%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM318+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:19:02 AM UTC 2025
% Result : Theorem 34.26s 34.47s
% Output : Proof 34.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 26 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 134 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 166 ( 73 ~; 57 |; 16 &)
% ( 17 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 63 ( 54 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
tff(n0_type,type,
n0: $i ).
tff(nn5_type,type,
nn5: $i ).
tff(n5_type,type,
n5: $i ).
tff(rdn_translate_type,type,
rdn_translate: ( $i * $i ) > $o ).
tff(rdn_neg_type,type,
rdn_neg: $i > $i ).
tff(rdn_pos_type,type,
rdn_pos: $i > $i ).
tff(rdnn_type,type,
rdnn: $i > $i ).
tff(1,plain,
( ~ sum(n5,nn5,n0)
<=> ~ sum(n5,nn5,n0) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ sum(n5,nn5,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n5_nn5_n0) ).
tff(3,plain,
~ sum(n5,nn5,n0),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [POS_X: $i,NEG_X: $i,RDN_X: $i] :
refl(( ( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) )
<=> ( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) )
<=> ! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
^ [POS_X: $i,NEG_X: $i,RDN_X: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
<=> ~ ( ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) ) )),
( ~ ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
<=> ~ ~ ( ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) ) )),
rewrite(( ~ ~ ( ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) )
<=> ( ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) ) )),
( ~ ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
<=> ( ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) ) )),
( ( ~ ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
| sum(POS_X,NEG_X,n0) )
<=> ( ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X))
| sum(POS_X,NEG_X,n0) ) )),
rewrite(( ( ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X))
| sum(POS_X,NEG_X,n0) )
<=> ( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) ) )),
( ( ~ ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
| sum(POS_X,NEG_X,n0) )
<=> ( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( ~ ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
| sum(POS_X,NEG_X,n0) )
<=> ! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( ~ ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
| sum(POS_X,NEG_X,n0) )
<=> ! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( ~ ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
| sum(POS_X,NEG_X,n0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,plain,
^ [POS_X: $i,NEG_X: $i,RDN_X: $i] :
rewrite(( ( ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
=> sum(POS_X,NEG_X,n0) )
<=> ( ~ ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
| sum(POS_X,NEG_X,n0) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
=> sum(POS_X,NEG_X,n0) )
<=> ! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( ~ ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
| sum(POS_X,NEG_X,n0) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,axiom,
! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
=> sum(POS_X,NEG_X,n0) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',sum_entry_point_posx_negx) ).
tff(12,plain,
! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( ~ ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
| sum(POS_X,NEG_X,n0) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( ~ ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
| sum(POS_X,NEG_X,n0) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( ~ ( rdn_translate(POS_X,rdn_pos(RDN_X))
& rdn_translate(NEG_X,rdn_neg(RDN_X)) )
| sum(POS_X,NEG_X,n0) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) ),
inference(modus_ponens,[status(thm)],[15,5]) ).
tff(17,plain,
( rdn_translate(nn5,rdn_neg(rdnn(n5)))
<=> rdn_translate(nn5,rdn_neg(rdnn(n5))) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdnn5) ).
tff(19,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( rdn_translate(n5,rdn_pos(rdnn(n5)))
<=> rdn_translate(n5,rdn_pos(rdnn(n5))) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn5) ).
tff(22,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) )
| sum(n5,nn5,n0)
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| ~ rdn_translate(nn5,rdn_neg(rdnn(n5))) )
<=> ( ~ ! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) )
| sum(n5,nn5,n0)
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| ~ rdn_translate(nn5,rdn_neg(rdnn(n5))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) )
| sum(n5,nn5,n0)
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| ~ rdn_translate(nn5,rdn_neg(rdnn(n5))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [POS_X: $i,NEG_X: $i,RDN_X: $i] :
( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(POS_X,rdn_pos(RDN_X))
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X)) )
| sum(n5,nn5,n0)
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| ~ rdn_translate(nn5,rdn_neg(rdnn(n5))) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,22,19,16,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM318+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n007.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
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri Jun 20 00:51:35 EDT 2025
% 0.12/0.35 % CPUTime :
% 34.26/34.47 % SZS status Theorem
% 34.26/34.47 % SZS output start Proof
% See solution above
% 34.45/34.68 % E exiting
%------------------------------------------------------------------------------