)
& int_leq(X3,n)
& int_less(X2,X3)
& int_leq(int_one,X2) )
| ~ sP0 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f379,plain,
( ~ spl7_1
| spl7_19 ),
inference(avatar_contradiction_clause,[],[f378]) ).
fof(f378,plain,
( $false
| ~ spl7_1
| spl7_19 ),
inference(subsumption_resolution,[],[f375,f78]) ).
fof(f78,plain,
( sP0
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f375,plain,
( ~ sP0
| spl7_19 ),
inference(resolution,[],[f308,f42]) ).
fof(f42,plain,
( int_leq(int_one,sK1)
| ~ sP0 ),
inference(cnf_transformation,[],[f32]) ).
fof(f308,plain,
( ~ int_leq(int_one,sK1)
| spl7_19 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f307,plain,
( spl7_19
<=> int_leq(int_one,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_19])]) ).
fof(f374,plain,
( ~ spl7_1
| spl7_18 ),
inference(avatar_contradiction_clause,[],[f373]) ).
fof(f373,plain,
( $false
| ~ spl7_1
| spl7_18 ),
inference(subsumption_resolution,[],[f370,f78]) ).
fof(f370,plain,
( ~ sP0
| ~ spl7_1
| spl7_18 ),
inference(resolution,[],[f362,f42]) ).
fof(f362,plain,
( ~ int_leq(int_one,sK1)
| ~ spl7_1
| spl7_18 ),
inference(resolution,[],[f336,f206]) ).
fof(f206,plain,
( int_less(sK1,sK2)
| ~ spl7_1 ),
inference(subsumption_resolution,[],[f43,f78]) ).
fof(f43,plain,
( int_less(sK1,sK2)
| ~ sP0 ),
inference(cnf_transformation,[],[f32]) ).
fof(f336,plain,
( ! [X0] :
( ~ int_less(X0,sK2)
| ~ int_leq(int_one,X0) )
| spl7_18 ),
inference(resolution,[],[f313,f57]) ).
fof(f57,plain,
! [X0] :
( int_less(int_zero,X0)
| ~ int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0] :
( ( int_less(int_zero,X0)
| ~ int_leq(int_one,X0) )
& ( int_leq(int_one,X0)
| ~ int_less(int_zero,X0) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( int_less(int_zero,X0)
<=> int_leq(int_one,X0) ),
file('/export/starexec/sandbox/tmp/tmp.QPKnhshnLL/Vampire---4.8_25743',one_successor_of_zero) ).
fof(f313,plain,
( ! [X0] :
( ~ int_less(int_zero,X0)
| ~ int_less(X0,sK2) )
| spl7_18 ),
inference(resolution,[],[f310,f67]) ).
fof(f67,plain,
! [X2,X0,X1] :
( int_less(X0,X2)
| ~ int_less(X1,X2)
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( int_less(X0,X2)
| ~ int_less(X1,X2)
| ~ int_less(X0,X1) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( int_less(X0,X2)
| ~ int_less(X1,X2)
| ~ int_less(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( int_less(X1,X2)
& int_less(X0,X1) )
=> int_less(X0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.QPKnhshnLL/Vampire---4.8_25743',int_less_transitive) ).
fof(f310,plain,
( ~ int_less(int_zero,sK2)
| spl7_18 ),
inference(resolution,[],[f305,f56]) ).
fof(f56,plain,
! [X0] :
( int_leq(int_one,X0)
| ~ int_less(int_zero,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f305,plain,
( ~ int_leq(int_one,sK2)
| spl7_18 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f304,plain,
( spl7_18
<=> int_leq(int_one,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_18])]) ).
fof(f309,plain,
( ~ spl7_8
| ~ spl7_18
| ~ spl7_19
| ~ spl7_1 ),
inference(avatar_split_clause,[],[f302,f77,f307,f304,f112]) ).
fof(f112,plain,
( spl7_8
<=> int_leq(sK1,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_8])]) ).
fof(f302,plain,
( ~ int_leq(int_one,sK1)
| ~ int_leq(int_one,sK2)
| ~ int_leq(sK1,n)
| ~ spl7_1 ),
inference(subsumption_resolution,[],[f301,f206]) ).
fof(f301,plain,
( ~ int_leq(int_one,sK1)
| ~ int_leq(int_one,sK2)
| ~ int_leq(sK1,n)
| ~ int_less(sK1,sK2)
| ~ spl7_1 ),
inference(subsumption_resolution,[],[f298,f205]) ).
fof(f205,plain,
( int_leq(sK2,n)
| ~ spl7_1 ),
inference(subsumption_resolution,[],[f44,f78]) ).
fof(f298,plain,
( ~ int_leq(int_one,sK1)
| ~ int_leq(sK2,n)
| ~ int_leq(int_one,sK2)
| ~ int_leq(sK1,n)
| ~ int_less(sK1,sK2)
| ~ spl7_1 ),
inference(trivial_inequality_removal,[],[f297]) ).
fof(f297,plain,
( real_zero != real_zero
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK2,n)
| ~ int_leq(int_one,sK2)
| ~ int_leq(sK1,n)
| ~ int_less(sK1,sK2)
| ~ spl7_1 ),
inference(superposition,[],[f204,f261]) ).
fof(f261,plain,
! [X0,X1] :
( real_zero = a(X0,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_less(X0,X1) ),
inference(subsumption_resolution,[],[f260,f73]) ).
fof(f260,plain,
! [X0,X1] :
( ~ int_leq(X1,n)
| ~ int_leq(X0,X0)
| ~ int_leq(int_one,X0)
| real_zero = a(X0,X1)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_less(X0,X1) ),
inference(duplicate_literal_removal,[],[f257]) ).
fof(f257,plain,
! [X0,X1] :
( ~ int_leq(X1,n)
| ~ int_leq(X0,X0)
| ~ int_leq(int_one,X0)
| real_zero = a(X0,X1)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ~ int_less(X0,X1)
| ~ int_less(X0,X1) ),
inference(superposition,[],[f203,f61]) ).
fof(f61,plain,
! [X0,X1] :
( plus(X0,sK5(X0,X1)) = X1
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( ( int_less(X0,X1)
| ! [X2] :
( ~ int_less(int_zero,X2)
| plus(X0,X2) != X1 ) )
& ( ( int_less(int_zero,sK5(X0,X1))
& plus(X0,sK5(X0,X1)) = X1 )
| ~ int_less(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f37,f38]) ).
fof(f38,plain,
! [X0,X1] :
( ? [X3] :
( int_less(int_zero,X3)
& plus(X0,X3) = X1 )
=> ( int_less(int_zero,sK5(X0,X1))
& plus(X0,sK5(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0,X1] :
( ( int_less(X0,X1)
| ! [X2] :
( ~ int_less(int_zero,X2)
| plus(X0,X2) != X1 ) )
& ( ? [X3] :
( int_less(int_zero,X3)
& plus(X0,X3) = X1 )
| ~ int_less(X0,X1) ) ),
inference(rectify,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( int_less(X0,X1)
| ! [X2] :
( ~ int_less(int_zero,X2)
| plus(X0,X2) != X1 ) )
& ( ? [X2] :
( int_less(int_zero,X2)
& plus(X0,X2) = X1 )
| ~ int_less(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( int_less(X0,X1)
<=> ? [X2] :
( int_less(int_zero,X2)
& plus(X0,X2) = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.QPKnhshnLL/Vampire---4.8_25743',plus_and_inverse) ).
fof(f203,plain,
! [X10,X8,X9] :
( ~ int_leq(plus(X10,sK5(X8,X9)),n)
| ~ int_leq(X8,X10)
| ~ int_leq(int_one,X8)
| real_zero = a(X8,X9)
| ~ int_leq(int_one,plus(X10,sK5(X8,X9)))
| ~ int_leq(X10,n)
| ~ int_leq(int_one,X10)
| ~ int_less(X8,X9) ),
inference(subsumption_resolution,[],[f123,f62]) ).
fof(f62,plain,
! [X0,X1] :
( int_less(int_zero,sK5(X0,X1))
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f123,plain,
! [X10,X8,X9] :
( real_zero = a(X8,X9)
| ~ int_leq(X8,X10)
| ~ int_leq(int_one,X8)
| ~ int_less(int_zero,sK5(X8,X9))
| ~ int_leq(plus(X10,sK5(X8,X9)),n)
| ~ int_leq(int_one,plus(X10,sK5(X8,X9)))
| ~ int_leq(X10,n)
| ~ int_leq(int_one,X10)
| ~ int_less(X8,X9) ),
inference(superposition,[],[f69,f61]) ).
fof(f69,plain,
! [X2,X3,X0] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3)
| ~ int_less(int_zero,X2)
| ~ int_leq(plus(X0,X2),n)
| ~ int_leq(int_one,plus(X0,X2))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(equality_resolution,[],[f52]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3)
| plus(X0,X2) != X1
| ~ int_less(int_zero,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3) )
| plus(X0,X2) != X1
| ~ int_less(int_zero,X2) )
& ! [X4] :
( real_one = a(X4,X4)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4) )
& ! [X5] :
( ! [X6] :
( a(plus(X6,X5),X6) = qr(plus(X6,X5),X6)
| ~ int_leq(X6,X1)
| ~ int_leq(int_one,X6) )
| plus(X1,X5) != X0
| ~ int_less(int_zero,X5) ) )
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(flattening,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( real_zero = a(X3,plus(X3,X2))
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3) )
| plus(X0,X2) != X1
| ~ int_less(int_zero,X2) )
& ! [X4] :
( real_one = a(X4,X4)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4) )
& ! [X5] :
( ! [X6] :
( a(plus(X6,X5),X6) = qr(plus(X6,X5),X6)
| ~ int_leq(X6,X1)
| ~ int_leq(int_one,X6) )
| plus(X1,X5) != X0
| ~ int_less(int_zero,X5) ) )
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( ( int_leq(X1,n)
& int_leq(int_one,X1)
& int_leq(X0,n)
& int_leq(int_one,X0) )
=> ( ! [X2] :
( ( plus(X0,X2) = X1
& int_less(int_zero,X2) )
=> ! [X3] :
( ( int_leq(X3,X0)
& int_leq(int_one,X3) )
=> real_zero = a(X3,plus(X3,X2)) ) )
& ! [X4] :
( ( int_leq(X4,X1)
& int_leq(int_one,X4) )
=> real_one = a(X4,X4) )
& ! [X5] :
( ( plus(X1,X5) = X0
& int_less(int_zero,X5) )
=> ! [X6] :
( ( int_leq(X6,X1)
& int_leq(int_one,X6) )
=> a(plus(X6,X5),X6) = qr(plus(X6,X5),X6) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( ( int_leq(X1,n)
& int_leq(int_one,X1)
& int_leq(X0,n)
& int_leq(int_one,X0) )
=> ( ! [X7] :
( ( plus(X0,X7) = X1
& int_less(int_zero,X7) )
=> ! [X2] :
( ( int_leq(X2,X0)
& int_leq(int_one,X2) )
=> real_zero = a(X2,plus(X2,X7)) ) )
& ! [X2] :
( ( int_leq(X2,X1)
& int_leq(int_one,X2) )
=> real_one = a(X2,X2) )
& ! [X7] :
( ( plus(X1,X7) = X0
& int_less(int_zero,X7) )
=> ! [X2] :
( ( int_leq(X2,X1)
& int_leq(int_one,X2) )
=> a(plus(X2,X7),X2) = qr(plus(X2,X7),X2) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QPKnhshnLL/Vampire---4.8_25743',qih) ).
fof(f204,plain,
( real_zero != a(sK1,sK2)
| ~ spl7_1 ),
inference(subsumption_resolution,[],[f45,f78]) ).
fof(f45,plain,
( real_zero != a(sK1,sK2)
| ~ sP0 ),
inference(cnf_transformation,[],[f32]) ).
fof(f225,plain,
( ~ spl7_5
| spl7_13
| ~ spl7_2
| ~ spl7_3
| ~ spl7_7 ),
inference(avatar_split_clause,[],[f224,f99,f84,f80,f221,f92]) ).
fof(f80,plain,
( spl7_2
<=> real_zero = sF6 ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
fof(f99,plain,
( spl7_7
<=> ! [X4,X1] :
( real_one = a(X4,X4)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_7])]) ).
fof(f224,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,sK3)
| ~ int_leq(sK3,X0) )
| ~ spl7_2
| ~ spl7_3
| ~ spl7_7 ),
inference(subsumption_resolution,[],[f217,f53]) ).
fof(f53,plain,
real_zero != real_one,
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
real_zero != real_one,
file('/export/starexec/sandbox/tmp/tmp.QPKnhshnLL/Vampire---4.8_25743',real_constants) ).
fof(f217,plain,
( ! [X0] :
( real_zero = real_one
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,sK3)
| ~ int_leq(sK3,X0) )
| ~ spl7_2
| ~ spl7_3
| ~ spl7_7 ),
inference(superposition,[],[f104,f100]) ).
fof(f100,plain,
( ! [X1,X4] :
( real_one = a(X4,X4)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1) )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f104,plain,
( real_zero = a(sK3,sK3)
| ~ spl7_2
| ~ spl7_3 ),
inference(backward_demodulation,[],[f103,f81]) ).
fof(f81,plain,
( real_zero = sF6
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f103,plain,
( sF6 = a(sK3,sK3)
| ~ spl7_3 ),
inference(backward_demodulation,[],[f74,f85]) ).
fof(f74,plain,
a(sK3,sK4) = sF6,
introduced(function_definition,[]) ).
fof(f200,plain,
( ~ spl7_1
| spl7_8
| ~ spl7_12 ),
inference(avatar_contradiction_clause,[],[f199]) ).
fof(f199,plain,
( $false
| ~ spl7_1
| spl7_8
| ~ spl7_12 ),
inference(subsumption_resolution,[],[f198,f78]) ).
fof(f198,plain,
( ~ sP0
| spl7_8
| ~ spl7_12 ),
inference(subsumption_resolution,[],[f192,f119]) ).
fof(f119,plain,
( ~ int_less(sK1,n)
| spl7_8 ),
inference(resolution,[],[f113,f65]) ).
fof(f65,plain,
! [X0,X1] :
( int_leq(X0,X1)
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f113,plain,
( ~ int_leq(sK1,n)
| spl7_8 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f192,plain,
( int_less(sK1,n)
| ~ sP0
| ~ spl7_12 ),
inference(backward_demodulation,[],[f43,f186]) ).
fof(f186,plain,
( n = sK2
| ~ spl7_12 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f185,plain,
( spl7_12
<=> n = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl7_12])]) ).
fof(f187,plain,
( ~ spl7_11
| spl7_12
| ~ spl7_1
| spl7_8 ),
inference(avatar_split_clause,[],[f179,f112,f77,f185,f182]) ).
fof(f179,plain,
( n = sK2
| ~ int_leq(sK2,n)
| ~ spl7_1
| spl7_8 ),
inference(resolution,[],[f176,f64]) ).
fof(f64,plain,
! [X0,X1] :
( int_less(X0,X1)
| X0 = X1
| ~ int_leq(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f176,plain,
( ~ int_less(sK2,n)
| ~ spl7_1
| spl7_8 ),
inference(subsumption_resolution,[],[f171,f78]) ).
fof(f171,plain,
( ~ int_less(sK2,n)
| ~ sP0
| spl7_8 ),
inference(resolution,[],[f138,f43]) ).
fof(f138,plain,
( ! [X0] :
( ~ int_less(sK1,X0)
| ~ int_less(X0,n) )
| spl7_8 ),
inference(resolution,[],[f119,f67]) ).
fof(f116,plain,
( ~ spl7_3
| ~ spl7_4
| ~ spl7_5
| ~ spl7_6 ),
inference(avatar_contradiction_clause,[],[f115]) ).
fof(f115,plain,
( $false
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5
| ~ spl7_6 ),
inference(subsumption_resolution,[],[f107,f102]) ).
fof(f107,plain,
( ~ int_leq(sK3,n)
| ~ spl7_5
| ~ spl7_6 ),
inference(resolution,[],[f97,f93]) ).
fof(f97,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f96,plain,
( spl7_6
<=> ! [X0] :
( ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).
fof(f101,plain,
( spl7_6
| spl7_7 ),
inference(avatar_split_clause,[],[f51,f99,f96]) ).
fof(f51,plain,
! [X0,X1,X4] :
( real_one = a(X4,X4)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f94,plain,
( spl7_1
| spl7_5 ),
inference(avatar_split_clause,[],[f46,f92,f77]) ).
fof(f46,plain,
( int_leq(int_one,sK3)
| sP0 ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
( ( real_zero = a(sK3,sK4)
& sK3 = sK4
& int_leq(sK4,n)
& int_leq(int_one,sK3) )
| sP0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f28,f33]) ).
fof(f33,plain,
( ? [X0,X1] :
( real_zero = a(X0,X1)
& X0 = X1
& int_leq(X1,n)
& int_leq(int_one,X0) )
=> ( real_zero = a(sK3,sK4)
& sK3 = sK4
& int_leq(sK4,n)
& int_leq(int_one,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
( ? [X0,X1] :
( real_zero = a(X0,X1)
& X0 = X1
& int_leq(X1,n)
& int_leq(int_one,X0) )
| sP0 ),
inference(definition_folding,[],[f19,f27]) ).
fof(f19,plain,
( ? [X0,X1] :
( real_zero = a(X0,X1)
& X0 = X1
& int_leq(X1,n)
& int_leq(int_one,X0) )
| ? [X2,X3] :
( real_zero != a(X2,X3)
& int_leq(X3,n)
& int_less(X2,X3)
& int_leq(int_one,X2) ) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
( ? [X0,X1] :
( real_zero = a(X0,X1)
& X0 = X1
& int_leq(X1,n)
& int_leq(int_one,X0) )
| ? [X2,X3] :
( real_zero != a(X2,X3)
& int_leq(X3,n)
& int_less(X2,X3)
& int_leq(int_one,X2) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
~ ( ! [X0,X1] :
( ( X0 = X1
& int_leq(X1,n)
& int_leq(int_one,X0) )
=> real_zero != a(X0,X1) )
& ! [X2,X3] :
( ( int_leq(X3,n)
& int_less(X2,X3)
& int_leq(int_one,X2) )
=> real_zero = a(X2,X3) ) ),
inference(rectify,[],[f14]) ).
fof(f14,negated_conjecture,
~ ( ! [X0,X1] :
( ( X0 = X1
& int_leq(X1,n)
& int_leq(int_one,X0) )
=> real_zero != a(X0,X1) )
& ! [X0,X1] :
( ( int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) )
=> real_zero = a(X0,X1) ) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
( ! [X0,X1] :
( ( X0 = X1
& int_leq(X1,n)
& int_leq(int_one,X0) )
=> real_zero != a(X0,X1) )
& ! [X0,X1] :
( ( int_leq(X1,n)
& int_less(X0,X1)
& int_leq(int_one,X0) )
=> real_zero = a(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.QPKnhshnLL/Vampire---4.8_25743',lti) ).
fof(f90,plain,
( spl7_1
| spl7_4 ),
inference(avatar_split_clause,[],[f47,f88,f77]) ).
fof(f47,plain,
( int_leq(sK4,n)
| sP0 ),
inference(cnf_transformation,[],[f34]) ).
fof(f86,plain,
( spl7_1
| spl7_3 ),
inference(avatar_split_clause,[],[f48,f84,f77]) ).
fof(f48,plain,
( sK3 = sK4
| sP0 ),
inference(cnf_transformation,[],[f34]) ).
fof(f82,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f75,f80,f77]) ).
fof(f75,plain,
( real_zero = sF6
| sP0 ),
inference(definition_folding,[],[f49,f74]) ).
fof(f49,plain,
( real_zero = a(sK3,sK4)
| sP0 ),
inference(cnf_transformation,[],[f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV492+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 10:10:05 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.35 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.QPKnhshnLL/Vampire---4.8_25743
% 0.14/0.36 % (25850)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.40 % (25854)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.21/0.42 % (25851)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.21/0.42 % (25855)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.21/0.42 % (25852)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.21/0.42 % (25856)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.21/0.42 % (25857)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.21/0.42 % (25853)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.21/0.49 % (25853)Refutation not found, incomplete strategy% (25853)------------------------------
% 0.21/0.49 % (25853)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.49 % (25853)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.49 % (25853)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.49
% 0.21/0.49 % (25853)Memory used [KB]: 1151
% 0.21/0.49 % (25853)Time elapsed: 0.076 s
% 0.21/0.49 % (25853)------------------------------
% 0.21/0.49 % (25853)------------------------------
% 0.21/0.53 % (25858)ott+10_5_av=off:bsr=on:br=off:drc=off:fsd=off:fsr=off:fde=unused:gsp=on:lcm=predicate:lma=on:nwc=2.5:sos=all:sp=occurrence:tgt=full:urr=on_375 on Vampire---4 for (375ds/0Mi)
% 0.21/0.53 % (25858)Refutation not found, incomplete strategy% (25858)------------------------------
% 0.21/0.53 % (25858)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.53 % (25858)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.53 % (25858)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.53
% 0.21/0.53 % (25858)Memory used [KB]: 1023
% 0.21/0.53 % (25858)Time elapsed: 0.003 s
% 0.21/0.53 % (25858)------------------------------
% 0.21/0.53 % (25858)------------------------------
% 1.47/0.56 % (25859)lrs-1010_3_aac=none:anc=none:er=known:fsd=off:fde=unused:gs=on:lcm=predicate:sos=on:sp=weighted_frequency:tgt=ground:stl=62_365 on Vampire---4 for (365ds/0Mi)
% 1.47/0.57 % (25859)First to succeed.
% 1.47/0.57 % (25859)Refutation found. Thanks to Tanya!
% 1.47/0.57 % SZS status Theorem for Vampire---4
% 1.47/0.57 % SZS output start Proof for Vampire---4
% See solution above
% 1.47/0.57 % (25859)------------------------------
% 1.47/0.57 % (25859)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 1.47/0.57 % (25859)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 1.47/0.57 % (25859)Termination reason: Refutation
% 1.47/0.57
% 1.47/0.57 % (25859)Memory used [KB]: 10234
% 1.47/0.57 % (25859)Time elapsed: 0.011 s
% 1.47/0.57 % (25859)------------------------------
% 1.47/0.57 % (25859)------------------------------
% 1.47/0.57 % (25850)Success in time 0.212 s
% 1.47/0.57 % Vampire---4.8 exiting
%------------------------------------------------------------------------------