%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN156-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:38:22 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 141
% Syntax : Number of formulae : 318 ( 73 unt; 0 typ; 0 def)
% Number of atoms : 1600 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 2230 (1035 ~;1029 |; 0 &)
% ( 166 <=>; 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 : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 26 ( 25 usr; 1 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/sandbox/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/sandbox/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,
( l0(a)
<=> l0(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
l0(a),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_20) ).
tff(17,plain,
l0(a),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( s0(d)
<=> s0(d) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
s0(d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_1) ).
tff(20,plain,
s0(d),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) )
<=> ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) )
<=> ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ( m1(a,a,a)
| ~ l0(a) )
<=> ( m1(a,a,a)
| ~ l0(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) )
<=> ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) )
<=> ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ) ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,axiom,
( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_023) ).
tff(27,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[27,21]) ).
tff(29,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[29,21]) ).
tff(31,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[30,21]) ).
tff(32,plain,
m1(a,a,a),
inference(unit_resolution,[status(thm)],[31,20,17]) ).
tff(33,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(34,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(35,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)],[34,33]) ).
tff(36,plain,
p2(a,a,a),
inference(unit_resolution,[status(thm)],[35,32,14]) ).
tff(37,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(38,plain,
( ( m3(a,a,a)
| ~ p2(a,a,a) )
<=> ( ~ p2(a,a,a)
| m3(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,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)],[38]) ).
tff(40,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)],[39,37]) ).
tff(41,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(42,plain,
( ~ ! [I: $i] :
( m3(I,I,I)
| ~ p2(I,I,I) )
| ~ p2(a,a,a)
| m3(a,a,a) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
m3(a,a,a),
inference(unit_resolution,[status(thm)],[42,36,7]) ).
tff(44,plain,
^ [I: $i,J: $i] :
refl(( ( k1(I)
| ~ n0(J,I) )
<=> ( k1(I)
| ~ n0(J,I) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_001) ).
tff(48,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( n0(b,a)
<=> n0(b,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
n0(b,a),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_37) ).
tff(53,plain,
n0(b,a),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,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(55,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(a)
| ~ n0(b,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(a)
| ~ n0(b,a) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
k1(a),
inference(unit_resolution,[status(thm)],[56,53,50]) ).
tff(58,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(59,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)],[58]) ).
tff(60,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(61,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(62,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)],[61]) ).
tff(63,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(64,plain,
! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
( m0(a,e,e)
<=> m0(a,e,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
m0(a,e,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_23) ).
tff(70,plain,
m0(a,e,e),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,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(72,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(73,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)],[72,71]) ).
tff(74,plain,
( ~ k1(a)
| n1(a,e,e) ),
inference(unit_resolution,[status(thm)],[73,70,67]) ).
tff(75,plain,
n1(a,e,e),
inference(unit_resolution,[status(thm)],[74,57]) ).
tff(76,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(77,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)],[76]) ).
tff(78,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(79,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(80,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)],[79]) ).
tff(81,axiom,
! [C: $i] :
( p2(C,e,C)
| ~ n1(C,e,e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_170) ).
tff(82,plain,
! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ),
inference(modus_ponens,[status(thm)],[84,77]) ).
tff(86,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(87,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(88,plain,
( ~ ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) )
| ~ n1(a,e,e)
| p2(a,e,a) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
p2(a,e,a),
inference(unit_resolution,[status(thm)],[88,85,75]) ).
tff(90,plain,
^ [H: $i,G: $i] :
refl(( ( ~ n0(H,G)
| l1(G,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],[]) ).
tff(91,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)],[90]) ).
tff(92,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(93,plain,
^ [H: $i,G: $i] :
rewrite(( ( l1(G,G)
| ~ n0(H,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],[]) ).
tff(94,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)],[93]) ).
tff(95,axiom,
! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_002) ).
tff(96,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(skolemize,[status(sab)],[97]) ).
tff(99,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[98,91]) ).
tff(100,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(101,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(b,a)
| l1(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(b,a)
| l1(a,a) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
l1(a,a),
inference(unit_resolution,[status(thm)],[102,53,99]) ).
tff(104,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(105,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)],[104]) ).
tff(106,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(107,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(108,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)],[107]) ).
tff(109,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(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) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
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) ),
inference(modus_ponens,[status(thm)],[110,106]) ).
tff(112,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)],[111]) ).
tff(113,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)],[112,105]) ).
tff(114,plain,
( ( ~ l0(a)
| p1(a,a,a) )
<=> ( ~ l0(a)
| p1(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,plain,
( ( p1(a,a,a)
| ~ l0(a) )
<=> ( ~ l0(a)
| p1(a,a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,axiom,
( p1(a,a,a)
| ~ l0(a) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_088) ).
tff(117,plain,
( ~ l0(a)
| p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
( ~ l0(a)
| p1(a,a,a) ),
inference(modus_ponens,[status(thm)],[117,114]) ).
tff(119,plain,
p1(a,a,a),
inference(unit_resolution,[status(thm)],[118,17]) ).
tff(120,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(121,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(122,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)],[121]) ).
tff(123,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)],[122,120]) ).
tff(124,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(125,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)],[124,123]) ).
tff(126,plain,
p2(a,e,e),
inference(unit_resolution,[status(thm)],[125,119,113,103,89]) ).
tff(127,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(128,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)],[127]) ).
tff(129,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(130,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(131,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(skolemize,[status(sab)],[131]) ).
tff(133,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[132,128]) ).
tff(134,plain,
( k0(e)
<=> k0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,axiom,
k0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(136,plain,
k0(e),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
( r0(e)
<=> r0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(138,axiom,
r0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_13) ).
tff(139,plain,
r0(e),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
( ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,plain,
( ( p1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) ) ),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(transitivity,[status(thm)],[143,141]) ).
tff(145,axiom,
( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_090) ).
tff(146,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[146,140]) ).
tff(148,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[147,140]) ).
tff(149,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[148,140]) ).
tff(150,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[149,140]) ).
tff(151,plain,
p1(e,e,e),
inference(unit_resolution,[status(thm)],[150,139,136]) ).
tff(152,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(153,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(154,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
n2(e),
inference(unit_resolution,[status(thm)],[154,151,133]) ).
tff(156,plain,
( ( ~ r0(e)
| m1(e,e,e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(157,plain,
( ( m1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,axiom,
( m1(e,e,e)
| ~ r0(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_012) ).
tff(159,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[159,156]) ).
tff(161,plain,
m1(e,e,e),
inference(unit_resolution,[status(thm)],[160,139]) ).
tff(162,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(163,plain,
( ( p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,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)],[163]) ).
tff(165,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)],[164,162]) ).
tff(166,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(167,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)],[166,165]) ).
tff(168,plain,
p2(e,e,e),
inference(unit_resolution,[status(thm)],[167,161,14]) ).
tff(169,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(170,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)],[169]) ).
tff(171,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(172,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(173,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)],[172]) ).
tff(174,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(175,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[175,171]) ).
tff(177,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(skolemize,[status(sab)],[176]) ).
tff(178,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[177,170]) ).
tff(179,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(180,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(181,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)],[180,179]) ).
tff(182,plain,
m3(e,e,e),
inference(unit_resolution,[status(thm)],[181,178,168,155]) ).
tff(183,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(184,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)],[183]) ).
tff(185,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(186,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(187,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)],[186]) ).
tff(188,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( p3(A,B,B)
| ~ m3(B,C,D)
| ~ p2(A,B,D) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_251) ).
tff(189,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)],[188,187]) ).
tff(190,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)],[189,185]) ).
tff(191,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)],[190]) ).
tff(192,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)],[191,184]) ).
tff(193,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(194,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(195,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)],[194]) ).
tff(196,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)],[195,193]) ).
tff(197,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(198,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)],[197,196]) ).
tff(199,plain,
p3(a,e,e),
inference(unit_resolution,[status(thm)],[198,192,182,126]) ).
tff(200,plain,
( ~ n4(a,e)
<=> ~ n4(a,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,axiom,
~ n4(a,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(202,plain,
~ n4(a,e),
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,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(204,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)],[203]) ).
tff(205,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(206,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(207,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)],[206]) ).
tff(208,axiom,
! [A: $i,J: $i] :
( n4(J,A)
| ~ p3(J,A,A)
| ~ n4(J,J) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_281) ).
tff(209,plain,
! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) ),
inference(modus_ponens,[status(thm)],[208,207]) ).
tff(210,plain,
! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) ),
inference(modus_ponens,[status(thm)],[209,205]) ).
tff(211,plain,
! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) ),
inference(skolemize,[status(sab)],[210]) ).
tff(212,plain,
! [A: $i,J: $i] :
( ~ n4(J,J)
| ~ p3(J,A,A)
| n4(J,A) ),
inference(modus_ponens,[status(thm)],[211,204]) ).
tff(213,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(214,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(215,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)],[214,213]) ).
tff(216,plain,
( ~ n4(a,a)
| ~ p3(a,e,e) ),
inference(unit_resolution,[status(thm)],[215,212,202]) ).
tff(217,plain,
~ n4(a,a),
inference(unit_resolution,[status(thm)],[216,199]) ).
tff(218,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(219,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)],[218]) ).
tff(220,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(221,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(222,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)],[221]) ).
tff(223,axiom,
! [I: $i,H: $i] :
( n4(H,H)
| ~ k4(I)
| ~ m3(H,H,H) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_284) ).
tff(224,plain,
! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) ),
inference(modus_ponens,[status(thm)],[223,222]) ).
tff(225,plain,
! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) ),
inference(modus_ponens,[status(thm)],[224,220]) ).
tff(226,plain,
! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) ),
inference(skolemize,[status(sab)],[225]) ).
tff(227,plain,
! [I: $i,H: $i] :
( n4(H,H)
| ~ m3(H,H,H)
| ~ k4(I) ),
inference(modus_ponens,[status(thm)],[226,219]) ).
tff(228,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(229,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)],[228]) ).
tff(230,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(231,axiom,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_240) ).
tff(232,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[231,230]) ).
tff(233,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(skolemize,[status(sab)],[232]) ).
tff(234,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[233,229]) ).
tff(235,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(236,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(237,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(e)
| ~ p2(e,e,e) ),
inference(modus_ponens,[status(thm)],[236,235]) ).
tff(238,plain,
n3(e),
inference(unit_resolution,[status(thm)],[237,234,168]) ).
tff(239,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(240,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)],[239]) ).
tff(241,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(242,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(243,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)],[242]) ).
tff(244,axiom,
! [D: $i,E: $i,F: $i,C: $i] :
( l1(C,D)
| ~ p0(E,C)
| ~ r0(F)
| ~ m0(D,C,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_003) ).
tff(245,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)],[244,243]) ).
tff(246,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)],[245,241]) ).
tff(247,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)],[246]) ).
tff(248,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)],[247,240]) ).
tff(249,plain,
( m0(e,b,c)
<=> m0(e,b,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(250,axiom,
m0(e,b,c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_27) ).
tff(251,plain,
m0(e,b,c),
inference(modus_ponens,[status(thm)],[250,249]) ).
tff(252,plain,
( p0(c,b)
<=> p0(c,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(253,axiom,
p0(c,b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_18) ).
tff(254,plain,
p0(c,b),
inference(modus_ponens,[status(thm)],[253,252]) ).
tff(255,plain,
( r0(b)
<=> r0(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(256,axiom,
r0(b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_9) ).
tff(257,plain,
r0(b),
inference(modus_ponens,[status(thm)],[256,255]) ).
tff(258,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(259,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(260,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)],[259]) ).
tff(261,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)],[260,258]) ).
tff(262,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(263,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)],[262,261]) ).
tff(264,plain,
l1(b,e),
inference(unit_resolution,[status(thm)],[263,257,254,251,248]) ).
tff(265,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(266,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)],[265]) ).
tff(267,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(268,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(269,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)],[268]) ).
tff(270,axiom,
! [H: $i,G: $i] :
( q2(G,G,H)
| ~ l1(H,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_186) ).
tff(271,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[270,269]) ).
tff(272,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[271,267]) ).
tff(273,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(skolemize,[status(sab)],[272]) ).
tff(274,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[273,266]) ).
tff(275,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(276,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(277,plain,
( ~ ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
| ~ l1(b,e)
| q2(e,e,b) ),
inference(modus_ponens,[status(thm)],[276,275]) ).
tff(278,plain,
q2(e,e,b),
inference(unit_resolution,[status(thm)],[277,274,264]) ).
tff(279,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(280,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)],[279]) ).
tff(281,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(282,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(283,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)],[282]) ).
tff(284,axiom,
! [I: $i,H: $i,G: $i] :
( q3(G,H)
| ~ q2(I,G,H)
| ~ n0(I,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_255) ).
tff(285,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[284,283]) ).
tff(286,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[285,281]) ).
tff(287,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(skolemize,[status(sab)],[286]) ).
tff(288,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[287,280]) ).
tff(289,plain,
( n0(e,e)
<=> n0(e,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(290,axiom,
n0(e,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_30) ).
tff(291,plain,
n0(e,e),
inference(modus_ponens,[status(thm)],[290,289]) ).
tff(292,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(293,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(294,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)],[293]) ).
tff(295,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)],[294,292]) ).
tff(296,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(297,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)],[296,295]) ).
tff(298,plain,
q3(e,b),
inference(unit_resolution,[status(thm)],[297,291,288,278]) ).
tff(299,plain,
( n0(c,d)
<=> n0(c,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(300,axiom,
n0(c,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_34) ).
tff(301,plain,
n0(c,d),
inference(modus_ponens,[status(thm)],[300,299]) ).
tff(302,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(303,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(304,plain,
( ( k4(c)
| ~ n0(c,d)
| ~ q3(e,b) )
<=> ( ~ q3(e,b)
| ~ n0(c,d)
| k4(c) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(305,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)],[304]) ).
tff(306,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)],[305,303]) ).
tff(307,axiom,
( k4(c)
| ~ n0(c,d)
| ~ q3(e,b)
| ~ n3(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_274) ).
tff(308,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[307,306]) ).
tff(309,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[308,302]) ).
tff(310,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[309,302]) ).
tff(311,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[310,302]) ).
tff(312,plain,
( ~ q3(e,b)
| ~ n0(c,d)
| k4(c)
| ~ n3(e) ),
inference(modus_ponens,[status(thm)],[311,302]) ).
tff(313,plain,
( ~ q3(e,b)
| k4(c)
| ~ n3(e) ),
inference(unit_resolution,[status(thm)],[312,301]) ).
tff(314,plain,
k4(c),
inference(unit_resolution,[status(thm)],[313,298,238]) ).
tff(315,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(316,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(317,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)],[316,315]) ).
tff(318,plain,
$false,
inference(unit_resolution,[status(thm)],[317,314,227,217,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN156-1 : TPTP v9.0.0. Released v1.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.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 12:28:10 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46 % SZS output start Proof
% See solution above
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------