TSTP Solution File: NUM341+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM341+1 : TPTP v8.1.0. Released v3.1.0.
% 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 : Sun Sep 18 13:03:34 EDT 2022
% Result : Theorem 15.50s 10.26s
% Output : Proof 15.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 43
% Syntax : Number of formulae : 87 ( 17 unt; 13 typ; 0 def)
% Number of atoms : 339 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 411 ( 174 ~; 105 |; 38 &)
% ( 91 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 28 ( 28 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 7 >; 6 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 174 ( 120 !; 30 ?; 174 :)
% Comments :
%------------------------------------------------------------------------------
tff(difference_type,type,
difference: ( $i * $i * $i ) > $o ).
tff(n126_type,type,
n126: $i ).
tff(nn126_type,type,
nn126: $i ).
tff(n0_type,type,
n0: $i ).
tff(sum_type,type,
sum: ( $i * $i * $i ) > $o ).
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(rdn_type,type,
rdn: ( $i * $i ) > $i ).
tff(rdnn_type,type,
rdnn: $i > $i ).
tff(n1_type,type,
n1: $i ).
tff(n2_type,type,
n2: $i ).
tff(n6_type,type,
n6: $i ).
tff(1,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(
( ( sum(Y,Z,X)
<=> difference(X,Y,Z) )
<=> ( sum(Y,Z,X)
<=> difference(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i,Y: $i,Z: $i] :
( sum(Y,Z,X)
<=> difference(X,Y,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( sum(Y,Z,X)
<=> difference(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i,Y: $i,Z: $i] :
( sum(Y,Z,X)
<=> difference(X,Y,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( sum(Y,Z,X)
<=> difference(X,Y,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i,Y: $i,Z: $i] :
( sum(Y,Z,X)
<=> difference(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',minus_entry_point) ).
tff(5,plain,
! [X: $i,Y: $i,Z: $i] :
( sum(Y,Z,X)
<=> difference(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i,Y: $i,Z: $i] :
( sum(Y,Z,X)
<=> difference(X,Y,Z) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i,Y: $i,Z: $i] :
( sum(Y,Z,X)
<=> difference(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( sum(Y,Z,X)
<=> difference(X,Y,Z) )
| ( sum(nn126,n126,n0)
<=> difference(n0,nn126,n126) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
( sum(nn126,n126,n0)
<=> difference(n0,nn126,n126) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(
( ( sum(X,Y,Z)
<=> ( ~ difference(Z,Y,X)
| ~ difference(Z,X,Y) ) )
<=> ( sum(X,Y,Z)
<=> ( ~ difference(Z,Y,X)
| ~ difference(Z,X,Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( ~ difference(Z,Y,X)
| ~ difference(Z,X,Y) ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( ~ difference(Z,Y,X)
| ~ difference(Z,X,Y) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(
monotonicity(
rewrite(
( ( difference(Z,Y,X)
& difference(Z,X,Y) )
<=> ~ ( ~ difference(Z,Y,X)
| ~ difference(Z,X,Y) ) )),
( ( ~ sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) )
<=> ( ~ sum(X,Y,Z)
<=> ~ ( ~ difference(Z,Y,X)
| ~ difference(Z,X,Y) ) ) )),
rewrite(
( ( ~ sum(X,Y,Z)
<=> ~ ( ~ difference(Z,Y,X)
| ~ difference(Z,X,Y) ) )
<=> ( sum(X,Y,Z)
<=> ( ~ difference(Z,Y,X)
| ~ difference(Z,X,Y) ) ) )),
( ( ~ sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) )
<=> ( sum(X,Y,Z)
<=> ( ~ difference(Z,Y,X)
| ~ difference(Z,X,Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( ~ difference(Z,Y,X)
| ~ difference(Z,X,Y) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(
( ~ ( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) )
<=> ( ~ sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [X: $i,Y: $i,Z: $i] :
~ ( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ~ ? [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) )
<=> ~ ? [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
~ ? [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_same_as_subtract) ).
tff(18,plain,
~ ? [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
~ ? [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ),
inference(modus_ponens,[status(thm)],[18,16]) ).
tff(20,plain,
~ ? [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ),
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
~ ? [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
~ ? [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ),
inference(modus_ponens,[status(thm)],[21,16]) ).
tff(23,plain,
~ ? [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ),
inference(modus_ponens,[status(thm)],[22,16]) ).
tff(24,plain,
~ ? [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(
$oeq(
~ ( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ),
~ ( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ))),
inference(bind,[status(th)],]) ).
tff(26,plain,
! [X: $i,Y: $i,Z: $i] :
~ ( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ),
inference(nnf-neg,[status(sab)],[24,25]) ).
tff(27,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ),
inference(modus_ponens,[status(thm)],[26,15]) ).
tff(28,plain,
! [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( ~ difference(Z,Y,X)
| ~ difference(Z,X,Y) ) ),
inference(modus_ponens,[status(thm)],[27,13]) ).
tff(29,plain,
! [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( ~ difference(Z,Y,X)
| ~ difference(Z,X,Y) ) ),
inference(modus_ponens,[status(thm)],[28,11]) ).
tff(30,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( ~ difference(Z,Y,X)
| ~ difference(Z,X,Y) ) )
| ( sum(nn126,n126,n0)
<=> ( ~ difference(n0,n126,nn126)
| ~ difference(n0,nn126,n126) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( sum(nn126,n126,n0)
<=> ( ~ difference(n0,n126,nn126)
| ~ difference(n0,nn126,n126) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( sum(X,Y,Z)
<=> ( ~ difference(Z,Y,X)
| ~ difference(Z,X,Y) ) )
| ( sum(n126,nn126,n0)
<=> ( ~ difference(n0,nn126,n126)
| ~ difference(n0,n126,nn126) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( sum(n126,nn126,n0)
<=> ( ~ difference(n0,nn126,n126)
| ~ difference(n0,n126,nn126) ) ),
inference(unit_resolution,[status(thm)],[32,29]) ).
tff(34,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(35,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)],[34]) ).
tff(36,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(37,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)],[36]) ).
tff(38,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(39,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(40,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)],[39]) ).
tff(41,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/sandbox2/benchmark/Axioms/NUM005+2.ax',sum_entry_point_posx_negx) ).
tff(42,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)],[41,40]) ).
tff(43,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)],[42,38]) ).
tff(44,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)],[43]) ).
tff(45,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)],[44,37]) ).
tff(46,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)],[45,35]) ).
tff(47,plain,
( rdn_translate(nn126,rdn_neg(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1)))))
<=> rdn_translate(nn126,rdn_neg(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1))))) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
rdn_translate(nn126,rdn_neg(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1))))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdnn126) ).
tff(49,plain,
rdn_translate(nn126,rdn_neg(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1))))),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
( rdn_translate(n126,rdn_pos(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1)))))
<=> rdn_translate(n126,rdn_pos(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1))))) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
rdn_translate(n126,rdn_pos(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1))))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn126) ).
tff(52,plain,
rdn_translate(n126,rdn_pos(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1))))),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,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(n126,nn126,n0)
| ~ rdn_translate(n126,rdn_pos(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1)))))
| ~ rdn_translate(nn126,rdn_neg(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1))))) )
<=> ( ~ ! [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(n126,nn126,n0)
| ~ rdn_translate(n126,rdn_pos(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1)))))
| ~ rdn_translate(nn126,rdn_neg(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,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(n126,nn126,n0)
| ~ rdn_translate(n126,rdn_pos(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1)))))
| ~ rdn_translate(nn126,rdn_neg(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,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(n126,nn126,n0)
| ~ rdn_translate(n126,rdn_pos(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1)))))
| ~ rdn_translate(nn126,rdn_neg(rdn(rdnn(n6),rdn(rdnn(n2),rdnn(n1))))) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
sum(n126,nn126,n0),
inference(unit_resolution,[status(thm)],[55,52,49,46]) ).
tff(57,plain,
( ~ ( sum(n126,nn126,n0)
<=> ( ~ difference(n0,nn126,n126)
| ~ difference(n0,n126,nn126) ) )
| ~ sum(n126,nn126,n0)
| ~ difference(n0,nn126,n126)
| ~ difference(n0,n126,nn126) ),
inference(tautology,[status(thm)],]) ).
tff(58,plain,
( ~ ( sum(n126,nn126,n0)
<=> ( ~ difference(n0,nn126,n126)
| ~ difference(n0,n126,nn126) ) )
| ~ difference(n0,nn126,n126)
| ~ difference(n0,n126,nn126) ),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
( ~ difference(n0,nn126,n126)
| ~ difference(n0,n126,nn126) ),
inference(unit_resolution,[status(thm)],[58,33]) ).
tff(60,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( sum(Y,Z,X)
<=> difference(X,Y,Z) )
| ( sum(n126,nn126,n0)
<=> difference(n0,n126,nn126) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( sum(n126,nn126,n0)
<=> difference(n0,n126,nn126) ),
inference(unit_resolution,[status(thm)],[60,7]) ).
tff(62,plain,
( ~ ( sum(n126,nn126,n0)
<=> difference(n0,n126,nn126) )
| ~ sum(n126,nn126,n0)
| difference(n0,n126,nn126) ),
inference(tautology,[status(thm)],]) ).
tff(63,plain,
( ~ ( sum(n126,nn126,n0)
<=> difference(n0,n126,nn126) )
| difference(n0,n126,nn126) ),
inference(unit_resolution,[status(thm)],[62,56]) ).
tff(64,plain,
difference(n0,n126,nn126),
inference(unit_resolution,[status(thm)],[63,61]) ).
tff(65,plain,
( ~ ( ~ difference(n0,nn126,n126)
| ~ difference(n0,n126,nn126) )
| ~ difference(n0,nn126,n126)
| ~ difference(n0,n126,nn126) ),
inference(tautology,[status(thm)],]) ).
tff(66,plain,
~ difference(n0,nn126,n126),
inference(unit_resolution,[status(thm)],[65,64,59]) ).
tff(67,plain,
( ~ difference(n0,n126,nn126)
| ~ difference(n0,nn126,n126)
| difference(n0,nn126,n126) ),
inference(tautology,[status(thm)],]) ).
tff(68,plain,
( ~ difference(n0,n126,nn126)
| ~ difference(n0,nn126,n126) ),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
( ~ ( sum(nn126,n126,n0)
<=> ( ~ difference(n0,n126,nn126)
| ~ difference(n0,nn126,n126) ) )
| sum(nn126,n126,n0)
| ~ ( ~ difference(n0,n126,nn126)
| ~ difference(n0,nn126,n126) ) ),
inference(tautology,[status(thm)],]) ).
tff(70,plain,
( ~ ( sum(nn126,n126,n0)
<=> ( ~ difference(n0,n126,nn126)
| ~ difference(n0,nn126,n126) ) )
| sum(nn126,n126,n0) ),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
sum(nn126,n126,n0),
inference(unit_resolution,[status(thm)],[70,31]) ).
tff(72,plain,
( ~ ( sum(nn126,n126,n0)
<=> difference(n0,nn126,n126) )
| ~ sum(nn126,n126,n0)
| difference(n0,nn126,n126) ),
inference(tautology,[status(thm)],]) ).
tff(73,plain,
( ~ ( sum(nn126,n126,n0)
<=> difference(n0,nn126,n126) )
| ~ sum(nn126,n126,n0) ),
inference(unit_resolution,[status(thm)],[72,66]) ).
tff(74,plain,
$false,
inference(unit_resolution,[status(thm)],[73,71,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM341+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 09:46:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 15.50/10.26 % SZS status Theorem
% 15.50/10.26 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------