TSTP Solution File: SWV007-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV007-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:09:36 EDT 2022
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 58
% Syntax : Number of formulae : 121 ( 30 unt; 7 typ; 0 def)
% Number of atoms : 579 ( 93 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 792 ( 362 ~; 371 |; 0 &)
% ( 59 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 35 ( 35 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 3 >; 1 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 269 ( 245 !; 0 ?; 269 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_than_type,type,
less_than: ( $i * $i ) > $o ).
tff(n_type,type,
n: $i ).
tff(successor_type,type,
successor: $i > $i ).
tff(m_type,type,
m: $i ).
tff(i_type,type,
i: $i ).
tff(a_type,type,
a: $i > $i ).
tff(k_type,type,
k: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( less_than(X,successor(X))
<=> less_than(X,successor(X)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : less_than(X,successor(X))
<=> ! [X: $i] : less_than(X,successor(X)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : less_than(X,successor(X))
<=> ! [X: $i] : less_than(X,successor(X)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : less_than(X,successor(X)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV001-0.ax',less_than_successor) ).
tff(5,plain,
! [X: $i] : less_than(X,successor(X)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : less_than(X,successor(X)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : less_than(X,successor(X)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : less_than(X,successor(X))
| less_than(n,successor(n)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
less_than(n,successor(n)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ less_than(X,Y)
| ~ less_than(Y,X) )
<=> ( ~ less_than(X,Y)
| ~ less_than(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV001-0.ax',anti_symmetry_of_less_than) ).
tff(14,plain,
! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(n,successor(n))
| ~ less_than(successor(n),n) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(n,successor(n))
| ~ less_than(successor(n),n) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( ~ less_than(successor(n),n)
| ~ less_than(n,successor(n)) )
<=> ( ~ less_than(n,successor(n))
| ~ less_than(successor(n),n) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(successor(n),n)
| ~ less_than(n,successor(n)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(n,successor(n))
| ~ less_than(successor(n),n) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(successor(n),n)
| ~ less_than(n,successor(n)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(n,successor(n))
| ~ less_than(successor(n),n) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(successor(n),n)
| ~ less_than(n,successor(n)) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(n,successor(n))
| ~ less_than(successor(n),n) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ less_than(successor(n),n),
inference(unit_resolution,[status(thm)],[22,16,9]) ).
tff(24,plain,
( ~ less_than(n,m)
<=> ~ less_than(n,m) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
~ less_than(n,m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
tff(26,plain,
~ less_than(n,m),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) )
<=> ( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( less_than(Z,Y)
| ( X != Y ) )
<=> ( ( X != Y )
| less_than(Z,Y) ) )),
( ( less_than(Z,Y)
| ( X != Y )
| ~ less_than(Z,X) )
<=> ( ( X != Y )
| less_than(Z,Y)
| ~ less_than(Z,X) ) )),
rewrite(
( ( ( X != Y )
| less_than(Z,Y)
| ~ less_than(Z,X) )
<=> ( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) ) )),
( ( less_than(Z,Y)
| ( X != Y )
| ~ less_than(Z,X) )
<=> ( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [Z: $i,Y: $i,X: $i] :
( less_than(Z,Y)
| ( X != Y )
| ~ less_than(Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [Z: $i,Y: $i,X: $i] :
( less_than(Z,Y)
| ( X != Y )
| ~ less_than(Z,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV001-0.ax',equal_and_less_than_transitivity2) ).
tff(33,plain,
! [Z: $i,Y: $i,X: $i] :
( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Z: $i,Y: $i,X: $i] :
( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] :
( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] :
( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) )
| ( successor(n) != m )
| ~ less_than(n,successor(n))
| less_than(n,m) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) )
| ( successor(n) != m )
| ~ less_than(n,successor(n))
| less_than(n,m) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) )
| ( successor(n) != m )
| ~ less_than(n,successor(n))
| less_than(n,m) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( X != Y )
| ~ less_than(Z,X)
| less_than(Z,Y) )
| ( successor(n) != m )
| ~ less_than(n,successor(n))
| less_than(n,m) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
successor(n) != m,
inference(unit_resolution,[status(thm)],[39,36,26,9]) ).
tff(41,plain,
( less_than(i,m)
<=> less_than(i,m) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
less_than(i,m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
tff(43,plain,
less_than(i,m),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(i,m)
| ~ less_than(m,i) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(i,m)
| ~ less_than(m,i) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( ~ less_than(m,i)
| ~ less_than(i,m) )
<=> ( ~ less_than(i,m)
| ~ less_than(m,i) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(m,i)
| ~ less_than(i,m) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(i,m)
| ~ less_than(m,i) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(m,i)
| ~ less_than(i,m) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(i,m)
| ~ less_than(m,i) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(m,i)
| ~ less_than(i,m) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(i,m)
| ~ less_than(m,i) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
~ less_than(m,i),
inference(unit_resolution,[status(thm)],[49,16,43]) ).
tff(51,plain,
^ [X: $i] :
refl(
( ( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) )
<=> ( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [X: $i] :
( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) )
<=> ! [X: $i] :
( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [X: $i] :
( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) )
<=> ! [X: $i] :
( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( less_than(X,i)
| ~ less_than(X,successor(n)) )
<=> ( less_than(X,i)
| ~ less_than(X,successor(n)) ) )),
( ( less_than(X,i)
| ~ less_than(X,successor(n))
| ~ less_than(a(X),a(k)) )
<=> ( less_than(X,i)
| ~ less_than(X,successor(n))
| ~ less_than(a(X),a(k)) ) )),
rewrite(
( ( less_than(X,i)
| ~ less_than(X,successor(n))
| ~ less_than(a(X),a(k)) )
<=> ( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) ) )),
( ( less_than(X,i)
| ~ less_than(X,successor(n))
| ~ less_than(a(X),a(k)) )
<=> ( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [X: $i] :
( less_than(X,i)
| ~ less_than(X,successor(n))
| ~ less_than(a(X),a(k)) )
<=> ! [X: $i] :
( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [X: $i] :
( less_than(X,i)
| ~ less_than(X,successor(n))
| ~ less_than(a(X),a(k)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
tff(57,plain,
! [X: $i] :
( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [X: $i] :
( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [X: $i] :
( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [X: $i] :
( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
( less_than(a(m),a(k))
<=> less_than(a(m),a(k)) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
less_than(a(m),a(k)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
tff(63,plain,
less_than(a(m),a(k)),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( ( ~ ! [X: $i] :
( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) )
| less_than(m,i)
| ~ less_than(a(m),a(k))
| ~ less_than(m,successor(n)) )
<=> ( ~ ! [X: $i] :
( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) )
| less_than(m,i)
| ~ less_than(a(m),a(k))
| ~ less_than(m,successor(n)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ~ ! [X: $i] :
( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) )
| less_than(m,i)
| ~ less_than(a(m),a(k))
| ~ less_than(m,successor(n)) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [X: $i] :
( less_than(X,i)
| ~ less_than(a(X),a(k))
| ~ less_than(X,successor(n)) )
| less_than(m,i)
| ~ less_than(a(m),a(k))
| ~ less_than(m,successor(n)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
~ less_than(m,successor(n)),
inference(unit_resolution,[status(thm)],[66,63,60,50]) ).
tff(68,plain,
^ [Y: $i,X: $i] :
refl(
( ( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
<=> ( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
<=> ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
<=> ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
^ [Y: $i,X: $i] :
rewrite(
( ( less_than(X,Y)
| less_than(Y,X)
| ( X = Y ) )
<=> ( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [Y: $i,X: $i] :
( less_than(X,Y)
| less_than(Y,X)
| ( X = Y ) )
<=> ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,axiom,
! [Y: $i,X: $i] :
( less_than(X,Y)
| less_than(Y,X)
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV001-0.ax',all_related) ).
tff(74,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ),
inference(modus_ponens,[status(thm)],[76,69]) ).
tff(78,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| ( successor(n) = m )
| less_than(m,successor(n))
| less_than(successor(n),m) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| ( successor(n) = m )
| less_than(m,successor(n))
| less_than(successor(n),m) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| ( successor(n) = m )
| less_than(m,successor(n))
| less_than(successor(n),m) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| ( successor(n) = m )
| less_than(m,successor(n))
| less_than(successor(n),m) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
( ( successor(n) = m )
| less_than(successor(n),m) ),
inference(unit_resolution,[status(thm)],[80,77,67]) ).
tff(82,plain,
less_than(successor(n),m),
inference(unit_resolution,[status(thm)],[81,40]) ).
tff(83,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) )
<=> ( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [Z: $i,Y: $i,X: $i] :
( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [Z: $i,Y: $i,X: $i] :
( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( less_than(Y,Z)
| ( X != Y ) )
<=> ( less_than(Y,Z)
| ( X != Y ) ) )),
( ( less_than(Y,Z)
| ( X != Y )
| ~ less_than(X,Z) )
<=> ( less_than(Y,Z)
| ( X != Y )
| ~ less_than(X,Z) ) )),
rewrite(
( ( less_than(Y,Z)
| ( X != Y )
| ~ less_than(X,Z) )
<=> ( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) ) )),
( ( less_than(Y,Z)
| ( X != Y )
| ~ less_than(X,Z) )
<=> ( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [Z: $i,Y: $i,X: $i] :
( less_than(Y,Z)
| ( X != Y )
| ~ less_than(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,axiom,
! [Z: $i,Y: $i,X: $i] :
( less_than(Y,Z)
| ( X != Y )
| ~ less_than(X,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV001-0.ax',equal_and_less_than_transitivity1) ).
tff(89,plain,
! [Z: $i,Y: $i,X: $i] :
( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [Z: $i,Y: $i,X: $i] :
( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [Z: $i,Y: $i,X: $i] :
( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [Z: $i,Y: $i,X: $i] :
( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) )
| less_than(m,successor(n))
| ~ less_than(n,successor(n))
| ( n != m ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) )
| less_than(m,successor(n))
| ~ less_than(n,successor(n))
| ( n != m ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) )
| less_than(m,successor(n))
| ~ less_than(n,successor(n))
| ( n != m ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( less_than(Y,Z)
| ~ less_than(X,Z)
| ( X != Y ) )
| less_than(m,successor(n))
| ~ less_than(n,successor(n))
| ( n != m ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
n != m,
inference(unit_resolution,[status(thm)],[95,92,67,9]) ).
tff(97,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| ( n = m )
| less_than(m,n)
| less_than(n,m) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| ( n = m )
| less_than(m,n)
| less_than(n,m) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| ( n = m )
| less_than(m,n)
| less_than(n,m) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| ( n = m )
| less_than(m,n)
| less_than(n,m) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
( ( n = m )
| less_than(m,n) ),
inference(unit_resolution,[status(thm)],[99,77,26]) ).
tff(101,plain,
less_than(m,n),
inference(unit_resolution,[status(thm)],[100,96]) ).
tff(102,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( less_than(X,Z)
| ~ less_than(X,Y) )
<=> ( ~ less_than(X,Y)
| less_than(X,Z) ) )),
( ( less_than(X,Z)
| ~ less_than(X,Y)
| ~ less_than(Y,Z) )
<=> ( ~ less_than(X,Y)
| less_than(X,Z)
| ~ less_than(Y,Z) ) )),
rewrite(
( ( ~ less_than(X,Y)
| less_than(X,Z)
| ~ less_than(Y,Z) )
<=> ( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ) )),
( ( less_than(X,Z)
| ~ less_than(X,Y)
| ~ less_than(Y,Z) )
<=> ( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(105,plain,
( ! [Z: $i,Y: $i,X: $i] :
( less_than(X,Z)
| ~ less_than(X,Y)
| ~ less_than(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,axiom,
! [Z: $i,Y: $i,X: $i] :
( less_than(X,Z)
| ~ less_than(X,Y)
| ~ less_than(Y,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV001-0.ax',transitivity_of_less_than) ).
tff(107,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ),
inference(modus_ponens,[status(thm)],[109,102]) ).
tff(111,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) )
| ~ less_than(m,n)
| ~ less_than(successor(n),m)
| less_than(successor(n),n) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) )
| ~ less_than(m,n)
| ~ less_than(successor(n),m)
| less_than(successor(n),n) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) )
| ~ less_than(m,n)
| ~ less_than(successor(n),m)
| less_than(successor(n),n) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) )
| ~ less_than(m,n)
| ~ less_than(successor(n),m)
| less_than(successor(n),n) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
$false,
inference(unit_resolution,[status(thm)],[113,110,101,82,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 01:08:41 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------