%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN144-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:20 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 158
% Syntax : Number of formulae : 349 ( 87 unt; 0 typ; 0 def)
% Number of atoms : 1957 ( 0 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 2776 (1292 ~;1288 |; 0 &)
% ( 196 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 124 ( 124 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 28 ( 27 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 813 ( 731 !; 0 ?; 813 :)
% Comments :
%------------------------------------------------------------------------------
tff(p4_type,type,
p4: ( $i * $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(e_type,type,
e: $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(r3_type,type,
r3: ( $i * $i * $i ) > $o ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(s0_type,type,
s0: $i > $o ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(n1_type,type,
n1: ( $i * $i * $i ) > $o ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(k0_type,type,
k0: $i > $o ).
tff(d_type,type,
d: $i ).
tff(r0_type,type,
r0: $i > $o ).
tff(m3_type,type,
m3: ( $i * $i * $i ) > $o ).
tff(k1_type,type,
k1: $i > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(l1_type,type,
l1: ( $i * $i ) > $o ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(n2_type,type,
n2: $i > $o ).
tff(k2_type,type,
k2: ( $i * $i ) > $o ).
tff(q1_type,type,
q1: ( $i * $i * $i ) > $o ).
tff(q2_type,type,
q2: ( $i * $i * $i ) > $o ).
tff(m2_type,type,
m2: $i > $o ).
tff(m5_type,type,
m5: ( $i * $i ) > $o ).
tff(1,plain,
^ [I: $i,H: $i] :
refl(( ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [I: $i,H: $i] :
trans(monotonicity(rewrite(( ( m1(H,I,H)
| ~ p0(H,I) )
<=> ( m1(H,I,H)
| ~ p0(H,I) ) )),
( ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) )),
rewrite(( ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) )),
( ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_029) ).
tff(7,plain,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( p0(b,c)
<=> p0(b,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
p0(b,c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_22) ).
tff(13,plain,
p0(b,c),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( s0(b)
<=> s0(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
s0(b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_5) ).
tff(16,plain,
s0(b),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) )
<=> ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( m1(b,c,b)
| ~ p0(b,c)
| ~ s0(b) )
<=> ( ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| m1(b,c,b)
| ~ p0(b,c)
| ~ s0(b) )
<=> ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| m1(b,c,b)
| ~ p0(b,c)
| ~ s0(b) )
<=> ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| m1(b,c,b)
| ~ p0(b,c)
| ~ s0(b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
m1(b,c,b),
inference(unit_resolution,[status(thm)],[22,16,13,10]) ).
tff(24,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(25,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)],[24]) ).
tff(26,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(27,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(28,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,b,c)
| ~ m1(b,c,b) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,b,c)
| ~ m1(b,c,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,b,c)
| ~ m1(b,c,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,b,c)
| ~ m1(b,c,b) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
p2(c,b,c),
inference(unit_resolution,[status(thm)],[33,30,23]) ).
tff(35,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
refl(( ( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
<=> ( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( n1(H,H,H)
| ~ m0(I,J,I) )
<=> ( n1(H,H,H)
| ~ m0(I,J,I) ) )),
( ( n1(H,H,H)
| ~ m0(I,J,I)
| ~ k0(H) )
<=> ( n1(H,H,H)
| ~ m0(I,J,I)
| ~ k0(H) ) )),
rewrite(( ( n1(H,H,H)
| ~ m0(I,J,I)
| ~ k0(H) )
<=> ( ~ k0(H)
| n1(H,H,H)
| ~ m0(I,J,I) ) )),
( ( n1(H,H,H)
| ~ m0(I,J,I)
| ~ k0(H) )
<=> ( ~ k0(H)
| n1(H,H,H)
| ~ m0(I,J,I) ) )),
( ( n1(H,H,H)
| ~ m0(I,J,I)
| ~ k0(H)
| ~ q0(A,J) )
<=> ( ~ k0(H)
| n1(H,H,H)
| ~ m0(I,J,I)
| ~ q0(A,J) ) )),
rewrite(( ( ~ k0(H)
| n1(H,H,H)
| ~ m0(I,J,I)
| ~ q0(A,J) )
<=> ( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ) )),
( ( n1(H,H,H)
| ~ m0(I,J,I)
| ~ k0(H)
| ~ q0(A,J) )
<=> ( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( n1(H,H,H)
| ~ m0(I,J,I)
| ~ k0(H)
| ~ q0(A,J) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [I: $i,A: $i,J: $i,H: $i] :
( n1(H,H,H)
| ~ m0(I,J,I)
| ~ k0(H)
| ~ q0(A,J) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_042) ).
tff(41,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( k0(b)
<=> k0(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
k0(b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_32) ).
tff(47,plain,
k0(b),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( m0(e,d,e)
<=> m0(e,d,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
m0(e,d,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_8) ).
tff(50,plain,
m0(e,d,e),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( q0(e,d)
<=> q0(e,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
q0(e,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_2) ).
tff(53,plain,
q0(e,d),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
| ~ k0(b)
| n1(b,b,b)
| ~ m0(e,d,e)
| ~ q0(e,d) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
| ~ k0(b)
| n1(b,b,b)
| ~ m0(e,d,e)
| ~ q0(e,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ( ~ k0(b)
| ~ q0(e,d)
| n1(b,b,b)
| ~ m0(e,d,e) )
<=> ( ~ k0(b)
| n1(b,b,b)
| ~ m0(e,d,e)
| ~ q0(e,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
| ~ k0(b)
| ~ q0(e,d)
| n1(b,b,b)
| ~ m0(e,d,e) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
| ~ k0(b)
| n1(b,b,b)
| ~ m0(e,d,e)
| ~ q0(e,d) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
| ~ k0(b)
| ~ q0(e,d)
| n1(b,b,b)
| ~ m0(e,d,e) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
| ~ k0(b)
| n1(b,b,b)
| ~ m0(e,d,e)
| ~ q0(e,d) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
| ~ k0(b)
| ~ q0(e,d)
| n1(b,b,b)
| ~ m0(e,d,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
| ~ k0(b)
| n1(b,b,b)
| ~ m0(e,d,e)
| ~ q0(e,d) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
n1(b,b,b),
inference(unit_resolution,[status(thm)],[59,53,50,47,44]) ).
tff(61,plain,
^ [D: $i,E: $i,C: $i] :
refl(( ( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
<=> ( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ) )),
inference(bind,[status(th)],[]) ).
tff(62,plain,
( ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
<=> ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
<=> ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
^ [D: $i,E: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( p2(C,D,D)
| ~ n1(E,D,E) )
<=> ( ~ n1(E,D,E)
| p2(C,D,D) ) )),
( ( p2(C,D,D)
| ~ n1(E,D,E)
| ~ p0(C,D) )
<=> ( ~ n1(E,D,E)
| p2(C,D,D)
| ~ p0(C,D) ) )),
rewrite(( ( ~ n1(E,D,E)
| p2(C,D,D)
| ~ p0(C,D) )
<=> ( ~ n1(E,D,E)
| ~ p0(C,D)
| p2(C,D,D) ) )),
( ( p2(C,D,D)
| ~ n1(E,D,E)
| ~ p0(C,D) )
<=> ( ~ n1(E,D,E)
| ~ p0(C,D)
| p2(C,D,D) ) )),
( ( p2(C,D,D)
| ~ n1(E,D,E)
| ~ p0(C,D)
| ~ p2(C,D,C) )
<=> ( ~ n1(E,D,E)
| ~ p0(C,D)
| p2(C,D,D)
| ~ p2(C,D,C) ) )),
rewrite(( ( ~ n1(E,D,E)
| ~ p0(C,D)
| p2(C,D,D)
| ~ p2(C,D,C) )
<=> ( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ) )),
( ( p2(C,D,D)
| ~ n1(E,D,E)
| ~ p0(C,D)
| ~ p2(C,D,C) )
<=> ( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [D: $i,E: $i,C: $i] :
( p2(C,D,D)
| ~ n1(E,D,E)
| ~ p0(C,D)
| ~ p2(C,D,C) )
<=> ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,axiom,
! [D: $i,E: $i,C: $i] :
( p2(C,D,D)
| ~ n1(E,D,E)
| ~ p0(C,D)
| ~ p2(C,D,C) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_152) ).
tff(67,plain,
! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,plain,
( p0(c,b)
<=> p0(c,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,axiom,
p0(c,b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_18) ).
tff(73,plain,
p0(c,b),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ( ~ ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
| ~ n1(b,b,b)
| ~ p0(c,b)
| ~ p2(c,b,c)
| p2(c,b,b) )
<=> ( ~ ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
| ~ n1(b,b,b)
| ~ p0(c,b)
| ~ p2(c,b,c)
| p2(c,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ( ~ n1(b,b,b)
| ~ p2(c,b,c)
| ~ p0(c,b)
| p2(c,b,b) )
<=> ( ~ n1(b,b,b)
| ~ p0(c,b)
| ~ p2(c,b,c)
| p2(c,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
( ( ~ ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
| ~ n1(b,b,b)
| ~ p2(c,b,c)
| ~ p0(c,b)
| p2(c,b,b) )
<=> ( ~ ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
| ~ n1(b,b,b)
| ~ p0(c,b)
| ~ p2(c,b,c)
| p2(c,b,b) ) ),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( ( ~ ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
| ~ n1(b,b,b)
| ~ p2(c,b,c)
| ~ p0(c,b)
| p2(c,b,b) )
<=> ( ~ ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
| ~ n1(b,b,b)
| ~ p0(c,b)
| ~ p2(c,b,c)
| p2(c,b,b) ) ),
inference(transitivity,[status(thm)],[76,74]) ).
tff(78,plain,
( ~ ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
| ~ n1(b,b,b)
| ~ p2(c,b,c)
| ~ p0(c,b)
| p2(c,b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
| ~ n1(b,b,b)
| ~ p0(c,b)
| ~ p2(c,b,c)
| p2(c,b,b) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( ~ p2(c,b,c)
| p2(c,b,b) ),
inference(unit_resolution,[status(thm)],[79,73,70,60]) ).
tff(81,plain,
p2(c,b,b),
inference(unit_resolution,[status(thm)],[80,34]) ).
tff(82,plain,
^ [B: $i,D: $i,C: $i] :
refl(( ( ~ p2(B,D,C)
| r3(B,C,B) )
<=> ( ~ p2(B,D,C)
| r3(B,C,B) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
^ [B: $i,D: $i,C: $i] :
rewrite(( ( r3(B,C,B)
| ~ p2(B,D,C) )
<=> ( ~ p2(B,D,C)
| r3(B,C,B) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [B: $i,D: $i,C: $i] :
( r3(B,C,B)
| ~ p2(B,D,C) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [B: $i,D: $i,C: $i] :
( r3(B,C,B)
| ~ p2(B,D,C) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_267) ).
tff(88,plain,
! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
( ( ~ ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
| ~ p2(c,b,b)
| r3(c,b,c) )
<=> ( ~ ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
| ~ p2(c,b,b)
| r3(c,b,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
| ~ p2(c,b,b)
| r3(c,b,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
| ~ p2(c,b,b)
| r3(c,b,c) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
r3(c,b,c),
inference(unit_resolution,[status(thm)],[94,91,81]) ).
tff(96,plain,
^ [H: $i,G: $i] :
refl(( ( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) )
<=> ( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) )
<=> ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) )
<=> ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
^ [H: $i,G: $i] :
trans(monotonicity(rewrite(( ( p4(G,G,H)
| ~ r0(G) )
<=> ( ~ r0(G)
| p4(G,G,H) ) )),
( ( p4(G,G,H)
| ~ r0(G)
| ~ r3(H,G,H) )
<=> ( ~ r0(G)
| p4(G,G,H)
| ~ r3(H,G,H) ) )),
rewrite(( ( ~ r0(G)
| p4(G,G,H)
| ~ r3(H,G,H) )
<=> ( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ) )),
( ( p4(G,G,H)
| ~ r0(G)
| ~ r3(H,G,H) )
<=> ( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [H: $i,G: $i] :
( p4(G,G,H)
| ~ r0(G)
| ~ r3(H,G,H) )
<=> ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,axiom,
! [H: $i,G: $i] :
( p4(G,G,H)
| ~ r0(G)
| ~ r3(H,G,H) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_285) ).
tff(102,plain,
! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ),
inference(modus_ponens,[status(thm)],[104,97]) ).
tff(106,plain,
( r0(b)
<=> r0(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,axiom,
r0(b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_9) ).
tff(108,plain,
r0(b),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
( ( ~ ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) )
| ~ r0(b)
| ~ r3(c,b,c)
| p4(b,b,c) )
<=> ( ~ ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) )
| ~ r0(b)
| ~ r3(c,b,c)
| p4(b,b,c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ~ ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) )
| ~ r0(b)
| ~ r3(c,b,c)
| p4(b,b,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) )
| ~ r0(b)
| ~ r3(c,b,c)
| p4(b,b,c) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
p4(b,b,c),
inference(unit_resolution,[status(thm)],[111,108,105,95]) ).
tff(113,plain,
^ [I: $i,J: $i] :
refl(( ( k1(I)
| ~ n0(J,I) )
<=> ( k1(I)
| ~ n0(J,I) ) )),
inference(bind,[status(th)],[]) ).
tff(114,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,axiom,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_001) ).
tff(117,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
( n0(b,a)
<=> n0(b,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,axiom,
n0(b,a),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_37) ).
tff(122,plain,
n0(b,a),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,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(124,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(a)
| ~ n0(b,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(a)
| ~ n0(b,a) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
k1(a),
inference(unit_resolution,[status(thm)],[125,122,119]) ).
tff(127,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(128,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)],[127]) ).
tff(129,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(130,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(131,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)],[130]) ).
tff(132,axiom,
! [D: $i,C: $i] :
( n1(C,e,e)
| ~ m0(C,D,e)
| ~ k1(C) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_040) ).
tff(133,plain,
! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ),
inference(modus_ponens,[status(thm)],[133,129]) ).
tff(135,plain,
! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ),
inference(skolemize,[status(sab)],[134]) ).
tff(136,plain,
! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ),
inference(modus_ponens,[status(thm)],[135,128]) ).
tff(137,plain,
( m0(a,e,e)
<=> m0(a,e,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,axiom,
m0(a,e,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_23) ).
tff(139,plain,
m0(a,e,e),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,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(141,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(142,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)],[141,140]) ).
tff(143,plain,
( ~ k1(a)
| n1(a,e,e) ),
inference(unit_resolution,[status(thm)],[142,139,136]) ).
tff(144,plain,
n1(a,e,e),
inference(unit_resolution,[status(thm)],[143,126]) ).
tff(145,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(146,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)],[145]) ).
tff(147,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(148,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(149,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)],[148]) ).
tff(150,axiom,
! [C: $i] :
( p2(C,e,C)
| ~ n1(C,e,e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_170) ).
tff(151,plain,
! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ),
inference(modus_ponens,[status(thm)],[151,147]) ).
tff(153,plain,
! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ),
inference(skolemize,[status(sab)],[152]) ).
tff(154,plain,
! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ),
inference(modus_ponens,[status(thm)],[153,146]) ).
tff(155,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(156,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(157,plain,
( ~ ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) )
| ~ n1(a,e,e)
| p2(a,e,a) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
p2(a,e,a),
inference(unit_resolution,[status(thm)],[157,154,144]) ).
tff(159,plain,
^ [H: $i,G: $i] :
refl(( ( ~ n0(H,G)
| l1(G,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],[]) ).
tff(160,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)],[159]) ).
tff(161,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(162,plain,
^ [H: $i,G: $i] :
rewrite(( ( l1(G,G)
| ~ n0(H,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],[]) ).
tff(163,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)],[162]) ).
tff(164,axiom,
! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_002) ).
tff(165,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[165,161]) ).
tff(167,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(skolemize,[status(sab)],[166]) ).
tff(168,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[167,160]) ).
tff(169,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(170,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(b,a)
| l1(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(171,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(b,a)
| l1(a,a) ),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
l1(a,a),
inference(unit_resolution,[status(thm)],[171,122,168]) ).
tff(173,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(174,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)],[173]) ).
tff(175,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(176,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(177,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)],[176]) ).
tff(178,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/sandbox/benchmark/Axioms/SYN001-0.ax',rule_146) ).
tff(179,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)],[178,177]) ).
tff(180,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)],[179,175]) ).
tff(181,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)],[180]) ).
tff(182,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)],[181,174]) ).
tff(183,plain,
( l0(a)
<=> l0(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(184,axiom,
l0(a),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_20) ).
tff(185,plain,
l0(a),
inference(modus_ponens,[status(thm)],[184,183]) ).
tff(186,plain,
( ( ~ l0(a)
| p1(a,a,a) )
<=> ( ~ l0(a)
| p1(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,plain,
( ( p1(a,a,a)
| ~ l0(a) )
<=> ( ~ l0(a)
| p1(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(188,axiom,
( p1(a,a,a)
| ~ l0(a) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_088) ).
tff(189,plain,
( ~ l0(a)
| p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
( ~ l0(a)
| p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[189,186]) ).
tff(191,plain,
p1(a,a,a),
inference(unit_resolution,[status(thm)],[190,185]) ).
tff(192,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(193,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(194,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)],[193]) ).
tff(195,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)],[194,192]) ).
tff(196,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(197,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)],[196,195]) ).
tff(198,plain,
p2(a,e,e),
inference(unit_resolution,[status(thm)],[197,191,182,172,158]) ).
tff(199,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(200,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)],[199]) ).
tff(201,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(202,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(203,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[202,201]) ).
tff(204,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(skolemize,[status(sab)],[203]) ).
tff(205,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[204,200]) ).
tff(206,plain,
( k0(e)
<=> k0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(207,axiom,
k0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(208,plain,
k0(e),
inference(modus_ponens,[status(thm)],[207,206]) ).
tff(209,plain,
( r0(e)
<=> r0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(210,axiom,
r0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_13) ).
tff(211,plain,
r0(e),
inference(modus_ponens,[status(thm)],[210,209]) ).
tff(212,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(213,plain,
( ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(214,plain,
( ( p1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(215,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) ) ),
inference(monotonicity,[status(thm)],[214]) ).
tff(216,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(transitivity,[status(thm)],[215,213]) ).
tff(217,axiom,
( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_090) ).
tff(218,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[217,216]) ).
tff(219,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[218,212]) ).
tff(220,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[219,212]) ).
tff(221,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[220,212]) ).
tff(222,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[221,212]) ).
tff(223,plain,
p1(e,e,e),
inference(unit_resolution,[status(thm)],[222,211,208]) ).
tff(224,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(225,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(226,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[225,224]) ).
tff(227,plain,
n2(e),
inference(unit_resolution,[status(thm)],[226,223,205]) ).
tff(228,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(229,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)],[228]) ).
tff(230,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(231,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(232,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)],[231]) ).
tff(233,axiom,
! [D: $i] :
( m3(D,e,e)
| ~ n2(e)
| ~ p2(D,e,e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_234) ).
tff(234,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[233,232]) ).
tff(235,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[234,230]) ).
tff(236,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(skolemize,[status(sab)],[235]) ).
tff(237,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[236,229]) ).
tff(238,plain,
( ( ~ ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
| ~ n2(e)
| ~ p2(a,e,e)
| m3(a,e,e) )
<=> ( ~ ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
| ~ n2(e)
| ~ p2(a,e,e)
| m3(a,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(239,plain,
( ~ ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
| ~ n2(e)
| ~ p2(a,e,e)
| m3(a,e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(240,plain,
( ~ ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
| ~ n2(e)
| ~ p2(a,e,e)
| m3(a,e,e) ),
inference(modus_ponens,[status(thm)],[239,238]) ).
tff(241,plain,
m3(a,e,e),
inference(unit_resolution,[status(thm)],[240,237,227,198]) ).
tff(242,plain,
^ [I: $i,A: $i,J: $i] :
refl(( ( ~ m0(J,A,I)
| q1(I,I,I) )
<=> ( ~ m0(J,A,I)
| q1(I,I,I) ) )),
inference(bind,[status(th)],[]) ).
tff(243,plain,
( ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) ) ),
inference(quant_intro,[status(thm)],[242]) ).
tff(244,plain,
( ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(245,plain,
^ [I: $i,A: $i,J: $i] :
rewrite(( ( q1(I,I,I)
| ~ m0(J,A,I) )
<=> ( ~ m0(J,A,I)
| q1(I,I,I) ) )),
inference(bind,[status(th)],[]) ).
tff(246,plain,
( ! [I: $i,A: $i,J: $i] :
( q1(I,I,I)
| ~ m0(J,A,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) ) ),
inference(quant_intro,[status(thm)],[245]) ).
tff(247,axiom,
! [I: $i,A: $i,J: $i] :
( q1(I,I,I)
| ~ m0(J,A,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_121) ).
tff(248,plain,
! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) ),
inference(modus_ponens,[status(thm)],[247,246]) ).
tff(249,plain,
! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) ),
inference(modus_ponens,[status(thm)],[248,244]) ).
tff(250,plain,
! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) ),
inference(skolemize,[status(sab)],[249]) ).
tff(251,plain,
! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) ),
inference(modus_ponens,[status(thm)],[250,243]) ).
tff(252,plain,
( m0(e,d,a)
<=> m0(e,d,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(253,axiom,
m0(e,d,a),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_4) ).
tff(254,plain,
m0(e,d,a),
inference(modus_ponens,[status(thm)],[253,252]) ).
tff(255,plain,
( ( ~ ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) )
| ~ m0(e,d,a)
| q1(a,a,a) )
<=> ( ~ ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) )
| ~ m0(e,d,a)
| q1(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(256,plain,
( ~ ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) )
| ~ m0(e,d,a)
| q1(a,a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(257,plain,
( ~ ! [I: $i,A: $i,J: $i] :
( ~ m0(J,A,I)
| q1(I,I,I) )
| ~ m0(e,d,a)
| q1(a,a,a) ),
inference(modus_ponens,[status(thm)],[256,255]) ).
tff(258,plain,
q1(a,a,a),
inference(unit_resolution,[status(thm)],[257,254,251]) ).
tff(259,plain,
^ [A: $i,J: $i] :
refl(( ( ~ q1(A,J,J)
| k2(J,J) )
<=> ( ~ q1(A,J,J)
| k2(J,J) ) )),
inference(bind,[status(th)],[]) ).
tff(260,plain,
( ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
<=> ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ) ),
inference(quant_intro,[status(thm)],[259]) ).
tff(261,plain,
( ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
<=> ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(262,plain,
^ [A: $i,J: $i] :
rewrite(( ( k2(J,J)
| ~ q1(A,J,J) )
<=> ( ~ q1(A,J,J)
| k2(J,J) ) )),
inference(bind,[status(th)],[]) ).
tff(263,plain,
( ! [A: $i,J: $i] :
( k2(J,J)
| ~ q1(A,J,J) )
<=> ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ) ),
inference(quant_intro,[status(thm)],[262]) ).
tff(264,axiom,
! [A: $i,J: $i] :
( k2(J,J)
| ~ q1(A,J,J) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_129) ).
tff(265,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(modus_ponens,[status(thm)],[264,263]) ).
tff(266,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(modus_ponens,[status(thm)],[265,261]) ).
tff(267,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(skolemize,[status(sab)],[266]) ).
tff(268,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(modus_ponens,[status(thm)],[267,260]) ).
tff(269,plain,
( ( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(a,a,a)
| k2(a,a) )
<=> ( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(a,a,a)
| k2(a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(270,plain,
( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(a,a,a)
| k2(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(271,plain,
( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(a,a,a)
| k2(a,a) ),
inference(modus_ponens,[status(thm)],[270,269]) ).
tff(272,plain,
k2(a,a),
inference(unit_resolution,[status(thm)],[271,268,258]) ).
tff(273,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(274,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)],[273]) ).
tff(275,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(276,axiom,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_181) ).
tff(277,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[276,275]) ).
tff(278,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(skolemize,[status(sab)],[277]) ).
tff(279,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[278,274]) ).
tff(280,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(281,plain,
( ( q2(e,e,e)
| ~ p1(e,e,e) )
<=> ( ~ p1(e,e,e)
| q2(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(282,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)],[281]) ).
tff(283,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)],[282,280]) ).
tff(284,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(285,plain,
( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) ),
inference(modus_ponens,[status(thm)],[284,283]) ).
tff(286,plain,
q2(e,e,e),
inference(unit_resolution,[status(thm)],[285,223,279]) ).
tff(287,plain,
^ [G: $i] :
refl(( ( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) )
<=> ( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) ) )),
inference(bind,[status(th)],[]) ).
tff(288,plain,
( ! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) )
<=> ! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) ) ),
inference(quant_intro,[status(thm)],[287]) ).
tff(289,plain,
( ! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) )
<=> ! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(290,plain,
^ [G: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( r3(a,a,e)
| ~ k2(a,a) )
<=> ( ~ k2(a,a)
| r3(a,a,e) ) )),
( ( r3(a,a,e)
| ~ k2(a,a)
| ~ q2(G,e,G) )
<=> ( ~ k2(a,a)
| r3(a,a,e)
| ~ q2(G,e,G) ) )),
rewrite(( ( ~ k2(a,a)
| r3(a,a,e)
| ~ q2(G,e,G) )
<=> ( ~ k2(a,a)
| r3(a,a,e)
| ~ q2(G,e,G) ) )),
( ( r3(a,a,e)
| ~ k2(a,a)
| ~ q2(G,e,G) )
<=> ( ~ k2(a,a)
| r3(a,a,e)
| ~ q2(G,e,G) ) )),
( ( r3(a,a,e)
| ~ k2(a,a)
| ~ q2(G,e,G)
| ~ m2(b) )
<=> ( ~ k2(a,a)
| r3(a,a,e)
| ~ q2(G,e,G)
| ~ m2(b) ) )),
rewrite(( ( ~ k2(a,a)
| r3(a,a,e)
| ~ q2(G,e,G)
| ~ m2(b) )
<=> ( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ q2(G,e,G) ) )),
( ( r3(a,a,e)
| ~ k2(a,a)
| ~ q2(G,e,G)
| ~ m2(b) )
<=> ( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ q2(G,e,G) ) )),
( ( r3(a,a,e)
| ~ k2(a,a)
| ~ q2(G,e,G)
| ~ m2(b)
| ~ m3(a,G,G) )
<=> ( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ q2(G,e,G)
| ~ m3(a,G,G) ) )),
rewrite(( ( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ q2(G,e,G)
| ~ m3(a,G,G) )
<=> ( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) ) )),
( ( r3(a,a,e)
| ~ k2(a,a)
| ~ q2(G,e,G)
| ~ m2(b)
| ~ m3(a,G,G) )
<=> ( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) ) )),
inference(bind,[status(th)],[]) ).
tff(291,plain,
( ! [G: $i] :
( r3(a,a,e)
| ~ k2(a,a)
| ~ q2(G,e,G)
| ~ m2(b)
| ~ m3(a,G,G) )
<=> ! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) ) ),
inference(quant_intro,[status(thm)],[290]) ).
tff(292,axiom,
! [G: $i] :
( r3(a,a,e)
| ~ k2(a,a)
| ~ q2(G,e,G)
| ~ m2(b)
| ~ m3(a,G,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_269) ).
tff(293,plain,
! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) ),
inference(modus_ponens,[status(thm)],[292,291]) ).
tff(294,plain,
! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) ),
inference(modus_ponens,[status(thm)],[293,289]) ).
tff(295,plain,
! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) ),
inference(skolemize,[status(sab)],[294]) ).
tff(296,plain,
! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) ),
inference(modus_ponens,[status(thm)],[295,288]) ).
tff(297,plain,
( n0(d,b)
<=> n0(d,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(298,axiom,
n0(d,b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_7) ).
tff(299,plain,
n0(d,b),
inference(modus_ponens,[status(thm)],[298,297]) ).
tff(300,plain,
( ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(b)
| ~ n0(d,b) )
<=> ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(b)
| ~ n0(d,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(301,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(b)
| ~ n0(d,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(302,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(b)
| ~ n0(d,b) ),
inference(modus_ponens,[status(thm)],[301,300]) ).
tff(303,plain,
k1(b),
inference(unit_resolution,[status(thm)],[302,299,119]) ).
tff(304,plain,
( ( m2(b)
| ~ k1(b) )
<=> ( m2(b)
| ~ k1(b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(305,axiom,
( m2(b)
| ~ k1(b) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_136) ).
tff(306,plain,
( m2(b)
| ~ k1(b) ),
inference(modus_ponens,[status(thm)],[305,304]) ).
tff(307,plain,
m2(b),
inference(unit_resolution,[status(thm)],[306,303]) ).
tff(308,plain,
( ( ~ ! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) )
| ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ q2(e,e,e)
| ~ m3(a,e,e) )
<=> ( ~ ! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) )
| ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ q2(e,e,e)
| ~ m3(a,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(309,plain,
( ( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,e,e)
| ~ q2(e,e,e) )
<=> ( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ q2(e,e,e)
| ~ m3(a,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(310,plain,
( ( ~ ! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) )
| ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,e,e)
| ~ q2(e,e,e) )
<=> ( ~ ! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) )
| ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ q2(e,e,e)
| ~ m3(a,e,e) ) ),
inference(monotonicity,[status(thm)],[309]) ).
tff(311,plain,
( ( ~ ! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) )
| ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,e,e)
| ~ q2(e,e,e) )
<=> ( ~ ! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) )
| ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ q2(e,e,e)
| ~ m3(a,e,e) ) ),
inference(transitivity,[status(thm)],[310,308]) ).
tff(312,plain,
( ~ ! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) )
| ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,e,e)
| ~ q2(e,e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(313,plain,
( ~ ! [G: $i] :
( ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ m3(a,G,G)
| ~ q2(G,e,G) )
| ~ m2(b)
| ~ k2(a,a)
| r3(a,a,e)
| ~ q2(e,e,e)
| ~ m3(a,e,e) ),
inference(modus_ponens,[status(thm)],[312,311]) ).
tff(314,plain,
( r3(a,a,e)
| ~ m3(a,e,e) ),
inference(unit_resolution,[status(thm)],[313,307,296,286,272]) ).
tff(315,plain,
r3(a,a,e),
inference(unit_resolution,[status(thm)],[314,241]) ).
tff(316,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
refl(( ( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) )
<=> ( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) ) )),
inference(bind,[status(th)],[]) ).
tff(317,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) ) ),
inference(quant_intro,[status(thm)],[316]) ).
tff(318,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(319,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
trans(monotonicity(rewrite(( ( p4(H,I,I)
| ~ r3(I,I,H) )
<=> ( ~ r3(I,I,H)
| p4(H,I,I) ) )),
( ( p4(H,I,I)
| ~ r3(I,I,H)
| ~ p4(J,J,A) )
<=> ( ~ r3(I,I,H)
| p4(H,I,I)
| ~ p4(J,J,A) ) )),
rewrite(( ( ~ r3(I,I,H)
| p4(H,I,I)
| ~ p4(J,J,A) )
<=> ( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) ) )),
( ( p4(H,I,I)
| ~ r3(I,I,H)
| ~ p4(J,J,A) )
<=> ( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) ) )),
inference(bind,[status(th)],[]) ).
tff(320,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( p4(H,I,I)
| ~ r3(I,I,H)
| ~ p4(J,J,A) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) ) ),
inference(quant_intro,[status(thm)],[319]) ).
tff(321,axiom,
! [I: $i,A: $i,J: $i,H: $i] :
( p4(H,I,I)
| ~ r3(I,I,H)
| ~ p4(J,J,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_288) ).
tff(322,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) ),
inference(modus_ponens,[status(thm)],[321,320]) ).
tff(323,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) ),
inference(modus_ponens,[status(thm)],[322,318]) ).
tff(324,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) ),
inference(skolemize,[status(sab)],[323]) ).
tff(325,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) ),
inference(modus_ponens,[status(thm)],[324,317]) ).
tff(326,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) )
| ~ p4(b,b,c)
| ~ r3(a,a,e)
| p4(e,a,a) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) )
| ~ p4(b,b,c)
| ~ r3(a,a,e)
| p4(e,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(327,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) )
| ~ p4(b,b,c)
| ~ r3(a,a,e)
| p4(e,a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(328,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ p4(J,J,A)
| ~ r3(I,I,H)
| p4(H,I,I) )
| ~ p4(b,b,c)
| ~ r3(a,a,e)
| p4(e,a,a) ),
inference(modus_ponens,[status(thm)],[327,326]) ).
tff(329,plain,
p4(e,a,a),
inference(unit_resolution,[status(thm)],[328,325,315,112]) ).
tff(330,plain,
( ~ m5(e,a)
<=> ~ m5(e,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(331,axiom,
~ m5(e,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(332,plain,
~ m5(e,a),
inference(modus_ponens,[status(thm)],[331,330]) ).
tff(333,plain,
^ [D: $i,E: $i,F: $i] :
refl(( ( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) )
<=> ( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) ) )),
inference(bind,[status(th)],[]) ).
tff(334,plain,
( ! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) )
<=> ! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) ) ),
inference(quant_intro,[status(thm)],[333]) ).
tff(335,plain,
( ! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) )
<=> ! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(336,plain,
^ [D: $i,E: $i,F: $i] :
trans(monotonicity(rewrite(( ( m5(D,E)
| ~ r0(D) )
<=> ( ~ r0(D)
| m5(D,E) ) )),
( ( m5(D,E)
| ~ r0(D)
| ~ p4(D,F,E) )
<=> ( ~ r0(D)
| m5(D,E)
| ~ p4(D,F,E) ) )),
rewrite(( ( ~ r0(D)
| m5(D,E)
| ~ p4(D,F,E) )
<=> ( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) ) )),
( ( m5(D,E)
| ~ r0(D)
| ~ p4(D,F,E) )
<=> ( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) ) )),
inference(bind,[status(th)],[]) ).
tff(337,plain,
( ! [D: $i,E: $i,F: $i] :
( m5(D,E)
| ~ r0(D)
| ~ p4(D,F,E) )
<=> ! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) ) ),
inference(quant_intro,[status(thm)],[336]) ).
tff(338,axiom,
! [D: $i,E: $i,F: $i] :
( m5(D,E)
| ~ r0(D)
| ~ p4(D,F,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_303) ).
tff(339,plain,
! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) ),
inference(modus_ponens,[status(thm)],[338,337]) ).
tff(340,plain,
! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) ),
inference(modus_ponens,[status(thm)],[339,335]) ).
tff(341,plain,
! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) ),
inference(skolemize,[status(sab)],[340]) ).
tff(342,plain,
! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) ),
inference(modus_ponens,[status(thm)],[341,334]) ).
tff(343,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) )
| ~ r0(e)
| m5(e,a)
| ~ p4(e,a,a) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) )
| ~ r0(e)
| m5(e,a)
| ~ p4(e,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(344,plain,
( ( ~ p4(e,a,a)
| ~ r0(e)
| m5(e,a) )
<=> ( ~ r0(e)
| m5(e,a)
| ~ p4(e,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(345,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) )
| ~ p4(e,a,a)
| ~ r0(e)
| m5(e,a) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) )
| ~ r0(e)
| m5(e,a)
| ~ p4(e,a,a) ) ),
inference(monotonicity,[status(thm)],[344]) ).
tff(346,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) )
| ~ p4(e,a,a)
| ~ r0(e)
| m5(e,a) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) )
| ~ r0(e)
| m5(e,a)
| ~ p4(e,a,a) ) ),
inference(transitivity,[status(thm)],[345,343]) ).
tff(347,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) )
| ~ p4(e,a,a)
| ~ r0(e)
| m5(e,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(348,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( ~ p4(D,F,E)
| ~ r0(D)
| m5(D,E) )
| ~ r0(e)
| m5(e,a)
| ~ p4(e,a,a) ),
inference(modus_ponens,[status(thm)],[347,346]) ).
tff(349,plain,
$false,
inference(unit_resolution,[status(thm)],[348,211,342,332,329]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN144-1 : TPTP v9.0.0. Released v1.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:28:07 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47 % SZS output start Proof
% See solution above
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------