TSTP Solution File: SYN156-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN156-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 23:53:59 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 171
% Syntax : Number of formulae : 368 ( 72 unt; 26 typ; 0 def)
% Number of atoms : 1684 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 2323 (1068 ~;1060 |; 0 &)
% ( 195 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 87 ( 87 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 21 >; 21 *; 0 +; 0 <<)
% Number of predicates : 27 ( 25 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 682 ( 617 !; 0 ?; 682 :)
% Comments :
%------------------------------------------------------------------------------
tff(m3_type,type,
m3: ( $i * $i * $i ) > $o ).
tff(a_type,type,
a: $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(s0_type,type,
s0: $i > $o ).
tff(d_type,type,
d: $i ).
tff(n4_type,type,
n4: ( $i * $i ) > $o ).
tff(p3_type,type,
p3: ( $i * $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(n1_type,type,
n1: ( $i * $i * $i ) > $o ).
tff(k1_type,type,
k1: $i > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(l1_type,type,
l1: ( $i * $i ) > $o ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(n2_type,type,
n2: $i > $o ).
tff(k0_type,type,
k0: $i > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(k4_type,type,
k4: $i > $o ).
tff(c_type,type,
c: $i ).
tff(n3_type,type,
n3: $i > $o ).
tff(q3_type,type,
q3: ( $i * $i ) > $o ).
tff(q2_type,type,
q2: ( $i * $i * $i ) > $o ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(1,plain,
^ [I: $i] :
refl(
( ( m3(I,I,I)
| ~ p2(I,I,I) )
<=> ( m3(I,I,I)
| ~ p2(I,I,I) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
<=> ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
<=> ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_238) ).
tff(5,plain,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,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(9,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)],[8]) ).
tff(10,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(11,axiom,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_176) ).
tff(12,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( m1(a,a,a)
<=> m1(a,a,a) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ( m1(a,a,a)
| $false
| $false )
<=> m1(a,a,a) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
l0(a),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_20) ).
tff(19,plain,
( l0(a)
<=> $true ),
inference(iff_true,[status(thm)],[18]) ).
tff(20,plain,
( ~ l0(a)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
( ~ l0(a)
<=> $false ),
inference(transitivity,[status(thm)],[20,17]) ).
tff(22,axiom,
s0(d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_1) ).
tff(23,plain,
( s0(d)
<=> $true ),
inference(iff_true,[status(thm)],[22]) ).
tff(24,plain,
( ~ s0(d)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ~ s0(d)
<=> $false ),
inference(transitivity,[status(thm)],[24,17]) ).
tff(26,plain,
( ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) )
<=> ( m1(a,a,a)
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[25,21]) ).
tff(27,plain,
( ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) )
<=> m1(a,a,a) ),
inference(transitivity,[status(thm)],[26,16]) ).
tff(28,plain,
( ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) )
<=> ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) )
<=> ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( m1(a,a,a)
| ~ l0(a) )
<=> ( m1(a,a,a)
| ~ l0(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) )
<=> ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) )
<=> ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,axiom,
( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_023) ).
tff(34,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[34,28]) ).
tff(36,plain,
m1(a,a,a),
inference(modus_ponens,[status(thm)],[35,27]) ).
tff(37,plain,
m1(a,a,a),
inference(modus_ponens,[status(thm)],[36,15]) ).
tff(38,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(a,a,a)
| ~ m1(a,a,a) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(a,a,a)
| ~ m1(a,a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(a,a,a)
| ~ m1(a,a,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(a,a,a)
| ~ m1(a,a,a) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
p2(a,a,a),
inference(unit_resolution,[status(thm)],[40,37,14]) ).
tff(42,plain,
( ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(a,a,a)
| m3(a,a,a) )
<=> ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(a,a,a)
| m3(a,a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( m3(a,a,a)
| ~ p2(a,a,a) )
<=> ( ~ p2(a,a,a)
| m3(a,a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| m3(a,a,a)
| ~ p2(a,a,a) )
<=> ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(a,a,a)
| m3(a,a,a) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| m3(a,a,a)
| ~ p2(a,a,a) )
<=> ( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(a,a,a)
| m3(a,a,a) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| m3(a,a,a)
| ~ p2(a,a,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(a,a,a)
| m3(a,a,a) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
m3(a,a,a),
inference(unit_resolution,[status(thm)],[47,41,7]) ).
tff(49,plain,
^ [I: $i,J: $i] :
refl(
( ( k1(I)
| ~ n0(J,I) )
<=> ( k1(I)
| ~ n0(J,I) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,axiom,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_001) ).
tff(53,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( n0(b,a)
<=> n0(b,a) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
n0(b,a),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_37) ).
tff(58,plain,
n0(b,a),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
( ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(a)
| ~ n0(b,a) )
<=> ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(a)
| ~ n0(b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(a)
| ~ n0(b,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(a)
| ~ n0(b,a) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
k1(a),
inference(unit_resolution,[status(thm)],[61,58,55]) ).
tff(63,plain,
^ [D: $i,C: $i] :
refl(
( ( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) )
<=> ( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) )
<=> ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) )
<=> ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
^ [D: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( n1(C,e,e)
| ~ m0(C,D,e) )
<=> ( ~ m0(C,D,e)
| n1(C,e,e) ) )),
( ( n1(C,e,e)
| ~ m0(C,D,e)
| ~ k1(C) )
<=> ( ~ m0(C,D,e)
| n1(C,e,e)
| ~ k1(C) ) )),
rewrite(
( ( ~ m0(C,D,e)
| n1(C,e,e)
| ~ k1(C) )
<=> ( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ) )),
( ( n1(C,e,e)
| ~ m0(C,D,e)
| ~ k1(C) )
<=> ( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [D: $i,C: $i] :
( n1(C,e,e)
| ~ m0(C,D,e)
| ~ k1(C) )
<=> ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,axiom,
! [D: $i,C: $i] :
( n1(C,e,e)
| ~ m0(C,D,e)
| ~ k1(C) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_040) ).
tff(69,plain,
! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ),
inference(modus_ponens,[status(thm)],[71,64]) ).
tff(73,plain,
( m0(a,e,e)
<=> m0(a,e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
m0(a,e,e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_23) ).
tff(75,plain,
m0(a,e,e),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
( ( ~ ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) )
| ~ k1(a)
| ~ m0(a,e,e)
| n1(a,e,e) )
<=> ( ~ ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) )
| ~ k1(a)
| ~ m0(a,e,e)
| n1(a,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ~ ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) )
| ~ k1(a)
| ~ m0(a,e,e)
| n1(a,e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) )
| ~ k1(a)
| ~ m0(a,e,e)
| n1(a,e,e) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
( ~ k1(a)
| n1(a,e,e) ),
inference(unit_resolution,[status(thm)],[78,75,72]) ).
tff(80,plain,
n1(a,e,e),
inference(unit_resolution,[status(thm)],[79,62]) ).
tff(81,plain,
^ [C: $i] :
refl(
( ( ~ n1(C,e,e)
| p2(C,e,C) )
<=> ( ~ n1(C,e,e)
| p2(C,e,C) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) )
<=> ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) )
<=> ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
^ [C: $i] :
rewrite(
( ( p2(C,e,C)
| ~ n1(C,e,e) )
<=> ( ~ n1(C,e,e)
| p2(C,e,C) ) )),
inference(bind,[status(th)],]) ).
tff(85,plain,
( ! [C: $i] :
( p2(C,e,C)
| ~ n1(C,e,e) )
<=> ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,axiom,
! [C: $i] :
( p2(C,e,C)
| ~ n1(C,e,e) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_170) ).
tff(87,plain,
! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ),
inference(modus_ponens,[status(thm)],[89,82]) ).
tff(91,plain,
( ( ~ ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) )
| ~ n1(a,e,e)
| p2(a,e,a) )
<=> ( ~ ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) )
| ~ n1(a,e,e)
| p2(a,e,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ~ ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) )
| ~ n1(a,e,e)
| p2(a,e,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
( ~ ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) )
| ~ n1(a,e,e)
| p2(a,e,a) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
p2(a,e,a),
inference(unit_resolution,[status(thm)],[93,90,80]) ).
tff(95,plain,
^ [H: $i,G: $i] :
refl(
( ( ~ n0(H,G)
| l1(G,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
^ [H: $i,G: $i] :
rewrite(
( ( l1(G,G)
| ~ n0(H,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],]) ).
tff(99,plain,
( ! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,axiom,
! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_002) ).
tff(101,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[101,97]) ).
tff(103,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(skolemize,[status(sab)],[102]) ).
tff(104,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[103,96]) ).
tff(105,plain,
( ( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(b,a)
| l1(a,a) )
<=> ( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(b,a)
| l1(a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(b,a)
| l1(a,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(b,a)
| l1(a,a) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
l1(a,a),
inference(unit_resolution,[status(thm)],[107,58,104]) ).
tff(109,plain,
^ [D: $i,E: $i,F: $i,C: $i] :
refl(
( ( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
<=> ( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ) )),
inference(bind,[status(th)],]) ).
tff(110,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
^ [D: $i,E: $i,F: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p2(C,D,D)
| ~ p1(C,E,F) )
<=> ( ~ p1(C,E,F)
| p2(C,D,D) ) )),
( ( p2(C,D,D)
| ~ p1(C,E,F)
| ~ l1(E,F) )
<=> ( ~ p1(C,E,F)
| p2(C,D,D)
| ~ l1(E,F) ) )),
rewrite(
( ( ~ p1(C,E,F)
| p2(C,D,D)
| ~ l1(E,F) )
<=> ( ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ) )),
( ( p2(C,D,D)
| ~ p1(C,E,F)
| ~ l1(E,F) )
<=> ( ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ) )),
( ( p2(C,D,D)
| ~ p1(C,E,F)
| ~ l1(E,F)
| ~ p2(C,D,C) )
<=> ( ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D)
| ~ p2(C,D,C) ) )),
rewrite(
( ( ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D)
| ~ p2(C,D,C) )
<=> ( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ) )),
( ( p2(C,D,D)
| ~ p1(C,E,F)
| ~ l1(E,F)
| ~ p2(C,D,C) )
<=> ( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ) )),
inference(bind,[status(th)],]) ).
tff(113,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( p2(C,D,D)
| ~ p1(C,E,F)
| ~ l1(E,F)
| ~ p2(C,D,C) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ) ),
inference(quant_intro,[status(thm)],[112]) ).
tff(114,axiom,
! [D: $i,E: $i,F: $i,C: $i] :
( p2(C,D,D)
| ~ p1(C,E,F)
| ~ l1(E,F)
| ~ p2(C,D,C) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_146) ).
tff(115,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ),
inference(modus_ponens,[status(thm)],[115,111]) ).
tff(117,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ),
inference(skolemize,[status(sab)],[116]) ).
tff(118,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ),
inference(modus_ponens,[status(thm)],[117,110]) ).
tff(119,plain,
( p1(a,a,a)
<=> p1(a,a,a) ),
inference(rewrite,[status(thm)],]) ).
tff(120,plain,
( ( $false
| p1(a,a,a) )
<=> p1(a,a,a) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
( ( ~ l0(a)
| p1(a,a,a) )
<=> ( $false
| p1(a,a,a) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(122,plain,
( ( ~ l0(a)
| p1(a,a,a) )
<=> p1(a,a,a) ),
inference(transitivity,[status(thm)],[121,120]) ).
tff(123,plain,
( ( p1(a,a,a)
| ~ l0(a) )
<=> ( ~ l0(a)
| p1(a,a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,axiom,
( p1(a,a,a)
| ~ l0(a) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_088) ).
tff(125,plain,
( ~ l0(a)
| p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
p1(a,a,a),
inference(modus_ponens,[status(thm)],[125,122]) ).
tff(127,plain,
p1(a,a,a),
inference(modus_ponens,[status(thm)],[126,119]) ).
tff(128,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
| ~ p1(a,a,a)
| ~ l1(a,a)
| ~ p2(a,e,a)
| p2(a,e,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
| ~ p1(a,a,a)
| ~ l1(a,a)
| ~ p2(a,e,a)
| p2(a,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(129,plain,
( ( ~ p2(a,e,a)
| ~ l1(a,a)
| ~ p1(a,a,a)
| p2(a,e,e) )
<=> ( ~ p1(a,a,a)
| ~ l1(a,a)
| ~ p2(a,e,a)
| p2(a,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
| ~ p2(a,e,a)
| ~ l1(a,a)
| ~ p1(a,a,a)
| p2(a,e,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
| ~ p1(a,a,a)
| ~ l1(a,a)
| ~ p2(a,e,a)
| p2(a,e,e) ) ),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
| ~ p2(a,e,a)
| ~ l1(a,a)
| ~ p1(a,a,a)
| p2(a,e,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
| ~ p1(a,a,a)
| ~ l1(a,a)
| ~ p2(a,e,a)
| p2(a,e,e) ) ),
inference(transitivity,[status(thm)],[130,128]) ).
tff(132,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
| ~ p2(a,e,a)
| ~ l1(a,a)
| ~ p1(a,a,a)
| p2(a,e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
| ~ p1(a,a,a)
| ~ l1(a,a)
| ~ p2(a,e,a)
| p2(a,e,e) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
p2(a,e,e),
inference(unit_resolution,[status(thm)],[133,127,118,108,94]) ).
tff(135,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(136,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)],[135]) ).
tff(137,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(138,axiom,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_137) ).
tff(139,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(skolemize,[status(sab)],[139]) ).
tff(141,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[140,136]) ).
tff(142,plain,
( p1(e,e,e)
<=> p1(e,e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(143,plain,
( ( $false
| $false
| p1(e,e,e) )
<=> p1(e,e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(144,axiom,
k0(e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(145,plain,
( k0(e)
<=> $true ),
inference(iff_true,[status(thm)],[144]) ).
tff(146,plain,
( ~ k0(e)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
( ~ k0(e)
<=> $false ),
inference(transitivity,[status(thm)],[146,17]) ).
tff(148,axiom,
r0(e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_13) ).
tff(149,plain,
( r0(e)
<=> $true ),
inference(iff_true,[status(thm)],[148]) ).
tff(150,plain,
( ~ r0(e)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
( ~ r0(e)
<=> $false ),
inference(transitivity,[status(thm)],[150,17]) ).
tff(152,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> ( $false
| $false
| p1(e,e,e) ) ),
inference(monotonicity,[status(thm)],[151,147]) ).
tff(153,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> p1(e,e,e) ),
inference(transitivity,[status(thm)],[152,143]) ).
tff(154,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(155,plain,
( ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(156,plain,
( ( p1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(157,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) ) ),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(transitivity,[status(thm)],[157,155]) ).
tff(159,axiom,
( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_090) ).
tff(160,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[160,154]) ).
tff(162,plain,
p1(e,e,e),
inference(modus_ponens,[status(thm)],[161,153]) ).
tff(163,plain,
p1(e,e,e),
inference(modus_ponens,[status(thm)],[162,142]) ).
tff(164,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(165,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(166,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
n2(e),
inference(unit_resolution,[status(thm)],[166,163,141]) ).
tff(168,plain,
( m1(e,e,e)
<=> m1(e,e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(169,plain,
( ( $false
| m1(e,e,e) )
<=> m1(e,e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(170,plain,
( ( ~ r0(e)
| m1(e,e,e) )
<=> ( $false
| m1(e,e,e) ) ),
inference(monotonicity,[status(thm)],[151]) ).
tff(171,plain,
( ( ~ r0(e)
| m1(e,e,e) )
<=> m1(e,e,e) ),
inference(transitivity,[status(thm)],[170,169]) ).
tff(172,plain,
( ( m1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(173,axiom,
( m1(e,e,e)
| ~ r0(e) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_012) ).
tff(174,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
m1(e,e,e),
inference(modus_ponens,[status(thm)],[174,171]) ).
tff(176,plain,
m1(e,e,e),
inference(modus_ponens,[status(thm)],[175,168]) ).
tff(177,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(178,plain,
( ( p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(179,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(transitivity,[status(thm)],[179,177]) ).
tff(181,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(182,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
p2(e,e,e),
inference(unit_resolution,[status(thm)],[182,176,14]) ).
tff(184,plain,
^ [D: $i] :
refl(
( ( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
<=> ( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) )),
inference(bind,[status(th)],]) ).
tff(185,plain,
( ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
<=> ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) ),
inference(quant_intro,[status(thm)],[184]) ).
tff(186,plain,
( ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
<=> ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(187,plain,
^ [D: $i] :
trans(
monotonicity(
rewrite(
( ( m3(D,e,e)
| ~ n2(e) )
<=> ( ~ n2(e)
| m3(D,e,e) ) )),
( ( m3(D,e,e)
| ~ n2(e)
| ~ p2(D,e,e) )
<=> ( ~ n2(e)
| m3(D,e,e)
| ~ p2(D,e,e) ) )),
rewrite(
( ( ~ n2(e)
| m3(D,e,e)
| ~ p2(D,e,e) )
<=> ( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) )),
( ( m3(D,e,e)
| ~ n2(e)
| ~ p2(D,e,e) )
<=> ( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) )),
inference(bind,[status(th)],]) ).
tff(188,plain,
( ! [D: $i] :
( m3(D,e,e)
| ~ n2(e)
| ~ p2(D,e,e) )
<=> ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) ),
inference(quant_intro,[status(thm)],[187]) ).
tff(189,axiom,
! [D: $i] :
( m3(D,e,e)
| ~ n2(e)
| ~ p2(D,e,e) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_234) ).
tff(190,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[189,188]) ).
tff(191,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[190,186]) ).
tff(192,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(skolemize,[status(sab)],[191]) ).
tff(193,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[192,185]) ).
tff(194,plain,
( ( ~ ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
| ~ n2(e)
| ~ p2(e,e,e)
| m3(e,e,e) )
<=> ( ~ ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
| ~ n2(e)
| ~ p2(e,e,e)
| m3(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(195,plain,
( ~ ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
| ~ n2(e)
| ~ p2(e,e,e)
| m3(e,e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(196,plain,
( ~ ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
| ~ n2(e)
| ~ p2(e,e,e)
| m3(e,e,e) ),
inference(modus_ponens,[status(thm)],[195,194]) ).
tff(197,plain,
m3(e,e,e),
inference(unit_resolution,[status(thm)],[196,193,183,167]) ).
tff(198,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(
( ( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
<=> ( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ) )),
inference(bind,[status(th)],]) ).
tff(199,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ) ),
inference(quant_intro,[status(thm)],[198]) ).
tff(200,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(201,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( p3(A,B,B)
| ~ m3(B,C,D) )
<=> ( ~ m3(B,C,D)
| p3(A,B,B) ) )),
( ( p3(A,B,B)
| ~ m3(B,C,D)
| ~ p2(A,B,D) )
<=> ( ~ m3(B,C,D)
| p3(A,B,B)
| ~ p2(A,B,D) ) )),
rewrite(
( ( ~ m3(B,C,D)
| p3(A,B,B)
| ~ p2(A,B,D) )
<=> ( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ) )),
( ( p3(A,B,B)
| ~ m3(B,C,D)
| ~ p2(A,B,D) )
<=> ( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ) )),
inference(bind,[status(th)],]) ).
tff(202,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( p3(A,B,B)
| ~ m3(B,C,D)
| ~ p2(A,B,D) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ) ),
inference(quant_intro,[status(thm)],[201]) ).
tff(203,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( p3(A,B,B)
| ~ m3(B,C,D)
| ~ p2(A,B,D) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_251) ).
tff(204,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ),
inference(modus_ponens,[status(thm)],[204,200]) ).
tff(206,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ),
inference(skolemize,[status(sab)],[205]) ).
tff(207,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ),
inference(modus_ponens,[status(thm)],[206,199]) ).
tff(208,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
| p3(a,e,e)
| ~ m3(e,e,e)
| ~ p2(a,e,e) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
| p3(a,e,e)
| ~ m3(e,e,e)
| ~ p2(a,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(209,plain,
( ( ~ p2(a,e,e)
| ~ m3(e,e,e)
| p3(a,e,e) )
<=> ( p3(a,e,e)
| ~ m3(e,e,e)
| ~ p2(a,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(210,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
| ~ p2(a,e,e)
| ~ m3(e,e,e)
| p3(a,e,e) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
| p3(a,e,e)
| ~ m3(e,e,e)
| ~ p2(a,e,e) ) ),
inference(monotonicity,[status(thm)],[209]) ).
tff(211,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
| ~ p2(a,e,e)
| ~ m3(e,e,e)
| p3(a,e,e) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
| p3(a,e,e)
| ~ m3(e,e,e)
| ~ p2(a,e,e) ) ),
inference(transitivity,[status(thm)],[210,208]) ).
tff(212,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
| ~ p2(a,e,e)
| ~ m3(e,e,e)
| p3(a,e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(213,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
| p3(a,e,e)
| ~ m3(e,e,e)
| ~ p2(a,e,e) ),
inference(modus_ponens,[status(thm)],[212,211]) ).
tff(214,plain,
p3(a,e,e),
inference(unit_resolution,[status(thm)],[213,207,197,134]) ).
tff(215,plain,
( ~ n4(a,e)
<=> ~ n4(a,e) ),
inference(rewrite,[status(thm)],]) ).
tff(216,axiom,
~ n4(a,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(217,plain,
~ n4(a,e),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
^ [A: $i,J: $i] :
refl(
( ( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) )
<=> ( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) ) )),
inference(bind,[status(th)],]) ).
tff(219,plain,
( ! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) )
<=> ! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) ) ),
inference(quant_intro,[status(thm)],[218]) ).
tff(220,plain,
( ! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) )
<=> ! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(221,plain,
^ [A: $i,J: $i] :
trans(
monotonicity(
rewrite(
( ( n4(J,A)
| ~ p3(J,A,A) )
<=> ( ~ p3(J,A,A)
| n4(J,A) ) )),
( ( n4(J,A)
| ~ p3(J,A,A)
| ~ n4(J,J) )
<=> ( ~ p3(J,A,A)
| n4(J,A)
| ~ n4(J,J) ) )),
rewrite(
( ( ~ p3(J,A,A)
| n4(J,A)
| ~ n4(J,J) )
<=> ( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) ) )),
( ( n4(J,A)
| ~ p3(J,A,A)
| ~ n4(J,J) )
<=> ( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) ) )),
inference(bind,[status(th)],]) ).
tff(222,plain,
( ! [A: $i,J: $i] :
( n4(J,A)
| ~ p3(J,A,A)
| ~ n4(J,J) )
<=> ! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) ) ),
inference(quant_intro,[status(thm)],[221]) ).
tff(223,axiom,
! [A: $i,J: $i] :
( n4(J,A)
| ~ p3(J,A,A)
| ~ n4(J,J) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_281) ).
tff(224,plain,
! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) ),
inference(modus_ponens,[status(thm)],[223,222]) ).
tff(225,plain,
! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) ),
inference(modus_ponens,[status(thm)],[224,220]) ).
tff(226,plain,
! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) ),
inference(skolemize,[status(sab)],[225]) ).
tff(227,plain,
! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) ),
inference(modus_ponens,[status(thm)],[226,219]) ).
tff(228,plain,
( ( ~ ! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) )
| ~ n4(a,a)
| ~ p3(a,e,e)
| n4(a,e) )
<=> ( ~ ! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) )
| ~ n4(a,a)
| ~ p3(a,e,e)
| n4(a,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(229,plain,
( ~ ! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) )
| ~ n4(a,a)
| ~ p3(a,e,e)
| n4(a,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(230,plain,
( ~ ! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) )
| ~ n4(a,a)
| ~ p3(a,e,e)
| n4(a,e) ),
inference(modus_ponens,[status(thm)],[229,228]) ).
tff(231,plain,
( ~ n4(a,a)
| ~ p3(a,e,e) ),
inference(unit_resolution,[status(thm)],[230,227,217]) ).
tff(232,plain,
~ n4(a,a),
inference(unit_resolution,[status(thm)],[231,214]) ).
tff(233,plain,
^ [I: $i,H: $i] :
refl(
( ( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) )
<=> ( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) ) )),
inference(bind,[status(th)],]) ).
tff(234,plain,
( ! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) )
<=> ! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) ) ),
inference(quant_intro,[status(thm)],[233]) ).
tff(235,plain,
( ! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) )
<=> ! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) ) ),
inference(rewrite,[status(thm)],]) ).
tff(236,plain,
^ [I: $i,H: $i] :
trans(
monotonicity(
rewrite(
( ( n4(H,H)
| ~ k4(I) )
<=> ( n4(H,H)
| ~ k4(I) ) )),
( ( n4(H,H)
| ~ k4(I)
| ~ m3(H,H,H) )
<=> ( n4(H,H)
| ~ k4(I)
| ~ m3(H,H,H) ) )),
rewrite(
( ( n4(H,H)
| ~ k4(I)
| ~ m3(H,H,H) )
<=> ( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) ) )),
( ( n4(H,H)
| ~ k4(I)
| ~ m3(H,H,H) )
<=> ( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) ) )),
inference(bind,[status(th)],]) ).
tff(237,plain,
( ! [I: $i,H: $i] :
( n4(H,H)
| ~ k4(I)
| ~ m3(H,H,H) )
<=> ! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) ) ),
inference(quant_intro,[status(thm)],[236]) ).
tff(238,axiom,
! [I: $i,H: $i] :
( n4(H,H)
| ~ k4(I)
| ~ m3(H,H,H) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_284) ).
tff(239,plain,
! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) ),
inference(modus_ponens,[status(thm)],[238,237]) ).
tff(240,plain,
! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) ),
inference(modus_ponens,[status(thm)],[239,235]) ).
tff(241,plain,
! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) ),
inference(skolemize,[status(sab)],[240]) ).
tff(242,plain,
! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) ),
inference(modus_ponens,[status(thm)],[241,234]) ).
tff(243,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(244,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)],[243]) ).
tff(245,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(246,axiom,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_240) ).
tff(247,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[246,245]) ).
tff(248,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(skolemize,[status(sab)],[247]) ).
tff(249,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[248,244]) ).
tff(250,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(e)
| ~ p2(e,e,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(e)
| ~ p2(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(251,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(e)
| ~ p2(e,e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(252,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(e)
| ~ p2(e,e,e) ),
inference(modus_ponens,[status(thm)],[251,250]) ).
tff(253,plain,
n3(e),
inference(unit_resolution,[status(thm)],[252,249,183]) ).
tff(254,plain,
^ [D: $i,E: $i,F: $i,C: $i] :
refl(
( ( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
<=> ( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) )),
inference(bind,[status(th)],]) ).
tff(255,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) ),
inference(quant_intro,[status(thm)],[254]) ).
tff(256,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) ),
inference(rewrite,[status(thm)],]) ).
tff(257,plain,
^ [D: $i,E: $i,F: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( l1(C,D)
| ~ p0(E,C) )
<=> ( ~ p0(E,C)
| l1(C,D) ) )),
( ( l1(C,D)
| ~ p0(E,C)
| ~ r0(F) )
<=> ( ~ p0(E,C)
| l1(C,D)
| ~ r0(F) ) )),
rewrite(
( ( ~ p0(E,C)
| l1(C,D)
| ~ r0(F) )
<=> ( ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) )),
( ( l1(C,D)
| ~ p0(E,C)
| ~ r0(F) )
<=> ( ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) )),
( ( l1(C,D)
| ~ p0(E,C)
| ~ r0(F)
| ~ m0(D,C,E) )
<=> ( ~ r0(F)
| ~ p0(E,C)
| l1(C,D)
| ~ m0(D,C,E) ) )),
rewrite(
( ( ~ r0(F)
| ~ p0(E,C)
| l1(C,D)
| ~ m0(D,C,E) )
<=> ( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) )),
( ( l1(C,D)
| ~ p0(E,C)
| ~ r0(F)
| ~ m0(D,C,E) )
<=> ( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) )),
inference(bind,[status(th)],]) ).
tff(258,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( l1(C,D)
| ~ p0(E,C)
| ~ r0(F)
| ~ m0(D,C,E) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) ),
inference(quant_intro,[status(thm)],[257]) ).
tff(259,axiom,
! [D: $i,E: $i,F: $i,C: $i] :
( l1(C,D)
| ~ p0(E,C)
| ~ r0(F)
| ~ m0(D,C,E) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_003) ).
tff(260,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ),
inference(modus_ponens,[status(thm)],[259,258]) ).
tff(261,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ),
inference(modus_ponens,[status(thm)],[260,256]) ).
tff(262,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ),
inference(skolemize,[status(sab)],[261]) ).
tff(263,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ),
inference(modus_ponens,[status(thm)],[262,255]) ).
tff(264,plain,
( m0(e,b,c)
<=> m0(e,b,c) ),
inference(rewrite,[status(thm)],]) ).
tff(265,axiom,
m0(e,b,c),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_27) ).
tff(266,plain,
m0(e,b,c),
inference(modus_ponens,[status(thm)],[265,264]) ).
tff(267,plain,
( p0(c,b)
<=> p0(c,b) ),
inference(rewrite,[status(thm)],]) ).
tff(268,axiom,
p0(c,b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_18) ).
tff(269,plain,
p0(c,b),
inference(modus_ponens,[status(thm)],[268,267]) ).
tff(270,plain,
( r0(b)
<=> r0(b) ),
inference(rewrite,[status(thm)],]) ).
tff(271,axiom,
r0(b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_9) ).
tff(272,plain,
r0(b),
inference(modus_ponens,[status(thm)],[271,270]) ).
tff(273,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(274,plain,
( ( ~ m0(e,b,c)
| ~ r0(b)
| ~ p0(c,b)
| l1(b,e) )
<=> ( ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(275,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ m0(e,b,c)
| ~ r0(b)
| ~ p0(c,b)
| l1(b,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) ) ),
inference(monotonicity,[status(thm)],[274]) ).
tff(276,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ m0(e,b,c)
| ~ r0(b)
| ~ p0(c,b)
| l1(b,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) ) ),
inference(transitivity,[status(thm)],[275,273]) ).
tff(277,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ m0(e,b,c)
| ~ r0(b)
| ~ p0(c,b)
| l1(b,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(278,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) ),
inference(modus_ponens,[status(thm)],[277,276]) ).
tff(279,plain,
l1(b,e),
inference(unit_resolution,[status(thm)],[278,272,269,266,263]) ).
tff(280,plain,
^ [H: $i,G: $i] :
refl(
( ( ~ l1(H,G)
| q2(G,G,H) )
<=> ( ~ l1(H,G)
| q2(G,G,H) ) )),
inference(bind,[status(th)],]) ).
tff(281,plain,
( ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
<=> ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ) ),
inference(quant_intro,[status(thm)],[280]) ).
tff(282,plain,
( ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
<=> ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ) ),
inference(rewrite,[status(thm)],]) ).
tff(283,plain,
^ [H: $i,G: $i] :
rewrite(
( ( q2(G,G,H)
| ~ l1(H,G) )
<=> ( ~ l1(H,G)
| q2(G,G,H) ) )),
inference(bind,[status(th)],]) ).
tff(284,plain,
( ! [H: $i,G: $i] :
( q2(G,G,H)
| ~ l1(H,G) )
<=> ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ) ),
inference(quant_intro,[status(thm)],[283]) ).
tff(285,axiom,
! [H: $i,G: $i] :
( q2(G,G,H)
| ~ l1(H,G) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_186) ).
tff(286,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[285,284]) ).
tff(287,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[286,282]) ).
tff(288,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(skolemize,[status(sab)],[287]) ).
tff(289,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[288,281]) ).
tff(290,plain,
( ( ~ ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
| ~ l1(b,e)
| q2(e,e,b) )
<=> ( ~ ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
| ~ l1(b,e)
| q2(e,e,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(291,plain,
( ~ ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
| ~ l1(b,e)
| q2(e,e,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(292,plain,
( ~ ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
| ~ l1(b,e)
| q2(e,e,b) ),
inference(modus_ponens,[status(thm)],[291,290]) ).
tff(293,plain,
q2(e,e,b),
inference(unit_resolution,[status(thm)],[292,289,279]) ).
tff(294,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(295,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)],[294]) ).
tff(296,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(297,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(298,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)],[297]) ).
tff(299,axiom,
! [I: $i,H: $i,G: $i] :
( q3(G,H)
| ~ q2(I,G,H)
| ~ n0(I,G) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_255) ).
tff(300,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[299,298]) ).
tff(301,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[300,296]) ).
tff(302,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(skolemize,[status(sab)],[301]) ).
tff(303,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[302,295]) ).
tff(304,plain,
( n0(e,e)
<=> n0(e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(305,axiom,
n0(e,e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_30) ).
tff(306,plain,
n0(e,e),
inference(modus_ponens,[status(thm)],[305,304]) ).
tff(307,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(308,plain,
( ( ~ q2(e,e,b)
| ~ n0(e,e)
| q3(e,b) )
<=> ( q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(309,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,b)
| ~ n0(e,e)
| q3(e,b) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) ) ),
inference(monotonicity,[status(thm)],[308]) ).
tff(310,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,b)
| ~ n0(e,e)
| q3(e,b) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) ) ),
inference(transitivity,[status(thm)],[309,307]) ).
tff(311,plain,
( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,b)
| ~ n0(e,e)
| q3(e,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(312,plain,
( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) ),
inference(modus_ponens,[status(thm)],[311,310]) ).
tff(313,plain,
q3(e,b),
inference(unit_resolution,[status(thm)],[312,306,303,293]) ).
tff(314,plain,
( ( ~ q3(e,b)
| k4(c)
| ~ n3(e) )
<=> ( ~ q3(e,b)
| k4(c)
| ~ n3(e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(315,plain,
( ( ~ q3(e,b)
| $false
| k4(c)
| ~ n3(e) )
<=> ( ~ q3(e,b)
| k4(c)
| ~ n3(e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(316,axiom,
n0(c,d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_34) ).
tff(317,plain,
( n0(c,d)
<=> $true ),
inference(iff_true,[status(thm)],[316]) ).
tff(318,plain,
( ~ n0(c,d)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[317]) ).
tff(319,plain,
( ~ n0(c,d)
<=> $false ),
inference(transitivity,[status(thm)],[318,17]) ).
tff(320,plain,
( ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) )
<=> ( ~ q3(e,b)
| $false
| k4(c)
| ~ n3(e) ) ),
inference(monotonicity,[status(thm)],[319]) ).
tff(321,plain,
( ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) )
<=> ( ~ q3(e,b)
| k4(c)
| ~ n3(e) ) ),
inference(transitivity,[status(thm)],[320,315]) ).
tff(322,plain,
( ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) )
<=> ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(323,plain,
( ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) )
<=> ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(324,plain,
( ( k4(c)
| ~ n0(c,d)
| ~ q3(e,b) )
<=> ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(325,plain,
( ( k4(c)
| ~ n0(c,d)
| ~ q3(e,b)
| ~ n3(e) )
<=> ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ) ),
inference(monotonicity,[status(thm)],[324]) ).
tff(326,plain,
( ( k4(c)
| ~ n0(c,d)
| ~ q3(e,b)
| ~ n3(e) )
<=> ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ) ),
inference(transitivity,[status(thm)],[325,323]) ).
tff(327,axiom,
( k4(c)
| ~ n0(c,d)
| ~ q3(e,b)
| ~ n3(e) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_274) ).
tff(328,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[327,326]) ).
tff(329,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[328,322]) ).
tff(330,plain,
( ~ q3(e,b)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[329,321]) ).
tff(331,plain,
( ~ q3(e,b)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[330,314]) ).
tff(332,plain,
( ~ q3(e,b)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[331,314]) ).
tff(333,plain,
( ~ q3(e,b)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[332,314]) ).
tff(334,plain,
( ~ q3(e,b)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[333,314]) ).
tff(335,plain,
( ~ q3(e,b)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[334,314]) ).
tff(336,plain,
( ~ q3(e,b)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[335,314]) ).
tff(337,plain,
( ~ q3(e,b)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[336,314]) ).
tff(338,plain,
k4(c),
inference(unit_resolution,[status(thm)],[337,313,253]) ).
tff(339,plain,
( ( ~ ! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) )
| n4(a,a)
| ~ m3(a,a,a)
| ~ k4(c) )
<=> ( ~ ! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) )
| n4(a,a)
| ~ m3(a,a,a)
| ~ k4(c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(340,plain,
( ~ ! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) )
| n4(a,a)
| ~ m3(a,a,a)
| ~ k4(c) ),
inference(quant_inst,[status(thm)],]) ).
tff(341,plain,
( ~ ! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) )
| n4(a,a)
| ~ m3(a,a,a)
| ~ k4(c) ),
inference(modus_ponens,[status(thm)],[340,339]) ).
tff(342,plain,
$false,
inference(unit_resolution,[status(thm)],[341,338,242,232,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN156-1 : 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 : n020.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 02:00:59 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.
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------