%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV023-1 : TPTP v9.0.0. Released v2.5.0.
% 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 05:08:58 AM UTC 2025
% Result : Unsatisfiable 0.23s 0.43s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 48
% Syntax : Number of formulae : 121 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 485 ( 157 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 526 ( 189 ~; 278 |; 0 &)
% ( 59 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 27 ( 27 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 142 ( 130 !; 0 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
tff(def_10_type,type,
def_10: ( $i * $i ) > $o ).
tff(plus_type,type,
plus: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(n0_type,type,
n0: $i ).
tff(minus_type,type,
minus: ( $i * $i ) > $i ).
tff(int_level_type,type,
int_level: $i > $i ).
tff(t_139_type,type,
t_139: $i ).
tff(level_type,type,
level: $i > $i ).
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(p_Reset_type,type,
p_Reset: $i > $o ).
tff(p_Rd_type,type,
p_Rd: $i > $o ).
tff(p_Wr_type,type,
p_Wr: $i > $o ).
tff(p_Empty_type,type,
p_Empty: $i > $o ).
tff(1,plain,
( ( n1 = plus(n0,n1) )
<=> ( n1 = plus(n0,n1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
n1 = plus(n0,n1),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax',axiom_20) ).
tff(3,plain,
n1 = plus(n0,n1),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
plus(n0,n1) = n1,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
plus(n0,plus(n0,n1)) = plus(n0,n1),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
plus(n0,n1) = plus(n0,plus(n0,n1)),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( def_10(plus(n0,n1),plus(n0,n1))
<=> def_10(plus(n0,n1),plus(n0,plus(n0,n1))) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( def_10(plus(n0,n1),plus(n0,plus(n0,n1)))
<=> def_10(plus(n0,n1),plus(n0,n1)) ),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
^ [X_t_32: $i] :
refl(( ( level(X_t_32) = int_level(X_t_32) )
<=> ( level(X_t_32) = int_level(X_t_32) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
<=> ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
<=> ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax',axiom_21) ).
tff(13,plain,
! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
( ~ ! [X_t_32: $i] : ( level(X_t_32) = int_level(X_t_32) )
| ( level(t_139) = int_level(t_139) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
level(t_139) = int_level(t_139),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
( ( level(t_139) = n1 )
<=> ( level(t_139) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
level(t_139) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_1) ).
tff(20,plain,
level(t_139) = n1,
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
n1 = level(t_139),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
plus(n0,plus(n0,n1)) = int_level(t_139),
inference(transitivity,[status(thm)],[5,4,21,17]) ).
tff(23,plain,
minus(plus(n0,plus(n0,n1)),plus(n0,n1)) = minus(int_level(t_139),n1),
inference(monotonicity,[status(thm)],[22,4]) ).
tff(24,plain,
minus(int_level(t_139),n1) = minus(plus(n0,plus(n0,n1)),plus(n0,n1)),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
int_level(t_139) = level(t_139),
inference(symmetry,[status(thm)],[17]) ).
tff(26,plain,
int_level(t_139) = plus(n0,n1),
inference(transitivity,[status(thm)],[25,20,3]) ).
tff(27,plain,
( gt(int_level(t_139),n0)
<=> gt(plus(n0,n1),n0) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( gt(plus(n0,n1),n0)
<=> gt(int_level(t_139),n0) ),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
^ [X_1: $i] :
refl(( gt(plus(X_1,n1),n0)
<=> gt(plus(X_1,n1),n0) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [X_1: $i] : gt(plus(X_1,n1),n0)
<=> ! [X_1: $i] : gt(plus(X_1,n1),n0) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [X_1: $i] : gt(plus(X_1,n1),n0)
<=> ! [X_1: $i] : gt(plus(X_1,n1),n0) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
! [X_1: $i] : gt(plus(X_1,n1),n0),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax',axiom_2) ).
tff(33,plain,
! [X_1: $i] : gt(plus(X_1,n1),n0),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [X_1: $i] : gt(plus(X_1,n1),n0),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [X_1: $i] : gt(plus(X_1,n1),n0),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [X_1: $i] : gt(plus(X_1,n1),n0)
| gt(plus(n0,n1),n0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
gt(plus(n0,n1),n0),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
gt(int_level(t_139),n0),
inference(modus_ponens,[status(thm)],[37,28]) ).
tff(39,plain,
( ~ p_Reset(t_139)
<=> ~ p_Reset(t_139) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
~ p_Reset(t_139),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_4) ).
tff(41,plain,
~ p_Reset(t_139),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( p_Rd(t_139)
<=> p_Rd(t_139) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
p_Rd(t_139),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_3) ).
tff(44,plain,
p_Rd(t_139),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( ~ p_Wr(t_139)
<=> ~ p_Wr(t_139) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
~ p_Wr(t_139),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_2) ).
tff(47,plain,
~ p_Wr(t_139),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
<=> ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
^ [X_t_42: $i] :
refl(( ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
<=> ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
<=> ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
<=> ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
^ [X_t_42: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( p_Reset(X_t_42)
| p_Wr(X_t_42)
| ~ p_Rd(X_t_42) )
<=> ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42) ) )),
( ( p_Reset(X_t_42)
| p_Wr(X_t_42)
| ~ p_Rd(X_t_42)
| ~ gt(int_level(X_t_42),n0) )
<=> ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0) ) )),
rewrite(( ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0) )
<=> ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0) ) )),
( ( p_Reset(X_t_42)
| p_Wr(X_t_42)
| ~ p_Rd(X_t_42)
| ~ gt(int_level(X_t_42),n0) )
<=> ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0) ) )),
( ( p_Reset(X_t_42)
| p_Wr(X_t_42)
| ~ p_Rd(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
<=> ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ) )),
rewrite(( ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
<=> ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ) )),
( ( p_Reset(X_t_42)
| p_Wr(X_t_42)
| ~ p_Rd(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
<=> ( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Wr(X_t_42)
| ~ p_Rd(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
<=> ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| p_Wr(X_t_42)
| ~ p_Rd(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax',axiom_71) ).
tff(55,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) ),
inference(modus_ponens,[status(thm)],[58,48]) ).
tff(60,plain,
( ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
| p_Reset(t_139)
| p_Wr(t_139)
| ~ p_Rd(t_139)
| ~ gt(int_level(t_139),n0)
| ( int_level(plus(t_139,n1)) = minus(int_level(t_139),n1) ) )
<=> ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
| p_Reset(t_139)
| p_Wr(t_139)
| ~ p_Rd(t_139)
| ~ gt(int_level(t_139),n0)
| ( int_level(plus(t_139,n1)) = minus(int_level(t_139),n1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ( p_Reset(t_139)
| ~ p_Rd(t_139)
| p_Wr(t_139)
| ~ gt(int_level(t_139),n0)
| ( int_level(plus(t_139,n1)) = minus(int_level(t_139),n1) ) )
<=> ( p_Reset(t_139)
| p_Wr(t_139)
| ~ p_Rd(t_139)
| ~ gt(int_level(t_139),n0)
| ( int_level(plus(t_139,n1)) = minus(int_level(t_139),n1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
( ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
| p_Reset(t_139)
| ~ p_Rd(t_139)
| p_Wr(t_139)
| ~ gt(int_level(t_139),n0)
| ( int_level(plus(t_139,n1)) = minus(int_level(t_139),n1) ) )
<=> ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
| p_Reset(t_139)
| p_Wr(t_139)
| ~ p_Rd(t_139)
| ~ gt(int_level(t_139),n0)
| ( int_level(plus(t_139,n1)) = minus(int_level(t_139),n1) ) ) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
| p_Reset(t_139)
| ~ p_Rd(t_139)
| p_Wr(t_139)
| ~ gt(int_level(t_139),n0)
| ( int_level(plus(t_139,n1)) = minus(int_level(t_139),n1) ) )
<=> ( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
| p_Reset(t_139)
| p_Wr(t_139)
| ~ p_Rd(t_139)
| ~ gt(int_level(t_139),n0)
| ( int_level(plus(t_139,n1)) = minus(int_level(t_139),n1) ) ) ),
inference(transitivity,[status(thm)],[62,60]) ).
tff(64,plain,
( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
| p_Reset(t_139)
| ~ p_Rd(t_139)
| p_Wr(t_139)
| ~ gt(int_level(t_139),n0)
| ( int_level(plus(t_139,n1)) = minus(int_level(t_139),n1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [X_t_42: $i] :
( p_Reset(X_t_42)
| ~ p_Rd(X_t_42)
| p_Wr(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ( int_level(plus(X_t_42,n1)) = minus(int_level(X_t_42),n1) ) )
| p_Reset(t_139)
| p_Wr(t_139)
| ~ p_Rd(t_139)
| ~ gt(int_level(t_139),n0)
| ( int_level(plus(t_139,n1)) = minus(int_level(t_139),n1) ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
( ~ gt(int_level(t_139),n0)
| ( int_level(plus(t_139,n1)) = minus(int_level(t_139),n1) ) ),
inference(unit_resolution,[status(thm)],[65,59,47,44,41]) ).
tff(67,plain,
int_level(plus(t_139,n1)) = minus(int_level(t_139),n1),
inference(unit_resolution,[status(thm)],[66,38]) ).
tff(68,plain,
int_level(plus(t_139,n1)) = minus(plus(n0,plus(n0,n1)),plus(n0,n1)),
inference(transitivity,[status(thm)],[67,24]) ).
tff(69,plain,
( ( int_level(plus(t_139,n1)) = n0 )
<=> ( minus(plus(n0,plus(n0,n1)),plus(n0,n1)) = n0 ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ( int_level(plus(t_139,n1)) != n0 )
<=> ( minus(plus(n0,plus(n0,n1)),plus(n0,n1)) != n0 ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ~ p_Empty(plus(t_139,n1))
<=> ~ p_Empty(plus(t_139,n1)) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,axiom,
~ p_Empty(plus(t_139,n1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quest_5) ).
tff(73,plain,
~ p_Empty(plus(t_139,n1)),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
^ [X_t_35: $i] :
refl(( ( p_Empty(X_t_35)
| ( int_level(X_t_35) != n0 ) )
<=> ( p_Empty(X_t_35)
| ( int_level(X_t_35) != n0 ) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [X_t_35: $i] :
( p_Empty(X_t_35)
| ( int_level(X_t_35) != n0 ) )
<=> ! [X_t_35: $i] :
( p_Empty(X_t_35)
| ( int_level(X_t_35) != n0 ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [X_t_35: $i] :
( p_Empty(X_t_35)
| ( int_level(X_t_35) != n0 ) )
<=> ! [X_t_35: $i] :
( p_Empty(X_t_35)
| ( int_level(X_t_35) != n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
^ [X_t_35: $i] :
rewrite(( ( ( int_level(X_t_35) != n0 )
| p_Empty(X_t_35) )
<=> ( p_Empty(X_t_35)
| ( int_level(X_t_35) != n0 ) ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [X_t_35: $i] :
( ( int_level(X_t_35) != n0 )
| p_Empty(X_t_35) )
<=> ! [X_t_35: $i] :
( p_Empty(X_t_35)
| ( int_level(X_t_35) != n0 ) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,axiom,
! [X_t_35: $i] :
( ( int_level(X_t_35) != n0 )
| p_Empty(X_t_35) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax',axiom_24) ).
tff(80,plain,
! [X_t_35: $i] :
( p_Empty(X_t_35)
| ( int_level(X_t_35) != n0 ) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [X_t_35: $i] :
( p_Empty(X_t_35)
| ( int_level(X_t_35) != n0 ) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
! [X_t_35: $i] :
( p_Empty(X_t_35)
| ( int_level(X_t_35) != n0 ) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [X_t_35: $i] :
( p_Empty(X_t_35)
| ( int_level(X_t_35) != n0 ) ),
inference(modus_ponens,[status(thm)],[82,75]) ).
tff(84,plain,
( ( ~ ! [X_t_35: $i] :
( p_Empty(X_t_35)
| ( int_level(X_t_35) != n0 ) )
| p_Empty(plus(t_139,n1))
| ( int_level(plus(t_139,n1)) != n0 ) )
<=> ( ~ ! [X_t_35: $i] :
( p_Empty(X_t_35)
| ( int_level(X_t_35) != n0 ) )
| p_Empty(plus(t_139,n1))
| ( int_level(plus(t_139,n1)) != n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [X_t_35: $i] :
( p_Empty(X_t_35)
| ( int_level(X_t_35) != n0 ) )
| p_Empty(plus(t_139,n1))
| ( int_level(plus(t_139,n1)) != n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [X_t_35: $i] :
( p_Empty(X_t_35)
| ( int_level(X_t_35) != n0 ) )
| p_Empty(plus(t_139,n1))
| ( int_level(plus(t_139,n1)) != n0 ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
int_level(plus(t_139,n1)) != n0,
inference(unit_resolution,[status(thm)],[86,83,73]) ).
tff(88,plain,
minus(plus(n0,plus(n0,n1)),plus(n0,n1)) != n0,
inference(modus_ponens,[status(thm)],[87,70]) ).
tff(89,plain,
^ [Y_4: $i,Z_5: $i] :
refl(( ( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) )
<=> ( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) )
<=> ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) )
<=> ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ! [Y_4: $i,Z_5: $i,X_3: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) )
<=> ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(93,plain,
( ! [Y_4: $i,Z_5: $i,X_3: $i] :
( def_10(Y_4,X_3)
| ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 ) )
<=> ! [Y_4: $i,Z_5: $i,X_3: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(94,plain,
( ! [Y_4: $i,Z_5: $i,X_3: $i] :
( def_10(Y_4,X_3)
| ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 ) )
<=> ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ) ),
inference(transitivity,[status(thm)],[93,92]) ).
tff(95,plain,
^ [Y_4: $i,Z_5: $i,X_3: $i] :
trans(monotonicity(rewrite(( ( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 ) )
<=> ( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 ) ) )),
( ( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 )
| def_10(Y_4,X_3) )
<=> ( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 )
| def_10(Y_4,X_3) ) )),
rewrite(( ( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 )
| def_10(Y_4,X_3) )
<=> ( def_10(Y_4,X_3)
| ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 ) ) )),
( ( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 )
| def_10(Y_4,X_3) )
<=> ( def_10(Y_4,X_3)
| ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 ) ) )),
inference(bind,[status(th)],[]) ).
tff(96,plain,
( ! [Y_4: $i,Z_5: $i,X_3: $i] :
( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 )
| def_10(Y_4,X_3) )
<=> ! [Y_4: $i,Z_5: $i,X_3: $i] :
( def_10(Y_4,X_3)
| ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 ) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ! [Y_4: $i,Z_5: $i,X_3: $i] :
( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 )
| def_10(Y_4,X_3) )
<=> ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,axiom,
! [Y_4: $i,Z_5: $i,X_3: $i] :
( ( minus(X_3,Y_4) = Z_5 )
| ( plus(Z_5,Y_4) != X_3 )
| def_10(Y_4,X_3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax',axiom_5) ).
tff(99,plain,
! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ),
inference(modus_ponens,[status(thm)],[99,91]) ).
tff(101,plain,
! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) ),
inference(modus_ponens,[status(thm)],[101,90]) ).
tff(103,plain,
( ( ~ ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) )
| def_10(plus(n0,n1),plus(n0,plus(n0,n1)))
| ( minus(plus(n0,plus(n0,n1)),plus(n0,n1)) = n0 ) )
<=> ( ~ ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) )
| def_10(plus(n0,n1),plus(n0,plus(n0,n1)))
| ( minus(plus(n0,plus(n0,n1)),plus(n0,n1)) = n0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
( ~ ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) )
| def_10(plus(n0,n1),plus(n0,plus(n0,n1)))
| ( minus(plus(n0,plus(n0,n1)),plus(n0,n1)) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [Y_4: $i,Z_5: $i] :
( def_10(Y_4,plus(Z_5,Y_4))
| ( minus(plus(Z_5,Y_4),Y_4) = Z_5 ) )
| def_10(plus(n0,n1),plus(n0,plus(n0,n1)))
| ( minus(plus(n0,plus(n0,n1)),plus(n0,n1)) = n0 ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
( def_10(plus(n0,n1),plus(n0,plus(n0,n1)))
| ( minus(plus(n0,plus(n0,n1)),plus(n0,n1)) = n0 ) ),
inference(unit_resolution,[status(thm)],[105,102]) ).
tff(107,plain,
def_10(plus(n0,n1),plus(n0,plus(n0,n1))),
inference(unit_resolution,[status(thm)],[106,88]) ).
tff(108,plain,
def_10(plus(n0,n1),plus(n0,n1)),
inference(modus_ponens,[status(thm)],[107,8]) ).
tff(109,plain,
^ [Y_4: $i] :
refl(( ~ def_10(Y_4,Y_4)
<=> ~ def_10(Y_4,Y_4) )),
inference(bind,[status(th)],[]) ).
tff(110,plain,
( ! [Y_4: $i] : ~ def_10(Y_4,Y_4)
<=> ! [Y_4: $i] : ~ def_10(Y_4,Y_4) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,plain,
( ! [Y_4: $i] : ~ def_10(Y_4,Y_4)
<=> ! [Y_4: $i] : ~ def_10(Y_4,Y_4) ),
inference(rewrite,[status(thm)],[]) ).
tff(112,plain,
( ! [Y_4: $i,X_3: $i] : ~ def_10(Y_4,Y_4)
<=> ! [Y_4: $i] : ~ def_10(Y_4,Y_4) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(113,plain,
( ! [Y_4: $i,X_3: $i] :
( ~ def_10(Y_4,X_3)
| ( X_3 != Y_4 ) )
<=> ! [Y_4: $i,X_3: $i] : ~ def_10(Y_4,Y_4) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(114,plain,
( ! [Y_4: $i,X_3: $i] :
( ~ def_10(Y_4,X_3)
| ( X_3 != Y_4 ) )
<=> ! [Y_4: $i] : ~ def_10(Y_4,Y_4) ),
inference(transitivity,[status(thm)],[113,112]) ).
tff(115,axiom,
! [Y_4: $i,X_3: $i] :
( ~ def_10(Y_4,X_3)
| ( X_3 != Y_4 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HWV003-0.ax',axiom_7) ).
tff(116,plain,
! [Y_4: $i] : ~ def_10(Y_4,Y_4),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
! [Y_4: $i] : ~ def_10(Y_4,Y_4),
inference(modus_ponens,[status(thm)],[116,111]) ).
tff(118,plain,
! [Y_4: $i] : ~ def_10(Y_4,Y_4),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [Y_4: $i] : ~ def_10(Y_4,Y_4),
inference(modus_ponens,[status(thm)],[118,110]) ).
tff(120,plain,
( ~ ! [Y_4: $i] : ~ def_10(Y_4,Y_4)
| ~ def_10(plus(n0,n1),plus(n0,n1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
$false,
inference(unit_resolution,[status(thm)],[120,119,108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : HWV023-1 : TPTP v9.0.0. Released v2.5.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 17:21:31 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.23/0.43 % SZS status Unsatisfiable
% 0.23/0.43 % SZS output start Proof
% See solution above
% 0.23/0.46 % E exiting
%------------------------------------------------------------------------------