TSTP Solution File: SYN009-4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN009-4 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 : Thu Sep 29 23:53:09 EDT 2022
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 43
% Syntax : Number of formulae : 89 ( 19 unt; 7 typ; 0 def)
% Number of atoms : 649 ( 0 equ)
% Maximal formula atoms : 22 ( 7 avg)
% Number of connectives : 964 ( 437 ~; 474 |; 0 &)
% ( 53 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 40 ( 40 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 6 >; 10 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 279 ( 249 !; 0 ?; 279 :)
% Comments :
%------------------------------------------------------------------------------
tff(q_type,type,
q: ( $i * $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(m_type,type,
m: ( $i * $i * $i ) > $o ).
tff(s_type,type,
s: $i > $o ).
tff(n_type,type,
n: ( $i * $i * $i ) > $o ).
tff(p_type,type,
p: ( $i * $i * $i ) > $o ).
tff(r_type,type,
r: ( $i * $i * $i ) > $o ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
<=> ( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z) )
<=> ( ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| m(X,Y,Z) )
<=> ( ~ s(Z)
| ~ s(Y)
| ~ s(X)
| m(X,Y,Z) ) )),
rewrite(
( ( ~ s(Z)
| ~ s(Y)
| ~ s(X)
| m(X,Y,Z) )
<=> ( m(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| m(X,Y,Z) )
<=> ( m(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| m(X,Y,Z)
| n(X,Y,Z) )
<=> ( m(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X)
| n(X,Y,Z) ) )),
rewrite(
( ( m(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X)
| n(X,Y,Z) )
<=> ( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| m(X,Y,Z)
| n(X,Y,Z) )
<=> ( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| m(X,Y,Z)
| n(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| m(X,Y,Z)
| n(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ n(c,c,c)
<=> ~ n(c,c,c) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
~ n(c,c,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
tff(13,plain,
~ n(c,c,c),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( s(c)
<=> s(c) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
s(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
tff(16,plain,
s(c),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| n(c,c,c)
| m(c,c,c)
| ~ s(c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| n(c,c,c)
| m(c,c,c)
| ~ s(c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( m(c,c,c)
| n(c,c,c)
| ~ s(c)
| ~ s(c)
| ~ s(c) )
<=> ( n(c,c,c)
| m(c,c,c)
| ~ s(c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| m(c,c,c)
| n(c,c,c)
| ~ s(c)
| ~ s(c)
| ~ s(c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| n(c,c,c)
| m(c,c,c)
| ~ s(c) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| m(c,c,c)
| n(c,c,c)
| ~ s(c)
| ~ s(c)
| ~ s(c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| n(c,c,c)
| m(c,c,c)
| ~ s(c) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| m(c,c,c)
| n(c,c,c)
| ~ s(c)
| ~ s(c)
| ~ s(c) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( m(X,Y,Z)
| n(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| n(c,c,c)
| m(c,c,c)
| ~ s(c) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
m(c,c,c),
inference(unit_resolution,[status(thm)],[22,16,13,10]) ).
tff(24,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ m(X,Y,Z)
| ~ q(X,Y,Z) )
<=> ( ~ m(X,Y,Z)
| ~ q(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ q(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ q(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ q(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ q(X,Y,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(
( ( ~ q(X,Y,Z)
| ~ m(X,Y,Z) )
<=> ( ~ m(X,Y,Z)
| ~ q(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ q(X,Y,Z)
| ~ m(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ q(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ q(X,Y,Z)
| ~ m(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
tff(30,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ q(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ q(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ q(X,Y,Z) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ q(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ q(X,Y,Z) )
| ~ m(c,c,c)
| ~ q(c,c,c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ q(X,Y,Z) )
| ~ m(c,c,c)
| ~ q(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ q(X,Y,Z) )
| ~ m(c,c,c)
| ~ q(c,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ q(X,Y,Z) )
| ~ m(c,c,c)
| ~ q(c,c,c) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
~ q(c,c,c),
inference(unit_resolution,[status(thm)],[36,33,23]) ).
tff(38,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ m(X,Y,Z)
| ~ p(X,Y,Z) )
<=> ( ~ m(X,Y,Z)
| ~ p(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ p(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ p(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ p(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ p(X,Y,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(
( ( ~ p(X,Y,Z)
| ~ m(X,Y,Z) )
<=> ( ~ m(X,Y,Z)
| ~ p(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ p(X,Y,Z)
| ~ m(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ p(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ p(X,Y,Z)
| ~ m(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
tff(44,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ p(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ p(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ p(X,Y,Z) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ p(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ p(X,Y,Z) )
| ~ m(c,c,c)
| ~ p(c,c,c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ p(X,Y,Z) )
| ~ m(c,c,c)
| ~ p(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ p(X,Y,Z) )
| ~ m(c,c,c)
| ~ p(c,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ p(X,Y,Z) )
| ~ m(c,c,c)
| ~ p(c,c,c) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
~ p(c,c,c),
inference(unit_resolution,[status(thm)],[50,47,23]) ).
tff(52,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ m(X,Y,Z)
| ~ r(X,Y,Z) )
<=> ( ~ m(X,Y,Z)
| ~ r(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ r(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ r(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ r(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ r(X,Y,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(
( ( ~ r(X,Y,Z)
| ~ m(X,Y,Z) )
<=> ( ~ m(X,Y,Z)
| ~ r(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ r(X,Y,Z)
| ~ m(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ r(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ r(X,Y,Z)
| ~ m(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
tff(58,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ r(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ r(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ r(X,Y,Z) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ r(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ r(X,Y,Z) )
| ~ m(c,c,c)
| ~ r(c,c,c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ r(X,Y,Z) )
| ~ m(c,c,c)
| ~ r(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ r(X,Y,Z) )
| ~ m(c,c,c)
| ~ r(c,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ m(X,Y,Z)
| ~ r(X,Y,Z) )
| ~ m(c,c,c)
| ~ r(c,c,c) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
~ r(c,c,c),
inference(unit_resolution,[status(thm)],[64,61,23]) ).
tff(66,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
<=> ( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z) )
<=> ( ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| p(X,Y,Z) )
<=> ( ~ s(Z)
| ~ s(Y)
| ~ s(X)
| p(X,Y,Z) ) )),
rewrite(
( ( ~ s(Z)
| ~ s(Y)
| ~ s(X)
| p(X,Y,Z) )
<=> ( p(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| p(X,Y,Z) )
<=> ( p(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| p(X,Y,Z)
| q(X,Y,Z) )
<=> ( p(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X)
| q(X,Y,Z) ) )),
rewrite(
( ( p(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X)
| q(X,Y,Z) )
<=> ( p(X,Y,Z)
| q(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| p(X,Y,Z)
| q(X,Y,Z) )
<=> ( p(X,Y,Z)
| q(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z) )
<=> ( p(X,Y,Z)
| q(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X)
| r(X,Y,Z) ) )),
rewrite(
( ( p(X,Y,Z)
| q(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X)
| r(X,Y,Z) )
<=> ( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
( ( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z) )
<=> ( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ s(X)
| ~ s(Y)
| ~ s(Z)
| p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
tff(72,plain,
! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| ~ s(c)
| r(c,c,c)
| p(c,c,c)
| q(c,c,c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| ~ s(c)
| r(c,c,c)
| p(c,c,c)
| q(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ( p(c,c,c)
| q(c,c,c)
| r(c,c,c)
| ~ s(c)
| ~ s(c)
| ~ s(c) )
<=> ( ~ s(c)
| r(c,c,c)
| p(c,c,c)
| q(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| p(c,c,c)
| q(c,c,c)
| r(c,c,c)
| ~ s(c)
| ~ s(c)
| ~ s(c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| ~ s(c)
| r(c,c,c)
| p(c,c,c)
| q(c,c,c) ) ),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| p(c,c,c)
| q(c,c,c)
| r(c,c,c)
| ~ s(c)
| ~ s(c)
| ~ s(c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| ~ s(c)
| r(c,c,c)
| p(c,c,c)
| q(c,c,c) ) ),
inference(transitivity,[status(thm)],[78,76]) ).
tff(80,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| p(c,c,c)
| q(c,c,c)
| r(c,c,c)
| ~ s(c)
| ~ s(c)
| ~ s(c) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( p(X,Y,Z)
| q(X,Y,Z)
| r(X,Y,Z)
| ~ s(Z)
| ~ s(Y)
| ~ s(X) )
| ~ s(c)
| r(c,c,c)
| p(c,c,c)
| q(c,c,c) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
$false,
inference(unit_resolution,[status(thm)],[81,16,75,65,51,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN009-4 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 00:57:34 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------