TSTP Solution File: ARI631_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ARI631_1 : TPTP v8.1.0. Released v6.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 17:02:22 EDT 2022
% Result : Theorem 0.15s 0.37s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 47
% Syntax : Number of formulae : 75 ( 55 unt; 4 typ; 0 def)
% Number of atoms : 90 ( 41 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 43 ( 24 ~; 4 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 29 ( 3 avg)
% Number arithmetic : 2085 ( 48 atm;1747 fun; 290 num; 0 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 4 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(w_type,type,
w: $real ).
tff(v_type,type,
v: $real ).
tff(u_type,type,
u: $real ).
tff(z_type,type,
z: $real ).
tff(1,plain,
( $lesseq($product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))))),$sum($product(u,$product(u,u)),$sum($product(3,$product(u,$product(u,v))),$sum($product(3,$product(u,$product(v,v))),$sum($product(3,$product(u,$product(u,z))),$sum($product(6,$product(u,$product(v,z))),$sum($product(3,$product(u,$product(z,z))),$sum($product(v,$product(v,v)),$sum($product(3,$product(v,$product(v,z))),$sum($product(3,$product(v,$product(z,z))),$product(z,$product(z,z))))))))))))
<=> $greatereq($sum($product(u,$product(u,u)),$sum($product(3,$product(u,$product(u,v))),$sum($product(3,$product(u,$product(v,v))),$sum($product(3,$product(u,$product(u,z))),$sum($product(6,$product(u,$product(v,z))),$sum($product(3,$product(u,$product(z,z))),$sum($product(v,$product(v,v)),$sum($product(3,$product(v,$product(v,z))),$sum($product(3,$product(v,$product(z,z))),$sum($product(z,$product(z,z)),$product(-1,$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w)))))))))))))))))),0) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
$sum($product(u,$product(u,u)),$sum($product(u,$product(u,v)),$sum($product(u,$product(u,z)),$sum($product(u,$product(u,v)),$sum($product(u,$product(v,v)),$sum($product(u,$product(v,z)),$sum($product(u,$product(u,z)),$sum($product(u,$product(v,z)),$sum($product(u,$product(z,z)),$sum($product(u,$product(u,v)),$sum($product(u,$product(v,v)),$sum($product(u,$product(v,z)),$sum($product(u,$product(v,v)),$sum($product(v,$product(v,v)),$sum($product(v,$product(v,z)),$sum($product(u,$product(v,z)),$sum($product(v,$product(v,z)),$sum($product(v,$product(z,z)),$sum($product(u,$product(u,z)),$sum($product(u,$product(v,z)),$sum($product(u,$product(z,z)),$sum($product(u,$product(v,z)),$sum($product(v,$product(v,z)),$sum($product(v,$product(z,z)),$sum($product(u,$product(z,z)),$sum($product(v,$product(z,z)),$product(z,$product(z,z)))))))))))))))))))))))))))) = $sum($product(u,$product(u,u)),$sum($product(3,$product(u,$product(u,v))),$sum($product(3,$product(u,$product(v,v))),$sum($product(3,$product(u,$product(u,z))),$sum($product(6,$product(u,$product(v,z))),$sum($product(3,$product(u,$product(z,z))),$sum($product(v,$product(v,v)),$sum($product(3,$product(v,$product(v,z))),$sum($product(3,$product(v,$product(z,z))),$product(z,$product(z,z))))))))))),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
$product(z,$product(v,z)) = $product(v,$product(z,z)),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
$product(z,$product(u,z)) = $product(u,$product(z,z)),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
$product(v,$product(u,z)) = $product(u,$product(v,z)),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
$product(z,$product(z,v)) = $product(v,$product(z,z)),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
$product(v,$product(z,v)) = $product(v,$product(v,z)),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
$product(u,$product(z,v)) = $product(u,$product(v,z)),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
$product(z,$product(v,v)) = $product(v,$product(v,z)),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
$product(z,$product(u,v)) = $product(u,$product(v,z)),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
$product(v,$product(u,v)) = $product(u,$product(v,v)),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
$product(z,$product(z,u)) = $product(u,$product(z,z)),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
$product(v,$product(z,u)) = $product(u,$product(v,z)),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
$product(u,$product(z,u)) = $product(u,$product(u,z)),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
$product(z,$product(v,u)) = $product(u,$product(v,z)),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
$product(v,$product(v,u)) = $product(u,$product(v,v)),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
$product(u,$product(v,u)) = $product(u,$product(u,v)),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
$product(z,$product(u,u)) = $product(u,$product(u,z)),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
$product(v,$product(u,u)) = $product(u,$product(u,v)),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
$sum($product(u,$product(u,u)),$sum($product(v,$product(u,u)),$sum($product(z,$product(u,u)),$sum($product(u,$product(v,u)),$sum($product(v,$product(v,u)),$sum($product(z,$product(v,u)),$sum($product(u,$product(z,u)),$sum($product(v,$product(z,u)),$sum($product(z,$product(z,u)),$sum($product(u,$product(u,v)),$sum($product(v,$product(u,v)),$sum($product(z,$product(u,v)),$sum($product(u,$product(v,v)),$sum($product(v,$product(v,v)),$sum($product(z,$product(v,v)),$sum($product(u,$product(z,v)),$sum($product(v,$product(z,v)),$sum($product(z,$product(z,v)),$sum($product(u,$product(u,z)),$sum($product(v,$product(u,z)),$sum($product(z,$product(u,z)),$sum($product(u,$product(v,z)),$sum($product(v,$product(v,z)),$sum($product(z,$product(v,z)),$sum($product(u,$product(z,z)),$sum($product(v,$product(z,z)),$product(z,$product(z,z)))))))))))))))))))))))))))) = $sum($product(u,$product(u,u)),$sum($product(u,$product(u,v)),$sum($product(u,$product(u,z)),$sum($product(u,$product(u,v)),$sum($product(u,$product(v,v)),$sum($product(u,$product(v,z)),$sum($product(u,$product(u,z)),$sum($product(u,$product(v,z)),$sum($product(u,$product(z,z)),$sum($product(u,$product(u,v)),$sum($product(u,$product(v,v)),$sum($product(u,$product(v,z)),$sum($product(u,$product(v,v)),$sum($product(v,$product(v,v)),$sum($product(v,$product(v,z)),$sum($product(u,$product(v,z)),$sum($product(v,$product(v,z)),$sum($product(v,$product(z,z)),$sum($product(u,$product(u,z)),$sum($product(u,$product(v,z)),$sum($product(u,$product(z,z)),$sum($product(u,$product(v,z)),$sum($product(v,$product(v,z)),$sum($product(v,$product(z,z)),$sum($product(u,$product(z,z)),$sum($product(v,$product(z,z)),$product(z,$product(z,z)))))))))))))))))))))))))))),
inference(monotonicity,[status(thm)],[19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3]) ).
tff(21,plain,
$sum($product(u,$product(u,u)),$sum($product(v,$product(u,u)),$sum($product(z,$product(u,u)),$sum($product(u,$product(v,u)),$sum($product(v,$product(v,u)),$sum($product(z,$product(v,u)),$sum($product(u,$product(z,u)),$sum($product(v,$product(z,u)),$sum($product(z,$product(z,u)),$sum($product(u,$product(u,v)),$sum($product(v,$product(u,v)),$sum($product(z,$product(u,v)),$sum($product(u,$product(v,v)),$sum($product(v,$product(v,v)),$sum($product(z,$product(v,v)),$sum($product(u,$product(z,v)),$sum($product(v,$product(z,v)),$sum($product(z,$product(z,v)),$sum($product(u,$product(u,z)),$sum($product(v,$product(u,z)),$sum($product(z,$product(u,z)),$sum($product(u,$product(v,z)),$sum($product(v,$product(v,z)),$sum($product(z,$product(v,z)),$sum($product(u,$product(z,z)),$sum($product(v,$product(z,z)),$product(z,$product(z,z)))))))))))))))))))))))))))) = $sum($product(u,$product(u,u)),$sum($product(3,$product(u,$product(u,v))),$sum($product(3,$product(u,$product(v,v))),$sum($product(3,$product(u,$product(u,z))),$sum($product(6,$product(u,$product(v,z))),$sum($product(3,$product(u,$product(z,z))),$sum($product(v,$product(v,v)),$sum($product(3,$product(v,$product(v,z))),$sum($product(3,$product(v,$product(z,z))),$product(z,$product(z,z))))))))))),
inference(transitivity,[status(thm)],[20,2]) ).
tff(22,plain,
$product($sum(u,$sum(v,z)),$product($sum(u,$sum(v,z)),$sum(u,$sum(v,z)))) = $sum($product(u,$product(u,u)),$sum($product(v,$product(u,u)),$sum($product(z,$product(u,u)),$sum($product(u,$product(v,u)),$sum($product(v,$product(v,u)),$sum($product(z,$product(v,u)),$sum($product(u,$product(z,u)),$sum($product(v,$product(z,u)),$sum($product(z,$product(z,u)),$sum($product(u,$product(u,v)),$sum($product(v,$product(u,v)),$sum($product(z,$product(u,v)),$sum($product(u,$product(v,v)),$sum($product(v,$product(v,v)),$sum($product(z,$product(v,v)),$sum($product(u,$product(z,v)),$sum($product(v,$product(z,v)),$sum($product(z,$product(z,v)),$sum($product(u,$product(u,z)),$sum($product(v,$product(u,z)),$sum($product(z,$product(u,z)),$sum($product(u,$product(v,z)),$sum($product(v,$product(v,z)),$sum($product(z,$product(v,z)),$sum($product(u,$product(z,z)),$sum($product(v,$product(z,z)),$product(z,$product(z,z)))))))))))))))))))))))))))),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
$product($sum(u,$sum(v,z)),$product($sum(u,$sum(v,z)),$sum(u,$sum(v,z)))) = $sum($product(u,$product(u,u)),$sum($product(3,$product(u,$product(u,v))),$sum($product(3,$product(u,$product(v,v))),$sum($product(3,$product(u,$product(u,z))),$sum($product(6,$product(u,$product(v,z))),$sum($product(3,$product(u,$product(z,z))),$sum($product(v,$product(v,v)),$sum($product(3,$product(v,$product(v,z))),$sum($product(3,$product(v,$product(z,z))),$product(z,$product(z,z))))))))))),
inference(transitivity,[status(thm)],[22,21]) ).
tff(24,plain,
( $lesseq($product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))))),$product($sum(u,$sum(v,z)),$product($sum(u,$sum(v,z)),$sum(u,$sum(v,z)))))
<=> $lesseq($product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))))),$sum($product(u,$product(u,u)),$sum($product(3,$product(u,$product(u,v))),$sum($product(3,$product(u,$product(v,v))),$sum($product(3,$product(u,$product(u,z))),$sum($product(6,$product(u,$product(v,z))),$sum($product(3,$product(u,$product(z,z))),$sum($product(v,$product(v,v)),$sum($product(3,$product(v,$product(v,z))),$sum($product(3,$product(v,$product(z,z))),$product(z,$product(z,z)))))))))))) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( $lesseq($product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))))),$product($sum(u,$sum(v,z)),$product($sum(u,$sum(v,z)),$sum(u,$sum(v,z)))))
<=> $greatereq($sum($product(u,$product(u,u)),$sum($product(3,$product(u,$product(u,v))),$sum($product(3,$product(u,$product(v,v))),$sum($product(3,$product(u,$product(u,z))),$sum($product(6,$product(u,$product(v,z))),$sum($product(3,$product(u,$product(z,z))),$sum($product(v,$product(v,v)),$sum($product(3,$product(v,$product(v,z))),$sum($product(3,$product(v,$product(z,z))),$sum($product(z,$product(z,z)),$product(-1,$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w)))))))))))))))))),0) ),
inference(transitivity,[status(thm)],[24,1]) ).
tff(26,plain,
( ~ ~ $lesseq($product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))))),$product($sum(u,$sum(v,z)),$product($sum(u,$sum(v,z)),$sum(u,$sum(v,z)))))
<=> $lesseq($product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))))),$product($sum(u,$sum(v,z)),$product($sum(u,$sum(v,z)),$sum(u,$sum(v,z))))) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( $less($product($sum(u,$sum(v,z)),$product($sum(u,$sum(v,z)),$sum(u,$sum(v,z)))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))))))
<=> ~ $lesseq($product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))))),$product($sum(u,$sum(v,z)),$product($sum(u,$sum(v,z)),$sum(u,$sum(v,z))))) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
$product($product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w)))))),$sum(1,$sum(u,$sum(v,w)))) = $product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))))),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
$sum($sum(u,$sum(v,w)),1) = $sum(1,$sum(u,$sum(v,w))),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
$sum($sum(u,v),w) = $sum(u,$sum(v,w)),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
$sum($sum($sum(u,v),w),1) = $sum($sum(u,$sum(v,w)),1),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
$sum($sum($sum(u,v),w),1) = $sum(1,$sum(u,$sum(v,w))),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
$product($product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))),$sum(1,$sum(u,$sum(v,w)))) = $product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w)))))),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
$product($product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w)))),$sum(1,$sum(u,$sum(v,w)))) = $product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
$product($sum($sum($sum(u,v),w),1),$sum($sum($sum(u,v),w),1)) = $product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w)))),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
$product($product($sum($sum($sum(u,v),w),1),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)) = $product($product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w)))),$sum(1,$sum(u,$sum(v,w)))),
inference(monotonicity,[status(thm)],[35,32]) ).
tff(37,plain,
$product($product($sum($sum($sum(u,v),w),1),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)) = $product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
$product($product($product($sum($sum($sum(u,v),w),1),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)) = $product($product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))),$sum(1,$sum(u,$sum(v,w)))),
inference(monotonicity,[status(thm)],[37,32]) ).
tff(39,plain,
$product($product($product($sum($sum($sum(u,v),w),1),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)) = $product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w)))))),
inference(transitivity,[status(thm)],[38,33]) ).
tff(40,plain,
$product($product($product($product($sum($sum($sum(u,v),w),1),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)) = $product($product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w)))))),$sum(1,$sum(u,$sum(v,w)))),
inference(monotonicity,[status(thm)],[39,32]) ).
tff(41,plain,
$product($product($product($product($sum($sum($sum(u,v),w),1),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)) = $product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))))),
inference(transitivity,[status(thm)],[40,28]) ).
tff(42,plain,
$product($product($sum(u,$sum(v,z)),$sum(u,$sum(v,z))),$sum(u,$sum(v,z))) = $product($sum(u,$sum(v,z)),$product($sum(u,$sum(v,z)),$sum(u,$sum(v,z)))),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
$sum($sum(u,v),z) = $sum(u,$sum(v,z)),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
$product($sum($sum(u,v),z),$sum($sum(u,v),z)) = $product($sum(u,$sum(v,z)),$sum(u,$sum(v,z))),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
$product($product($sum($sum(u,v),z),$sum($sum(u,v),z)),$sum($sum(u,v),z)) = $product($product($sum(u,$sum(v,z)),$sum(u,$sum(v,z))),$sum(u,$sum(v,z))),
inference(monotonicity,[status(thm)],[44,43]) ).
tff(46,plain,
$product($product($sum($sum(u,v),z),$sum($sum(u,v),z)),$sum($sum(u,v),z)) = $product($sum(u,$sum(v,z)),$product($sum(u,$sum(v,z)),$sum(u,$sum(v,z)))),
inference(transitivity,[status(thm)],[45,42]) ).
tff(47,plain,
( $less($product($product($sum($sum(u,v),z),$sum($sum(u,v),z)),$sum($sum(u,v),z)),$product($product($product($product($sum($sum($sum(u,v),w),1),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)))
<=> $less($product($sum(u,$sum(v,z)),$product($sum(u,$sum(v,z)),$sum(u,$sum(v,z)))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w)))))))) ),
inference(monotonicity,[status(thm)],[46,41]) ).
tff(48,plain,
( $less($product($product($sum($sum(u,v),z),$sum($sum(u,v),z)),$sum($sum(u,v),z)),$product($product($product($product($sum($sum($sum(u,v),w),1),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)))
<=> ~ $lesseq($product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))))),$product($sum(u,$sum(v,z)),$product($sum(u,$sum(v,z)),$sum(u,$sum(v,z))))) ),
inference(transitivity,[status(thm)],[47,27]) ).
tff(49,plain,
( ~ $less($product($product($sum($sum(u,v),z),$sum($sum(u,v),z)),$sum($sum(u,v),z)),$product($product($product($product($sum($sum($sum(u,v),w),1),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)))
<=> ~ ~ $lesseq($product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))))),$product($sum(u,$sum(v,z)),$product($sum(u,$sum(v,z)),$sum(u,$sum(v,z))))) ),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
( ~ $less($product($product($sum($sum(u,v),z),$sum($sum(u,v),z)),$sum($sum(u,v),z)),$product($product($product($product($sum($sum($sum(u,v),w),1),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)))
<=> $lesseq($product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))))),$product($sum(u,$sum(v,z)),$product($sum(u,$sum(v,z)),$sum(u,$sum(v,z))))) ),
inference(transitivity,[status(thm)],[49,26]) ).
tff(51,axiom,
~ $less($product($product($sum($sum(u,v),z),$sum($sum(u,v),z)),$sum($sum(u,v),z)),$product($product($product($product($sum($sum($sum(u,v),w),1),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1)),$sum($sum($sum(u,v),w),1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion) ).
tff(52,plain,
$lesseq($product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w))))))),$product($sum(u,$sum(v,z)),$product($sum(u,$sum(v,z)),$sum(u,$sum(v,z))))),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
$greatereq($sum($product(u,$product(u,u)),$sum($product(3,$product(u,$product(u,v))),$sum($product(3,$product(u,$product(v,v))),$sum($product(3,$product(u,$product(u,z))),$sum($product(6,$product(u,$product(v,z))),$sum($product(3,$product(u,$product(z,z))),$sum($product(v,$product(v,v)),$sum($product(3,$product(v,$product(v,z))),$sum($product(3,$product(v,$product(z,z))),$sum($product(z,$product(z,z)),$product(-1,$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w)))))))))))))))))),0),
inference(modus_ponens,[status(thm)],[52,25]) ).
tff(54,plain,
( ~ $lesseq(w,$sum(1,z))
<=> ~ $greatereq($sum(z,$product(-1,w)),-1) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( $less($sum(1,z),w)
<=> ~ $lesseq(w,$sum(1,z)) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
$less($sum(1,z),w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_03) ).
tff(57,plain,
~ $lesseq(w,$sum(1,z)),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
~ $greatereq($sum(z,$product(-1,w)),-1),
inference(modus_ponens,[status(thm)],[57,54]) ).
tff(59,plain,
( $greater(z,0)
<=> ~ $lesseq(z,0) ),
inference(rewrite,[status(thm)],]) ).
tff(60,axiom,
$greater(z,0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_02) ).
tff(61,plain,
~ $lesseq(z,0),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
( ~ $lesseq(v,u)
<=> ~ $greatereq($sum(u,$product(-1,v)),0) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( $less(u,v)
<=> ~ $lesseq(v,u) ),
inference(rewrite,[status(thm)],]) ).
tff(64,axiom,
$less(u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis_01) ).
tff(65,plain,
~ $lesseq(v,u),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
~ $greatereq($sum(u,$product(-1,v)),0),
inference(modus_ponens,[status(thm)],[65,62]) ).
tff(67,plain,
( $greater(u,0)
<=> ~ $lesseq(u,0) ),
inference(rewrite,[status(thm)],]) ).
tff(68,axiom,
$greater(u,0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis) ).
tff(69,plain,
~ $lesseq(u,0),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
( ~ $greatereq($sum($product(u,$product(u,u)),$sum($product(3,$product(u,$product(u,v))),$sum($product(3,$product(u,$product(v,v))),$sum($product(3,$product(u,$product(u,z))),$sum($product(6,$product(u,$product(v,z))),$sum($product(3,$product(u,$product(z,z))),$sum($product(v,$product(v,v)),$sum($product(3,$product(v,$product(v,z))),$sum($product(3,$product(v,$product(z,z))),$sum($product(z,$product(z,z)),$product(-1,$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$product($sum(1,$sum(u,$sum(v,w))),$sum(1,$sum(u,$sum(v,w)))))))))))))))))),0)
| $lesseq(u,0)
| $greatereq($sum(u,$product(-1,v)),0)
| $lesseq(z,0)
| $greatereq($sum(z,$product(-1,w)),-1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(71,plain,
$false,
inference(unit_resolution,[status(thm)],[70,69,66,61,58,53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ARI631_1 : TPTP v8.1.0. Released v6.3.0.
% 0.00/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n025.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Aug 30 01:14:44 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 0.15/0.37 % SZS status Theorem
% 0.15/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------