%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n026.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 2.98s 1.13s
% Output : Refutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 13
% Syntax : Number of formulae : 122 ( 12 unt; 1 def)
% Number of atoms : 493 ( 106 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 617 ( 246 ~; 264 |; 83 &)
% ( 3 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 180 ( 161 !; 19 ?)
% 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(f6,axiom,
! [X0,X1] : plus(X0,X1) = plus(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_commutative) ).
fof(f7,axiom,
! [X0] : plus(X0,int_zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_zero) ).
fof(f8,axiom,
! [X0,X1,X2,X3] :
( ( int_less(X0,X1)
& int_leq(X2,X3) )
=> int_leq(plus(X0,X2),plus(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_and_order1) ).
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] :
( ! [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(f18,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,[],[f17]) ).
fof(f19,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(f20,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,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( X0 != X1
| ~ int_less(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f22,plain,
! [X0,X1,X2] :
( int_less(X0,X2)
| ~ int_less(X0,X1)
| ~ int_less(X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f23,plain,
! [X0,X1,X2] :
( int_less(X0,X2)
| ~ int_less(X0,X1)
| ~ int_less(X1,X2) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( int_leq(plus(X0,X2),plus(X1,X3))
| ~ int_less(X0,X1)
| ~ int_leq(X2,X3) ),
inference(ennf_transformation,[],[f8]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( int_leq(plus(X0,X2),plus(X1,X3))
| ~ int_less(X0,X1)
| ~ int_leq(X2,X3) ),
inference(flattening,[],[f24]) ).
fof(f26,definition,
( ? [X2,X3] :
( real_zero = a(X2,X3)
& int_leq(int_one,X2)
& int_leq(X3,n)
& X2 = X3 )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f27,plain,
( ? [X0,X1] :
( real_zero != a(X0,X1)
& int_leq(int_one,X0)
& int_less(X0,X1)
& int_leq(X1,n) )
| sP0 ),
inference(definition_folding,[],[f20,f26]) ).
fof(f28,plain,
( ? [X2,X3] :
( real_zero = a(X2,X3)
& int_leq(int_one,X2)
& int_leq(X3,n)
& X2 = X3 )
| ~ sP0 ),
inference(nnf_transformation,[],[f26]) ).
fof(f29,plain,
( ? [X0,X1] :
( real_zero = a(X0,X1)
& int_leq(int_one,X0)
& int_leq(X1,n)
& X0 = X1 )
| ~ sP0 ),
inference(rectify,[],[f28]) ).
fof(f30,plain,
( ( real_zero = a(sK1,sK2)
& int_leq(int_one,sK1)
& int_leq(sK2,n)
& sK1 = sK2 )
| ~ sP0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f29]) ).
fof(f31,plain,
( ( real_zero != a(sK3,sK4)
& int_leq(int_one,sK3)
& int_less(sK3,sK4)
& int_leq(sK4,n) )
| sP0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f27]) ).
fof(f32,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(f33,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,[],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ( int_less(X0,X1)
| ! [X2] :
( plus(X0,X2) != X1
| ~ int_less(int_zero,X2) ) )
& ( ( plus(X0,sK5(X0,X1)) = X1
& int_less(int_zero,sK5(X0,X1)) )
| ~ int_less(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1))],[f33]) ).
fof(f35,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(f36,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,[],[f35]) ).
fof(f37,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(f38,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,[],[f18]) ).
fof(f39,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,[],[f18]) ).
fof(f41,plain,
( sK1 = sK2
| ~ sP0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f42,plain,
( int_leq(sK2,n)
| ~ sP0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f43,plain,
( int_leq(int_one,sK1)
| ~ sP0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f44,plain,
( real_zero = a(sK1,sK2)
| ~ sP0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f45,plain,
( int_leq(sK4,n)
| sP0 ),
inference(cnf_transformation,[],[f31]) ).
fof(f46,plain,
( int_less(sK3,sK4)
| sP0 ),
inference(cnf_transformation,[],[f31]) ).
fof(f47,plain,
( int_leq(int_one,sK3)
| sP0 ),
inference(cnf_transformation,[],[f31]) ).
fof(f48,plain,
( real_zero != a(sK3,sK4)
| sP0 ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
! [X0,X1] :
( X0 != X1
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f50,plain,
! [X0,X1] :
( int_less(int_zero,sK5(X0,X1))
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
! [X0,X1] :
( plus(X0,sK5(X0,X1)) = X1
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
! [X0] : plus(X0,int_zero) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f54,plain,
! [X0,X1] :
( int_less(X0,X1)
| int_leq(X1,X0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f55,plain,
! [X0,X1] :
( int_less(X0,X1)
| X0 = X1
| ~ int_leq(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f56,plain,
! [X0,X1] :
( int_leq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f57,plain,
! [X0,X1] :
( int_leq(X0,X1)
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f58,plain,
! [X0] :
( int_leq(int_one,X0)
| ~ int_less(int_zero,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f59,plain,
! [X0] :
( int_less(int_zero,X0)
| ~ int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f61,plain,
! [X2,X0,X1] :
( int_less(X0,X2)
| ~ int_less(X0,X1)
| ~ int_less(X1,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f62,plain,
! [X2,X3,X0,X1] :
( int_leq(plus(X0,X2),plus(X1,X3))
| ~ int_less(X0,X1)
| ~ int_leq(X2,X3) ),
inference(cnf_transformation,[],[f25]) ).
fof(f63,plain,
! [X0,X1] : plus(X0,X1) = plus(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f64,plain,
real_zero != real_one,
inference(cnf_transformation,[],[f11]) ).
fof(f66,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,[],[f38]) ).
fof(f67,plain,
! [X1] : ~ int_less(X1,X1),
inference(equality_resolution,[],[f49]) ).
fof(f69,plain,
! [X1] : int_leq(X1,X1),
inference(equality_resolution,[],[f56]) ).
fof(f70,plain,
( int_leq(sK1,n)
| ~ sP0
| ~ sP0 ),
inference(superposition,[],[f42,f41]) ).
fof(f71,plain,
( int_leq(sK1,n)
| ~ sP0 ),
inference(duplicate_literal_removal,[],[f70]) ).
fof(f72,plain,
( real_zero = a(sK1,sK1)
| ~ sP0
| ~ sP0 ),
inference(superposition,[],[f44,f41]) ).
fof(f73,plain,
( real_zero = a(sK1,sK1)
| ~ sP0 ),
inference(duplicate_literal_removal,[],[f72]) ).
fof(f76,plain,
! [X0] : plus(int_zero,X0) = X0,
inference(superposition,[],[f63,f53]) ).
fof(f93,plain,
! [X0,X1] :
( ~ int_less(X1,X0)
| ~ int_less(X0,X1) ),
inference(resolution,[],[f61,f67]) ).
fof(f98,plain,
( ~ int_less(sK4,sK3)
| sP0 ),
inference(resolution,[],[f93,f46]) ).
fof(f112,plain,
! [X2,X0,X1] :
( int_leq(plus(X1,X2),X0)
| ~ int_less(X1,X0)
| ~ int_leq(X2,int_zero) ),
inference(superposition,[],[f62,f53]) ).
fof(f117,plain,
! [X0] :
( ~ int_less(sK4,X0)
| sP0
| ~ int_less(X0,sK3) ),
inference(resolution,[],[f98,f61]) ).
fof(f118,plain,
( ~ int_leq(sK4,sK3)
| sK3 = sK4
| sP0 ),
inference(resolution,[],[f98,f55]) ).
fof(f121,plain,
! [X0,X1] :
( real_zero = real_one
| ~ sP0
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) ),
inference(superposition,[],[f73,f39]) ).
fof(f122,plain,
! [X0,X1] :
( ~ sP0
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) ),
inference(forward_subsumption_resolution,[],[f121,f64]) ).
fof(f124,plain,
! [X0,X1] :
( ~ int_leq(sK1,X0)
| ~ sP0
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) ),
inference(forward_subsumption_resolution,[],[f122,f43]) ).
fof(f127,plain,
! [X0] :
( ~ int_less(X0,sK3)
| sP0
| sK4 = X0
| ~ int_leq(sK4,X0) ),
inference(resolution,[],[f117,f55]) ).
fof(f128,plain,
! [X0] :
( int_leq(X0,sK4)
| ~ int_less(X0,sK3)
| sP0 ),
inference(resolution,[],[f117,f54]) ).
fof(f133,plain,
! [X2,X0,X1] :
( real_zero = a(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,X2)
| ~ int_less(int_zero,sK5(X1,X0))
| ~ int_leq(int_one,X2)
| ~ int_leq(X2,n)
| ~ int_leq(int_one,plus(X2,sK5(X1,X0)))
| ~ int_leq(plus(X2,sK5(X1,X0)),n)
| ~ int_less(X1,X0) ),
inference(superposition,[],[f66,f51]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ~ int_leq(plus(X2,sK5(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,sK5(X1,X0)))
| real_zero = a(X1,X0)
| ~ int_less(X1,X0) ),
inference(forward_subsumption_resolution,[],[f133,f50]) ).
fof(f177,plain,
! [X0,X1] :
( int_leq(X0,X1)
| ~ int_less(int_zero,X1)
| ~ int_leq(X0,int_zero) ),
inference(superposition,[],[f112,f76]) ).
fof(f211,plain,
! [X0] :
( int_leq(sK3,X0)
| sK4 = X0
| ~ int_leq(sK4,X0)
| sP0 ),
inference(resolution,[],[f127,f54]) ).
fof(f250,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,[],[f135,f51]) ).
fof(f254,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,[],[f250]) ).
fof(f255,plain,
! [X0,X1] :
( real_zero = a(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_less(X1,X0) ),
inference(forward_subsumption_resolution,[],[f254,f69]) ).
fof(f388,plain,
( ~ int_less(int_zero,sK3)
| ~ int_leq(sK4,int_zero)
| sK3 = sK4
| sP0 ),
inference(resolution,[],[f177,f118]) ).
fof(f392,plain,
( ~ int_leq(sK4,int_zero)
| sK3 = sK4
| sP0
| ~ int_leq(int_one,sK3) ),
inference(resolution,[],[f388,f59]) ).
fof(f396,plain,
( ~ int_leq(sK4,int_zero)
| sK3 = sK4
| sP0 ),
inference(forward_subsumption_resolution,[],[f392,f47]) ).
fof(f625,plain,
! [X0] :
( ~ sP0
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK1,n) ),
inference(resolution,[],[f124,f69]) ).
fof(f646,plain,
! [X0] :
( ~ sP0
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(sK1,n) ),
inference(forward_subsumption_resolution,[],[f625,f43]) ).
fof(f649,plain,
! [X0] :
( ~ sP0
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) ),
inference(forward_subsumption_resolution,[],[f646,f71]) ).
fof(f776,plain,
( real_zero != real_zero
| sP0
| ~ int_leq(int_one,sK3)
| ~ int_leq(sK3,n)
| ~ int_leq(int_one,sK4)
| ~ int_leq(sK4,n)
| ~ int_less(sK3,sK4) ),
inference(superposition,[],[f48,f255]) ).
fof(f777,plain,
( sP0
| ~ int_leq(int_one,sK3)
| ~ int_leq(sK3,n)
| ~ int_leq(int_one,sK4)
| ~ int_leq(sK4,n)
| ~ int_less(sK3,sK4) ),
inference(trivial_inequality_removal,[],[f776]) ).
fof(f784,plain,
( sP0
| ~ int_leq(sK3,n)
| ~ int_leq(int_one,sK4)
| ~ int_leq(sK4,n)
| ~ int_less(sK3,sK4) ),
inference(forward_subsumption_resolution,[],[f777,f47]) ).
fof(f785,plain,
( sP0
| ~ int_leq(sK3,n)
| ~ int_leq(int_one,sK4)
| ~ int_less(sK3,sK4) ),
inference(forward_subsumption_resolution,[],[f784,f45]) ).
fof(f786,plain,
( ~ int_leq(sK3,n)
| sP0
| ~ int_leq(int_one,sK4) ),
inference(forward_subsumption_resolution,[],[f785,f46]) ).
fof(f788,plain,
( sP0
| ~ int_leq(int_one,sK4)
| n = sK4
| ~ int_leq(sK4,n)
| sP0 ),
inference(resolution,[],[f786,f211]) ).
fof(f794,plain,
( ~ int_less(sK3,n)
| ~ int_leq(int_one,sK4)
| sP0 ),
inference(resolution,[],[f786,f57]) ).
fof(f798,plain,
( sP0
| ~ int_leq(int_one,sK4)
| n = sK4
| ~ int_leq(sK4,n) ),
inference(duplicate_literal_removal,[],[f788]) ).
fof(f800,plain,
( ~ int_leq(int_one,sK4)
| sP0
| n = sK4 ),
inference(forward_subsumption_resolution,[],[f798,f45]) ).
fof(f863,plain,
( ~ int_less(int_zero,sK4)
| n = sK4
| sP0 ),
inference(resolution,[],[f800,f58]) ).
fof(f903,plain,
( int_leq(sK4,int_zero)
| sP0
| n = sK4 ),
inference(resolution,[],[f863,f54]) ).
fof(f959,plain,
( sP0
| n = sK4
| sK3 = sK4
| sP0 ),
inference(resolution,[],[f903,f396]) ).
fof(f964,plain,
( sK3 = sK4
| n = sK4
| sP0 ),
inference(duplicate_literal_removal,[],[f959]) ).
fof(f1046,plain,
( int_less(sK3,sK3)
| sP0
| n = sK4
| sP0 ),
inference(superposition,[],[f46,f964]) ).
fof(f1137,plain,
( int_less(sK3,sK3)
| sP0
| n = sK4 ),
inference(duplicate_literal_removal,[],[f1046]) ).
fof(f1142,plain,
( n = sK4
| sP0 ),
inference(forward_subsumption_resolution,[],[f1137,f67]) ).
fof(f1161,plain,
( ~ int_less(sK3,sK4)
| ~ int_leq(int_one,sK4)
| sP0
| sP0 ),
inference(superposition,[],[f794,f1142]) ).
fof(f1168,plain,
( ~ int_less(sK3,sK4)
| ~ int_leq(int_one,sK4)
| sP0 ),
inference(duplicate_literal_removal,[],[f1161]) ).
fof(f1171,plain,
( ~ int_leq(int_one,sK4)
| sP0 ),
inference(forward_subsumption_resolution,[],[f1168,f46]) ).
fof(f1174,plain,
( sP0
| ~ int_less(int_one,sK3)
| sP0 ),
inference(resolution,[],[f1171,f128]) ).
fof(f1185,plain,
( ~ int_less(int_one,sK4)
| sP0 ),
inference(resolution,[],[f1171,f57]) ).
fof(f1196,plain,
( ~ int_less(int_one,sK3)
| sP0 ),
inference(duplicate_literal_removal,[],[f1174]) ).
fof(f1242,plain,
( sP0
| int_one = sK3
| ~ int_leq(int_one,sK3) ),
inference(resolution,[],[f1196,f55]) ).
fof(f1244,plain,
( int_one = sK3
| sP0 ),
inference(forward_subsumption_resolution,[],[f1242,f47]) ).
fof(f1364,plain,
( ~ int_less(sK3,sK4)
| sP0
| sP0 ),
inference(superposition,[],[f1185,f1244]) ).
fof(f1371,plain,
( ~ int_less(sK3,sK4)
| sP0 ),
inference(duplicate_literal_removal,[],[f1364]) ).
fof(f1379,plain,
sP0,
inference(forward_subsumption_resolution,[],[f1371,f46]) ).
fof(f1384,plain,
! [X0] :
( ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) ),
inference(forward_subsumption_resolution,[],[f649,f1379]) ).
fof(f1386,plain,
( ~ int_leq(sK1,n)
| ~ sP0 ),
inference(resolution,[],[f1384,f43]) ).
fof(f1411,plain,
~ sP0,
inference(forward_subsumption_resolution,[],[f1386,f71]) ).
fof(f1412,plain,
$false,
inference(forward_subsumption_resolution,[],[f1411,f1379]) ).
%------------------------------------------------------------------------------
%----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 THM
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 11:17:12 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.98/1.13 % (3791350)Detected formulas, will run a generic FOF schedule.
% 2.98/1.13 % (3791361)dis-21_1_sil=8000:lcm=predicate:random_seed=3161329514: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)
% 2.98/1.13 % (3791356)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=1214128563:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.98/1.13 % (3791360)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=832264939:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.98/1.13 % (3791357)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=3710330851:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.98/1.13 % (3791355)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=1520334580:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.98/1.13 % (3791361)Instruction limit reached!
% 2.98/1.13 % (3791361)------------------------------
% 2.98/1.13 % (3791361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.13 % (3791361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.13 % (3791361)CaDiCaL version: 2.1.3
% 2.98/1.13 % (3791361)Termination reason: Instruction limit
% 2.98/1.13 % (3791361)Termination phase: Saturation
% 2.98/1.13 % (3791361)Time elapsed: 0.044 s
% 2.98/1.13 % (3791361)Peak memory usage: 89 MB
% 2.98/1.13 % (3791361)Instructions burned: 130 (million)
% 2.98/1.13 % (3791358)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1641481218:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.98/1.13 % (3791359)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3458498882:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.98/1.13 % (3791358)Refutation not found, incomplete strategy
% 2.98/1.13 % (3791358)------------------------------
% 2.98/1.13 % (3791358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.13 % (3791358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.13 % (3791358)CaDiCaL version: 2.1.3
% 2.98/1.13 % (3791358)Termination reason: Refutation not found, incomplete strategy
% 2.98/1.13 % (3791358)Time elapsed: 0.005 s
% 2.98/1.13 % (3791358)Peak memory usage: 88 MB
% 2.98/1.13 % (3791358)Instructions burned: 5 (million)
% 2.98/1.13 % (3791359)First to succeed.
% 2.98/1.13 % (3791359)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3791350"
% 2.98/1.13 % (3791369)lrs+10_1_sil=8000:sp=occurrence:random_seed=2342124083:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.98/1.13 % (3791360)Instruction limit reached!
% 2.98/1.13 % (3791360)------------------------------
% 2.98/1.13 % (3791360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.13 % (3791360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.13 % (3791360)CaDiCaL version: 2.1.3
% 2.98/1.13 % (3791360)Termination reason: Instruction limit
% 2.98/1.13 % (3791360)Termination phase: Saturation
% 2.98/1.13 % (3791360)Time elapsed: 0.100 s
% 2.98/1.13 % (3791360)Peak memory usage: 89 MB
% 2.98/1.13 % (3791360)Instructions burned: 139 (million)
% 2.98/1.13 % (3791369)Also succeeded, but the first one will report.
% 2.98/1.13 % (3791371)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1783838249:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.98/1.13 % (3791358)------------------------------
% 2.98/1.13 % (3791358)------------------------------
% 2.98/1.13 % (3791359)Refutation found. Thanks to Tanya!
% 2.98/1.13 % SZS status Theorem for theBenchmark
% 2.98/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 3.87/1.32 % (3791359)------------------------------
% 3.87/1.32 % (3791359)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.87/1.32 % (3791359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.87/1.32 % (3791359)CaDiCaL version: 2.1.3
% 3.87/1.32 % (3791359)Termination reason: Refutation
% 3.87/1.32 % (3791359)Time elapsed: 0.041 s
% 3.87/1.32 % (3791359)Peak memory usage: 89 MB
% 3.87/1.32 % (3791359)Instructions burned: 64 (million)
% 3.87/1.32 % (3791359)------------------------------
% 3.87/1.32 % (3791359)------------------------------
% 3.87/1.32 % (3791350)Success in time 0.453 s
% 3.87/1.32 % Vampire exiting
%------------------------------------------------------------------------------