%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV492+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 01:24:26 PM UTC 2026
% Result : Theorem 0.19s 0.31s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 26
% Syntax : Number of formulae : 188 ( 12 unt; 17 def)
% Number of atoms : 613 ( 92 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 727 ( 302 ~; 332 |; 53 &)
% ( 20 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 18 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 119 ( 0 sgn 110 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( int_leq(X0,X1)
<=> ( int_less(X0,X1)
| X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_leq) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( int_less(X0,X1)
& int_less(X1,X2) )
=> int_less(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_transitive) ).
fof(f3,axiom,
! [X0,X1] :
( int_less(X0,X1)
=> X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_irreflexive) ).
fof(f4,axiom,
! [X0,X1] :
( int_less(X0,X1)
| int_leq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_total) ).
fof(f9,axiom,
! [X0,X1] :
( int_less(X0,X1)
<=> ? [X2] :
( plus(X0,X2) = X1
& int_less(int_zero,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_and_inverse) ).
fof(f10,axiom,
! [X0] :
( int_less(int_zero,X0)
<=> int_leq(int_one,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_successor_of_zero) ).
fof(f11,axiom,
real_zero != real_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',real_constants) ).
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) = qr(plus(X3,X2),X3) ) )
& ! [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/sandbox2/benchmark/theBenchmark.p',qih) ).
fof(f13,conjecture,
( ! [X0,X1] :
( ( int_leq(int_one,X0)
& int_less(X0,X1)
& int_leq(X1,n) )
=> a(X0,X1) = real_zero )
& ! [X0,X1] :
( ( int_leq(int_one,X0)
& int_leq(X1,n)
& X0 = X1 )
=> a(X0,X1) != real_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lti) ).
fof(f14,negated_conjecture,
~ ( ! [X0,X1] :
( ( int_leq(int_one,X0)
& int_less(X0,X1)
& int_leq(X1,n) )
=> a(X0,X1) = real_zero )
& ! [X0,X1] :
( ( int_leq(int_one,X0)
& int_leq(X1,n)
& X0 = X1 )
=> a(X0,X1) != real_zero ) ),
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) = qr(plus(X3,X2),X3) ) )
& ! [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] :
( ( int_leq(int_one,X0)
& int_less(X0,X1)
& int_leq(X1,n) )
=> a(X0,X1) = real_zero )
& ! [X2,X3] :
( ( int_leq(int_one,X2)
& int_leq(X3,n)
& X2 = X3 )
=> real_zero != a(X2,X3) ) ),
inference(rectify,[],[f14]) ).
fof(f17,plain,
! [X0,X1,X2] :
( int_less(X0,X2)
| ~ int_less(X0,X1)
| ~ int_less(X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f18,plain,
! [X0,X1,X2] :
( int_less(X0,X2)
| ~ int_less(X0,X1)
| ~ int_less(X1,X2) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( X0 != X1
| ~ int_less(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f22,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( a(plus(X3,X2),X3) = qr(plus(X3,X2),X3)
| ~ 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(f23,plain,
! [X0,X1] :
( ( ! [X2] :
( ! [X3] :
( a(plus(X3,X2),X3) = qr(plus(X3,X2),X3)
| ~ 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,[],[f22]) ).
fof(f24,plain,
( ? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(int_one,X0)
& int_less(X0,X1)
& int_leq(X1,n) )
| ? [X2,X3] :
( real_zero = a(X2,X3)
& int_leq(int_one,X2)
& int_leq(X3,n)
& X2 = X3 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f25,plain,
( ? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(int_one,X0)
& int_less(X0,X1)
& int_leq(X1,n) )
| ? [X2,X3] :
( real_zero = a(X2,X3)
& int_leq(int_one,X2)
& int_leq(X3,n)
& X2 = X3 ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( int_less(X0,X1)
| X0 = X1
| ~ int_leq(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
fof(f27,plain,
! [X0,X1] :
( X0 != X1
| int_leq(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0,X1] :
( ~ int_less(X0,X1)
| int_leq(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ int_less(X0,X1)
| ~ int_less(X1,X2)
| int_less(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X0,X1] :
( ~ int_less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X0,X1] :
( int_less(X0,X1)
| int_leq(X1,X0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f36,plain,
! [X0,X1] :
( int_less(int_zero,sK0(X0,X1))
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f37,plain,
! [X0,X1] :
( ~ int_less(X0,X1)
| plus(X0,sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f39,plain,
! [X0] :
( ~ int_leq(int_one,X0)
| int_less(int_zero,X0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f40,plain,
! [X0] :
( ~ int_less(int_zero,X0)
| int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f41,plain,
real_zero != real_one,
inference(cnf_transformation,[],[f11]) ).
fof(f43,plain,
! [X0,X1,X6,X5] :
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| plus(X0,X5) != X1
| ~ int_less(int_zero,X5)
| ~ int_leq(X6,X0)
| ~ int_leq(int_one,X6)
| real_zero = a(X6,plus(X6,X5)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
! [X0,X1,X4] :
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4)
| real_one = a(X4,X4) ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
( real_zero = a(sK1,sK2)
| int_leq(sK4,n) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
( real_zero = a(sK1,sK2)
| int_less(sK3,sK4) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
( real_zero = a(sK1,sK2)
| int_leq(int_one,sK3) ),
inference(cnf_transformation,[],[f25]) ).
fof(f48,plain,
( real_zero = a(sK1,sK2)
| real_zero != a(sK3,sK4) ),
inference(cnf_transformation,[],[f25]) ).
fof(f49,plain,
( int_leq(int_one,sK1)
| int_leq(sK4,n) ),
inference(cnf_transformation,[],[f25]) ).
fof(f50,plain,
( int_leq(int_one,sK1)
| int_less(sK3,sK4) ),
inference(cnf_transformation,[],[f25]) ).
fof(f51,plain,
( int_leq(int_one,sK1)
| int_leq(int_one,sK3) ),
inference(cnf_transformation,[],[f25]) ).
fof(f52,plain,
( int_leq(int_one,sK1)
| real_zero != a(sK3,sK4) ),
inference(cnf_transformation,[],[f25]) ).
fof(f53,plain,
( int_leq(sK2,n)
| int_leq(sK4,n) ),
inference(cnf_transformation,[],[f25]) ).
fof(f54,plain,
( int_leq(sK2,n)
| int_less(sK3,sK4) ),
inference(cnf_transformation,[],[f25]) ).
fof(f55,plain,
( int_leq(sK2,n)
| int_leq(int_one,sK3) ),
inference(cnf_transformation,[],[f25]) ).
fof(f56,plain,
( int_leq(sK2,n)
| real_zero != a(sK3,sK4) ),
inference(cnf_transformation,[],[f25]) ).
fof(f57,plain,
( sK1 = sK2
| int_leq(sK4,n) ),
inference(cnf_transformation,[],[f25]) ).
fof(f58,plain,
( sK1 = sK2
| int_less(sK3,sK4) ),
inference(cnf_transformation,[],[f25]) ).
fof(f59,plain,
( sK1 = sK2
| int_leq(int_one,sK3) ),
inference(cnf_transformation,[],[f25]) ).
fof(f60,plain,
( sK1 = sK2
| real_zero != a(sK3,sK4) ),
inference(cnf_transformation,[],[f25]) ).
fof(f61,plain,
! [X1] : int_leq(X1,X1),
inference(equality_resolution,[],[f27]) ).
fof(f62,plain,
! [X1] : ~ int_less(X1,X1),
inference(equality_resolution,[],[f30]) ).
fof(f64,plain,
! [X0,X6,X5] :
( ~ int_leq(int_one,X6)
| ~ int_leq(int_one,plus(X0,X5))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X5)
| ~ int_leq(X6,X0)
| ~ int_leq(plus(X0,X5),n)
| real_zero = a(X6,plus(X6,X5)) ),
inference(equality_resolution,[],[f43]) ).
fof(f67,definition,
( spl5_1
<=> int_leq(sK4,n) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f69,plain,
( int_leq(sK4,n)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f71,definition,
( spl5_2
<=> real_zero = a(sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f73,plain,
( real_zero = a(sK1,sK2)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f45,f71,f67]) ).
fof(f76,definition,
( spl5_3
<=> int_less(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f78,plain,
( int_less(sK3,sK4)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,plain,
( spl5_3
| spl5_2 ),
inference(avatar_split_clause,[],[f46,f71,f76]) ).
fof(f81,definition,
( spl5_4
<=> int_leq(int_one,sK3) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f83,plain,
( int_leq(int_one,sK3)
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,plain,
( spl5_4
| spl5_2 ),
inference(avatar_split_clause,[],[f47,f71,f81]) ).
fof(f86,definition,
( spl5_5
<=> real_zero = a(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f88,plain,
( real_zero != a(sK3,sK4)
| spl5_5 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,plain,
( ~ spl5_5
| spl5_2 ),
inference(avatar_split_clause,[],[f48,f71,f86]) ).
fof(f91,definition,
( spl5_6
<=> int_leq(int_one,sK1) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f93,plain,
( int_leq(int_one,sK1)
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,plain,
( spl5_1
| spl5_6 ),
inference(avatar_split_clause,[],[f49,f91,f67]) ).
fof(f95,plain,
( spl5_3
| spl5_6 ),
inference(avatar_split_clause,[],[f50,f91,f76]) ).
fof(f96,plain,
( spl5_4
| spl5_6 ),
inference(avatar_split_clause,[],[f51,f91,f81]) ).
fof(f97,plain,
( ~ spl5_5
| spl5_6 ),
inference(avatar_split_clause,[],[f52,f91,f86]) ).
fof(f99,definition,
( spl5_7
<=> int_leq(sK2,n) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
fof(f101,plain,
( int_leq(sK2,n)
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl5_1
| spl5_7 ),
inference(avatar_split_clause,[],[f53,f99,f67]) ).
fof(f103,plain,
( spl5_3
| spl5_7 ),
inference(avatar_split_clause,[],[f54,f99,f76]) ).
fof(f104,plain,
( spl5_4
| spl5_7 ),
inference(avatar_split_clause,[],[f55,f99,f81]) ).
fof(f105,plain,
( ~ spl5_5
| spl5_7 ),
inference(avatar_split_clause,[],[f56,f99,f86]) ).
fof(f107,definition,
( spl5_8
<=> sK1 = sK2 ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
fof(f109,plain,
( sK1 = sK2
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,plain,
( spl5_1
| spl5_8 ),
inference(avatar_split_clause,[],[f57,f107,f67]) ).
fof(f111,plain,
( spl5_3
| spl5_8 ),
inference(avatar_split_clause,[],[f58,f107,f76]) ).
fof(f112,plain,
( spl5_4
| spl5_8 ),
inference(avatar_split_clause,[],[f59,f107,f81]) ).
fof(f113,plain,
( ~ spl5_5
| spl5_8 ),
inference(avatar_split_clause,[],[f60,f107,f86]) ).
fof(f115,definition,
( spl5_9
<=> ! [X0] :
( ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
fof(f116,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,definition,
( spl5_10
<=> ! [X4,X1] :
( ~ int_leq(X1,n)
| real_one = a(X4,X4)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X1) ) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
fof(f119,plain,
( ! [X1,X4] :
( ~ int_leq(int_one,X1)
| real_one = a(X4,X4)
| ~ int_leq(int_one,X4)
| ~ int_leq(X4,X1)
| ~ int_leq(X1,n) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f120,plain,
( spl5_9
| spl5_10 ),
inference(avatar_split_clause,[],[f44,f118,f115]) ).
fof(f121,plain,
( int_leq(sK1,n)
| ~ spl5_7
| ~ spl5_8 ),
inference(superposition,[],[f101,f109]) ).
fof(f122,plain,
( real_zero = a(sK1,sK1)
| ~ spl5_2
| ~ spl5_8 ),
inference(forward_demodulation,[],[f73,f109]) ).
fof(f123,plain,
( ~ int_leq(sK1,n)
| ~ spl5_6
| ~ spl5_9 ),
inference(resolution,[],[f116,f93]) ).
fof(f125,plain,
( $false
| ~ spl5_6
| ~ spl5_7
| ~ spl5_8
| ~ spl5_9 ),
inference(forward_subsumption_resolution,[],[f123,f121]) ).
fof(f126,plain,
( ~ spl5_6
| ~ spl5_7
| ~ spl5_8
| ~ spl5_9 ),
inference(avatar_contradiction_clause,[],[f125]) ).
fof(f146,plain,
! [X0] :
( ~ int_leq(int_zero,X0)
| int_zero = X0
| int_leq(int_one,X0) ),
inference(resolution,[],[f26,f40]) ).
fof(f178,plain,
( ! [X0] :
( real_one = a(X0,X0)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,sK1)
| ~ int_leq(sK1,n) )
| ~ spl5_6
| ~ spl5_10 ),
inference(resolution,[],[f119,f93]) ).
fof(f188,plain,
( ! [X0] :
( ~ int_leq(int_one,X0)
| real_one = a(X0,X0)
| ~ int_leq(X0,sK1) )
| ~ spl5_6
| ~ spl5_7
| ~ spl5_8
| ~ spl5_10 ),
inference(forward_subsumption_resolution,[],[f178,f121]) ).
fof(f220,plain,
( real_one = a(sK1,sK1)
| ~ int_leq(sK1,sK1)
| ~ spl5_6
| ~ spl5_7
| ~ spl5_8
| ~ spl5_10 ),
inference(resolution,[],[f188,f93]) ).
fof(f233,plain,
( real_one = a(sK1,sK1)
| ~ spl5_6
| ~ spl5_7
| ~ spl5_8
| ~ spl5_10 ),
inference(forward_subsumption_resolution,[],[f220,f61]) ).
fof(f234,plain,
( real_zero = real_one
| ~ spl5_2
| ~ spl5_6
| ~ spl5_7
| ~ spl5_8
| ~ spl5_10 ),
inference(forward_demodulation,[],[f233,f122]) ).
fof(f235,plain,
( $false
| ~ spl5_2
| ~ spl5_6
| ~ spl5_7
| ~ spl5_8
| ~ spl5_10 ),
inference(forward_subsumption_resolution,[],[f234,f41]) ).
fof(f236,plain,
( ~ spl5_2
| ~ spl5_6
| ~ spl5_7
| ~ spl5_8
| ~ spl5_10 ),
inference(avatar_contradiction_clause,[],[f235]) ).
fof(f246,plain,
( sK4 = plus(sK3,sK0(sK3,sK4))
| ~ spl5_3 ),
inference(resolution,[],[f78,f37]) ).
fof(f247,plain,
( ! [X0] :
( ~ int_less(sK4,X0)
| int_less(sK3,X0) )
| ~ spl5_3 ),
inference(resolution,[],[f78,f29]) ).
fof(f250,plain,
( ! [X0,X1] :
( ~ int_leq(sK3,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ~ int_less(int_zero,X1)
| ~ int_leq(int_one,plus(X0,X1))
| ~ int_leq(plus(X0,X1),n)
| real_zero = a(sK3,plus(sK3,X1)) )
| ~ spl5_4 ),
inference(resolution,[],[f83,f64]) ).
fof(f252,plain,
( int_less(int_zero,sK3)
| ~ spl5_4 ),
inference(resolution,[],[f83,f39]) ).
fof(f255,definition,
( spl5_19
<=> int_leq(sK3,n) ),
introduced(definition,[new_symbols(definition,[spl5_19])],[avatar_definition]) ).
fof(f266,plain,
( ! [X0] :
( int_less(int_zero,X0)
| ~ int_less(sK3,X0) )
| ~ spl5_4 ),
inference(resolution,[],[f252,f29]) ).
fof(f270,plain,
( ! [X0] :
( ~ int_leq(sK4,X0)
| sK4 = X0
| int_less(sK3,X0) )
| ~ spl5_3 ),
inference(resolution,[],[f247,f26]) ).
fof(f271,plain,
( ! [X0] :
( int_less(sK3,X0)
| int_leq(X0,sK4) )
| ~ spl5_3 ),
inference(resolution,[],[f247,f31]) ).
fof(f328,plain,
( ! [X0] :
( ~ int_leq(sK3,n)
| ~ int_leq(int_one,sK3)
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,plus(sK3,X0))
| ~ int_leq(plus(sK3,X0),n)
| real_zero = a(sK3,plus(sK3,X0)) )
| ~ spl5_4 ),
inference(resolution,[],[f250,f61]) ).
fof(f337,definition,
( spl5_25
<=> int_leq(int_one,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_25])],[avatar_definition]) ).
fof(f338,plain,
( int_leq(int_one,sK4)
| ~ spl5_25 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f339,plain,
( ~ int_leq(int_one,sK4)
| spl5_25 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f691,definition,
( spl5_40
<=> n = sK4 ),
introduced(definition,[new_symbols(definition,[spl5_40])],[avatar_definition]) ).
fof(f693,plain,
( n = sK4
| ~ spl5_40 ),
inference(avatar_component_clause,[],[f691]) ).
fof(f759,plain,
( ! [X0] :
( ~ int_leq(sK3,n)
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,plus(sK3,X0))
| ~ int_leq(plus(sK3,X0),n)
| real_zero = a(sK3,plus(sK3,X0)) )
| ~ spl5_4 ),
inference(forward_subsumption_resolution,[],[f328,f83]) ).
fof(f764,definition,
( spl5_55
<=> ! [X0] :
( ~ int_less(int_zero,X0)
| real_zero = a(sK3,plus(sK3,X0))
| ~ int_leq(plus(sK3,X0),n)
| ~ int_leq(int_one,plus(sK3,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl5_55])],[avatar_definition]) ).
fof(f765,plain,
( ! [X0] :
( ~ int_leq(plus(sK3,X0),n)
| real_zero = a(sK3,plus(sK3,X0))
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,plus(sK3,X0)) )
| ~ spl5_55 ),
inference(avatar_component_clause,[],[f764]) ).
fof(f766,plain,
( spl5_55
| ~ spl5_19
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f759,f81,f255,f764]) ).
fof(f933,plain,
( ~ int_less(sK3,int_zero)
| ~ spl5_4 ),
inference(resolution,[],[f266,f62]) ).
fof(f948,plain,
( int_leq(int_zero,sK4)
| ~ spl5_3
| ~ spl5_4 ),
inference(resolution,[],[f933,f271]) ).
fof(f957,plain,
( int_zero = sK4
| int_leq(int_one,sK4)
| ~ spl5_3
| ~ spl5_4 ),
inference(resolution,[],[f948,f146]) ).
fof(f966,definition,
( spl5_71
<=> int_zero = sK4 ),
introduced(definition,[new_symbols(definition,[spl5_71])],[avatar_definition]) ).
fof(f968,plain,
( int_zero = sK4
| ~ spl5_71 ),
inference(avatar_component_clause,[],[f966]) ).
fof(f970,plain,
( int_zero = sK4
| ~ spl5_3
| ~ spl5_4
| spl5_25 ),
inference(forward_subsumption_resolution,[],[f957,f339]) ).
fof(f975,plain,
( spl5_71
| ~ spl5_3
| ~ spl5_4
| spl5_25 ),
inference(avatar_split_clause,[],[f970,f337,f81,f76,f966]) ).
fof(f999,plain,
( ~ int_less(sK3,sK4)
| ~ spl5_4
| ~ spl5_71 ),
inference(superposition,[],[f933,f968]) ).
fof(f1004,plain,
( $false
| ~ spl5_3
| ~ spl5_4
| ~ spl5_71 ),
inference(forward_subsumption_resolution,[],[f999,f78]) ).
fof(f1005,plain,
( ~ spl5_3
| ~ spl5_4
| ~ spl5_71 ),
inference(avatar_contradiction_clause,[],[f1004]) ).
fof(f1025,definition,
( spl5_75
<=> int_less(int_zero,sK0(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl5_75])],[avatar_definition]) ).
fof(f1026,plain,
( int_less(int_zero,sK0(sK3,sK4))
| ~ spl5_75 ),
inference(avatar_component_clause,[],[f1025]) ).
fof(f1027,plain,
( ~ int_less(int_zero,sK0(sK3,sK4))
| spl5_75 ),
inference(avatar_component_clause,[],[f1025]) ).
fof(f1050,plain,
( ~ int_less(sK3,sK4)
| spl5_75 ),
inference(resolution,[],[f1027,f36]) ).
fof(f1064,plain,
( $false
| ~ spl5_3
| spl5_75 ),
inference(forward_subsumption_resolution,[],[f1050,f78]) ).
fof(f1065,plain,
( ~ spl5_3
| spl5_75 ),
inference(avatar_contradiction_clause,[],[f1064]) ).
fof(f1342,definition,
( spl5_109
<=> int_less(sK3,n) ),
introduced(definition,[new_symbols(definition,[spl5_109])],[avatar_definition]) ).
fof(f1344,plain,
( int_less(sK3,n)
| ~ spl5_109 ),
inference(avatar_component_clause,[],[f1342]) ).
fof(f1447,plain,
( n = sK4
| int_less(sK3,n)
| ~ spl5_1
| ~ spl5_3 ),
inference(resolution,[],[f270,f69]) ).
fof(f1458,plain,
( spl5_109
| spl5_40
| ~ spl5_1
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f1447,f76,f67,f691,f1342]) ).
fof(f1463,plain,
( int_less(sK3,n)
| ~ spl5_3
| ~ spl5_40 ),
inference(superposition,[],[f78,f693]) ).
fof(f1488,plain,
( spl5_109
| ~ spl5_3
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f1463,f691,f76,f1342]) ).
fof(f1497,plain,
( int_leq(sK3,n)
| ~ spl5_109 ),
inference(resolution,[],[f1344,f28]) ).
fof(f2275,plain,
( ~ int_leq(sK4,n)
| real_zero = a(sK3,sK4)
| ~ int_less(int_zero,sK0(sK3,sK4))
| ~ int_leq(int_one,sK4)
| ~ spl5_3
| ~ spl5_55 ),
inference(superposition,[],[f765,f246]) ).
fof(f2282,plain,
( real_zero = a(sK3,sK4)
| ~ int_less(int_zero,sK0(sK3,sK4))
| ~ int_leq(int_one,sK4)
| ~ spl5_1
| ~ spl5_3
| ~ spl5_55 ),
inference(forward_subsumption_resolution,[],[f2275,f69]) ).
fof(f2283,plain,
( ~ int_less(int_zero,sK0(sK3,sK4))
| ~ int_leq(int_one,sK4)
| ~ spl5_1
| ~ spl5_3
| spl5_5
| ~ spl5_55 ),
inference(forward_subsumption_resolution,[],[f2282,f88]) ).
fof(f2284,plain,
( ~ int_leq(int_one,sK4)
| ~ spl5_1
| ~ spl5_3
| spl5_5
| ~ spl5_55
| ~ spl5_75 ),
inference(forward_subsumption_resolution,[],[f2283,f1026]) ).
fof(f2285,plain,
( $false
| ~ spl5_1
| ~ spl5_3
| spl5_5
| ~ spl5_25
| ~ spl5_55
| ~ spl5_75 ),
inference(forward_subsumption_resolution,[],[f2284,f338]) ).
fof(f2286,plain,
( ~ spl5_1
| ~ spl5_3
| spl5_5
| ~ spl5_25
| ~ spl5_55
| ~ spl5_75 ),
inference(avatar_contradiction_clause,[],[f2285]) ).
fof(f2289,plain,
( spl5_19
| ~ spl5_109 ),
inference(avatar_split_clause,[],[f1497,f1342,f255]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f74]) ).
cnf(s2,plain,
( spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f79]) ).
cnf(s3,plain,
( spl5_2
| spl5_4 ),
inference(sat_conversion,[],[f84]) ).
cnf(s4,plain,
( spl5_2
| ~ spl5_5 ),
inference(sat_conversion,[],[f89]) ).
cnf(s5,plain,
( spl5_1
| spl5_6 ),
inference(sat_conversion,[],[f94]) ).
cnf(s6,plain,
( spl5_3
| spl5_6 ),
inference(sat_conversion,[],[f95]) ).
cnf(s7,plain,
( spl5_4
| spl5_6 ),
inference(sat_conversion,[],[f96]) ).
cnf(s8,plain,
( ~ spl5_5
| spl5_6 ),
inference(sat_conversion,[],[f97]) ).
cnf(s9,plain,
( spl5_1
| spl5_7 ),
inference(sat_conversion,[],[f102]) ).
cnf(s10,plain,
( spl5_3
| spl5_7 ),
inference(sat_conversion,[],[f103]) ).
cnf(s11,plain,
( spl5_4
| spl5_7 ),
inference(sat_conversion,[],[f104]) ).
cnf(s12,plain,
( ~ spl5_5
| spl5_7 ),
inference(sat_conversion,[],[f105]) ).
cnf(s13,plain,
( spl5_1
| spl5_8 ),
inference(sat_conversion,[],[f110]) ).
cnf(s14,plain,
( spl5_3
| spl5_8 ),
inference(sat_conversion,[],[f111]) ).
cnf(s15,plain,
( spl5_4
| spl5_8 ),
inference(sat_conversion,[],[f112]) ).
cnf(s16,plain,
( ~ spl5_5
| spl5_8 ),
inference(sat_conversion,[],[f113]) ).
cnf(s17,plain,
( spl5_9
| spl5_10 ),
inference(sat_conversion,[],[f120]) ).
cnf(s18,plain,
( ~ spl5_6
| ~ spl5_7
| ~ spl5_8
| ~ spl5_9 ),
inference(sat_conversion,[],[f126]) ).
cnf(s22,plain,
( ~ spl5_2
| ~ spl5_6
| ~ spl5_7
| ~ spl5_8
| ~ spl5_10 ),
inference(sat_conversion,[],[f236]) ).
cnf(s43,plain,
( ~ spl5_4
| ~ spl5_19
| spl5_55 ),
inference(sat_conversion,[],[f766]) ).
cnf(s61,plain,
( ~ spl5_3
| ~ spl5_4
| spl5_25
| spl5_71 ),
inference(sat_conversion,[],[f975]) ).
cnf(s64,plain,
( ~ spl5_3
| ~ spl5_4
| ~ spl5_71 ),
inference(sat_conversion,[],[f1005]) ).
cnf(s71,plain,
( ~ spl5_3
| spl5_75 ),
inference(sat_conversion,[],[f1065]) ).
cnf(s104,plain,
( ~ spl5_1
| ~ spl5_3
| spl5_40
| spl5_109 ),
inference(sat_conversion,[],[f1458]) ).
cnf(s106,plain,
( ~ spl5_3
| ~ spl5_40
| spl5_109 ),
inference(sat_conversion,[],[f1488]) ).
cnf(s167,plain,
( ~ spl5_1
| ~ spl5_3
| spl5_5
| ~ spl5_25
| ~ spl5_55
| ~ spl5_75 ),
inference(sat_conversion,[],[f2286]) ).
cnf(s170,plain,
( spl5_19
| ~ spl5_109 ),
inference(sat_conversion,[],[f2289]) ).
cnf(s173,plain,
( ~ spl5_6
| ~ spl5_7
| ~ spl5_2
| ~ spl5_8 ),
inference(rat,[],[s17,s18,s22]) ).
cnf(s174,plain,
spl5_1,
inference(rat,[],[s173,s1,s5,s9,s13]) ).
cnf(s175,plain,
( spl5_109
| ~ spl5_3 ),
inference(rat,[],[s104,s106,s174]) ).
cnf(s176,plain,
spl5_2,
inference(rat,[],[s175,s170,s43,s167,s71,s61,s64,s2,s3,s4,s174]) ).
cnf(s177,plain,
( spl5_8
| ~ spl5_3 ),
inference(rat,[],[s167,s43,s61,s64,s15,s16,s71,s170,s175,s174]) ).
cnf(s178,plain,
( spl5_7
| ~ spl5_3 ),
inference(rat,[],[s167,s43,s61,s64,s11,s12,s71,s170,s175,s174]) ).
cnf(s179,plain,
~ spl5_3,
inference(rat,[],[s167,s43,s61,s64,s7,s8,s173,s178,s177,s170,s175,s71,s174,s176]) ).
cnf(s180,plain,
spl5_8,
inference(rat,[],[s14,s179]) ).
cnf(s181,plain,
spl5_7,
inference(rat,[],[s10,s179]) ).
cnf(s182,plain,
spl5_6,
inference(rat,[],[s6,s179]) ).
cnf(s183,plain,
$false,
inference(rat,[],[s173,s180,s176,s182,s181]) ).
fof(f2290,plain,
$false,
inference(avatar_sat_refutation,[],[s183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV492+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n008.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Mon Sep 28 11:15:10 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.31 % (2183792)Will run a generic schedule for satisfiability detection.
% 0.19/0.31 % (2183798)% WARNING: option uhcvi not known.
% 0.19/0.31 % (2183798)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2420109569:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.31 % (2183797)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=900839725_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.31 % (2183802)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3710705649:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.31 % (2183799)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3817697227:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.31 % (2183800)dis+10_1_sil=32000:sp=arity:random_seed=3518671498:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.31 % (2183801)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3698496421:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.31 % (2183803)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1770699851:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.31 % TRYING [1]
% 0.19/0.31 % TRYING [2]
% 0.19/0.31 % TRYING [3]
% 0.19/0.31 % TRYING [4]
% 0.19/0.31 % TRYING [5]
% 0.19/0.31 % TRYING [6]
% 0.19/0.31 % (2183798) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2183792-2183798"...
% 0.19/0.31 % (2183798)...printing done.
% 0.19/0.31 % (2183798)Refutation found. Thanks to Tanya!
% 0.19/0.31 % SZS status Theorem for theBenchmark
% 0.19/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.31 % (2183798)------------------------------
% 0.19/0.31 % (2183798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.31 % (2183798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.31 % (2183798)CaDiCaL version: 2.1.3
% 0.19/0.31 % (2183798)Termination reason: Refutation
% 0.19/0.31 % (2183798)Time elapsed: 0.033 s
% 0.19/0.31 % (2183798)Peak memory usage: 14 MB
% 0.19/0.31 % (2183798)Instructions burned: 82 (million)
% 0.19/0.31 % (2183792)Success in time 0.064 s
% 0.19/0.31 % Vampire exiting
%------------------------------------------------------------------------------