%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV069+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:31:26 AM UTC 2025
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 37
% Syntax : Number of formulae : 96 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 240 ( 49 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 215 ( 75 ~; 52 |; 38 &)
% ( 45 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 74 ( 67 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(minus_type,type,
minus: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(n5_type,type,
n5: $i ).
tff(n0_type,type,
n0: $i ).
tff(n4_type,type,
n4: $i ).
tff(pred_type,type,
pred: $i > $i ).
tff(succ_type,type,
succ: $i > $i ).
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(n135300_type,type,
n135300: $i ).
tff(pv10_type,type,
pv10: $i ).
tff(1,plain,
( ! [X: $i] : ( pred(succ(X)) = X )
<=> ! [X: $i] : ( pred(succ(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ! [X: $i] : ( pred(succ(X)) = X )
<=> ! [X: $i] : ( pred(succ(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
! [X: $i] : ( pred(succ(X)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_succ) ).
tff(4,plain,
! [X: $i] : ( pred(succ(X)) = X ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
! [X: $i] : ( pred(succ(X)) = X ),
inference(skolemize,[status(sab)],[4]) ).
tff(6,plain,
! [X: $i] : ( pred(succ(X)) = X ),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( ~ ! [X: $i] : ( pred(succ(X)) = X )
| ( pred(succ(n4)) = n4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(8,plain,
pred(succ(n4)) = n4,
inference(unit_resolution,[status(thm)],[7,6]) ).
tff(9,plain,
( ( succ(succ(succ(succ(n0)))) = n4 )
<=> ( succ(succ(succ(succ(n0)))) = n4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
succ(succ(succ(succ(n0)))) = n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_4) ).
tff(11,plain,
succ(succ(succ(succ(n0)))) = n4,
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
n4 = succ(succ(succ(succ(n0)))),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
succ(n4) = succ(succ(succ(succ(succ(n0))))),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
succ(succ(succ(succ(succ(n0))))) = succ(n4),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( ( succ(succ(succ(succ(succ(n0))))) = n5 )
<=> ( succ(succ(succ(succ(succ(n0))))) = n5 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
succ(succ(succ(succ(succ(n0))))) = n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_5) ).
tff(17,plain,
succ(succ(succ(succ(succ(n0))))) = n5,
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
n5 = succ(succ(succ(succ(succ(n0))))),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
n5 = succ(n4),
inference(transitivity,[status(thm)],[18,14]) ).
tff(20,plain,
pred(n5) = pred(succ(n4)),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
^ [X: $i] :
refl(( ( minus(X,n1) = pred(X) )
<=> ( minus(X,n1) = pred(X) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X: $i] : ( minus(X,n1) = pred(X) )
<=> ! [X: $i] : ( minus(X,n1) = pred(X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] : ( minus(X,n1) = pred(X) )
<=> ! [X: $i] : ( minus(X,n1) = pred(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [X: $i] : ( minus(X,n1) = pred(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
tff(25,plain,
! [X: $i] : ( minus(X,n1) = pred(X) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i] : ( minus(X,n1) = pred(X) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] : ( minus(X,n1) = pred(X) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [X: $i] : ( minus(X,n1) = pred(X) )
| ( minus(n5,n1) = pred(n5) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
minus(n5,n1) = pred(n5),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
minus(n5,n1) = n4,
inference(transitivity,[status(thm)],[29,20,8]) ).
tff(31,plain,
( leq(n0,minus(n5,n1))
<=> leq(n0,n4) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( leq(n0,n4)
<=> leq(n0,minus(n5,n1)) ),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( gt(n4,n0)
<=> gt(n4,n0) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
gt(n4,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_0) ).
tff(35,plain,
gt(n4,n0),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ gt(Y,X)
| leq(X,Y) )
<=> ( ~ gt(Y,X)
| leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
^ [X: $i,Y: $i] :
rewrite(( ( gt(Y,X)
=> leq(X,Y) )
<=> ( ~ gt(Y,X)
| leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [X: $i,Y: $i] :
( gt(Y,X)
=> leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [X: $i,Y: $i] :
( gt(Y,X)
=> leq(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt1) ).
tff(42,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(n4,n0)
| leq(n0,n4) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(n4,n0)
| leq(n0,n4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(n4,n0)
| leq(n0,n4) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(n4,n0)
| leq(n0,n4) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
leq(n0,n4),
inference(unit_resolution,[status(thm)],[48,45,35]) ).
tff(50,plain,
leq(n0,minus(n5,n1)),
inference(modus_ponens,[status(thm)],[49,32]) ).
tff(51,plain,
( ~ ! [X: $i] : ( pred(succ(X)) = X )
| ( pred(succ(n0)) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
pred(succ(n0)) = n0,
inference(unit_resolution,[status(thm)],[51,6]) ).
tff(53,plain,
( ( succ(n0) = n1 )
<=> ( succ(n0) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
tff(55,plain,
succ(n0) = n1,
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
n1 = succ(n0),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
pred(n1) = pred(succ(n0)),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
pred(n1) = n0,
inference(transitivity,[status(thm)],[57,52]) ).
tff(59,plain,
( leq(n0,pred(n1))
<=> leq(n0,n0) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
^ [X: $i,Y: $i] :
refl(( ( leq(X,pred(Y))
<=> gt(Y,X) )
<=> ( leq(X,pred(Y))
<=> gt(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) )
<=> ! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) )
<=> ! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt_pred) ).
tff(64,plain,
! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
( ~ ! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) )
| ( leq(n0,pred(n1))
<=> gt(n1,n0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
( leq(n0,pred(n1))
<=> gt(n1,n0) ),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
( gt(n1,n0)
<=> gt(n1,n0) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
gt(n1,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_0) ).
tff(71,plain,
gt(n1,n0),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( ~ ( leq(n0,pred(n1))
<=> gt(n1,n0) )
| leq(n0,pred(n1))
| ~ gt(n1,n0) ),
inference(tautology,[status(thm)],[]) ).
tff(73,plain,
( ~ ( leq(n0,pred(n1))
<=> gt(n1,n0) )
| leq(n0,pred(n1)) ),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
leq(n0,pred(n1)),
inference(unit_resolution,[status(thm)],[73,68]) ).
tff(75,plain,
leq(n0,n0),
inference(modus_ponens,[status(thm)],[74,59]) ).
tff(76,plain,
( leq(pv10,minus(n135300,n1))
<=> leq(pv10,minus(n135300,n1)) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ~ ( ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) )
=> ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,minus(n5,n1))
& leq(pv10,minus(n135300,n1)) ) )
<=> ~ ( ~ ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) )
| ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,minus(n5,n1))
& leq(pv10,minus(n135300,n1)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
~ ( ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) )
=> ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,minus(n5,n1))
& leq(pv10,minus(n135300,n1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_array_0010) ).
tff(79,plain,
~ ( ~ ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) )
| ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,minus(n5,n1))
& leq(pv10,minus(n135300,n1)) ) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ),
inference(or_elim,[status(thm)],[79]) ).
tff(81,plain,
leq(pv10,minus(n135300,n1)),
inference(and_elim,[status(thm)],[80]) ).
tff(82,plain,
leq(pv10,minus(n135300,n1)),
inference(modus_ponens,[status(thm)],[81,76]) ).
tff(83,plain,
( leq(n0,pv10)
<=> leq(n0,pv10) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
leq(n0,pv10),
inference(and_elim,[status(thm)],[80]) ).
tff(85,plain,
leq(n0,pv10),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( ~ ~ ( ~ leq(n0,n0)
| ~ leq(n0,pv10)
| ~ leq(n0,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1)) )
<=> ( ~ leq(n0,n0)
| ~ leq(n0,pv10)
| ~ leq(n0,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,minus(n5,n1))
& leq(pv10,minus(n135300,n1)) )
<=> ~ ( ~ leq(n0,n0)
| ~ leq(n0,pv10)
| ~ leq(n0,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ~ ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,minus(n5,n1))
& leq(pv10,minus(n135300,n1)) )
<=> ~ ~ ( ~ leq(n0,n0)
| ~ leq(n0,pv10)
| ~ leq(n0,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1)) ) ),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ~ ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,minus(n5,n1))
& leq(pv10,minus(n135300,n1)) )
<=> ( ~ leq(n0,n0)
| ~ leq(n0,pv10)
| ~ leq(n0,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1)) ) ),
inference(transitivity,[status(thm)],[88,86]) ).
tff(90,plain,
( ~ ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,minus(n5,n1))
& leq(pv10,minus(n135300,n1)) )
<=> ~ ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,minus(n5,n1))
& leq(pv10,minus(n135300,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
~ ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,minus(n5,n1))
& leq(pv10,minus(n135300,n1)) ),
inference(or_elim,[status(thm)],[79]) ).
tff(92,plain,
~ ( leq(n0,n0)
& leq(n0,pv10)
& leq(n0,minus(n5,n1))
& leq(pv10,minus(n135300,n1)) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
( ~ leq(n0,n0)
| ~ leq(n0,pv10)
| ~ leq(n0,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1)) ),
inference(modus_ponens,[status(thm)],[92,89]) ).
tff(94,plain,
( ~ leq(n0,n0)
| ~ leq(n0,minus(n5,n1)) ),
inference(unit_resolution,[status(thm)],[93,85,82]) ).
tff(95,plain,
~ leq(n0,minus(n5,n1)),
inference(unit_resolution,[status(thm)],[94,75]) ).
tff(96,plain,
$false,
inference(unit_resolution,[status(thm)],[95,50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV069+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 09:26:48 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% See solution above
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------