TSTP Solution File: ARI621_3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI621_3 : TPTP v8.1.0. Released v5.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 : Tue Sep 6 17:02:20 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 36
% Syntax : Number of formulae : 96 ( 22 unt; 2 typ; 0 def)
% Number of atoms : 1138 ( 430 equ)
% Maximal formula atoms : 36 ( 12 avg)
% Number of connectives : 2275 (1251 ~; 868 |; 91 &)
% ( 63 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number arithmetic : 1844 ( 176 atm; 347 fun;1137 num; 184 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 1 usr; 9 con; 0-2 aty)
% Number of variables : 184 ( 160 !; 18 ?; 184 :)
% Comments :
%------------------------------------------------------------------------------
tff(pow2_type,type,
pow2: $real > $o ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $real > $real ).
tff(1,plain,
^ [X: $real] :
refl(
( ~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
<=> ~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
<=> ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $real] :
rewrite(
( ~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
<=> ~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
<=> ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
<=> ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [X: $real] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( $greatereq(X,2)
& ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
& pow2(tptp_fun_Y_0(X)) )
<=> ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )),
( ( ( X = 1 )
| ~ pow2(X)
| ( $greatereq(X,2)
& ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
& pow2(tptp_fun_Y_0(X)) ) )
<=> ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) ) )),
rewrite(
( ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
<=> ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) ) )),
( ( ( X = 1 )
| ~ pow2(X)
| ( $greatereq(X,2)
& ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
& pow2(tptp_fun_Y_0(X)) ) )
<=> ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) ) )),
rewrite(
( ( pow2(X)
| ( ( X != 1 )
& ( ~ $greatereq(X,2)
| ! [Y: $real] :
~ ( ( $sum(X,$product(-2,Y)) = 0 )
& pow2(Y) ) ) ) )
<=> ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )),
( ( ( ( X = 1 )
| ~ pow2(X)
| ( $greatereq(X,2)
& ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
& pow2(tptp_fun_Y_0(X)) ) )
& ( pow2(X)
| ( ( X != 1 )
& ( ~ $greatereq(X,2)
| ! [Y: $real] :
~ ( ( $sum(X,$product(-2,Y)) = 0 )
& pow2(Y) ) ) ) ) )
<=> ( ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
& ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) )),
rewrite(
( ( ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
& ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
<=> ~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) )),
( ( ( ( X = 1 )
| ~ pow2(X)
| ( $greatereq(X,2)
& ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
& pow2(tptp_fun_Y_0(X)) ) )
& ( pow2(X)
| ( ( X != 1 )
& ( ~ $greatereq(X,2)
| ! [Y: $real] :
~ ( ( $sum(X,$product(-2,Y)) = 0 )
& pow2(Y) ) ) ) ) )
<=> ~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [X: $real] :
( ( ( X = 1 )
| ~ pow2(X)
| ( $greatereq(X,2)
& ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
& pow2(tptp_fun_Y_0(X)) ) )
& ( pow2(X)
| ( ( X != 1 )
& ( ~ $greatereq(X,2)
| ! [Y: $real] :
~ ( ( $sum(X,$product(-2,Y)) = 0 )
& pow2(Y) ) ) ) ) )
<=> ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [X: $real] :
rewrite(
( ( ( ~ pow2(X)
| ( X = 1 )
| ( $greatereq(X,2)
& ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
& pow2(tptp_fun_Y_0(X)) ) )
& ( pow2(X)
| ( ( X != 1 )
& ( ~ $greatereq(X,2)
| ! [Y: $real] :
~ ( ( $sum(X,$product(-2,Y)) = 0 )
& pow2(Y) ) ) ) ) )
<=> ( ( ( X = 1 )
| ~ pow2(X)
| ( $greatereq(X,2)
& ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
& pow2(tptp_fun_Y_0(X)) ) )
& ( pow2(X)
| ( ( X != 1 )
& ( ~ $greatereq(X,2)
| ! [Y: $real] :
~ ( ( $sum(X,$product(-2,Y)) = 0 )
& pow2(Y) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [X: $real] :
( ( ~ pow2(X)
| ( X = 1 )
| ( $greatereq(X,2)
& ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
& pow2(tptp_fun_Y_0(X)) ) )
& ( pow2(X)
| ( ( X != 1 )
& ( ~ $greatereq(X,2)
| ! [Y: $real] :
~ ( ( $sum(X,$product(-2,Y)) = 0 )
& pow2(Y) ) ) ) ) )
<=> ! [X: $real] :
( ( ( X = 1 )
| ~ pow2(X)
| ( $greatereq(X,2)
& ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
& pow2(tptp_fun_Y_0(X)) ) )
& ( pow2(X)
| ( ( X != 1 )
& ( ~ $greatereq(X,2)
| ! [Y: $real] :
~ ( ( $sum(X,$product(-2,Y)) = 0 )
& pow2(Y) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $real] :
rewrite(
( ( pow2(X)
<=> ( ( X = 1 )
| ( $greatereq(X,2)
& ? [Y: $real] :
( ( $sum($product(2,Y),$product(-1,X)) = 0 )
& pow2(Y) ) ) ) )
<=> ( pow2(X)
<=> ( ( X = 1 )
| ( $greatereq(X,2)
& ? [Y: $real] :
( ( $sum(X,$product(-2,Y)) = 0 )
& pow2(Y) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $real] :
( pow2(X)
<=> ( ( X = 1 )
| ( $greatereq(X,2)
& ? [Y: $real] :
( ( $sum($product(2,Y),$product(-1,X)) = 0 )
& pow2(Y) ) ) ) )
<=> ! [X: $real] :
( pow2(X)
<=> ( ( X = 1 )
| ( $greatereq(X,2)
& ? [Y: $real] :
( ( $sum(X,$product(-2,Y)) = 0 )
& pow2(Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [X: $real] :
rewrite(
( ( pow2(X)
<=> ( ( X = 1 )
| ( $lesseq(2,X)
& ? [Y: $real] :
( ( $product(2,Y) = X )
& pow2(Y) ) ) ) )
<=> ( pow2(X)
<=> ( ( X = 1 )
| ( $greatereq(X,2)
& ? [Y: $real] :
( ( $sum($product(2,Y),$product(-1,X)) = 0 )
& pow2(Y) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [X: $real] :
( pow2(X)
<=> ( ( X = 1 )
| ( $lesseq(2,X)
& ? [Y: $real] :
( ( $product(2,Y) = X )
& pow2(Y) ) ) ) )
<=> ! [X: $real] :
( pow2(X)
<=> ( ( X = 1 )
| ( $greatereq(X,2)
& ? [Y: $real] :
( ( $sum($product(2,Y),$product(-1,X)) = 0 )
& pow2(Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [X: $real] :
( pow2(X)
<=> ( ( X = 1 )
| ( $lesseq(2,X)
& ? [Y: $real] :
( ( $product(2,Y) = X )
& pow2(Y) ) ) ) )
<=> ! [X: $real] :
( pow2(X)
<=> ( ( X = 1 )
| ( $lesseq(2,X)
& ? [Y: $real] :
( ( $product(2,Y) = X )
& pow2(Y) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ( ! [X: $real] :
( pow2(X)
<=> ( ( X = 1 )
| ( $lesseq(2,X)
& ? [Y: $real] :
( ( $product(2,Y) = X )
& pow2(Y) ) ) ) )
=> ~ pow2(12) )
<=> ~ ( ~ pow2(12)
| ~ ! [X: $real] :
( pow2(X)
<=> ( ( X = 1 )
| ( $lesseq(2,X)
& ? [Y: $real] :
( ( $product(2,Y) = X )
& pow2(Y) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
~ ( ! [X: $real] :
( pow2(X)
<=> ( ( X = 1 )
| ( $lesseq(2,X)
& ? [Y: $real] :
( ( $product(2,Y) = X )
& pow2(Y) ) ) ) )
=> ~ pow2(12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_pow_of_2_10) ).
tff(17,plain,
~ ( ~ pow2(12)
| ~ ! [X: $real] :
( pow2(X)
<=> ( ( X = 1 )
| ( $lesseq(2,X)
& ? [Y: $real] :
( ( $product(2,Y) = X )
& pow2(Y) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [X: $real] :
( pow2(X)
<=> ( ( X = 1 )
| ( $lesseq(2,X)
& ? [Y: $real] :
( ( $product(2,Y) = X )
& pow2(Y) ) ) ) ),
inference(or_elim,[status(thm)],[17]) ).
tff(19,plain,
! [X: $real] :
( pow2(X)
<=> ( ( X = 1 )
| ( $lesseq(2,X)
& ? [Y: $real] :
( ( $product(2,Y) = X )
& pow2(Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
! [X: $real] :
( pow2(X)
<=> ( ( X = 1 )
| ( $greatereq(X,2)
& ? [Y: $real] :
( ( $sum($product(2,Y),$product(-1,X)) = 0 )
& pow2(Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[19,13]) ).
tff(21,plain,
! [X: $real] :
( pow2(X)
<=> ( ( X = 1 )
| ( $greatereq(X,2)
& ? [Y: $real] :
( ( $sum(X,$product(-2,Y)) = 0 )
& pow2(Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,11]) ).
tff(22,plain,
! [X: $real] :
( ( ~ pow2(X)
| ( X = 1 )
| ( $greatereq(X,2)
& ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
& pow2(tptp_fun_Y_0(X)) ) )
& ( pow2(X)
| ( ( X != 1 )
& ( ~ $greatereq(X,2)
| ! [Y: $real] :
~ ( ( $sum(X,$product(-2,Y)) = 0 )
& pow2(Y) ) ) ) ) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [X: $real] :
( ( ( X = 1 )
| ~ pow2(X)
| ( $greatereq(X,2)
& ( $sum(X,$product(-2,tptp_fun_Y_0(X))) = 0 )
& pow2(tptp_fun_Y_0(X)) ) )
& ( pow2(X)
| ( ( X != 1 )
& ( ~ $greatereq(X,2)
| ! [Y: $real] :
~ ( ( $sum(X,$product(-2,Y)) = 0 )
& pow2(Y) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[22,9]) ).
tff(24,plain,
! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[23,7]) ).
tff(25,plain,
! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,5]) ).
tff(26,plain,
( ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ~ pow2(3)
| ~ ( ~ pow2(tptp_fun_Y_0(3))
| ( tptp_fun_Y_0(3) != 3/2 ) ) )
| ~ ( pow2(3)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 3/2 ) ) ) ) )
<=> ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ~ pow2(3)
| ~ ( ~ pow2(tptp_fun_Y_0(3))
| ( tptp_fun_Y_0(3) != 3/2 ) ) )
| ~ ( pow2(3)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 3/2 ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ~ ( ~ ( ( 3 = 1 )
| ~ pow2(3)
| ~ ( ~ $greatereq(3,2)
| ( $sum(3,$product(-2,tptp_fun_Y_0(3))) != 0 )
| ~ pow2(tptp_fun_Y_0(3)) ) )
| ~ ( pow2(3)
| ~ ( ( 3 = 1 )
| ~ ( ~ $greatereq(3,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(3,$product(-2,Y)) != 0 ) ) ) ) ) )
<=> ~ ( ~ ( ~ pow2(3)
| ~ ( ~ pow2(tptp_fun_Y_0(3))
| ( tptp_fun_Y_0(3) != 3/2 ) ) )
| ~ ( pow2(3)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 3/2 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ( 3 = 1 )
| ~ pow2(3)
| ~ ( ~ $greatereq(3,2)
| ( $sum(3,$product(-2,tptp_fun_Y_0(3))) != 0 )
| ~ pow2(tptp_fun_Y_0(3)) ) )
| ~ ( pow2(3)
| ~ ( ( 3 = 1 )
| ~ ( ~ $greatereq(3,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(3,$product(-2,Y)) != 0 ) ) ) ) ) ) )
<=> ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ~ pow2(3)
| ~ ( ~ pow2(tptp_fun_Y_0(3))
| ( tptp_fun_Y_0(3) != 3/2 ) ) )
| ~ ( pow2(3)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 3/2 ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ( 3 = 1 )
| ~ pow2(3)
| ~ ( ~ $greatereq(3,2)
| ( $sum(3,$product(-2,tptp_fun_Y_0(3))) != 0 )
| ~ pow2(tptp_fun_Y_0(3)) ) )
| ~ ( pow2(3)
| ~ ( ( 3 = 1 )
| ~ ( ~ $greatereq(3,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(3,$product(-2,Y)) != 0 ) ) ) ) ) ) )
<=> ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ~ pow2(3)
| ~ ( ~ pow2(tptp_fun_Y_0(3))
| ( tptp_fun_Y_0(3) != 3/2 ) ) )
| ~ ( pow2(3)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 3/2 ) ) ) ) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ( 3 = 1 )
| ~ pow2(3)
| ~ ( ~ $greatereq(3,2)
| ( $sum(3,$product(-2,tptp_fun_Y_0(3))) != 0 )
| ~ pow2(tptp_fun_Y_0(3)) ) )
| ~ ( pow2(3)
| ~ ( ( 3 = 1 )
| ~ ( ~ $greatereq(3,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(3,$product(-2,Y)) != 0 ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ~ pow2(3)
| ~ ( ~ pow2(tptp_fun_Y_0(3))
| ( tptp_fun_Y_0(3) != 3/2 ) ) )
| ~ ( pow2(3)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 3/2 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
~ ( ~ ( ~ pow2(3)
| ~ ( ~ pow2(tptp_fun_Y_0(3))
| ( tptp_fun_Y_0(3) != 3/2 ) ) )
| ~ ( pow2(3)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 3/2 ) ) ) ),
inference(unit_resolution,[status(thm)],[31,25]) ).
tff(33,plain,
( ~ ( ~ pow2(3)
| ~ ( ~ pow2(tptp_fun_Y_0(3))
| ( tptp_fun_Y_0(3) != 3/2 ) ) )
| ~ ( pow2(3)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 3/2 ) ) )
| ~ pow2(3)
| ~ ( ~ pow2(tptp_fun_Y_0(3))
| ( tptp_fun_Y_0(3) != 3/2 ) ) ),
inference(tautology,[status(thm)],]) ).
tff(34,plain,
( ~ pow2(3)
| ~ ( ~ pow2(tptp_fun_Y_0(3))
| ( tptp_fun_Y_0(3) != 3/2 ) ) ),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
( ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ~ pow2(6)
| ~ ( ~ pow2(tptp_fun_Y_0(6))
| ( tptp_fun_Y_0(6) != 3 ) ) )
| ~ ( pow2(6)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 3 ) ) ) ) )
<=> ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ~ pow2(6)
| ~ ( ~ pow2(tptp_fun_Y_0(6))
| ( tptp_fun_Y_0(6) != 3 ) ) )
| ~ ( pow2(6)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 3 ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ~ ( ~ ( ( 6 = 1 )
| ~ pow2(6)
| ~ ( ~ $greatereq(6,2)
| ( $sum(6,$product(-2,tptp_fun_Y_0(6))) != 0 )
| ~ pow2(tptp_fun_Y_0(6)) ) )
| ~ ( pow2(6)
| ~ ( ( 6 = 1 )
| ~ ( ~ $greatereq(6,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(6,$product(-2,Y)) != 0 ) ) ) ) ) )
<=> ~ ( ~ ( ~ pow2(6)
| ~ ( ~ pow2(tptp_fun_Y_0(6))
| ( tptp_fun_Y_0(6) != 3 ) ) )
| ~ ( pow2(6)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 3 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ( 6 = 1 )
| ~ pow2(6)
| ~ ( ~ $greatereq(6,2)
| ( $sum(6,$product(-2,tptp_fun_Y_0(6))) != 0 )
| ~ pow2(tptp_fun_Y_0(6)) ) )
| ~ ( pow2(6)
| ~ ( ( 6 = 1 )
| ~ ( ~ $greatereq(6,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(6,$product(-2,Y)) != 0 ) ) ) ) ) ) )
<=> ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ~ pow2(6)
| ~ ( ~ pow2(tptp_fun_Y_0(6))
| ( tptp_fun_Y_0(6) != 3 ) ) )
| ~ ( pow2(6)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 3 ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ( 6 = 1 )
| ~ pow2(6)
| ~ ( ~ $greatereq(6,2)
| ( $sum(6,$product(-2,tptp_fun_Y_0(6))) != 0 )
| ~ pow2(tptp_fun_Y_0(6)) ) )
| ~ ( pow2(6)
| ~ ( ( 6 = 1 )
| ~ ( ~ $greatereq(6,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(6,$product(-2,Y)) != 0 ) ) ) ) ) ) )
<=> ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ~ pow2(6)
| ~ ( ~ pow2(tptp_fun_Y_0(6))
| ( tptp_fun_Y_0(6) != 3 ) ) )
| ~ ( pow2(6)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 3 ) ) ) ) ) ),
inference(transitivity,[status(thm)],[37,35]) ).
tff(39,plain,
( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ( 6 = 1 )
| ~ pow2(6)
| ~ ( ~ $greatereq(6,2)
| ( $sum(6,$product(-2,tptp_fun_Y_0(6))) != 0 )
| ~ pow2(tptp_fun_Y_0(6)) ) )
| ~ ( pow2(6)
| ~ ( ( 6 = 1 )
| ~ ( ~ $greatereq(6,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(6,$product(-2,Y)) != 0 ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ~ pow2(6)
| ~ ( ~ pow2(tptp_fun_Y_0(6))
| ( tptp_fun_Y_0(6) != 3 ) ) )
| ~ ( pow2(6)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 3 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
~ ( ~ ( ~ pow2(6)
| ~ ( ~ pow2(tptp_fun_Y_0(6))
| ( tptp_fun_Y_0(6) != 3 ) ) )
| ~ ( pow2(6)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 3 ) ) ) ),
inference(unit_resolution,[status(thm)],[40,25]) ).
tff(42,plain,
( ~ ( ~ pow2(6)
| ~ ( ~ pow2(tptp_fun_Y_0(6))
| ( tptp_fun_Y_0(6) != 3 ) ) )
| ~ ( pow2(6)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 3 ) ) )
| ~ pow2(6)
| ~ ( ~ pow2(tptp_fun_Y_0(6))
| ( tptp_fun_Y_0(6) != 3 ) ) ),
inference(tautology,[status(thm)],]) ).
tff(43,plain,
( ~ pow2(6)
| ~ ( ~ pow2(tptp_fun_Y_0(6))
| ( tptp_fun_Y_0(6) != 3 ) ) ),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
( ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ~ pow2(12)
| ~ ( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 ) ) )
| ~ ( pow2(12)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 6 ) ) ) ) )
<=> ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ~ pow2(12)
| ~ ( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 ) ) )
| ~ ( pow2(12)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 6 ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ~ ( ~ ( ( 12 = 1 )
| ~ pow2(12)
| ~ ( ~ $greatereq(12,2)
| ( $sum(12,$product(-2,tptp_fun_Y_0(12))) != 0 )
| ~ pow2(tptp_fun_Y_0(12)) ) )
| ~ ( pow2(12)
| ~ ( ( 12 = 1 )
| ~ ( ~ $greatereq(12,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(12,$product(-2,Y)) != 0 ) ) ) ) ) )
<=> ~ ( ~ ( ~ pow2(12)
| ~ ( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 ) ) )
| ~ ( pow2(12)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 6 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ( 12 = 1 )
| ~ pow2(12)
| ~ ( ~ $greatereq(12,2)
| ( $sum(12,$product(-2,tptp_fun_Y_0(12))) != 0 )
| ~ pow2(tptp_fun_Y_0(12)) ) )
| ~ ( pow2(12)
| ~ ( ( 12 = 1 )
| ~ ( ~ $greatereq(12,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(12,$product(-2,Y)) != 0 ) ) ) ) ) ) )
<=> ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ~ pow2(12)
| ~ ( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 ) ) )
| ~ ( pow2(12)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 6 ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ( 12 = 1 )
| ~ pow2(12)
| ~ ( ~ $greatereq(12,2)
| ( $sum(12,$product(-2,tptp_fun_Y_0(12))) != 0 )
| ~ pow2(tptp_fun_Y_0(12)) ) )
| ~ ( pow2(12)
| ~ ( ( 12 = 1 )
| ~ ( ~ $greatereq(12,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(12,$product(-2,Y)) != 0 ) ) ) ) ) ) )
<=> ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ~ pow2(12)
| ~ ( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 ) ) )
| ~ ( pow2(12)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 6 ) ) ) ) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ( 12 = 1 )
| ~ pow2(12)
| ~ ( ~ $greatereq(12,2)
| ( $sum(12,$product(-2,tptp_fun_Y_0(12))) != 0 )
| ~ pow2(tptp_fun_Y_0(12)) ) )
| ~ ( pow2(12)
| ~ ( ( 12 = 1 )
| ~ ( ~ $greatereq(12,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(12,$product(-2,Y)) != 0 ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ~ pow2(12)
| ~ ( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 ) ) )
| ~ ( pow2(12)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 6 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
~ ( ~ ( ~ pow2(12)
| ~ ( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 ) ) )
| ~ ( pow2(12)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 6 ) ) ) ),
inference(unit_resolution,[status(thm)],[49,25]) ).
tff(51,plain,
( ~ ( ~ pow2(12)
| ~ ( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 ) ) )
| ~ ( pow2(12)
| ! [Y: $real] :
( ~ pow2(Y)
| ( Y != 6 ) ) )
| ~ pow2(12)
| ~ ( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 ) ) ),
inference(tautology,[status(thm)],]) ).
tff(52,plain,
( ~ pow2(12)
| ~ ( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 ) ) ),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
( pow2(12)
<=> pow2(12) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
pow2(12),
inference(or_elim,[status(thm)],[17]) ).
tff(55,plain,
pow2(12),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
( ~ ( ~ pow2(12)
| ~ ( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 ) ) )
| ~ pow2(12)
| ~ ( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 ) ) ),
inference(tautology,[status(thm)],]) ).
tff(57,plain,
( ~ ( ~ pow2(12)
| ~ ( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 ) ) )
| ~ ( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 ) ) ),
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
~ ( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 ) ),
inference(unit_resolution,[status(thm)],[57,52]) ).
tff(59,plain,
( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 )
| ( tptp_fun_Y_0(12) = 6 ) ),
inference(tautology,[status(thm)],]) ).
tff(60,plain,
tptp_fun_Y_0(12) = 6,
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
6 = tptp_fun_Y_0(12),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( pow2(6)
<=> pow2(tptp_fun_Y_0(12)) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( pow2(tptp_fun_Y_0(12))
<=> pow2(6) ),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
( ~ pow2(tptp_fun_Y_0(12))
| ( tptp_fun_Y_0(12) != 6 )
| pow2(tptp_fun_Y_0(12)) ),
inference(tautology,[status(thm)],]) ).
tff(65,plain,
pow2(tptp_fun_Y_0(12)),
inference(unit_resolution,[status(thm)],[64,58]) ).
tff(66,plain,
pow2(6),
inference(modus_ponens,[status(thm)],[65,63]) ).
tff(67,plain,
( ~ ( ~ pow2(6)
| ~ ( ~ pow2(tptp_fun_Y_0(6))
| ( tptp_fun_Y_0(6) != 3 ) ) )
| ~ pow2(6)
| ~ ( ~ pow2(tptp_fun_Y_0(6))
| ( tptp_fun_Y_0(6) != 3 ) ) ),
inference(tautology,[status(thm)],]) ).
tff(68,plain,
~ ( ~ pow2(tptp_fun_Y_0(6))
| ( tptp_fun_Y_0(6) != 3 ) ),
inference(unit_resolution,[status(thm)],[67,66,43]) ).
tff(69,plain,
( ~ pow2(tptp_fun_Y_0(6))
| ( tptp_fun_Y_0(6) != 3 )
| ( tptp_fun_Y_0(6) = 3 ) ),
inference(tautology,[status(thm)],]) ).
tff(70,plain,
tptp_fun_Y_0(6) = 3,
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
3 = tptp_fun_Y_0(6),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( pow2(3)
<=> pow2(tptp_fun_Y_0(6)) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( pow2(tptp_fun_Y_0(6))
<=> pow2(3) ),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ~ pow2(tptp_fun_Y_0(6))
| ( tptp_fun_Y_0(6) != 3 )
| pow2(tptp_fun_Y_0(6)) ),
inference(tautology,[status(thm)],]) ).
tff(75,plain,
pow2(tptp_fun_Y_0(6)),
inference(unit_resolution,[status(thm)],[74,68]) ).
tff(76,plain,
pow2(3),
inference(modus_ponens,[status(thm)],[75,73]) ).
tff(77,plain,
( ~ ( ~ pow2(3)
| ~ ( ~ pow2(tptp_fun_Y_0(3))
| ( tptp_fun_Y_0(3) != 3/2 ) ) )
| ~ pow2(3)
| ~ ( ~ pow2(tptp_fun_Y_0(3))
| ( tptp_fun_Y_0(3) != 3/2 ) ) ),
inference(tautology,[status(thm)],]) ).
tff(78,plain,
~ ( ~ pow2(tptp_fun_Y_0(3))
| ( tptp_fun_Y_0(3) != 3/2 ) ),
inference(unit_resolution,[status(thm)],[77,76,34]) ).
tff(79,plain,
( ~ pow2(tptp_fun_Y_0(3))
| ( tptp_fun_Y_0(3) != 3/2 )
| ( tptp_fun_Y_0(3) = 3/2 ) ),
inference(tautology,[status(thm)],]) ).
tff(80,plain,
tptp_fun_Y_0(3) = 3/2,
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
3/2 = tptp_fun_Y_0(3),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
( pow2(3/2)
<=> pow2(tptp_fun_Y_0(3)) ),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
( pow2(tptp_fun_Y_0(3))
<=> pow2(3/2) ),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( ~ pow2(tptp_fun_Y_0(3))
| ( tptp_fun_Y_0(3) != 3/2 )
| pow2(tptp_fun_Y_0(3)) ),
inference(tautology,[status(thm)],]) ).
tff(85,plain,
pow2(tptp_fun_Y_0(3)),
inference(unit_resolution,[status(thm)],[84,78]) ).
tff(86,plain,
pow2(3/2),
inference(modus_ponens,[status(thm)],[85,83]) ).
tff(87,plain,
( ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ pow2(3/2) )
<=> ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ pow2(3/2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ~ ( ~ ( ( 3/2 = 1 )
| ~ pow2(3/2)
| ~ ( ~ $greatereq(3/2,2)
| ( $sum(3/2,$product(-2,tptp_fun_Y_0(3/2))) != 0 )
| ~ pow2(tptp_fun_Y_0(3/2)) ) )
| ~ ( pow2(3/2)
| ~ ( ( 3/2 = 1 )
| ~ ( ~ $greatereq(3/2,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(3/2,$product(-2,Y)) != 0 ) ) ) ) ) )
<=> ~ pow2(3/2) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ( 3/2 = 1 )
| ~ pow2(3/2)
| ~ ( ~ $greatereq(3/2,2)
| ( $sum(3/2,$product(-2,tptp_fun_Y_0(3/2))) != 0 )
| ~ pow2(tptp_fun_Y_0(3/2)) ) )
| ~ ( pow2(3/2)
| ~ ( ( 3/2 = 1 )
| ~ ( ~ $greatereq(3/2,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(3/2,$product(-2,Y)) != 0 ) ) ) ) ) ) )
<=> ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ pow2(3/2) ) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ( 3/2 = 1 )
| ~ pow2(3/2)
| ~ ( ~ $greatereq(3/2,2)
| ( $sum(3/2,$product(-2,tptp_fun_Y_0(3/2))) != 0 )
| ~ pow2(tptp_fun_Y_0(3/2)) ) )
| ~ ( pow2(3/2)
| ~ ( ( 3/2 = 1 )
| ~ ( ~ $greatereq(3/2,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(3/2,$product(-2,Y)) != 0 ) ) ) ) ) ) )
<=> ( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ pow2(3/2) ) ),
inference(transitivity,[status(thm)],[89,87]) ).
tff(91,plain,
( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ ( ~ ( ( 3/2 = 1 )
| ~ pow2(3/2)
| ~ ( ~ $greatereq(3/2,2)
| ( $sum(3/2,$product(-2,tptp_fun_Y_0(3/2))) != 0 )
| ~ pow2(tptp_fun_Y_0(3/2)) ) )
| ~ ( pow2(3/2)
| ~ ( ( 3/2 = 1 )
| ~ ( ~ $greatereq(3/2,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(3/2,$product(-2,Y)) != 0 ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
( ~ ! [X: $real] :
~ ( ~ ( ( X = 1 )
| ~ pow2(X)
| ~ ( ~ $greatereq(X,2)
| ( $sum(X,$product(-2,tptp_fun_Y_0(X))) != 0 )
| ~ pow2(tptp_fun_Y_0(X)) ) )
| ~ ( pow2(X)
| ~ ( ( X = 1 )
| ~ ( ~ $greatereq(X,2)
| ! [Y: $real] :
( ~ pow2(Y)
| ( $sum(X,$product(-2,Y)) != 0 ) ) ) ) ) )
| ~ pow2(3/2) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
~ pow2(3/2),
inference(unit_resolution,[status(thm)],[92,25]) ).
tff(94,plain,
$false,
inference(unit_resolution,[status(thm)],[93,86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ARI621_3 : TPTP v8.1.0. Released v5.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 00:49:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------