%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV002-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:31:19 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 33
% Syntax : Number of formulae : 78 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 373 ( 37 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 477 ( 200 ~; 238 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 18 ( 18 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 137 ( 126 !; 0 ?; 137 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_than_type,type,
less_than: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i > $i ).
tff(q_type,type,
q: $i ).
tff(j_type,type,
j: $i ).
tff(k_type,type,
k: $i ).
tff(i_type,type,
i: $i ).
tff(1,plain,
( less_than(a(q),a(j))
<=> less_than(a(q),a(j)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
less_than(a(q),a(j)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
tff(3,plain,
less_than(a(q),a(j)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( less_than(a(j),a(k))
<=> less_than(a(j),a(k)) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
less_than(a(j),a(k)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
tff(6,plain,
less_than(a(j),a(k)),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,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(8,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(9,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(10,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)],[9]) ).
tff(11,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(12,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) )
| ~ less_than(a(j),a(k))
| ~ less_than(a(q),a(j))
| less_than(a(q),a(k)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) )
| ~ less_than(a(j),a(k))
| ~ less_than(a(q),a(j))
| less_than(a(q),a(k)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) )
| ~ less_than(a(j),a(k))
| ~ less_than(a(q),a(j))
| less_than(a(q),a(k)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ less_than(Y,Z)
| ~ less_than(X,Y)
| less_than(X,Z) )
| ~ less_than(a(j),a(k))
| ~ less_than(a(q),a(j))
| less_than(a(q),a(k)) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
less_than(a(q),a(k)),
inference(unit_resolution,[status(thm)],[18,15,6,3]) ).
tff(20,plain,
( ~ less_than(q,i)
<=> ~ less_than(q,i) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
~ less_than(q,i),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
tff(22,plain,
~ less_than(q,i),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
^ [X: $i] :
refl(( ( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) )
<=> ( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) )
<=> ! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) )
<=> ! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( less_than(X,i)
| ~ less_than(X,j) )
<=> ( ~ less_than(X,j)
| less_than(X,i) ) )),
( ( less_than(X,i)
| ~ less_than(X,j)
| ~ less_than(a(X),a(k)) )
<=> ( ~ less_than(X,j)
| less_than(X,i)
| ~ less_than(a(X),a(k)) ) )),
rewrite(( ( ~ less_than(X,j)
| less_than(X,i)
| ~ less_than(a(X),a(k)) )
<=> ( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) ) )),
( ( less_than(X,i)
| ~ less_than(X,j)
| ~ less_than(a(X),a(k)) )
<=> ( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [X: $i] :
( less_than(X,i)
| ~ less_than(X,j)
| ~ less_than(a(X),a(k)) )
<=> ! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,axiom,
! [X: $i] :
( less_than(X,i)
| ~ less_than(X,j)
| ~ less_than(a(X),a(k)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
tff(29,plain,
! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) ),
inference(modus_ponens,[status(thm)],[31,24]) ).
tff(33,plain,
( ( ~ ! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) )
| less_than(q,i)
| ~ less_than(a(q),a(k))
| ~ less_than(q,j) )
<=> ( ~ ! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) )
| less_than(q,i)
| ~ less_than(a(q),a(k))
| ~ less_than(q,j) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ( ~ less_than(a(q),a(k))
| ~ less_than(q,j)
| less_than(q,i) )
<=> ( less_than(q,i)
| ~ less_than(a(q),a(k))
| ~ less_than(q,j) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ( ~ ! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) )
| ~ less_than(a(q),a(k))
| ~ less_than(q,j)
| less_than(q,i) )
<=> ( ~ ! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) )
| less_than(q,i)
| ~ less_than(a(q),a(k))
| ~ less_than(q,j) ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( ~ ! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) )
| ~ less_than(a(q),a(k))
| ~ less_than(q,j)
| less_than(q,i) )
<=> ( ~ ! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) )
| less_than(q,i)
| ~ less_than(a(q),a(k))
| ~ less_than(q,j) ) ),
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,plain,
( ~ ! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) )
| ~ less_than(a(q),a(k))
| ~ less_than(q,j)
| less_than(q,i) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [X: $i] :
( ~ less_than(a(X),a(k))
| ~ less_than(X,j)
| less_than(X,i) )
| less_than(q,i)
| ~ less_than(a(q),a(k))
| ~ less_than(q,j) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( ~ less_than(a(q),a(k))
| ~ less_than(q,j) ),
inference(unit_resolution,[status(thm)],[38,32,22]) ).
tff(40,plain,
~ less_than(q,j),
inference(unit_resolution,[status(thm)],[39,19]) ).
tff(41,plain,
( ~ less_than(j,q)
<=> ~ less_than(j,q) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
~ less_than(j,q),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
tff(43,plain,
~ less_than(j,q),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,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(45,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)],[44]) ).
tff(46,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(47,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(48,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)],[47]) ).
tff(49,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(50,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| less_than(j,q)
| less_than(q,j)
| ( j = q ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| less_than(j,q)
| less_than(q,j)
| ( j = q ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( ( j = q )
| less_than(q,j)
| less_than(j,q) )
<=> ( less_than(j,q)
| less_than(q,j)
| ( j = q ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| ( j = q )
| less_than(q,j)
| less_than(j,q) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| less_than(j,q)
| less_than(q,j)
| ( j = q ) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| ( j = q )
| less_than(q,j)
| less_than(j,q) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| less_than(j,q)
| less_than(q,j)
| ( j = q ) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| ( j = q )
| less_than(q,j)
| less_than(j,q) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| less_than(Y,X)
| less_than(X,Y) )
| less_than(j,q)
| less_than(q,j)
| ( j = q ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( less_than(q,j)
| ( j = q ) ),
inference(unit_resolution,[status(thm)],[59,53,43]) ).
tff(61,plain,
j = q,
inference(unit_resolution,[status(thm)],[60,40]) ).
tff(62,plain,
a(j) = a(q),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
a(q) = a(j),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
( less_than(a(j),a(q))
<=> less_than(a(q),a(j)) ),
inference(monotonicity,[status(thm)],[62,63]) ).
tff(65,plain,
( less_than(a(q),a(j))
<=> less_than(a(j),a(q)) ),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
less_than(a(j),a(q)),
inference(modus_ponens,[status(thm)],[3,65]) ).
tff(67,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(68,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)],[67]) ).
tff(69,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(70,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(71,plain,
! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(a(j),a(q))
| ~ less_than(a(q),a(j)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(a(j),a(q))
| ~ less_than(a(q),a(j)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(a(j),a(q))
| ~ less_than(a(q),a(j)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [Y: $i,X: $i] :
( ~ less_than(X,Y)
| ~ less_than(Y,X) )
| ~ less_than(a(j),a(q))
| ~ less_than(a(q),a(j)) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
~ less_than(a(j),a(q)),
inference(unit_resolution,[status(thm)],[76,73,3]) ).
tff(78,plain,
$false,
inference(unit_resolution,[status(thm)],[77,66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV002-1 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n002.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 : Fri Jun 20 09:22:46 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
% 0.13/0.40 % E exiting
%------------------------------------------------------------------------------