TSTP Solution File: SYN214-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN214-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 23:54:14 EDT 2022
% Result : Unsatisfiable 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 113
% Syntax : Number of formulae : 226 ( 46 unt; 23 typ; 0 def)
% Number of atoms : 939 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1292 ( 596 ~; 588 |; 0 &)
% ( 108 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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 : 35 ( 19 >; 16 *; 0 +; 0 <<)
% Number of predicates : 25 ( 23 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 430 ( 391 !; 0 ?; 430 :)
% Comments :
%------------------------------------------------------------------------------
tff(r4_type,type,
r4: $i > $o ).
tff(d_type,type,
d: $i ).
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(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(n1_type,type,
n1: ( $i * $i * $i ) > $o ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(l4_type,type,
l4: $i > $o ).
tff(c_type,type,
c: $i ).
tff(p3_type,type,
p3: ( $i * $i * $i ) > $o ).
tff(n2_type,type,
n2: $i > $o ).
tff(k1_type,type,
k1: $i > $o ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(s5_type,type,
s5: $i > $o ).
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,F: $i] :
refl(
( ( n3(D)
| ~ p2(E,F,D) )
<=> ( n3(D)
| ~ p2(E,F,D) ) )),
inference(bind,[status(th)],]) ).
tff(59,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)],[58]) ).
tff(60,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(61,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(62,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
^ [B: $i] :
refl(
( ( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ( p2(B,B,B)
| ~ n1(d,d,B) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,axiom,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_153) ).
tff(69,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
( n1(d,d,d)
<=> n1(d,d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ( n1(d,d,d)
| $false )
<=> n1(d,d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
q0(d,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_25) ).
tff(75,plain,
( q0(d,d)
<=> $true ),
inference(iff_true,[status(thm)],[74]) ).
tff(76,plain,
( ~ q0(d,d)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( ~ q0(d,d)
<=> $false ),
inference(transitivity,[status(thm)],[76,10]) ).
tff(78,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> ( n1(d,d,d)
| $false ) ),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> n1(d,d,d) ),
inference(transitivity,[status(thm)],[78,73]) ).
tff(80,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> ( n1(d,d,d)
| ~ q0(d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,axiom,
( n1(d,d,d)
| ~ q0(d,d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_045) ).
tff(82,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[82,80]) ).
tff(84,plain,
n1(d,d,d),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
n1(d,d,d),
inference(modus_ponens,[status(thm)],[84,72]) ).
tff(86,plain,
( ( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) )
<=> ( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
p2(d,d,d),
inference(unit_resolution,[status(thm)],[88,85,71]) ).
tff(90,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(d)
| ~ p2(d,d,d) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(d)
| ~ p2(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(d)
| ~ p2(d,d,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(d)
| ~ p2(d,d,d) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
n3(d),
inference(unit_resolution,[status(thm)],[92,89,64]) ).
tff(94,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(95,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)],[94]) ).
tff(96,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(97,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(98,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)],[97]) ).
tff(99,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(100,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(modus_ponens,[status(thm)],[102,95]) ).
tff(104,plain,
( p0(b,d)
<=> p0(b,d) ),
inference(rewrite,[status(thm)],]) ).
tff(105,axiom,
p0(b,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_10) ).
tff(106,plain,
p0(b,d),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
( ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,d)
| ~ q3(e,e)
| ~ n3(d)
| r4(d) )
<=> ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,d)
| ~ q3(e,e)
| ~ n3(d)
| r4(d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ( ~ p0(b,d)
| ~ n3(d)
| ~ q3(e,e)
| r4(d) )
<=> ( ~ p0(b,d)
| ~ q3(e,e)
| ~ n3(d)
| r4(d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,d)
| ~ n3(d)
| ~ q3(e,e)
| r4(d) )
<=> ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,d)
| ~ q3(e,e)
| ~ n3(d)
| r4(d) ) ),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,d)
| ~ n3(d)
| ~ q3(e,e)
| r4(d) )
<=> ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,d)
| ~ q3(e,e)
| ~ n3(d)
| r4(d) ) ),
inference(transitivity,[status(thm)],[109,107]) ).
tff(111,plain,
( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,d)
| ~ n3(d)
| ~ q3(e,e)
| r4(d) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,d)
| ~ q3(e,e)
| ~ n3(d)
| r4(d) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
r4(d),
inference(unit_resolution,[status(thm)],[112,106,103,93,57]) ).
tff(114,plain,
^ [H: $i] :
refl(
( ( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
<=> ( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) )),
inference(bind,[status(th)],]) ).
tff(115,plain,
( ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
<=> ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,plain,
( ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
<=> ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
^ [H: $i] :
trans(
monotonicity(
rewrite(
( ( p3(H,H,H)
| ~ k1(H) )
<=> ( ~ k1(H)
| p3(H,H,H) ) )),
( ( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) )
<=> ( ~ k1(H)
| p3(H,H,H)
| ~ n2(H) ) )),
rewrite(
( ( ~ k1(H)
| p3(H,H,H)
| ~ n2(H) )
<=> ( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) )),
( ( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) )
<=> ( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) )),
inference(bind,[status(th)],]) ).
tff(118,plain,
( ! [H: $i] :
( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) )
<=> ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,axiom,
! [H: $i] :
( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_249) ).
tff(120,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[120,116]) ).
tff(122,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(skolemize,[status(sab)],[121]) ).
tff(123,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[122,115]) ).
tff(124,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( n2(A)
| ~ p1(B,C,A) )
<=> ( n2(A)
| ~ p1(B,C,A) ) )),
inference(bind,[status(th)],]) ).
tff(125,plain,
( ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
<=> ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,plain,
( ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
<=> ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,axiom,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_137) ).
tff(128,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(skolemize,[status(sab)],[128]) ).
tff(130,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[129,125]) ).
tff(131,plain,
^ [I: $i,A: $i,J: $i] :
refl(
( ( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
<=> ( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) )),
inference(bind,[status(th)],]) ).
tff(132,plain,
( ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
( ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
^ [I: $i,A: $i,J: $i] :
trans(
monotonicity(
rewrite(
( ( p1(I,I,I)
| ~ l0(I) )
<=> ( ~ l0(I)
| p1(I,I,I) ) )),
( ( p1(I,I,I)
| ~ l0(I)
| ~ m0(J,A,I) )
<=> ( ~ l0(I)
| p1(I,I,I)
| ~ m0(J,A,I) ) )),
rewrite(
( ( ~ l0(I)
| p1(I,I,I)
| ~ m0(J,A,I) )
<=> ( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) )),
( ( p1(I,I,I)
| ~ l0(I)
| ~ m0(J,A,I) )
<=> ( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) )),
inference(bind,[status(th)],]) ).
tff(135,plain,
( ! [I: $i,A: $i,J: $i] :
( p1(I,I,I)
| ~ l0(I)
| ~ m0(J,A,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) ),
inference(quant_intro,[status(thm)],[134]) ).
tff(136,axiom,
! [I: $i,A: $i,J: $i] :
( p1(I,I,I)
| ~ l0(I)
| ~ m0(J,A,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_086) ).
tff(137,plain,
! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[137,133]) ).
tff(139,plain,
! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ),
inference(skolemize,[status(sab)],[138]) ).
tff(140,plain,
! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[139,132]) ).
tff(141,plain,
( m0(e,b,c)
<=> m0(e,b,c) ),
inference(rewrite,[status(thm)],]) ).
tff(142,axiom,
m0(e,b,c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_27) ).
tff(143,plain,
m0(e,b,c),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
( l0(c)
<=> l0(c) ),
inference(rewrite,[status(thm)],]) ).
tff(145,axiom,
l0(c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_24) ).
tff(146,plain,
l0(c),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
( ( ~ ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
| ~ l0(c)
| ~ m0(e,b,c)
| p1(c,c,c) )
<=> ( ~ ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
| ~ l0(c)
| ~ m0(e,b,c)
| p1(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(148,plain,
( ~ ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
| ~ l0(c)
| ~ m0(e,b,c)
| p1(c,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
( ~ ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
| ~ l0(c)
| ~ m0(e,b,c)
| p1(c,c,c) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
p1(c,c,c),
inference(unit_resolution,[status(thm)],[149,146,143,140]) ).
tff(151,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(c)
| ~ p1(c,c,c) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(c)
| ~ p1(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(c)
| ~ p1(c,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(153,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(c)
| ~ p1(c,c,c) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
n2(c),
inference(unit_resolution,[status(thm)],[153,150,130]) ).
tff(155,plain,
^ [I: $i,J: $i] :
refl(
( ( k1(I)
| ~ n0(J,I) )
<=> ( k1(I)
| ~ n0(J,I) ) )),
inference(bind,[status(th)],]) ).
tff(156,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,axiom,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_001) ).
tff(159,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(skolemize,[status(sab)],[159]) ).
tff(161,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[160,156]) ).
tff(162,plain,
( n0(d,c)
<=> n0(d,c) ),
inference(rewrite,[status(thm)],]) ).
tff(163,axiom,
n0(d,c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_26) ).
tff(164,plain,
n0(d,c),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
( ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) )
<=> ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(166,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(167,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
k1(c),
inference(unit_resolution,[status(thm)],[167,164,161]) ).
tff(169,plain,
( ( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(c)
| ~ n2(c)
| p3(c,c,c) )
<=> ( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(c)
| ~ n2(c)
| p3(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(170,plain,
( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(c)
| ~ n2(c)
| p3(c,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(c)
| ~ n2(c)
| p3(c,c,c) ),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
p3(c,c,c),
inference(unit_resolution,[status(thm)],[171,168,154,123]) ).
tff(173,plain,
^ [B: $i,A: $i,J: $i] :
refl(
( ( l4(J)
| ~ p3(A,B,J) )
<=> ( l4(J)
| ~ p3(A,B,J) ) )),
inference(bind,[status(th)],]) ).
tff(174,plain,
( ! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) )
<=> ! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) ) ),
inference(quant_intro,[status(thm)],[173]) ).
tff(175,plain,
( ! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) )
<=> ! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) ) ),
inference(rewrite,[status(thm)],]) ).
tff(176,axiom,
! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_277) ).
tff(177,plain,
! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) ),
inference(modus_ponens,[status(thm)],[176,175]) ).
tff(178,plain,
! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) ),
inference(skolemize,[status(sab)],[177]) ).
tff(179,plain,
! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) ),
inference(modus_ponens,[status(thm)],[178,174]) ).
tff(180,plain,
( ( ~ ! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) )
| l4(c)
| ~ p3(c,c,c) )
<=> ( ~ ! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) )
| l4(c)
| ~ p3(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(181,plain,
( ~ ! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) )
| l4(c)
| ~ p3(c,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(182,plain,
( ~ ! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) )
| l4(c)
| ~ p3(c,c,c) ),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
l4(c),
inference(unit_resolution,[status(thm)],[182,179,172]) ).
tff(184,plain,
( ~ s5(c)
<=> ~ s5(c) ),
inference(rewrite,[status(thm)],]) ).
tff(185,axiom,
~ s5(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(186,plain,
~ s5(c),
inference(modus_ponens,[status(thm)],[185,184]) ).
tff(187,plain,
^ [I: $i,H: $i] :
refl(
( ( ~ l4(H)
| ~ r4(I)
| s5(H) )
<=> ( ~ l4(H)
| ~ r4(I)
| s5(H) ) )),
inference(bind,[status(th)],]) ).
tff(188,plain,
( ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
<=> ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) ) ),
inference(quant_intro,[status(thm)],[187]) ).
tff(189,plain,
( ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
<=> ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) ) ),
inference(rewrite,[status(thm)],]) ).
tff(190,plain,
^ [I: $i,H: $i] :
rewrite(
( ( s5(H)
| ~ l4(H)
| ~ r4(I) )
<=> ( ~ l4(H)
| ~ r4(I)
| s5(H) ) )),
inference(bind,[status(th)],]) ).
tff(191,plain,
( ! [I: $i,H: $i] :
( s5(H)
| ~ l4(H)
| ~ r4(I) )
<=> ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) ) ),
inference(quant_intro,[status(thm)],[190]) ).
tff(192,axiom,
! [I: $i,H: $i] :
( s5(H)
| ~ l4(H)
| ~ r4(I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_329) ).
tff(193,plain,
! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) ),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) ),
inference(modus_ponens,[status(thm)],[193,189]) ).
tff(195,plain,
! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) ),
inference(skolemize,[status(sab)],[194]) ).
tff(196,plain,
! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) ),
inference(modus_ponens,[status(thm)],[195,188]) ).
tff(197,plain,
( ( ~ ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
| s5(c)
| ~ r4(d)
| ~ l4(c) )
<=> ( ~ ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
| s5(c)
| ~ r4(d)
| ~ l4(c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(198,plain,
( ( ~ l4(c)
| ~ r4(d)
| s5(c) )
<=> ( s5(c)
| ~ r4(d)
| ~ l4(c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(199,plain,
( ( ~ ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
| ~ l4(c)
| ~ r4(d)
| s5(c) )
<=> ( ~ ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
| s5(c)
| ~ r4(d)
| ~ l4(c) ) ),
inference(monotonicity,[status(thm)],[198]) ).
tff(200,plain,
( ( ~ ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
| ~ l4(c)
| ~ r4(d)
| s5(c) )
<=> ( ~ ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
| s5(c)
| ~ r4(d)
| ~ l4(c) ) ),
inference(transitivity,[status(thm)],[199,197]) ).
tff(201,plain,
( ~ ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
| ~ l4(c)
| ~ r4(d)
| s5(c) ),
inference(quant_inst,[status(thm)],]) ).
tff(202,plain,
( ~ ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
| s5(c)
| ~ r4(d)
| ~ l4(c) ),
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
$false,
inference(unit_resolution,[status(thm)],[202,196,186,183,113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN214-1 : TPTP v8.1.0. Released v1.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.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
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 02:10:41 EDT 2022
% 0.13/0.35 % 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.
% 0.21/0.49 % SZS status Unsatisfiable
% 0.21/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------