TSTP Solution File: SYN162-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN162-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 23:54:00 EDT 2022
% Result : Unsatisfiable 0.19s 0.49s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 72
% Syntax : Number of formulae : 145 ( 27 unt; 16 typ; 0 def)
% Number of atoms : 585 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 808 ( 372 ~; 363 |; 0 &)
% ( 73 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 13 >; 12 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 2 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 250 ( 229 !; 0 ?; 250 :)
% Comments :
%------------------------------------------------------------------------------
tff(q3_type,type,
q3: ( $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(q2_type,type,
q2: ( $i * $i * $i ) > $o ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(k0_type,type,
k0: $i > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(n3_type,type,
n3: $i > $o ).
tff(c_type,type,
c: $i ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(r4_type,type,
r4: $i > $o ).
tff(n5_type,type,
n5: ( $i * $i ) > $o ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(1,plain,
^ [I: $i] :
refl(
( ( q2(I,I,I)
| ~ p1(I,I,I) )
<=> ( q2(I,I,I)
| ~ p1(I,I,I) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
<=> ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
<=> ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_181) ).
tff(5,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( p1(e,e,e)
<=> p1(e,e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
( ( $false
| $false
| p1(e,e,e) )
<=> p1(e,e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
k0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(12,plain,
( k0(e)
<=> $true ),
inference(iff_true,[status(thm)],[11]) ).
tff(13,plain,
( ~ k0(e)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ~ k0(e)
<=> $false ),
inference(transitivity,[status(thm)],[13,10]) ).
tff(15,axiom,
r0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_13) ).
tff(16,plain,
( r0(e)
<=> $true ),
inference(iff_true,[status(thm)],[15]) ).
tff(17,plain,
( ~ r0(e)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ~ r0(e)
<=> $false ),
inference(transitivity,[status(thm)],[17,10]) ).
tff(19,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> ( $false
| $false
| p1(e,e,e) ) ),
inference(monotonicity,[status(thm)],[18,14]) ).
tff(20,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> p1(e,e,e) ),
inference(transitivity,[status(thm)],[19,9]) ).
tff(21,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( p1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,axiom,
( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_090) ).
tff(27,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[27,21]) ).
tff(29,plain,
p1(e,e,e),
inference(modus_ponens,[status(thm)],[28,20]) ).
tff(30,plain,
p1(e,e,e),
inference(modus_ponens,[status(thm)],[29,8]) ).
tff(31,plain,
( ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) )
<=> ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( q2(e,e,e)
| ~ p1(e,e,e) )
<=> ( ~ p1(e,e,e)
| q2(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| q2(e,e,e)
| ~ p1(e,e,e) )
<=> ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| q2(e,e,e)
| ~ p1(e,e,e) )
<=> ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| q2(e,e,e)
| ~ p1(e,e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
q2(e,e,e),
inference(unit_resolution,[status(thm)],[36,30,7]) ).
tff(38,plain,
^ [I: $i,H: $i,G: $i] :
refl(
( ( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
<=> ( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
<=> ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
<=> ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
^ [I: $i,H: $i,G: $i] :
trans(
monotonicity(
rewrite(
( ( q3(G,H)
| ~ q2(I,G,H) )
<=> ( ~ q2(I,G,H)
| q3(G,H) ) )),
( ( q3(G,H)
| ~ q2(I,G,H)
| ~ n0(I,G) )
<=> ( ~ q2(I,G,H)
| q3(G,H)
| ~ n0(I,G) ) )),
rewrite(
( ( ~ q2(I,G,H)
| q3(G,H)
| ~ n0(I,G) )
<=> ( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) )),
( ( q3(G,H)
| ~ q2(I,G,H)
| ~ n0(I,G) )
<=> ( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [I: $i,H: $i,G: $i] :
( q3(G,H)
| ~ q2(I,G,H)
| ~ n0(I,G) )
<=> ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [I: $i,H: $i,G: $i] :
( q3(G,H)
| ~ q2(I,G,H)
| ~ n0(I,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_255) ).
tff(44,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( n0(e,e)
<=> n0(e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
n0(e,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_30) ).
tff(50,plain,
n0(e,e),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( ~ q2(e,e,e)
| ~ n0(e,e)
| q3(e,e) )
<=> ( q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,e)
| ~ n0(e,e)
| q3(e,e) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,e)
| ~ n0(e,e)
| q3(e,e) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,e)
| ~ n0(e,e)
| q3(e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
q3(e,e),
inference(unit_resolution,[status(thm)],[56,50,47,37]) ).
tff(58,plain,
^ [D: $i,E: $i] :
refl(
( ( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ( p2(D,E,D)
| ~ m1(E,D,E) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,axiom,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_176) ).
tff(62,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
( m1(c,c,c)
<=> m1(c,c,c) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ( $false
| m1(c,c,c) )
<=> m1(c,c,c) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
l0(c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_24) ).
tff(68,plain,
( l0(c)
<=> $true ),
inference(iff_true,[status(thm)],[67]) ).
tff(69,plain,
( ~ l0(c)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ~ l0(c)
<=> $false ),
inference(transitivity,[status(thm)],[69,10]) ).
tff(71,plain,
( ( ~ l0(c)
| m1(c,c,c) )
<=> ( $false
| m1(c,c,c) ) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( ( ~ l0(c)
| m1(c,c,c) )
<=> m1(c,c,c) ),
inference(transitivity,[status(thm)],[71,66]) ).
tff(73,plain,
( ( m1(c,c,c)
| ~ l0(c) )
<=> ( ~ l0(c)
| m1(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
( m1(c,c,c)
| ~ l0(c) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_020) ).
tff(75,plain,
( ~ l0(c)
| m1(c,c,c) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
m1(c,c,c),
inference(modus_ponens,[status(thm)],[75,72]) ).
tff(77,plain,
m1(c,c,c),
inference(modus_ponens,[status(thm)],[76,65]) ).
tff(78,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ( p2(c,c,c)
| ~ m1(c,c,c) )
<=> ( ~ m1(c,c,c)
| p2(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,c,c)
| ~ m1(c,c,c) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) ) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,c,c)
| ~ m1(c,c,c) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) ) ),
inference(transitivity,[status(thm)],[80,78]) ).
tff(82,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,c,c)
| ~ m1(c,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(c,c,c)
| p2(c,c,c) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
p2(c,c,c),
inference(unit_resolution,[status(thm)],[83,77,64]) ).
tff(85,plain,
^ [D: $i,E: $i,F: $i] :
refl(
( ( n3(D)
| ~ p2(E,F,D) )
<=> ( n3(D)
| ~ p2(E,F,D) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
<=> ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
<=> ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,axiom,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_240) ).
tff(89,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(c)
| ~ p2(c,c,c) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(c)
| ~ p2(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(c)
| ~ p2(c,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(94,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(c)
| ~ p2(c,c,c) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
n3(c),
inference(unit_resolution,[status(thm)],[94,91,84]) ).
tff(96,plain,
( ~ n5(c,c)
<=> ~ n5(c,c) ),
inference(rewrite,[status(thm)],]) ).
tff(97,axiom,
~ n5(c,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(98,plain,
~ n5(c,c),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
^ [B: $i] :
refl(
( ( n5(B,B)
| ~ r4(B) )
<=> ( n5(B,B)
| ~ r4(B) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [B: $i] :
( n5(B,B)
| ~ r4(B) )
<=> ! [B: $i] :
( n5(B,B)
| ~ r4(B) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [B: $i] :
( n5(B,B)
| ~ r4(B) )
<=> ! [B: $i] :
( n5(B,B)
| ~ r4(B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,axiom,
! [B: $i] :
( n5(B,B)
| ~ r4(B) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_314) ).
tff(103,plain,
! [B: $i] :
( n5(B,B)
| ~ r4(B) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
! [B: $i] :
( n5(B,B)
| ~ r4(B) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [B: $i] :
( n5(B,B)
| ~ r4(B) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
( ( ~ ! [B: $i] :
( n5(B,B)
| ~ r4(B) )
| n5(c,c)
| ~ r4(c) )
<=> ( ~ ! [B: $i] :
( n5(B,B)
| ~ r4(B) )
| n5(c,c)
| ~ r4(c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ~ ! [B: $i] :
( n5(B,B)
| ~ r4(B) )
| n5(c,c)
| ~ r4(c) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
( ~ ! [B: $i] :
( n5(B,B)
| ~ r4(B) )
| n5(c,c)
| ~ r4(c) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
~ r4(c),
inference(unit_resolution,[status(thm)],[108,105,98]) ).
tff(110,plain,
^ [I: $i,J: $i,H: $i,G: $i] :
refl(
( ( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
<=> ( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) )),
inference(bind,[status(th)],]) ).
tff(111,plain,
( ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
<=> ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,plain,
( ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
<=> ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
^ [I: $i,J: $i,H: $i,G: $i] :
trans(
monotonicity(
rewrite(
( ( r4(G)
| ~ n3(G)
| ~ q3(H,I) )
<=> ( ~ n3(G)
| ~ q3(H,I)
| r4(G) ) )),
( ( r4(G)
| ~ n3(G)
| ~ q3(H,I)
| ~ p0(J,G) )
<=> ( ~ n3(G)
| ~ q3(H,I)
| r4(G)
| ~ p0(J,G) ) )),
rewrite(
( ( ~ n3(G)
| ~ q3(H,I)
| r4(G)
| ~ p0(J,G) )
<=> ( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) )),
( ( r4(G)
| ~ n3(G)
| ~ q3(H,I)
| ~ p0(J,G) )
<=> ( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [I: $i,J: $i,H: $i,G: $i] :
( r4(G)
| ~ n3(G)
| ~ q3(H,I)
| ~ p0(J,G) )
<=> ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,axiom,
! [I: $i,J: $i,H: $i,G: $i] :
( r4(G)
| ~ n3(G)
| ~ q3(H,I)
| ~ p0(J,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_298) ).
tff(116,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(modus_ponens,[status(thm)],[116,112]) ).
tff(118,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(modus_ponens,[status(thm)],[118,111]) ).
tff(120,plain,
( p0(b,c)
<=> p0(b,c) ),
inference(rewrite,[status(thm)],]) ).
tff(121,axiom,
p0(b,c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_22) ).
tff(122,plain,
p0(b,c),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
( ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,c)
| r4(c)
| ~ q3(e,e)
| ~ n3(c) )
<=> ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,c)
| r4(c)
| ~ q3(e,e)
| ~ n3(c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ( ~ p0(b,c)
| ~ n3(c)
| ~ q3(e,e)
| r4(c) )
<=> ( ~ p0(b,c)
| r4(c)
| ~ q3(e,e)
| ~ n3(c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,plain,
( ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,c)
| ~ n3(c)
| ~ q3(e,e)
| r4(c) )
<=> ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,c)
| r4(c)
| ~ q3(e,e)
| ~ n3(c) ) ),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,c)
| ~ n3(c)
| ~ q3(e,e)
| r4(c) )
<=> ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,c)
| r4(c)
| ~ q3(e,e)
| ~ n3(c) ) ),
inference(transitivity,[status(thm)],[125,123]) ).
tff(127,plain,
( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,c)
| ~ n3(c)
| ~ q3(e,e)
| r4(c) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,c)
| r4(c)
| ~ q3(e,e)
| ~ n3(c) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
$false,
inference(unit_resolution,[status(thm)],[128,122,119,109,95,57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN162-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.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 : Mon Sep 5 02:00:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.19/0.49 % SZS status Unsatisfiable
% 0.19/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------