%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV009-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 : Sat Jun 21 05:31:20 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 37
% Syntax : Number of formulae : 82 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 647 ( 0 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 995 ( 468 ~; 474 |; 0 &)
% ( 53 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 38 ( 38 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 168 ( 152 !; 0 ?; 168 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_type,type,
less: ( $i * $i ) > $o ).
tff(i_type,type,
i: $i ).
tff(p_type,type,
p: $i ).
tff(less_or_equal_type,type,
less_or_equal: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i > $i ).
tff(q_type,type,
q: $i ).
tff(n_type,type,
n: $i ).
tff(j_type,type,
j: $i ).
tff(m_type,type,
m: $i ).
tff(1,plain,
( ~ less_or_equal(a(p),a(q))
<=> ~ less_or_equal(a(p),a(q)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ less_or_equal(a(p),a(q)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
tff(3,plain,
~ less_or_equal(a(p),a(q)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) )
<=> ( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) )
<=> ! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) )
<=> ! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ less_or_equal(i,X)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,n) )
<=> ( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) ) )),
( ( ~ less_or_equal(i,X)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,n)
| less_or_equal(a(X),a(Y)) )
<=> ( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X)
| less_or_equal(a(X),a(Y)) ) )),
rewrite(( ( ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X)
| less_or_equal(a(X),a(Y)) )
<=> ( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) ) )),
( ( ~ less_or_equal(i,X)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,n)
| less_or_equal(a(X),a(Y)) )
<=> ( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [Y: $i,X: $i] :
( ~ less_or_equal(i,X)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,n)
| less_or_equal(a(X),a(Y)) )
<=> ! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [Y: $i,X: $i] :
( ~ less_or_equal(i,X)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,n)
| less_or_equal(a(X),a(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
tff(10,plain,
! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( less_or_equal(q,n)
<=> less_or_equal(q,n) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
less_or_equal(q,n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
tff(16,plain,
less_or_equal(q,n),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( less_or_equal(p,q)
<=> less_or_equal(p,q) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
less_or_equal(p,q),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
tff(19,plain,
less_or_equal(p,q),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(i,p)
| ~ less_or_equal(p,q)
| ~ less_or_equal(q,n) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(i,p)
| ~ less_or_equal(p,q)
| ~ less_or_equal(q,n) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ( ~ less_or_equal(p,q)
| less_or_equal(a(p),a(q))
| ~ less_or_equal(q,n)
| ~ less_or_equal(i,p) )
<=> ( less_or_equal(a(p),a(q))
| ~ less_or_equal(i,p)
| ~ less_or_equal(p,q)
| ~ less_or_equal(q,n) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) )
| ~ less_or_equal(p,q)
| less_or_equal(a(p),a(q))
| ~ less_or_equal(q,n)
| ~ less_or_equal(i,p) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(i,p)
| ~ less_or_equal(p,q)
| ~ less_or_equal(q,n) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) )
| ~ less_or_equal(p,q)
| less_or_equal(a(p),a(q))
| ~ less_or_equal(q,n)
| ~ less_or_equal(i,p) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(i,p)
| ~ less_or_equal(p,q)
| ~ less_or_equal(q,n) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) )
| ~ less_or_equal(p,q)
| less_or_equal(a(p),a(q))
| ~ less_or_equal(q,n)
| ~ less_or_equal(i,p) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less_or_equal(i,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(i,p)
| ~ less_or_equal(p,q)
| ~ less_or_equal(q,n) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ less_or_equal(i,p),
inference(unit_resolution,[status(thm)],[25,19,16,13,3]) ).
tff(27,plain,
^ [Y: $i,X: $i] :
refl(( ( less(Y,X)
| less_or_equal(X,Y) )
<=> ( less(Y,X)
| less_or_equal(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) )
<=> ! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) )
<=> ! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
^ [Y: $i,X: $i] :
rewrite(( ( less_or_equal(X,Y)
| less(Y,X) )
<=> ( less(Y,X)
| less_or_equal(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [Y: $i,X: $i] :
( less_or_equal(X,Y)
| less(Y,X) )
<=> ! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [Y: $i,X: $i] :
( less_or_equal(X,Y)
| less(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
tff(33,plain,
! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) )
| less(p,i)
| less_or_equal(i,p) )
<=> ( ~ ! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) )
| less(p,i)
| less_or_equal(i,p) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) )
| less(p,i)
| less_or_equal(i,p) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) )
| less(p,i)
| less_or_equal(i,p) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
less(p,i),
inference(unit_resolution,[status(thm)],[39,36,26]) ).
tff(41,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) )
<=> ( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) )
<=> ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) )
<=> ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
^ [Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ less_or_equal(m,X)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,j) )
<=> ( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(m,X) ) )),
( ( ~ less_or_equal(m,X)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,j)
| less_or_equal(a(X),a(Y)) )
<=> ( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(m,X)
| less_or_equal(a(X),a(Y)) ) )),
rewrite(( ( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(m,X)
| less_or_equal(a(X),a(Y)) )
<=> ( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) ) )),
( ( ~ less_or_equal(m,X)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,j)
| less_or_equal(a(X),a(Y)) )
<=> ( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [Y: $i,X: $i] :
( ~ less_or_equal(m,X)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,j)
| less_or_equal(a(X),a(Y)) )
<=> ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [Y: $i,X: $i] :
( ~ less_or_equal(m,X)
| ~ less_or_equal(X,Y)
| ~ less_or_equal(Y,j)
| less_or_equal(a(X),a(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
tff(47,plain,
! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( less_or_equal(m,p)
<=> less_or_equal(m,p) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
less_or_equal(m,p),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
tff(53,plain,
less_or_equal(m,p),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(p,q)
| ~ less_or_equal(m,p)
| ~ less_or_equal(q,j) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(p,q)
| ~ less_or_equal(m,p)
| ~ less_or_equal(q,j) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( ~ less_or_equal(q,j)
| ~ less_or_equal(p,q)
| less_or_equal(a(p),a(q))
| ~ less_or_equal(m,p) )
<=> ( less_or_equal(a(p),a(q))
| ~ less_or_equal(p,q)
| ~ less_or_equal(m,p)
| ~ less_or_equal(q,j) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) )
| ~ less_or_equal(q,j)
| ~ less_or_equal(p,q)
| less_or_equal(a(p),a(q))
| ~ less_or_equal(m,p) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(p,q)
| ~ less_or_equal(m,p)
| ~ less_or_equal(q,j) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) )
| ~ less_or_equal(q,j)
| ~ less_or_equal(p,q)
| less_or_equal(a(p),a(q))
| ~ less_or_equal(m,p) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(p,q)
| ~ less_or_equal(m,p)
| ~ less_or_equal(q,j) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) )
| ~ less_or_equal(q,j)
| ~ less_or_equal(p,q)
| less_or_equal(a(p),a(q))
| ~ less_or_equal(m,p) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_or_equal(Y,j)
| ~ less_or_equal(X,Y)
| less_or_equal(a(X),a(Y))
| ~ less_or_equal(m,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(p,q)
| ~ less_or_equal(m,p)
| ~ less_or_equal(q,j) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
~ less_or_equal(q,j),
inference(unit_resolution,[status(thm)],[59,53,19,50,3]) ).
tff(61,plain,
( ( ~ ! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) )
| less(j,q)
| less_or_equal(q,j) )
<=> ( ~ ! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) )
| less(j,q)
| less_or_equal(q,j) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) )
| less(j,q)
| less_or_equal(q,j) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [Y: $i,X: $i] :
( less(Y,X)
| less_or_equal(X,Y) )
| less(j,q)
| less_or_equal(q,j) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
less(j,q),
inference(unit_resolution,[status(thm)],[63,36,60]) ).
tff(65,plain,
^ [Y: $i,X: $i] :
refl(( ( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) )
<=> ( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) )
<=> ! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) )
<=> ! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
^ [Y: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ less_or_equal(m,X)
| ~ less(X,i) )
<=> ( ~ less(X,i)
| ~ less_or_equal(m,X) ) )),
( ( ~ less_or_equal(m,X)
| ~ less(X,i)
| ~ less(j,Y) )
<=> ( ~ less(X,i)
| ~ less_or_equal(m,X)
| ~ less(j,Y) ) )),
rewrite(( ( ~ less(X,i)
| ~ less_or_equal(m,X)
| ~ less(j,Y) )
<=> ( ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) ) )),
( ( ~ less_or_equal(m,X)
| ~ less(X,i)
| ~ less(j,Y) )
<=> ( ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) ) )),
( ( ~ less_or_equal(m,X)
| ~ less(X,i)
| ~ less(j,Y)
| ~ less_or_equal(Y,n) )
<=> ( ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X)
| ~ less_or_equal(Y,n) ) )),
rewrite(( ( ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X)
| ~ less_or_equal(Y,n) )
<=> ( ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) ) )),
( ( ~ less_or_equal(m,X)
| ~ less(X,i)
| ~ less(j,Y)
| ~ less_or_equal(Y,n) )
<=> ( ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) ) )),
( ( ~ less_or_equal(m,X)
| ~ less(X,i)
| ~ less(j,Y)
| ~ less_or_equal(Y,n)
| less_or_equal(a(X),a(Y)) )
<=> ( ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X)
| less_or_equal(a(X),a(Y)) ) )),
rewrite(( ( ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X)
| less_or_equal(a(X),a(Y)) )
<=> ( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) ) )),
( ( ~ less_or_equal(m,X)
| ~ less(X,i)
| ~ less(j,Y)
| ~ less_or_equal(Y,n)
| less_or_equal(a(X),a(Y)) )
<=> ( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [Y: $i,X: $i] :
( ~ less_or_equal(m,X)
| ~ less(X,i)
| ~ less(j,Y)
| ~ less_or_equal(Y,n)
| less_or_equal(a(X),a(Y)) )
<=> ! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,axiom,
! [Y: $i,X: $i] :
( ~ less_or_equal(m,X)
| ~ less(X,i)
| ~ less(j,Y)
| ~ less_or_equal(Y,n)
| less_or_equal(a(X),a(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
tff(71,plain,
! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) ),
inference(modus_ponens,[status(thm)],[73,66]) ).
tff(75,plain,
( ( ~ ! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(q,n)
| ~ less(p,i)
| ~ less_or_equal(m,p)
| ~ less(j,q) )
<=> ( ~ ! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(q,n)
| ~ less(p,i)
| ~ less_or_equal(m,p)
| ~ less(j,q) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
( ( less_or_equal(a(p),a(q))
| ~ less_or_equal(q,n)
| ~ less(j,q)
| ~ less(p,i)
| ~ less_or_equal(m,p) )
<=> ( less_or_equal(a(p),a(q))
| ~ less_or_equal(q,n)
| ~ less(p,i)
| ~ less_or_equal(m,p)
| ~ less(j,q) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ( ~ ! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(q,n)
| ~ less(j,q)
| ~ less(p,i)
| ~ less_or_equal(m,p) )
<=> ( ~ ! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(q,n)
| ~ less(p,i)
| ~ less_or_equal(m,p)
| ~ less(j,q) ) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ( ~ ! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(q,n)
| ~ less(j,q)
| ~ less(p,i)
| ~ less_or_equal(m,p) )
<=> ( ~ ! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(q,n)
| ~ less(p,i)
| ~ less_or_equal(m,p)
| ~ less(j,q) ) ),
inference(transitivity,[status(thm)],[77,75]) ).
tff(79,plain,
( ~ ! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(q,n)
| ~ less(j,q)
| ~ less(p,i)
| ~ less_or_equal(m,p) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [Y: $i,X: $i] :
( less_or_equal(a(X),a(Y))
| ~ less_or_equal(Y,n)
| ~ less(j,Y)
| ~ less(X,i)
| ~ less_or_equal(m,X) )
| less_or_equal(a(p),a(q))
| ~ less_or_equal(q,n)
| ~ less(p,i)
| ~ less_or_equal(m,p)
| ~ less(j,q) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
( ~ less(p,i)
| ~ less(j,q) ),
inference(unit_resolution,[status(thm)],[80,53,16,74,3]) ).
tff(82,plain,
$false,
inference(unit_resolution,[status(thm)],[81,64,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWV009-1 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n016.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:21:32 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.36 % SZS status Unsatisfiable
% 0.18/0.36 % SZS output start Proof
% See solution above
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------