TSTP Solution File: DAT046_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT046_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 : Fri Sep 16 14:36:30 EDT 2022
% Result : Theorem 0.13s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 52
% Syntax : Number of formulae : 115 ( 36 unt; 4 typ; 0 def)
% Number of atoms : 369 ( 157 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 364 ( 117 ~; 85 |; 0 &)
% ( 162 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number arithmetic : 746 ( 37 atm; 179 fun; 431 num; 99 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 9 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 3 usr; 6 con; 0-2 aty)
% Number of variables : 185 ( 162 !; 0 ?; 185 :)
% Comments :
%------------------------------------------------------------------------------
tff(count_type,type,
count: collection > $int ).
tff(add_type,type,
add: ( $int * collection ) > collection ).
tff(empty_type,type,
empty: collection ).
tff(in_type,type,
in: ( $int * collection ) > $o ).
tff(1,plain,
^ [X6: collection] :
refl(
( $greatereq(count(X6),0)
<=> $greatereq(count(X6),0) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X6: collection] : $greatereq(count(X6),0)
<=> ! [X6: collection] : $greatereq(count(X6),0) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X6: collection] : $greatereq(count(X6),0)
<=> ! [X6: collection] : $greatereq(count(X6),0) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X6: collection] : $greatereq(count(X6),0),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax1) ).
tff(5,plain,
! [X6: collection] : $greatereq(count(X6),0),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X6: collection] : $greatereq(count(X6),0),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X6: collection] : $greatereq(count(X6),0),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X6: collection] : $greatereq(count(X6),0)
| $greatereq(count(empty),0) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
$greatereq(count(empty),0),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X8: $int,X9: collection] :
refl(
( ( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) )
<=> ( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) )
<=> ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [X8: $int,X9: collection] :
rewrite(
( ( ~ in(X8,X9)
<=> ( $sum(count(add(X8,X9)),$product(-1,count(X9))) = 1 ) )
<=> ( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(add(X8,X9)),$product(-1,count(X9))) = 1 ) )
<=> ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [X8: $int,X9: collection] :
rewrite(
( ( ~ in(X8,X9)
<=> ( count(add(X8,X9)) = $sum(1,count(X9)) ) )
<=> ( ~ in(X8,X9)
<=> ( $sum(count(add(X8,X9)),$product(-1,count(X9))) = 1 ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( count(add(X8,X9)) = $sum(1,count(X9)) ) )
<=> ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(add(X8,X9)),$product(-1,count(X9))) = 1 ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( count(add(X8,X9)) = $sum(1,count(X9)) ) )
<=> ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( count(add(X8,X9)) = $sum(1,count(X9)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
^ [X8: $int,X9: collection] :
rewrite(
( ( ~ in(X8,X9)
<=> ( count(add(X8,X9)) = $sum(count(X9),1) ) )
<=> ( ~ in(X8,X9)
<=> ( count(add(X8,X9)) = $sum(1,count(X9)) ) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( count(add(X8,X9)) = $sum(count(X9),1) ) )
<=> ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( count(add(X8,X9)) = $sum(1,count(X9)) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,axiom,
! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( count(add(X8,X9)) = $sum(count(X9),1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax3) ).
tff(20,plain,
! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( count(add(X8,X9)) = $sum(1,count(X9)) ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( count(add(X8,X9)) = $sum(1,count(X9)) ) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(add(X8,X9)),$product(-1,count(X9))) = 1 ) ),
inference(modus_ponens,[status(thm)],[21,15]) ).
tff(23,plain,
! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) ),
inference(modus_ponens,[status(thm)],[22,13]) ).
tff(24,plain,
! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) ),
inference(modus_ponens,[status(thm)],[24,11]) ).
tff(26,plain,
( ~ ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) )
| ( ~ in(3,empty)
<=> ( $sum(count(empty),$product(-1,count(add(3,empty)))) = -1 ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ in(3,empty)
<=> ( $sum(count(empty),$product(-1,count(add(3,empty)))) = -1 ) ),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
^ [U: $int] :
refl(
( ~ in(U,empty)
<=> ~ in(U,empty) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [U: $int] : ~ in(U,empty)
<=> ! [U: $int] : ~ in(U,empty) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [U: $int] : ~ in(U,empty)
<=> ! [U: $int] : ~ in(U,empty) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
! [U: $int] : ~ in(U,empty),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=0.ax',ax1) ).
tff(32,plain,
! [U: $int] : ~ in(U,empty),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [U: $int] : ~ in(U,empty),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [U: $int] : ~ in(U,empty),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ~ ! [U: $int] : ~ in(U,empty)
| ~ in(3,empty) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
~ in(3,empty),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
( ~ ( ~ in(3,empty)
<=> ( $sum(count(empty),$product(-1,count(add(3,empty)))) = -1 ) )
| in(3,empty)
| ( $sum(count(empty),$product(-1,count(add(3,empty)))) = -1 ) ),
inference(tautology,[status(thm)],]) ).
tff(38,plain,
$sum(count(empty),$product(-1,count(add(3,empty)))) = -1,
inference(unit_resolution,[status(thm)],[37,36,27]) ).
tff(39,plain,
( ( $sum(count(empty),$product(-1,count(add(3,empty)))) != -1 )
| $lesseq($sum(count(empty),$product(-1,count(add(3,empty)))),-1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(40,plain,
$lesseq($sum(count(empty),$product(-1,count(add(3,empty)))),-1),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
( ( ~ ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) )
| ( ~ in(1,add(3,empty))
<=> ( $sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))) = 1 ) ) )
<=> ( ~ ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) )
| ( ~ in(1,add(3,empty))
<=> ( $sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))) = 1 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ( ~ in(1,add(3,empty))
<=> ( $sum(count(add(3,empty)),$product(-1,count(add(1,add(3,empty))))) = -1 ) )
<=> ( ~ in(1,add(3,empty))
<=> ( $sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))) = 1 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( ~ ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) )
| ( ~ in(1,add(3,empty))
<=> ( $sum(count(add(3,empty)),$product(-1,count(add(1,add(3,empty))))) = -1 ) ) )
<=> ( ~ ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) )
| ( ~ in(1,add(3,empty))
<=> ( $sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))) = 1 ) ) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ( ~ ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) )
| ( ~ in(1,add(3,empty))
<=> ( $sum(count(add(3,empty)),$product(-1,count(add(1,add(3,empty))))) = -1 ) ) )
<=> ( ~ ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) )
| ( ~ in(1,add(3,empty))
<=> ( $sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))) = 1 ) ) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ~ ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) )
| ( ~ in(1,add(3,empty))
<=> ( $sum(count(add(3,empty)),$product(-1,count(add(1,add(3,empty))))) = -1 ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [X8: $int,X9: collection] :
( ~ in(X8,X9)
<=> ( $sum(count(X9),$product(-1,count(add(X8,X9)))) = -1 ) )
| ( ~ in(1,add(3,empty))
<=> ( $sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))) = 1 ) ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
( ~ in(1,add(3,empty))
<=> ( $sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))) = 1 ) ),
inference(unit_resolution,[status(thm)],[46,25]) ).
tff(48,plain,
^ [Z: $int,X1: collection,X2: $int] :
refl(
( ( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
<=> ( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
<=> ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
^ [Z: $int,X1: collection,X2: $int] :
rewrite(
( ( ( in(Z,X1)
| ( $sum(Z,$product(-1,X2)) = 0 ) )
<=> in(Z,add(X2,X1)) )
<=> ( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(Z,$product(-1,X2)) = 0 ) )
<=> in(Z,add(X2,X1)) )
<=> ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
^ [Z: $int,X1: collection,X2: $int] :
rewrite(
( ( ( ( Z = X2 )
| in(Z,X1) )
<=> in(Z,add(X2,X1)) )
<=> ( ( in(Z,X1)
| ( $sum(Z,$product(-1,X2)) = 0 ) )
<=> in(Z,add(X2,X1)) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [Z: $int,X1: collection,X2: $int] :
( ( ( Z = X2 )
| in(Z,X1) )
<=> in(Z,add(X2,X1)) )
<=> ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(Z,$product(-1,X2)) = 0 ) )
<=> in(Z,add(X2,X1)) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [Z: $int,X1: collection,X2: $int] :
( ( ( Z = X2 )
| in(Z,X1) )
<=> in(Z,add(X2,X1)) )
<=> ! [Z: $int,X1: collection,X2: $int] :
( ( ( Z = X2 )
| in(Z,X1) )
<=> in(Z,add(X2,X1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
^ [Z: $int,X1: collection,X2: $int] :
rewrite(
( ( ( in(Z,X1)
| ( Z = X2 ) )
<=> in(Z,add(X2,X1)) )
<=> ( ( ( Z = X2 )
| in(Z,X1) )
<=> in(Z,add(X2,X1)) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( Z = X2 ) )
<=> in(Z,add(X2,X1)) )
<=> ! [Z: $int,X1: collection,X2: $int] :
( ( ( Z = X2 )
| in(Z,X1) )
<=> in(Z,add(X2,X1)) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( Z = X2 ) )
<=> in(Z,add(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=0.ax',ax4) ).
tff(58,plain,
! [Z: $int,X1: collection,X2: $int] :
( ( ( Z = X2 )
| in(Z,X1) )
<=> in(Z,add(X2,X1)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [Z: $int,X1: collection,X2: $int] :
( ( ( Z = X2 )
| in(Z,X1) )
<=> in(Z,add(X2,X1)) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(Z,$product(-1,X2)) = 0 ) )
<=> in(Z,add(X2,X1)) ),
inference(modus_ponens,[status(thm)],[59,53]) ).
tff(61,plain,
! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) ),
inference(modus_ponens,[status(thm)],[60,51]) ).
tff(62,plain,
! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) ),
inference(modus_ponens,[status(thm)],[62,49]) ).
tff(64,plain,
( ( ~ ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
| ( in(1,empty)
<=> in(1,add(3,empty)) ) )
<=> ( ~ ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
| ( in(1,empty)
<=> in(1,add(3,empty)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ( ( in(1,empty)
| ( $sum(3,$product(-1,1)) = 0 ) )
<=> in(1,add(3,empty)) )
<=> ( in(1,empty)
<=> in(1,add(3,empty)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ( ~ ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
| ( ( in(1,empty)
| ( $sum(3,$product(-1,1)) = 0 ) )
<=> in(1,add(3,empty)) ) )
<=> ( ~ ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
| ( in(1,empty)
<=> in(1,add(3,empty)) ) ) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ( ~ ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
| ( ( in(1,empty)
| ( $sum(3,$product(-1,1)) = 0 ) )
<=> in(1,add(3,empty)) ) )
<=> ( ~ ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
| ( in(1,empty)
<=> in(1,add(3,empty)) ) ) ),
inference(transitivity,[status(thm)],[66,64]) ).
tff(68,plain,
( ~ ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
| ( ( in(1,empty)
| ( $sum(3,$product(-1,1)) = 0 ) )
<=> in(1,add(3,empty)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
( ~ ! [Z: $int,X1: collection,X2: $int] :
( ( in(Z,X1)
| ( $sum(X2,$product(-1,Z)) = 0 ) )
<=> in(Z,add(X2,X1)) )
| ( in(1,empty)
<=> in(1,add(3,empty)) ) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
( in(1,empty)
<=> in(1,add(3,empty)) ),
inference(unit_resolution,[status(thm)],[69,63]) ).
tff(71,plain,
( ~ ! [U: $int] : ~ in(U,empty)
| ~ in(1,empty) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
~ in(1,empty),
inference(unit_resolution,[status(thm)],[71,34]) ).
tff(73,plain,
( ~ ( in(1,empty)
<=> in(1,add(3,empty)) )
| in(1,empty)
| ~ in(1,add(3,empty)) ),
inference(tautology,[status(thm)],]) ).
tff(74,plain,
~ in(1,add(3,empty)),
inference(unit_resolution,[status(thm)],[73,72,70]) ).
tff(75,plain,
( ~ ( ~ in(1,add(3,empty))
<=> ( $sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))) = 1 ) )
| in(1,add(3,empty))
| ( $sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))) = 1 ) ),
inference(tautology,[status(thm)],]) ).
tff(76,plain,
$sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))) = 1,
inference(unit_resolution,[status(thm)],[75,74,47]) ).
tff(77,plain,
( ( $sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))) != 1 )
| $greatereq($sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))),1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(78,plain,
$greatereq($sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))),1),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
( $greatereq(count(add(1,add(3,empty))),2)
| ~ $greatereq($sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))),1)
| ~ $greatereq(count(empty),0)
| ~ $lesseq($sum(count(empty),$product(-1,count(add(3,empty)))),-1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(80,plain,
$greatereq(count(add(1,add(3,empty))),2),
inference(unit_resolution,[status(thm)],[79,78,40,9]) ).
tff(81,plain,
^ [X7: collection] :
refl(
( ( ( X7 = empty )
<=> ( count(X7) = 0 ) )
<=> ( ( X7 = empty )
<=> ( count(X7) = 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) )
<=> ! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) )
<=> ! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax2) ).
tff(85,plain,
! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
( ( ~ ! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) )
| ( count(empty) = 0 ) )
<=> ( ~ ! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) )
| ( count(empty) = 0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( $true
<=> ( count(empty) = 0 ) )
<=> ( count(empty) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ( empty = empty )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ( ( empty = empty )
<=> ( count(empty) = 0 ) )
<=> ( $true
<=> ( count(empty) = 0 ) ) ),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
( ( ( empty = empty )
<=> ( count(empty) = 0 ) )
<=> ( count(empty) = 0 ) ),
inference(transitivity,[status(thm)],[91,89]) ).
tff(93,plain,
( ( ~ ! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) )
| ( ( empty = empty )
<=> ( count(empty) = 0 ) ) )
<=> ( ~ ! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) )
| ( count(empty) = 0 ) ) ),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( ( ~ ! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) )
| ( ( empty = empty )
<=> ( count(empty) = 0 ) ) )
<=> ( ~ ! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) )
| ( count(empty) = 0 ) ) ),
inference(transitivity,[status(thm)],[93,88]) ).
tff(95,plain,
( ~ ! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) )
| ( ( empty = empty )
<=> ( count(empty) = 0 ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
( ~ ! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) )
| ( count(empty) = 0 ) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
count(empty) = 0,
inference(unit_resolution,[status(thm)],[96,87]) ).
tff(98,plain,
( ( count(empty) != 0 )
| $lesseq(count(empty),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(99,plain,
$lesseq(count(empty),0),
inference(unit_resolution,[status(thm)],[98,97]) ).
tff(100,plain,
( ( $sum(count(empty),$product(-1,count(add(3,empty)))) != -1 )
| $greatereq($sum(count(empty),$product(-1,count(add(3,empty)))),-1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(101,plain,
$greatereq($sum(count(empty),$product(-1,count(add(3,empty)))),-1),
inference(unit_resolution,[status(thm)],[100,38]) ).
tff(102,plain,
( ( $sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))) != 1 )
| $lesseq($sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))),1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(103,plain,
$lesseq($sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))),1),
inference(unit_resolution,[status(thm)],[102,76]) ).
tff(104,plain,
( $lesseq(count(add(1,add(3,empty))),2)
| ~ $lesseq($sum(count(add(1,add(3,empty))),$product(-1,count(add(3,empty)))),1)
| ~ $lesseq(count(empty),0)
| ~ $greatereq($sum(count(empty),$product(-1,count(add(3,empty)))),-1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(105,plain,
$lesseq(count(add(1,add(3,empty))),2),
inference(unit_resolution,[status(thm)],[104,103,101,99]) ).
tff(106,plain,
( ( count(add(1,add(3,empty))) != 2 )
<=> ( count(add(1,add(3,empty))) != 2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,axiom,
count(add(1,add(3,empty))) != 2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(108,plain,
count(add(1,add(3,empty))) != 2,
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
( ( count(add(1,add(3,empty))) = 2 )
| ~ $lesseq(count(add(1,add(3,empty))),2)
| ~ $greatereq(count(add(1,add(3,empty))),2) ),
inference(theory_lemma,[status(thm)],]) ).
tff(110,plain,
( ~ $lesseq(count(add(1,add(3,empty))),2)
| ~ $greatereq(count(add(1,add(3,empty))),2) ),
inference(unit_resolution,[status(thm)],[109,108]) ).
tff(111,plain,
$false,
inference(unit_resolution,[status(thm)],[110,105,80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : DAT046_1 : TPTP v8.1.0. Released v5.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n019.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 : Wed Aug 31 01:48:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------