%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV490+3 : 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 1.08s 0.94s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 12
% Syntax : Number of formulae : 107 ( 21 unt; 0 def)
% Number of atoms : 458 ( 118 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 629 ( 278 ~; 263 |; 64 &)
% ( 3 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 175 ( 168 !; 7 ?)
% 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) = 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/sandbox2/benchmark/theBenchmark.p',qii) ).
fof(f13,conjecture,
! [X0,X1] :
( ( int_leq(int_one,X0)
& int_leq(X0,n)
& int_leq(int_one,X1)
& int_leq(X1,n) )
=> ( ( X0 != X1
=> a(X0,X1) = real_zero )
& ( X0 = X1
=> a(X0,X1) != real_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',di) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ( int_leq(int_one,X0)
& int_leq(X0,n)
& int_leq(int_one,X1)
& int_leq(X1,n) )
=> ( ( X0 != X1
=> a(X0,X1) = real_zero )
& ( 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) = 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)
& X0 != X1 )
| ( real_zero = 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)
& X0 != X1 )
| ( real_zero = 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(f21,plain,
! [X0,X1,X2] :
( int_less(X0,X2)
| ~ int_less(X0,X1)
| ~ int_less(X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f22,plain,
! [X0,X1,X2] :
( int_less(X0,X2)
| ~ int_less(X0,X1)
| ~ int_less(X1,X2) ),
inference(flattening,[],[f21]) ).
fof(f23,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(f24,plain,
! [X0,X1,X2,X3] :
( int_leq(plus(X0,X2),plus(X1,X3))
| ~ int_less(X0,X1)
| ~ int_leq(X2,X3) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
( ( ( real_zero != a(sK0,sK1)
& sK0 != sK1 )
| ( real_zero = 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(f31,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(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(f40,plain,
( sK0 != sK1
| real_zero = a(sK0,sK1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
( real_zero != a(sK0,sK1)
| sK0 = sK1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f43,plain,
! [X0,X1] :
( X0 != X1
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f44,plain,
! [X0,X1] :
( int_less(int_zero,sK2(X0,X1))
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f45,plain,
! [X0,X1] :
( plus(X0,sK2(X0,X1)) = X1
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f47,plain,
! [X0] : plus(X0,int_zero) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f48,plain,
! [X0,X1] :
( int_less(X0,X1)
| int_leq(X1,X0) ),
inference(cnf_transformation,[],[f4]) ).
fof(f49,plain,
! [X0,X1] :
( int_less(X0,X1)
| X0 = X1
| ~ int_leq(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f50,plain,
! [X0,X1] :
( int_leq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f52,plain,
! [X0] :
( int_leq(int_one,X0)
| ~ int_less(int_zero,X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f53,plain,
! [X0] :
( int_less(int_zero,X0)
| ~ int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f55,plain,
! [X2,X0,X1] :
( int_less(X0,X2)
| ~ int_less(X0,X1)
| ~ int_less(X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( int_leq(plus(X0,X2),plus(X1,X3))
| ~ int_less(X0,X1)
| ~ int_leq(X2,X3) ),
inference(cnf_transformation,[],[f24]) ).
fof(f57,plain,
! [X0,X1] : plus(X0,X1) = plus(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f58,plain,
real_zero != real_one,
inference(cnf_transformation,[],[f11]) ).
fof(f59,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(f60,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(f61,plain,
! [X1] : ~ int_less(X1,X1),
inference(equality_resolution,[],[f43]) ).
fof(f63,plain,
! [X1] : int_leq(X1,X1),
inference(equality_resolution,[],[f50]) ).
fof(f68,plain,
! [X0] : plus(int_zero,X0) = X0,
inference(superposition,[],[f57,f47]) ).
fof(f83,plain,
! [X0,X1] :
( ~ int_less(X1,X0)
| ~ int_less(X0,X1) ),
inference(resolution,[],[f55,f61]) ).
fof(f89,plain,
! [X0,X1] :
( ~ int_less(X0,X1)
| X0 = X1
| ~ int_leq(X1,X0) ),
inference(resolution,[],[f83,f49]) ).
fof(f110,plain,
! [X2,X0,X1] :
( int_leq(plus(X1,X2),X0)
| ~ int_less(X1,X0)
| ~ int_leq(X2,int_zero) ),
inference(superposition,[],[f56,f47]) ).
fof(f125,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,[],[f59,f45]) ).
fof(f127,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,[],[f125,f44]) ).
fof(f131,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,[],[f60,f45]) ).
fof(f133,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,[],[f131,f44]) ).
fof(f160,plain,
! [X0,X1] :
( int_leq(X0,X1)
| ~ int_less(int_zero,X1)
| ~ int_leq(X0,int_zero) ),
inference(superposition,[],[f110,f68]) ).
fof(f247,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,[],[f127,f45]) ).
fof(f251,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,[],[f247]) ).
fof(f253,plain,
! [X0,X1] :
( real_zero = a(X0,X1)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n)
| ~ int_leq(X1,n)
| ~ int_less(X1,X0) ),
inference(forward_subsumption_resolution,[],[f251,f63]) ).
fof(f259,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,[],[f133,f45]) ).
fof(f263,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,[],[f259]) ).
fof(f265,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,[],[f263,f63]) ).
fof(f283,plain,
! [X0,X1] :
( X0 = X1
| ~ int_leq(X1,X0)
| X0 = X1
| ~ int_leq(X0,X1) ),
inference(resolution,[],[f89,f49]) ).
fof(f287,plain,
! [X0,X1] :
( ~ int_leq(X1,X0)
| X0 = X1
| ~ int_leq(X0,X1) ),
inference(duplicate_literal_removal,[],[f283]) ).
fof(f606,plain,
( real_zero != real_zero
| sK0 = sK1
| ~ int_leq(int_one,sK1)
| ~ int_leq(int_one,sK0)
| ~ int_leq(sK0,n)
| ~ int_leq(sK1,n)
| ~ int_less(sK1,sK0) ),
inference(superposition,[],[f41,f253]) ).
fof(f609,plain,
( sK0 = sK1
| ~ int_leq(int_one,sK1)
| ~ int_leq(int_one,sK0)
| ~ int_leq(sK0,n)
| ~ int_leq(sK1,n)
| ~ int_less(sK1,sK0) ),
inference(trivial_inequality_removal,[],[f606]) ).
fof(f611,plain,
( sK0 = sK1
| ~ int_leq(int_one,sK0)
| ~ int_leq(sK0,n)
| ~ int_leq(sK1,n)
| ~ int_less(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f609,f36]) ).
fof(f612,plain,
( sK0 = sK1
| ~ int_leq(sK0,n)
| ~ int_leq(sK1,n)
| ~ int_less(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f611,f38]) ).
fof(f613,plain,
( sK0 = sK1
| ~ int_leq(sK1,n)
| ~ int_less(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f612,f37]) ).
fof(f614,plain,
( ~ int_less(sK1,sK0)
| sK0 = sK1 ),
inference(forward_subsumption_resolution,[],[f613,f35]) ).
fof(f616,plain,
( sK0 = sK1
| sK0 = sK1
| ~ int_leq(sK1,sK0) ),
inference(resolution,[],[f614,f49]) ).
fof(f618,plain,
( ~ int_leq(sK1,sK0)
| sK0 = sK1 ),
inference(duplicate_literal_removal,[],[f616]) ).
fof(f620,plain,
( real_zero != real_zero
| sK0 = sK1
| ~ int_leq(int_one,sK0)
| ~ int_leq(sK0,n)
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK1,n)
| ~ int_less(sK0,sK1) ),
inference(superposition,[],[f41,f265]) ).
fof(f623,plain,
( sK0 = sK1
| ~ int_leq(int_one,sK0)
| ~ int_leq(sK0,n)
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK1,n)
| ~ int_less(sK0,sK1) ),
inference(trivial_inequality_removal,[],[f620]) ).
fof(f625,plain,
( sK0 = sK1
| ~ int_leq(sK0,n)
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK1,n)
| ~ int_less(sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f623,f38]) ).
fof(f626,plain,
( sK0 = sK1
| ~ int_leq(int_one,sK1)
| ~ int_leq(sK1,n)
| ~ int_less(sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f625,f37]) ).
fof(f627,plain,
( sK0 = sK1
| ~ int_leq(sK1,n)
| ~ int_less(sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f626,f36]) ).
fof(f628,plain,
( ~ int_less(sK0,sK1)
| sK0 = sK1 ),
inference(forward_subsumption_resolution,[],[f627,f35]) ).
fof(f631,plain,
( sK0 = sK1
| int_leq(sK1,sK0) ),
inference(resolution,[],[f628,f48]) ).
fof(f697,plain,
sK0 = sK1,
inference(forward_subsumption_resolution,[],[f631,f618]) ).
fof(f700,plain,
( sK0 != sK0
| real_zero = a(sK0,sK0) ),
inference(superposition,[],[f40,f697]) ).
fof(f714,plain,
real_zero = a(sK0,sK0),
inference(trivial_inequality_removal,[],[f700]) ).
fof(f728,plain,
! [X0,X1] :
( real_zero = real_one
| ~ int_leq(int_one,sK0)
| ~ int_leq(sK0,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) ),
inference(superposition,[],[f33,f714]) ).
fof(f729,plain,
! [X0,X1] :
( ~ int_leq(int_one,sK0)
| ~ int_leq(sK0,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) ),
inference(forward_subsumption_resolution,[],[f728,f58]) ).
fof(f731,plain,
! [X0,X1] :
( ~ int_leq(sK0,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) ),
inference(forward_subsumption_resolution,[],[f729,f38]) ).
fof(f877,plain,
( ~ int_leq(sK0,n)
| ~ int_leq(int_one,sK0)
| ~ int_leq(int_one,n)
| ~ int_leq(n,n) ),
inference(factoring,[],[f731]) ).
fof(f878,plain,
( ~ int_leq(int_one,sK0)
| ~ int_leq(int_one,n)
| ~ int_leq(n,n) ),
inference(forward_subsumption_resolution,[],[f877,f37]) ).
fof(f886,plain,
( ~ int_leq(int_one,n)
| ~ int_leq(n,n) ),
inference(forward_subsumption_resolution,[],[f878,f38]) ).
fof(f890,plain,
~ int_leq(int_one,n),
inference(forward_subsumption_resolution,[],[f886,f63]) ).
fof(f893,plain,
~ int_less(int_zero,n),
inference(resolution,[],[f890,f52]) ).
fof(f902,plain,
int_leq(n,int_zero),
inference(resolution,[],[f893,f48]) ).
fof(f955,plain,
( ~ int_leq(n,sK0)
| n = sK0 ),
inference(resolution,[],[f287,f37]) ).
fof(f1028,plain,
( n = sK0
| ~ int_less(int_zero,sK0)
| ~ int_leq(n,int_zero) ),
inference(resolution,[],[f955,f160]) ).
fof(f1031,plain,
( ~ int_less(int_zero,sK0)
| n = sK0 ),
inference(forward_subsumption_resolution,[],[f1028,f902]) ).
fof(f1087,plain,
( n = sK0
| ~ int_leq(int_one,sK0) ),
inference(resolution,[],[f1031,f53]) ).
fof(f1092,plain,
n = sK0,
inference(forward_subsumption_resolution,[],[f1087,f38]) ).
fof(f1094,plain,
int_leq(int_one,n),
inference(superposition,[],[f38,f1092]) ).
fof(f1129,plain,
$false,
inference(forward_subsumption_resolution,[],[f1094,f890]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV490+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n026.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 11:17:27 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 1.08/0.94 % (3791786)Detected formulas, will run a generic FOF schedule.
% 1.08/0.94 % (3791795)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=879054273:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.08/0.94 % (3791795)First to succeed.
% 1.08/0.94 % (3791795)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3791786"
% 1.08/0.94 % (3791792)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=1715277130:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.08/0.94 % (3791793)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=1830999968:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.08/0.94 % (3791791)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=1072756542:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.08/0.94 % (3791796)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2090336462:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.08/0.94 % (3791794)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2883524640:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.08/0.94 % (3791797)dis-21_1_sil=8000:lcm=predicate:random_seed=3188537379: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)
% 1.08/0.94 % (3791794)Instruction limit reached!
% 1.08/0.94 % (3791794)------------------------------
% 1.08/0.94 % (3791794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.08/0.94 % (3791794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.94 % (3791794)CaDiCaL version: 2.1.3
% 1.08/0.94 % (3791794)Termination reason: Instruction limit
% 1.08/0.94 % (3791794)Termination phase: Saturation
% 1.08/0.94 % (3791794)Time elapsed: 0.058 s
% 1.08/0.94 % (3791794)Peak memory usage: 88 MB
% 1.08/0.94 % (3791794)Instructions burned: 109 (million)
% 1.08/0.94 % (3791797)Instruction limit reached!
% 1.08/0.94 % (3791797)------------------------------
% 1.08/0.94 % (3791797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.08/0.94 % (3791797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.94 % (3791797)CaDiCaL version: 2.1.3
% 1.08/0.94 % (3791797)Termination reason: Instruction limit
% 1.08/0.94 % (3791797)Termination phase: Saturation
% 1.08/0.94 % (3791797)Time elapsed: 0.080 s
% 1.08/0.94 % (3791797)Peak memory usage: 88 MB
% 1.08/0.94 % (3791797)Instructions burned: 129 (million)
% 1.08/0.94 % (3791796)Instruction limit reached!
% 1.08/0.94 % (3791796)------------------------------
% 1.08/0.94 % (3791796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.08/0.94 % (3791796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.94 % (3791796)CaDiCaL version: 2.1.3
% 1.08/0.94 % (3791796)Termination reason: Instruction limit
% 1.08/0.94 % (3791796)Termination phase: Saturation
% 1.08/0.94 % (3791796)Time elapsed: 0.097 s
% 1.08/0.94 % (3791796)Peak memory usage: 90 MB
% 1.08/0.94 % (3791796)Instructions burned: 140 (million)
% 1.08/0.94 % (3791795)Refutation found. Thanks to Tanya!
% 1.08/0.94 % SZS status Theorem for theBenchmark
% 1.08/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.14 % (3791795)------------------------------
% 0.21/1.14 % (3791795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.14 % (3791795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.14 % (3791795)CaDiCaL version: 2.1.3
% 0.21/1.14 % (3791795)Termination reason: Refutation
% 0.21/1.14 % (3791795)Time elapsed: 0.020 s
% 0.21/1.14 % (3791795)Peak memory usage: 89 MB
% 0.21/1.14 % (3791795)Instructions burned: 58 (million)
% 0.21/1.14 % (3791795)------------------------------
% 0.21/1.14 % (3791795)------------------------------
% 0.21/1.14 % (3791786)Success in time 0.282 s
% 0.21/1.14 % Vampire exiting
%------------------------------------------------------------------------------