%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV491+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:16:02 PM UTC 2026
% Result : Theorem 4.43s 1.51s
% Output : Refutation 6.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of formulae : 115 ( 16 unt; 7 def)
% Number of atoms : 489 ( 103 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 658 ( 284 ~; 278 |; 66 &)
% ( 9 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 124 ( 0 sgn 117 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( int_leq(X0,X1)
<=> ( int_less(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_leq) ).
fof(f3,axiom,
! [X0,X1] :
( int_less(X0,X1)
=> X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_irreflexive) ).
fof(f9,axiom,
! [X0,X1] :
( int_less(X0,X1)
<=> ? [X2] :
( plus(X0,X2) = X1
& int_less(int_zero,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_and_inverse) ).
fof(f12,axiom,
! [X0,X1] :
( ( int_leq(int_one,X0)
& int_leq(X0,n)
& int_leq(int_one,X1)
& int_leq(X1,n) )
=> ( ! [X2] :
( ( int_less(int_zero,X2)
& X0 = plus(X1,X2) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(plus(X3,X2),X3) = real_zero ) )
& ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(X3,X3) = real_one )
& ! [X2] :
( ( int_less(int_zero,X2)
& X1 = plus(X0,X2) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X0) )
=> a(X3,plus(X3,X2)) = real_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qih) ).
fof(f13,conjecture,
! [X0,X1] :
( ( int_leq(int_one,X0)
& int_leq(X0,n)
& int_leq(int_one,X1)
& int_leq(X1,n) )
=> ( ( int_less(X0,X1)
=> a(X0,X1) = real_zero )
& ( int_less(X1,X0)
=> a(X0,X1) = real_zero )
& ( X0 = X1
=> a(X0,X1) = real_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diag) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ( int_leq(int_one,X0)
& int_leq(X0,n)
& int_leq(int_one,X1)
& int_leq(X1,n) )
=> ( ( int_less(X0,X1)
=> a(X0,X1) = real_zero )
& ( int_less(X1,X0)
=> a(X0,X1) = real_zero )
& ( X0 = X1
=> a(X0,X1) = real_one ) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( int_leq(int_one,X0)
& int_leq(X0,n)
& int_leq(int_one,X1)
& int_leq(X1,n) )
=> ( ! [X2] :
( ( int_less(int_zero,X2)
& X0 = plus(X1,X2) )
=> ! [X3] :
( ( int_leq(int_one,X3)
& int_leq(X3,X1) )
=> a(plus(X3,X2),X3) = real_zero ) )
& ! [X4] :
( ( int_leq(int_one,X4)
& int_leq(X4,X1) )
=> real_one = a(X4,X4) )
& ! [X5] :
( ( int_less(int_zero,X5)
& plus(X0,X5) = X1 )
=> ! [X6] :
( ( int_leq(int_one,X6)
& int_leq(X6,X0) )
=> real_zero = a(X6,plus(X6,X5)) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f16,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( a(plus(X3,X2),X3) = real_zero
| ~ int_leq(int_one,X3)
| ~ int_leq(X3,X1) )
| ~ int_less(int_zero,X2)
| plus(X1,X2) != X0 )
& ! [X4] :
( real_one = a(X4,X4)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1) )
& ! [X5] :
( ! [X6] :
( real_zero = a(X6,plus(X6,X5))
| ~ int_leq(int_one,X6)
| ~ int_leq(X6,X0) )
| ~ int_less(int_zero,X5)
| plus(X0,X5) != X1 ) )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( a(plus(X3,X2),X3) = real_zero
| ~ int_leq(int_one,X3)
| ~ int_leq(X3,X1) )
| ~ int_less(int_zero,X2)
| plus(X1,X2) != X0 )
& ! [X4] :
( real_one = a(X4,X4)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1) )
& ! [X5] :
( ! [X6] :
( real_zero = a(X6,plus(X6,X5))
| ~ int_leq(int_one,X6)
| ~ int_leq(X6,X0) )
| ~ int_less(int_zero,X5)
| plus(X0,X5) != X1 ) )
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
? [X0,X1] :
( ( ( real_zero != a(X0,X1)
& int_less(X0,X1) )
| ( real_zero != a(X0,X1)
& int_less(X1,X0) )
| ( real_one != a(X0,X1)
& X0 = X1 ) )
& int_leq(int_one,X0)
& int_leq(X0,n)
& int_leq(int_one,X1)
& int_leq(X1,n) ),
inference(ennf_transformation,[],[f14]) ).
fof(f19,plain,
? [X0,X1] :
( ( ( real_zero != a(X0,X1)
& int_less(X0,X1) )
| ( real_zero != a(X0,X1)
& int_less(X1,X0) )
| ( real_one != a(X0,X1)
& X0 = X1 ) )
& int_leq(int_one,X0)
& int_leq(X0,n)
& int_leq(int_one,X1)
& int_leq(X1,n) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( X0 != X1
| ~ int_less(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f25,plain,
( ( ( real_zero != a(sK0,sK1)
& int_less(sK0,sK1) )
| ( real_zero != a(sK0,sK1)
& int_less(sK1,sK0) )
| ( real_one != a(sK0,sK1)
& sK0 = sK1 ) )
& int_leq(int_one,sK0)
& int_leq(sK0,n)
& int_leq(int_one,sK1)
& int_leq(sK1,n) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f19]) ).
fof(f26,plain,
! [X0,X1] :
( ( int_less(X0,X1)
| ! [X2] :
( plus(X0,X2) != X1
| ~ int_less(int_zero,X2) ) )
& ( ? [X2] :
( plus(X0,X2) = X1
& int_less(int_zero,X2) )
| ~ int_less(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f27,plain,
! [X0,X1] :
( ( int_less(X0,X1)
| ! [X2] :
( plus(X0,X2) != X1
| ~ int_less(int_zero,X2) ) )
& ( ? [X3] :
( plus(X0,X3) = X1
& int_less(int_zero,X3) )
| ~ int_less(X0,X1) ) ),
inference(rectify,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ( int_less(X0,X1)
| ! [X2] :
( plus(X0,X2) != X1
| ~ int_less(int_zero,X2) ) )
& ( ( plus(X0,sK2(X0,X1)) = X1
& int_less(int_zero,sK2(X0,X1)) )
| ~ int_less(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1))],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ( int_leq(X0,X1)
| ( ~ int_less(X0,X1)
& X0 != X1 ) )
& ( int_less(X0,X1)
| X0 = X1
| ~ int_leq(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f30,plain,
! [X0,X1] :
( ( int_leq(X0,X1)
| ( ~ int_less(X0,X1)
& X0 != X1 ) )
& ( int_less(X0,X1)
| X0 = X1
| ~ int_leq(X0,X1) ) ),
inference(flattening,[],[f29]) ).
fof(f32,plain,
! [X0,X1,X6,X5] :
( real_zero = a(X6,plus(X6,X5))
| ~ int_leq(int_one,X6)
| ~ int_leq(X6,X0)
| ~ int_less(int_zero,X5)
| plus(X0,X5) != X1
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X0,X1,X4] :
( real_one = a(X4,X4)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n) ),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( real_zero = a(plus(X3,X2),X3)
| ~ int_leq(int_one,X3)
| ~ int_leq(X3,X1)
| ~ int_less(int_zero,X2)
| plus(X1,X2) != X0
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n) ),
inference(cnf_transformation,[],[f17]) ).
fof(f35,plain,
int_leq(sK1,n),
inference(cnf_transformation,[],[f25]) ).
fof(f36,plain,
int_leq(int_one,sK1),
inference(cnf_transformation,[],[f25]) ).
fof(f37,plain,
int_leq(sK0,n),
inference(cnf_transformation,[],[f25]) ).
fof(f38,plain,
int_leq(int_one,sK0),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
( int_less(sK0,sK1)
| int_less(sK1,sK0)
| sK0 = sK1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f40,plain,
( int_less(sK0,sK1)
| int_less(sK1,sK0)
| real_one != a(sK0,sK1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f45,plain,
( real_zero != a(sK0,sK1)
| real_zero != a(sK0,sK1)
| sK0 = sK1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
( real_zero != a(sK0,sK1)
| real_zero != a(sK0,sK1)
| real_one != a(sK0,sK1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f48,plain,
! [X0,X1] :
( int_less(int_zero,sK2(X0,X1))
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
! [X0,X1] :
( plus(X0,sK2(X0,X1)) = X1
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f53,plain,
! [X0,X1] :
( X0 != X1
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f55,plain,
! [X0,X1] :
( int_leq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f63,plain,
! [X2,X3,X1] :
( real_zero = a(plus(X3,X2),X3)
| ~ int_leq(int_one,X3)
| ~ int_leq(X3,X1)
| ~ int_less(int_zero,X2)
| ~ int_leq(int_one,plus(X1,X2))
| ~ int_leq(plus(X1,X2),n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n) ),
inference(equality_resolution,[],[f34]) ).
fof(f64,plain,
! [X0,X6,X5] :
( real_zero = a(X6,plus(X6,X5))
| ~ int_leq(int_one,X6)
| ~ int_leq(X6,X0)
| ~ int_less(int_zero,X5)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,plus(X0,X5))
| ~ int_leq(plus(X0,X5),n) ),
inference(equality_resolution,[],[f32]) ).
fof(f66,plain,
! [X1] : ~ int_less(X1,X1),
inference(equality_resolution,[],[f53]) ).
fof(f67,plain,
! [X1] : int_leq(X1,X1),
inference(equality_resolution,[],[f55]) ).
fof(f68,plain,
( real_zero != a(sK0,sK1)
| sK0 = sK1 ),
inference(duplicate_literal_removal,[],[f45]) ).
fof(f69,plain,
( real_zero != a(sK0,sK1)
| real_one != a(sK0,sK1) ),
inference(duplicate_literal_removal,[],[f46]) ).
fof(f71,definition,
( spl3_1
<=> sK0 = sK1 ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f73,plain,
( sK0 = sK1
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f75,definition,
( spl3_2
<=> int_less(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f77,plain,
( int_less(sK1,sK0)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl3_3
<=> int_less(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f81,plain,
( int_less(sK0,sK1)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,plain,
( spl3_1
| spl3_2
| spl3_3 ),
inference(avatar_split_clause,[],[f39,f79,f75,f71]) ).
fof(f84,definition,
( spl3_4
<=> real_one = a(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f86,plain,
( real_one != a(sK0,sK1)
| spl3_4 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( ~ spl3_4
| spl3_2
| spl3_3 ),
inference(avatar_split_clause,[],[f40,f79,f75,f84]) ).
fof(f89,definition,
( spl3_5
<=> real_zero = a(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f91,plain,
( real_zero != a(sK0,sK1)
| spl3_5 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f96,plain,
( spl3_1
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f68,f89,f71]) ).
fof(f97,plain,
( ~ spl3_4
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f69,f89,f84]) ).
fof(f99,definition,
( spl3_6
<=> ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) ) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f100,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) )
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl3_7
<=> ! [X4,X1] :
( real_one = a(X4,X4)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4) ) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f103,plain,
( ! [X1,X4] :
( real_one = a(X4,X4)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4) )
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f104,plain,
( spl3_6
| spl3_7 ),
inference(avatar_split_clause,[],[f33,f102,f99]) ).
fof(f105,plain,
( ~ int_leq(sK1,n)
| ~ spl3_6 ),
inference(resolution,[],[f100,f36]) ).
fof(f110,plain,
( $false
| ~ spl3_6 ),
inference(forward_subsumption_resolution,[],[f105,f35]) ).
fof(f111,plain,
~ spl3_6,
inference(avatar_contradiction_clause,[],[f110]) ).
fof(f196,plain,
! [X2,X0,X1] :
( real_zero = a(X0,X1)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2)
| ~ int_less(int_zero,sK2(X1,X0))
| ~ int_leq(int_one,plus(X2,sK2(X1,X0)))
| ~ int_leq(plus(X2,sK2(X1,X0)),n)
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,n)
| ~ int_less(X1,X0) ),
inference(superposition,[],[f63,f49]) ).
fof(f198,plain,
! [X2,X0,X1] :
( ~ int_leq(plus(X2,sK2(X1,X0)),n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2)
| ~ int_leq(int_one,plus(X2,sK2(X1,X0)))
| real_zero = a(X0,X1)
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,n)
| ~ int_less(X1,X0) ),
inference(forward_subsumption_resolution,[],[f196,f48]) ).
fof(f206,plain,
! [X2,X0,X1] :
( real_zero = a(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2)
| ~ int_less(int_zero,sK2(X1,X0))
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,plus(X2,sK2(X1,X0)))
| ~ int_leq(plus(X2,sK2(X1,X0)),n)
| ~ int_less(X1,X0) ),
inference(superposition,[],[f64,f49]) ).
fof(f208,plain,
! [X2,X0,X1] :
( ~ int_leq(plus(X2,sK2(X1,X0)),n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2)
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,plus(X2,sK2(X1,X0)))
| real_zero = a(X1,X0)
| ~ int_less(X1,X0) ),
inference(forward_subsumption_resolution,[],[f206,f48]) ).
fof(f397,plain,
! [X0,X1] :
( ~ int_leq(X0,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X1)
| ~ int_leq(int_one,X0)
| real_zero = a(X0,X1)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_less(X1,X0)
| ~ int_less(X1,X0) ),
inference(superposition,[],[f198,f49]) ).
fof(f401,plain,
! [X0,X1] :
( ~ int_leq(X0,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X1)
| ~ int_leq(int_one,X0)
| real_zero = a(X0,X1)
| ~ int_leq(X1,n)
| ~ int_less(X1,X0) ),
inference(duplicate_literal_removal,[],[f397]) ).
fof(f404,plain,
! [X0,X1] :
( ~ int_leq(X0,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_one,X0)
| real_zero = a(X0,X1)
| ~ int_leq(X1,n)
| ~ int_less(X1,X0) ),
inference(forward_subsumption_resolution,[],[f401,f67]) ).
fof(f414,plain,
! [X0,X1] :
( ~ int_leq(X0,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X1)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X0)
| real_zero = a(X1,X0)
| ~ int_less(X1,X0)
| ~ int_less(X1,X0) ),
inference(superposition,[],[f208,f49]) ).
fof(f418,plain,
! [X0,X1] :
( ~ int_leq(X0,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X0)
| real_zero = a(X1,X0)
| ~ int_less(X1,X0) ),
inference(duplicate_literal_removal,[],[f414]) ).
fof(f421,plain,
! [X0,X1] :
( ~ int_leq(X0,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X0)
| real_zero = a(X1,X0)
| ~ int_less(X1,X0) ),
inference(forward_subsumption_resolution,[],[f418,f67]) ).
fof(f1648,plain,
! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(int_one,sK0)
| real_zero = a(sK0,X0)
| ~ int_leq(X0,n)
| ~ int_less(X0,sK0) ),
inference(resolution,[],[f404,f37]) ).
fof(f1651,plain,
! [X0] :
( real_zero = a(sK0,X0)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_less(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f1648,f38]) ).
fof(f1675,plain,
! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,sK1)
| real_zero = a(X0,sK1)
| ~ int_less(X0,sK1) ),
inference(resolution,[],[f421,f35]) ).
fof(f1676,plain,
! [X0] :
( ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| real_zero = a(X0,sK1)
| ~ int_less(X0,sK1) ),
inference(forward_subsumption_resolution,[],[f1675,f36]) ).
fof(f2661,plain,
( real_zero != real_zero
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK1,n)
| ~ int_less(sK1,sK0)
| spl3_5 ),
inference(superposition,[],[f91,f1651]) ).
fof(f2666,plain,
( ~ int_leq(int_one,sK1)
| ~ int_leq(sK1,n)
| ~ int_less(sK1,sK0)
| spl3_5 ),
inference(trivial_inequality_removal,[],[f2661]) ).
fof(f3304,plain,
( real_one != a(sK0,sK0)
| ~ spl3_1
| spl3_4 ),
inference(forward_demodulation,[],[f86,f73]) ).
fof(f3346,plain,
( ! [X0] :
( real_one != real_one
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(sK0,X0)
| ~ int_leq(int_one,sK0) )
| ~ spl3_1
| spl3_4
| ~ spl3_7 ),
inference(superposition,[],[f3304,f103]) ).
fof(f3348,plain,
( ! [X0] :
( ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(sK0,X0)
| ~ int_leq(int_one,sK0) )
| ~ spl3_1
| spl3_4
| ~ spl3_7 ),
inference(trivial_inequality_removal,[],[f3346]) ).
fof(f3349,plain,
( ! [X0] :
( ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(sK0,X0) )
| ~ spl3_1
| spl3_4
| ~ spl3_7 ),
inference(forward_subsumption_resolution,[],[f3348,f38]) ).
fof(f3382,plain,
( ~ int_leq(int_one,sK0)
| ~ int_leq(sK0,sK0)
| ~ spl3_1
| spl3_4
| ~ spl3_7 ),
inference(resolution,[],[f3349,f37]) ).
fof(f3385,plain,
( ~ int_leq(sK0,sK0)
| ~ spl3_1
| spl3_4
| ~ spl3_7 ),
inference(forward_subsumption_resolution,[],[f3382,f38]) ).
fof(f3389,plain,
( $false
| ~ spl3_1
| spl3_4
| ~ spl3_7 ),
inference(forward_subsumption_resolution,[],[f3385,f67]) ).
fof(f3390,plain,
( ~ spl3_1
| spl3_4
| ~ spl3_7 ),
inference(avatar_contradiction_clause,[],[f3389]) ).
fof(f3477,plain,
( ~ int_leq(int_one,sK0)
| real_zero = a(sK0,sK1)
| ~ int_less(sK0,sK1) ),
inference(resolution,[],[f1676,f37]) ).
fof(f3479,plain,
( real_zero = a(sK0,sK1)
| ~ int_less(sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f3477,f38]) ).
fof(f3486,plain,
( ~ int_less(sK0,sK1)
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f3479,f91]) ).
fof(f3492,plain,
( $false
| ~ spl3_3
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f3486,f81]) ).
fof(f3493,plain,
( ~ spl3_3
| spl3_5 ),
inference(avatar_contradiction_clause,[],[f3492]) ).
fof(f3501,plain,
( int_less(sK0,sK0)
| ~ spl3_1
| ~ spl3_2 ),
inference(forward_demodulation,[],[f77,f73]) ).
fof(f3530,plain,
( ~ int_leq(sK1,n)
| ~ int_less(sK1,sK0)
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f2666,f36]) ).
fof(f3533,plain,
( $false
| ~ spl3_1
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f3501,f66]) ).
fof(f3534,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[],[f3533]) ).
fof(f3550,plain,
( ~ int_less(sK1,sK0)
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f3530,f35]) ).
fof(f3567,plain,
( $false
| ~ spl3_2
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f3550,f77]) ).
fof(f3568,plain,
( ~ spl3_2
| spl3_5 ),
inference(avatar_contradiction_clause,[],[f3567]) ).
cnf(s1,plain,
( spl3_1
| spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f82]) ).
cnf(s2,plain,
( spl3_2
| spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f87]) ).
cnf(s7,plain,
( spl3_1
| ~ spl3_5 ),
inference(sat_conversion,[],[f96]) ).
cnf(s8,plain,
( ~ spl3_4
| ~ spl3_5 ),
inference(sat_conversion,[],[f97]) ).
cnf(s9,plain,
( spl3_6
| spl3_7 ),
inference(sat_conversion,[],[f104]) ).
cnf(s11,plain,
~ spl3_6,
inference(sat_conversion,[],[f111]) ).
cnf(s93,plain,
( ~ spl3_1
| spl3_4
| ~ spl3_7 ),
inference(sat_conversion,[],[f3390]) ).
cnf(s95,plain,
( ~ spl3_3
| spl3_5 ),
inference(sat_conversion,[],[f3493]) ).
cnf(s97,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f3534]) ).
cnf(s103,plain,
( ~ spl3_2
| spl3_5 ),
inference(sat_conversion,[],[f3568]) ).
cnf(s112,plain,
spl3_7,
inference(rat,[],[s9,s11]) ).
cnf(s113,plain,
spl3_1,
inference(rat,[],[s1,s95,s103,s7]) ).
cnf(s115,plain,
~ spl3_2,
inference(rat,[],[s97,s113]) ).
cnf(s116,plain,
spl3_4,
inference(rat,[],[s93,s112,s113]) ).
cnf(s118,plain,
~ spl3_5,
inference(rat,[],[s8,s116]) ).
cnf(s119,plain,
spl3_3,
inference(rat,[],[s2,s115,s116]) ).
cnf(s120,plain,
$false,
inference(rat,[],[s95,s118,s119]) ).
fof(f3581,plain,
$false,
inference(avatar_sat_refutation,[],[s120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV491+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n010.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 11:15:02 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.43/1.51 % (1859131)Detected formulas, will run a generic FOF schedule.
% 4.43/1.51 % (1859241)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=302268849:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.43/1.51 % (1859240)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=705011524:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.43/1.51 % (1859239)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1229906202:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.43/1.51 % (1859243)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=677728503:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.43/1.51 % (1859244)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2945772698:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.43/1.51 % (1859245)dis-21_1_sil=8000:lcm=predicate:random_seed=3377923117:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.43/1.51 % (1859242)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1068945617:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.43/1.51 % (1859243)Instruction limit reached!
% 4.43/1.51 % (1859243)------------------------------
% 4.43/1.51 % (1859243)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.51 % (1859243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.51 % (1859243)CaDiCaL version: 2.1.3
% 4.43/1.51 % (1859243)Termination reason: Instruction limit
% 4.43/1.51 % (1859243)Termination phase: Saturation
% 4.43/1.51 % (1859243)Time elapsed: 0.071 s
% 4.43/1.51 % (1859243)Peak memory usage: 88 MB
% 4.43/1.51 % (1859243)Instructions burned: 119 (million)
% 4.43/1.51 % (1859245)Instruction limit reached!
% 4.43/1.51 % (1859245)------------------------------
% 4.43/1.51 % (1859245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.51 % (1859245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.51 % (1859245)CaDiCaL version: 2.1.3
% 4.43/1.51 % (1859245)Termination reason: Instruction limit
% 4.43/1.51 % (1859245)Termination phase: Saturation
% 4.43/1.51 % (1859245)Time elapsed: 0.082 s
% 4.43/1.51 % (1859245)Peak memory usage: 88 MB
% 4.43/1.51 % (1859245)Instructions burned: 130 (million)
% 4.43/1.51 % (1859242)Instruction limit reached!
% 4.43/1.51 % (1859242)------------------------------
% 4.43/1.51 % (1859242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.51 % (1859242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.51 % (1859242)CaDiCaL version: 2.1.3
% 4.43/1.51 % (1859242)Termination reason: Instruction limit
% 4.43/1.51 % (1859242)Termination phase: Saturation
% 4.43/1.51 % (1859242)Time elapsed: 0.070 s
% 4.43/1.51 % (1859242)Peak memory usage: 89 MB
% 4.43/1.51 % (1859242)Instructions burned: 111 (million)
% 4.43/1.51 % (1859244)Instruction limit reached!
% 4.43/1.51 % (1859244)------------------------------
% 4.43/1.51 % (1859244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.51 % (1859244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.51 % (1859244)CaDiCaL version: 2.1.3
% 4.43/1.51 % (1859244)Termination reason: Instruction limit
% 4.43/1.51 % (1859244)Termination phase: Saturation
% 4.43/1.51 % (1859244)Time elapsed: 0.095 s
% 4.43/1.51 % (1859244)Peak memory usage: 89 MB
% 4.43/1.51 % (1859244)Instructions burned: 139 (million)
% 4.43/1.51 % (1859280)lrs+10_1_sil=8000:sp=occurrence:random_seed=818178303:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.43/1.51 % (1859281)lrs+10_1_sil=32000:urr=on:br=off:random_seed=773074489:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.43/1.51 % (1859282)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4034795210:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.43/1.51 % (1859283)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2153881832:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.43/1.51 % (1859281)Instruction limit reached!
% 4.43/1.51 % (1859281)------------------------------
% 4.43/1.51 % (1859281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.51 % (1859281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.51 % (1859281)CaDiCaL version: 2.1.3
% 4.43/1.51 % (1859281)Termination reason: Instruction limit
% 4.43/1.51 % (1859281)Termination phase: Saturation
% 4.43/1.51 % (1859281)Time elapsed: 0.080 s
% 4.43/1.51 % (1859281)Peak memory usage: 90 MB
% 4.43/1.51 % (1859281)Instructions burned: 157 (million)
% 4.43/1.51 % (1859282)First to succeed.
% 4.43/1.51 % (1859282)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1859131"
% 4.43/1.51 % (1859241)Also succeeded, but the first one will report.
% 4.43/1.51 % (1859283)Instruction limit reached!
% 4.43/1.51 % (1859283)------------------------------
% 4.43/1.51 % (1859283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.51 % (1859283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.51 % (1859283)CaDiCaL version: 2.1.3
% 4.43/1.51 % (1859283)Termination reason: Instruction limit
% 4.43/1.51 % (1859283)Termination phase: Saturation
% 4.43/1.51 % (1859283)Time elapsed: 0.074 s
% 4.43/1.51 % (1859283)Peak memory usage: 92 MB
% 4.43/1.51 % (1859283)Instructions burned: 248 (million)
% 4.43/1.51 % (1859280)Instruction limit reached!
% 4.43/1.51 % (1859280)------------------------------
% 4.43/1.51 % (1859280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.51 % (1859280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.51 % (1859280)CaDiCaL version: 2.1.3
% 4.43/1.51 % (1859280)Termination reason: Instruction limit
% 4.43/1.51 % (1859280)Termination phase: Saturation
% 4.43/1.51 % (1859280)Time elapsed: 0.182 s
% 4.43/1.51 % (1859280)Peak memory usage: 91 MB
% 4.43/1.51 % (1859280)Instructions burned: 285 (million)
% 4.43/1.51 % (1859288)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1373296954:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.43/1.51 % (1859289)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4159899833:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.43/1.51 % (1859290)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3424991976:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.43/1.51 % (1859240)Also succeeded, but the first one will report.
% 4.43/1.51 % (1859288)Instruction limit reached!
% 4.43/1.51 % (1859288)------------------------------
% 4.43/1.51 % (1859288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.43/1.51 % (1859288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.43/1.51 % (1859288)CaDiCaL version: 2.1.3
% 4.43/1.51 % (1859288)Termination reason: Instruction limit
% 4.43/1.51 % (1859288)Termination phase: Saturation
% 4.43/1.51 % (1859288)Time elapsed: 0.172 s
% 4.43/1.51 % (1859288)Peak memory usage: 88 MB
% 4.43/1.51 % (1859288)Instructions burned: 294 (million)
% 4.43/1.51 % (1859239)Also succeeded, but the first one will report.
% 4.43/1.51 % (1859282)Refutation found. Thanks to Tanya!
% 4.43/1.51 % SZS status Theorem for theBenchmark
% 4.43/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 6.54/1.77 % (1859282)------------------------------
% 6.54/1.77 % (1859282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.54/1.77 % (1859282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.54/1.77 % (1859282)CaDiCaL version: 2.1.3
% 6.54/1.77 % (1859282)Termination reason: Refutation
% 6.54/1.77 % (1859282)Time elapsed: 0.129 s
% 6.54/1.77 % (1859282)Peak memory usage: 91 MB
% 6.54/1.77 % (1859282)Instructions burned: 182 (million)
% 6.54/1.77 % (1859282)------------------------------
% 6.54/1.77 % (1859282)------------------------------
% 6.54/1.77 % (1859131)Success in time 0.847 s
% 6.54/1.77 % Vampire exiting
%------------------------------------------------------------------------------