TSTP Solution File: PUZ056-2.005 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ056-2.005 : TPTP v8.1.0. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 : Sun Sep 18 14:11:09 EDT 2022
% Result : Unsatisfiable 2.48s 1.84s
% Output : Proof 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 117
% Syntax : Number of formulae : 245 ( 56 unt; 5 typ; 0 def)
% Number of atoms : 2792 ( 0 equ)
% Maximal formula atoms : 34 ( 11 avg)
% Number of connectives : 4787 (2364 ~;2256 |; 0 &)
% ( 167 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 129 ( 129 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 2 >; 5 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-5 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 1470 (1416 !; 0 ?;1470 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_type,type,
p: ( $i * $i * $i * $i * $i ) > $o ).
tff(s2_type,type,
s2: $i ).
tff(s0_type,type,
s0: $i ).
tff(s1_type,type,
s1: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(1,plain,
( p(s0,s0,s0,s0,s0)
<=> p(s0,s0,s0,s0,s0) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
p(s0,s0,s0,s0,s0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',init) ).
tff(3,plain,
p(s0,s0,s0,s0,s0),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
refl(
( ( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
<=> ( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
<=> ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
<=> ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule1) ).
tff(8,plain,
! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s0,s0,s0,s0)
| p(s2,s0,s0,s0,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s0,s0,s0,s0)
| p(s2,s0,s0,s0,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s0,s0,s0,s0)
| p(s2,s0,s0,s0,s0) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s0,s0,s0,s0)
| p(s2,s0,s0,s0,s0) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
p(s2,s0,s0,s0,s0),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( neq(s2,s1)
<=> neq(s2,s1) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
neq(s2,s1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',neq8) ).
tff(17,plain,
neq(s2,s1),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( neq(s2,s0)
<=> neq(s2,s0) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
neq(s2,s0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',neq7) ).
tff(20,plain,
neq(s2,s0),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
refl(
( ( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
<=> ( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
<=> ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
<=> ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
^ [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ p(T0,I,T2,T3,T4)
| ~ neq(T0,I) )
<=> ( ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) ) )),
( ( ~ p(T0,I,T2,T3,T4)
| ~ neq(T0,I)
| ~ neq(T0,J) )
<=> ( ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4)
| ~ neq(T0,J) ) )),
rewrite(
( ( ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4)
| ~ neq(T0,J) )
<=> ( ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) ) )),
( ( ~ p(T0,I,T2,T3,T4)
| ~ neq(T0,I)
| ~ neq(T0,J) )
<=> ( ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) ) )),
( ( ~ p(T0,I,T2,T3,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| p(T0,J,T2,T3,T4) )
<=> ( ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4)
| p(T0,J,T2,T3,T4) ) )),
rewrite(
( ( ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4)
| p(T0,J,T2,T3,T4) )
<=> ( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) ) )),
( ( ~ p(T0,I,T2,T3,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| p(T0,J,T2,T3,T4) )
<=> ( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( ~ p(T0,I,T2,T3,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| p(T0,J,T2,T3,T4) )
<=> ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( ~ p(T0,I,T2,T3,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| p(T0,J,T2,T3,T4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule2) ).
tff(27,plain,
! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s0,s0)
| p(s2,s1,s0,s0,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s0,s0)
| p(s2,s1,s0,s0,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( p(s2,s1,s0,s0,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s0,s0) )
<=> ( ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s0,s0)
| p(s2,s1,s0,s0,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s2,s1,s0,s0,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s0,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s0,s0)
| p(s2,s1,s0,s0,s0) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s2,s1,s0,s0,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s0,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s0,s0)
| p(s2,s1,s0,s0,s0) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s2,s1,s0,s0,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s0,s0) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s0,s0)
| p(s2,s1,s0,s0,s0) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
p(s2,s1,s0,s0,s0),
inference(unit_resolution,[status(thm)],[36,30,20,17,14]) ).
tff(38,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s1,s0,s0,s0)
| p(s1,s1,s0,s0,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s1,s0,s0,s0)
| p(s1,s1,s0,s0,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s1,s0,s0,s0)
| p(s1,s1,s0,s0,s0) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s1,s0,s0,s0)
| p(s1,s1,s0,s0,s0) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
p(s1,s1,s0,s0,s0),
inference(unit_resolution,[status(thm)],[40,10,37]) ).
tff(42,plain,
( neq(s1,s2)
<=> neq(s1,s2) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
neq(s1,s2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',neq6) ).
tff(44,plain,
neq(s1,s2),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( neq(s1,s0)
<=> neq(s1,s0) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
neq(s1,s0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',neq4) ).
tff(47,plain,
neq(s1,s0),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
^ [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
refl(
( ( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
<=> ( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
<=> ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
<=> ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
^ [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ p(T0,T1,I,T3,T4)
| ~ neq(T0,I) )
<=> ( ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ) )),
( ( ~ p(T0,T1,I,T3,T4)
| ~ neq(T0,I)
| ~ neq(T0,J) )
<=> ( ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4)
| ~ neq(T0,J) ) )),
rewrite(
( ( ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4)
| ~ neq(T0,J) )
<=> ( ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ) )),
( ( ~ p(T0,T1,I,T3,T4)
| ~ neq(T0,I)
| ~ neq(T0,J) )
<=> ( ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ) )),
( ( ~ p(T0,T1,I,T3,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I) )
<=> ( ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4)
| ~ neq(T1,I) ) )),
rewrite(
( ( ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4)
| ~ neq(T1,I) )
<=> ( ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ) )),
( ( ~ p(T0,T1,I,T3,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I) )
<=> ( ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ) )),
( ( ~ p(T0,T1,I,T3,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J) )
<=> ( ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4)
| ~ neq(T1,J) ) )),
rewrite(
( ( ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4)
| ~ neq(T1,J) )
<=> ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ) )),
( ( ~ p(T0,T1,I,T3,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J) )
<=> ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ) )),
( ( ~ p(T0,T1,I,T3,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| p(T0,T1,J,T3,T4) )
<=> ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4)
| p(T0,T1,J,T3,T4) ) )),
rewrite(
( ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4)
| p(T0,T1,J,T3,T4) )
<=> ( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ) )),
( ( ~ p(T0,T1,I,T3,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| p(T0,T1,J,T3,T4) )
<=> ( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ p(T0,T1,I,T3,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| p(T0,T1,J,T3,T4) )
<=> ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,axiom,
! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ p(T0,T1,I,T3,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| p(T0,T1,J,T3,T4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule3) ).
tff(54,plain,
! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) ),
inference(modus_ponens,[status(thm)],[56,49]) ).
tff(58,plain,
( ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s1,s2,s0,s0)
| ~ p(s1,s1,s0,s0,s0) )
<=> ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s1,s2,s0,s0)
| ~ p(s1,s1,s0,s0,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( p(s1,s1,s2,s0,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ p(s1,s1,s0,s0,s0) )
<=> ( ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s1,s2,s0,s0)
| ~ p(s1,s1,s0,s0,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| p(s1,s1,s2,s0,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ p(s1,s1,s0,s0,s0) )
<=> ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s1,s2,s0,s0)
| ~ p(s1,s1,s0,s0,s0) ) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| p(s1,s1,s2,s0,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ p(s1,s1,s0,s0,s0) )
<=> ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s1,s2,s0,s0)
| ~ p(s1,s1,s0,s0,s0) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| p(s1,s1,s2,s0,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ p(s1,s1,s0,s0,s0) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s1,s2,s0,s0)
| ~ p(s1,s1,s0,s0,s0) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
p(s1,s1,s2,s0,s0),
inference(unit_resolution,[status(thm)],[63,57,47,44,41]) ).
tff(65,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s1,s2,s0,s0)
| p(s0,s1,s2,s0,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s1,s2,s0,s0)
| p(s0,s1,s2,s0,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s1,s2,s0,s0)
| p(s0,s1,s2,s0,s0) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s1,s2,s0,s0)
| p(s0,s1,s2,s0,s0) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
p(s0,s1,s2,s0,s0),
inference(unit_resolution,[status(thm)],[67,10,64]) ).
tff(69,plain,
( neq(s0,s2)
<=> neq(s0,s2) ),
inference(rewrite,[status(thm)],]) ).
tff(70,axiom,
neq(s0,s2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',neq3) ).
tff(71,plain,
neq(s0,s2),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( neq(s0,s1)
<=> neq(s0,s1) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
neq(s0,s1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',neq2) ).
tff(74,plain,
neq(s0,s1),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| p(s0,s2,s2,s0,s0)
| ~ p(s0,s1,s2,s0,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| p(s0,s2,s2,s0,s0)
| ~ p(s0,s1,s2,s0,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
( ( p(s0,s2,s2,s0,s0)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ p(s0,s1,s2,s0,s0) )
<=> ( ~ neq(s0,s1)
| ~ neq(s0,s2)
| p(s0,s2,s2,s0,s0)
| ~ p(s0,s1,s2,s0,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s0,s2,s2,s0,s0)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ p(s0,s1,s2,s0,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| p(s0,s2,s2,s0,s0)
| ~ p(s0,s1,s2,s0,s0) ) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s0,s2,s2,s0,s0)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ p(s0,s1,s2,s0,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| p(s0,s2,s2,s0,s0)
| ~ p(s0,s1,s2,s0,s0) ) ),
inference(transitivity,[status(thm)],[77,75]) ).
tff(79,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s0,s2,s2,s0,s0)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ p(s0,s1,s2,s0,s0) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| p(s0,s2,s2,s0,s0)
| ~ p(s0,s1,s2,s0,s0) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
p(s0,s2,s2,s0,s0),
inference(unit_resolution,[status(thm)],[80,30,74,71,68]) ).
tff(82,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s2,s2,s0,s0)
| p(s2,s2,s2,s0,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s2,s2,s0,s0)
| p(s2,s2,s2,s0,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s2,s2,s0,s0)
| p(s2,s2,s2,s0,s0) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s2,s2,s0,s0)
| p(s2,s2,s2,s0,s0) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
p(s2,s2,s2,s0,s0),
inference(unit_resolution,[status(thm)],[84,10,81]) ).
tff(86,plain,
^ [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
refl(
( ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
<=> ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
<=> ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
( ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
<=> ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
^ [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,I) )
<=> ( ~ neq(T0,I)
| ~ p(T0,T1,T2,I,T4) ) )),
( ( ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,I)
| ~ neq(T0,J) )
<=> ( ~ neq(T0,I)
| ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,J) ) )),
rewrite(
( ( ~ neq(T0,I)
| ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,J) )
<=> ( ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,T2,I,T4) ) )),
( ( ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,I)
| ~ neq(T0,J) )
<=> ( ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,T2,I,T4) ) )),
( ( ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I) )
<=> ( ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,T2,I,T4)
| ~ neq(T1,I) ) )),
rewrite(
( ( ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,T2,I,T4)
| ~ neq(T1,I) )
<=> ( ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,T2,I,T4) ) )),
( ( ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I) )
<=> ( ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,T2,I,T4) ) )),
( ( ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J) )
<=> ( ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,T2,I,T4)
| ~ neq(T1,J) ) )),
rewrite(
( ( ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,T2,I,T4)
| ~ neq(T1,J) )
<=> ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,T2,I,T4) ) )),
( ( ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J) )
<=> ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,T2,I,T4) ) )),
( ( ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I) )
<=> ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,T2,I,T4)
| ~ neq(T2,I) ) )),
rewrite(
( ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,T2,I,T4)
| ~ neq(T2,I) )
<=> ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) ) )),
( ( ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I) )
<=> ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) ) )),
( ( ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I)
| ~ neq(T2,J) )
<=> ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4)
| ~ neq(T2,J) ) )),
rewrite(
( ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4)
| ~ neq(T2,J) )
<=> ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) ) )),
( ( ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I)
| ~ neq(T2,J) )
<=> ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) ) )),
( ( ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I)
| ~ neq(T2,J)
| p(T0,T1,T2,J,T4) )
<=> ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4)
| p(T0,T1,T2,J,T4) ) )),
rewrite(
( ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4)
| p(T0,T1,T2,J,T4) )
<=> ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) ) )),
( ( ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I)
| ~ neq(T2,J)
| p(T0,T1,T2,J,T4) )
<=> ( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I)
| ~ neq(T2,J)
| p(T0,T1,T2,J,T4) )
<=> ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,axiom,
! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ p(T0,T1,T2,I,T4)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I)
| ~ neq(T2,J)
| p(T0,T1,T2,J,T4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule4) ).
tff(92,plain,
! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) ),
inference(modus_ponens,[status(thm)],[94,87]) ).
tff(96,plain,
( ( ~ ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s2,s2,s0,s0)
| p(s2,s2,s2,s1,s0) )
<=> ( ~ ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s2,s2,s0,s0)
| p(s2,s2,s2,s1,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
( ( ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| p(s2,s2,s2,s1,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s2,s2,s0,s0) )
<=> ( ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s2,s2,s0,s0)
| p(s2,s2,s2,s1,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ( ~ ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| p(s2,s2,s2,s1,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s2,s2,s0,s0) )
<=> ( ~ ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s2,s2,s0,s0)
| p(s2,s2,s2,s1,s0) ) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
( ( ~ ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| p(s2,s2,s2,s1,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s2,s2,s0,s0) )
<=> ( ~ ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s2,s2,s0,s0)
| p(s2,s2,s2,s1,s0) ) ),
inference(transitivity,[status(thm)],[98,96]) ).
tff(100,plain,
( ~ ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| p(s2,s2,s2,s1,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s2,s2,s0,s0) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s2,s2,s0,s0)
| p(s2,s2,s2,s1,s0) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
p(s2,s2,s2,s1,s0),
inference(unit_resolution,[status(thm)],[101,95,20,17,85]) ).
tff(103,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s2,s2,s1,s0)
| p(s1,s2,s2,s1,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s2,s2,s1,s0)
| p(s1,s2,s2,s1,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s2,s2,s1,s0)
| p(s1,s2,s2,s1,s0) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s2,s2,s1,s0)
| p(s1,s2,s2,s1,s0) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
p(s1,s2,s2,s1,s0),
inference(unit_resolution,[status(thm)],[105,10,102]) ).
tff(107,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s0,s2,s1,s0)
| ~ p(s1,s2,s2,s1,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s0,s2,s1,s0)
| ~ p(s1,s2,s2,s1,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ( p(s1,s0,s2,s1,s0)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ p(s1,s2,s2,s1,s0) )
<=> ( ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s0,s2,s1,s0)
| ~ p(s1,s2,s2,s1,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s1,s0,s2,s1,s0)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ p(s1,s2,s2,s1,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s0,s2,s1,s0)
| ~ p(s1,s2,s2,s1,s0) ) ),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s1,s0,s2,s1,s0)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ p(s1,s2,s2,s1,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s0,s2,s1,s0)
| ~ p(s1,s2,s2,s1,s0) ) ),
inference(transitivity,[status(thm)],[109,107]) ).
tff(111,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s1,s0,s2,s1,s0)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ p(s1,s2,s2,s1,s0) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s0,s2,s1,s0)
| ~ p(s1,s2,s2,s1,s0) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
p(s1,s0,s2,s1,s0),
inference(unit_resolution,[status(thm)],[112,30,47,44,106]) ).
tff(114,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s0,s2,s1,s0)
| p(s0,s0,s2,s1,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s0,s2,s1,s0)
| p(s0,s0,s2,s1,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s0,s2,s1,s0)
| p(s0,s0,s2,s1,s0) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s0,s2,s1,s0)
| p(s0,s0,s2,s1,s0) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
p(s0,s0,s2,s1,s0),
inference(unit_resolution,[status(thm)],[116,10,113]) ).
tff(118,plain,
( ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| p(s0,s0,s1,s1,s0)
| ~ p(s0,s0,s2,s1,s0) )
<=> ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| p(s0,s0,s1,s1,s0)
| ~ p(s0,s0,s2,s1,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
( ( p(s0,s0,s1,s1,s0)
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ p(s0,s0,s2,s1,s0) )
<=> ( ~ neq(s0,s1)
| ~ neq(s0,s2)
| p(s0,s0,s1,s1,s0)
| ~ p(s0,s0,s2,s1,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,plain,
( ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| p(s0,s0,s1,s1,s0)
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ p(s0,s0,s2,s1,s0) )
<=> ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| p(s0,s0,s1,s1,s0)
| ~ p(s0,s0,s2,s1,s0) ) ),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
( ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| p(s0,s0,s1,s1,s0)
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ p(s0,s0,s2,s1,s0) )
<=> ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| p(s0,s0,s1,s1,s0)
| ~ p(s0,s0,s2,s1,s0) ) ),
inference(transitivity,[status(thm)],[120,118]) ).
tff(122,plain,
( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| p(s0,s0,s1,s1,s0)
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ p(s0,s0,s2,s1,s0) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| p(s0,s0,s1,s1,s0)
| ~ p(s0,s0,s2,s1,s0) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
p(s0,s0,s1,s1,s0),
inference(unit_resolution,[status(thm)],[123,57,74,71,117]) ).
tff(125,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s0,s1,s1,s0)
| p(s2,s0,s1,s1,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s0,s1,s1,s0)
| p(s2,s0,s1,s1,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s0,s1,s1,s0)
| p(s2,s0,s1,s1,s0) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s0,s1,s1,s0)
| p(s2,s0,s1,s1,s0) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
p(s2,s0,s1,s1,s0),
inference(unit_resolution,[status(thm)],[127,10,124]) ).
tff(129,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s1,s1,s0)
| p(s2,s1,s1,s1,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s1,s1,s0)
| p(s2,s1,s1,s1,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,plain,
( ( p(s2,s1,s1,s1,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s1,s1,s0) )
<=> ( ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s1,s1,s0)
| p(s2,s1,s1,s1,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(131,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s2,s1,s1,s1,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s1,s1,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s1,s1,s0)
| p(s2,s1,s1,s1,s0) ) ),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s2,s1,s1,s1,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s1,s1,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s1,s1,s0)
| p(s2,s1,s1,s1,s0) ) ),
inference(transitivity,[status(thm)],[131,129]) ).
tff(133,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s2,s1,s1,s1,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s1,s1,s0) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s1,s1,s0)
| p(s2,s1,s1,s1,s0) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
p(s2,s1,s1,s1,s0),
inference(unit_resolution,[status(thm)],[134,30,20,17,128]) ).
tff(136,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s1,s1,s1,s0)
| p(s1,s1,s1,s1,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s1,s1,s1,s0)
| p(s1,s1,s1,s1,s0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(137,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s1,s1,s1,s0)
| p(s1,s1,s1,s1,s0) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s1,s1,s1,s0)
| p(s1,s1,s1,s1,s0) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
p(s1,s1,s1,s1,s0),
inference(unit_resolution,[status(thm)],[138,10,135]) ).
tff(140,plain,
^ [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
refl(
( ( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) )
<=> ( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) ) )),
inference(bind,[status(th)],]) ).
tff(141,plain,
( ! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) )
<=> ! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) ) ),
inference(quant_intro,[status(thm)],[140]) ).
tff(142,plain,
( ! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) )
<=> ! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,plain,
^ [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I) )
<=> ( ~ neq(T0,I)
| ~ p(T0,T1,T2,T3,I) ) )),
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J) )
<=> ( ~ neq(T0,I)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,J) ) )),
rewrite(
( ( ~ neq(T0,I)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,J) )
<=> ( ~ neq(T0,I)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I) ) )),
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J) )
<=> ( ~ neq(T0,I)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I) ) )),
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I) )
<=> ( ~ neq(T0,I)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T1,I) ) )),
rewrite(
( ( ~ neq(T0,I)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T1,I) )
<=> ( ~ neq(T0,I)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T1,I) ) )),
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I) )
<=> ( ~ neq(T0,I)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T1,I) ) )),
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J) )
<=> ( ~ neq(T0,I)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T1,I)
| ~ neq(T1,J) ) )),
rewrite(
( ( ~ neq(T0,I)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T1,I)
| ~ neq(T1,J) )
<=> ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T1,I) ) )),
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J) )
<=> ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T1,I) ) )),
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I) )
<=> ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T1,I)
| ~ neq(T2,I) ) )),
rewrite(
( ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T1,I)
| ~ neq(T2,I) )
<=> ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T2,I)
| ~ neq(T1,I) ) )),
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I) )
<=> ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T2,I)
| ~ neq(T1,I) ) )),
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I)
| ~ neq(T2,J) )
<=> ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T2,I)
| ~ neq(T1,I)
| ~ neq(T2,J) ) )),
rewrite(
( ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T2,I)
| ~ neq(T1,I)
| ~ neq(T2,J) )
<=> ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) ) )),
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I)
| ~ neq(T2,J) )
<=> ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) ) )),
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I)
| ~ neq(T2,J)
| ~ neq(T3,I) )
<=> ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I)
| ~ neq(T3,I) ) )),
rewrite(
( ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I)
| ~ neq(T3,I) )
<=> ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) ) )),
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I)
| ~ neq(T2,J)
| ~ neq(T3,I) )
<=> ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) ) )),
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I)
| ~ neq(T2,J)
| ~ neq(T3,I)
| ~ neq(T3,J) )
<=> ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I)
| ~ neq(T3,J) ) )),
rewrite(
( ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I)
| ~ neq(T3,J) )
<=> ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) ) )),
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I)
| ~ neq(T2,J)
| ~ neq(T3,I)
| ~ neq(T3,J) )
<=> ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) ) )),
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I)
| ~ neq(T2,J)
| ~ neq(T3,I)
| ~ neq(T3,J)
| p(T0,T1,T2,T3,J) )
<=> ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I)
| p(T0,T1,T2,T3,J) ) )),
rewrite(
( ( ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I)
| p(T0,T1,T2,T3,J) )
<=> ( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) ) )),
( ( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I)
| ~ neq(T2,J)
| ~ neq(T3,I)
| ~ neq(T3,J)
| p(T0,T1,T2,T3,J) )
<=> ( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) ) )),
inference(bind,[status(th)],]) ).
tff(144,plain,
( ! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I)
| ~ neq(T2,J)
| ~ neq(T3,I)
| ~ neq(T3,J)
| p(T0,T1,T2,T3,J) )
<=> ! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) ) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,axiom,
! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( ~ p(T0,T1,T2,T3,I)
| ~ neq(T0,I)
| ~ neq(T0,J)
| ~ neq(T1,I)
| ~ neq(T1,J)
| ~ neq(T2,I)
| ~ neq(T2,J)
| ~ neq(T3,I)
| ~ neq(T3,J)
| p(T0,T1,T2,T3,J) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule5) ).
tff(146,plain,
! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) ),
inference(modus_ponens,[status(thm)],[146,142]) ).
tff(148,plain,
! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) ),
inference(skolemize,[status(sab)],[147]) ).
tff(149,plain,
! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) ),
inference(modus_ponens,[status(thm)],[148,141]) ).
tff(150,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ p(s1,s1,s1,s1,s0)
| p(s1,s1,s1,s1,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ p(s1,s1,s1,s1,s0)
| p(s1,s1,s1,s1,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(151,plain,
( ( p(s1,s1,s1,s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s2)
| ~ p(s1,s1,s1,s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s0) )
<=> ( ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ p(s1,s1,s1,s1,s0)
| p(s1,s1,s1,s1,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) )
| p(s1,s1,s1,s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s2)
| ~ p(s1,s1,s1,s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ p(s1,s1,s1,s1,s0)
| p(s1,s1,s1,s1,s2) ) ),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) )
| p(s1,s1,s1,s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s2)
| ~ p(s1,s1,s1,s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s0) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ p(s1,s1,s1,s1,s0)
| p(s1,s1,s1,s1,s2) ) ),
inference(transitivity,[status(thm)],[152,150]) ).
tff(154,plain,
( ~ ! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) )
| p(s1,s1,s1,s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s2)
| ~ p(s1,s1,s1,s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s0) ),
inference(quant_inst,[status(thm)],]) ).
tff(155,plain,
( ~ ! [T3: $i,T2: $i,I: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,T2,T3,J)
| ~ neq(T0,I)
| ~ neq(T1,J)
| ~ neq(T0,J)
| ~ p(T0,T1,T2,T3,I)
| ~ neq(T3,J)
| ~ neq(T3,I)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ neq(T1,I) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ p(s1,s1,s1,s1,s0)
| p(s1,s1,s1,s1,s2) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
p(s1,s1,s1,s1,s2),
inference(unit_resolution,[status(thm)],[155,149,47,44,139]) ).
tff(157,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s1,s1,s1,s2)
| p(s0,s1,s1,s1,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s1,s1,s1,s2)
| p(s0,s1,s1,s1,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s1,s1,s1,s2)
| p(s0,s1,s1,s1,s2) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s1,s1,s1,s2)
| p(s0,s1,s1,s1,s2) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
p(s0,s1,s1,s1,s2),
inference(unit_resolution,[status(thm)],[159,10,156]) ).
tff(161,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s0,s1)
| ~ p(s0,s1,s1,s1,s2)
| ~ neq(s0,s2)
| p(s0,s2,s1,s1,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s0,s1)
| ~ p(s0,s1,s1,s1,s2)
| ~ neq(s0,s2)
| p(s0,s2,s1,s1,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(162,plain,
( ( p(s0,s2,s1,s1,s2)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ p(s0,s1,s1,s1,s2) )
<=> ( ~ neq(s0,s1)
| ~ p(s0,s1,s1,s1,s2)
| ~ neq(s0,s2)
| p(s0,s2,s1,s1,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(163,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s0,s2,s1,s1,s2)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ p(s0,s1,s1,s1,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s0,s1)
| ~ p(s0,s1,s1,s1,s2)
| ~ neq(s0,s2)
| p(s0,s2,s1,s1,s2) ) ),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s0,s2,s1,s1,s2)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ p(s0,s1,s1,s1,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s0,s1)
| ~ p(s0,s1,s1,s1,s2)
| ~ neq(s0,s2)
| p(s0,s2,s1,s1,s2) ) ),
inference(transitivity,[status(thm)],[163,161]) ).
tff(165,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s0,s2,s1,s1,s2)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ p(s0,s1,s1,s1,s2) ),
inference(quant_inst,[status(thm)],]) ).
tff(166,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s0,s1)
| ~ p(s0,s1,s1,s1,s2)
| ~ neq(s0,s2)
| p(s0,s2,s1,s1,s2) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
p(s0,s2,s1,s1,s2),
inference(unit_resolution,[status(thm)],[166,30,74,71,160]) ).
tff(168,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s2,s1,s1,s2)
| p(s2,s2,s1,s1,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s2,s1,s1,s2)
| p(s2,s2,s1,s1,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(169,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s2,s1,s1,s2)
| p(s2,s2,s1,s1,s2) ),
inference(quant_inst,[status(thm)],]) ).
tff(170,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s2,s1,s1,s2)
| p(s2,s2,s1,s1,s2) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
p(s2,s2,s1,s1,s2),
inference(unit_resolution,[status(thm)],[170,10,167]) ).
tff(172,plain,
( ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| p(s2,s2,s0,s1,s2)
| ~ p(s2,s2,s1,s1,s2) )
<=> ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| p(s2,s2,s0,s1,s2)
| ~ p(s2,s2,s1,s1,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(173,plain,
( ( p(s2,s2,s0,s1,s2)
| ~ neq(s2,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ neq(s2,s1)
| ~ p(s2,s2,s1,s1,s2) )
<=> ( ~ neq(s2,s1)
| ~ neq(s2,s0)
| p(s2,s2,s0,s1,s2)
| ~ p(s2,s2,s1,s1,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(174,plain,
( ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| p(s2,s2,s0,s1,s2)
| ~ neq(s2,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ neq(s2,s1)
| ~ p(s2,s2,s1,s1,s2) )
<=> ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| p(s2,s2,s0,s1,s2)
| ~ p(s2,s2,s1,s1,s2) ) ),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
( ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| p(s2,s2,s0,s1,s2)
| ~ neq(s2,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ neq(s2,s1)
| ~ p(s2,s2,s1,s1,s2) )
<=> ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| p(s2,s2,s0,s1,s2)
| ~ p(s2,s2,s1,s1,s2) ) ),
inference(transitivity,[status(thm)],[174,172]) ).
tff(176,plain,
( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| p(s2,s2,s0,s1,s2)
| ~ neq(s2,s0)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ neq(s2,s1)
| ~ p(s2,s2,s1,s1,s2) ),
inference(quant_inst,[status(thm)],]) ).
tff(177,plain,
( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| p(s2,s2,s0,s1,s2)
| ~ p(s2,s2,s1,s1,s2) ),
inference(modus_ponens,[status(thm)],[176,175]) ).
tff(178,plain,
p(s2,s2,s0,s1,s2),
inference(unit_resolution,[status(thm)],[177,57,20,17,171]) ).
tff(179,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s2,s0,s1,s2)
| p(s1,s2,s0,s1,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s2,s0,s1,s2)
| p(s1,s2,s0,s1,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(180,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s2,s0,s1,s2)
| p(s1,s2,s0,s1,s2) ),
inference(quant_inst,[status(thm)],]) ).
tff(181,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s2,s0,s1,s2)
| p(s1,s2,s0,s1,s2) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
p(s1,s2,s0,s1,s2),
inference(unit_resolution,[status(thm)],[181,10,178]) ).
tff(183,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s1,s0)
| p(s1,s0,s0,s1,s2)
| ~ neq(s1,s2)
| ~ p(s1,s2,s0,s1,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s1,s0)
| p(s1,s0,s0,s1,s2)
| ~ neq(s1,s2)
| ~ p(s1,s2,s0,s1,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(184,plain,
( ( p(s1,s0,s0,s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ p(s1,s2,s0,s1,s2) )
<=> ( ~ neq(s1,s0)
| p(s1,s0,s0,s1,s2)
| ~ neq(s1,s2)
| ~ p(s1,s2,s0,s1,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(185,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s1,s0,s0,s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ p(s1,s2,s0,s1,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s1,s0)
| p(s1,s0,s0,s1,s2)
| ~ neq(s1,s2)
| ~ p(s1,s2,s0,s1,s2) ) ),
inference(monotonicity,[status(thm)],[184]) ).
tff(186,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s1,s0,s0,s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ p(s1,s2,s0,s1,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s1,s0)
| p(s1,s0,s0,s1,s2)
| ~ neq(s1,s2)
| ~ p(s1,s2,s0,s1,s2) ) ),
inference(transitivity,[status(thm)],[185,183]) ).
tff(187,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s1,s0,s0,s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ p(s1,s2,s0,s1,s2) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s1,s0)
| p(s1,s0,s0,s1,s2)
| ~ neq(s1,s2)
| ~ p(s1,s2,s0,s1,s2) ),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
p(s1,s0,s0,s1,s2),
inference(unit_resolution,[status(thm)],[188,30,47,44,182]) ).
tff(190,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s0,s0,s1,s2)
| p(s0,s0,s0,s1,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s0,s0,s1,s2)
| p(s0,s0,s0,s1,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(191,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s0,s0,s1,s2)
| p(s0,s0,s0,s1,s2) ),
inference(quant_inst,[status(thm)],]) ).
tff(192,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s0,s0,s1,s2)
| p(s0,s0,s0,s1,s2) ),
inference(modus_ponens,[status(thm)],[191,190]) ).
tff(193,plain,
p(s0,s0,s0,s1,s2),
inference(unit_resolution,[status(thm)],[192,10,189]) ).
tff(194,plain,
( ( ~ ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
| ~ neq(s0,s1)
| p(s0,s0,s0,s2,s2)
| ~ neq(s0,s2)
| ~ p(s0,s0,s0,s1,s2) )
<=> ( ~ ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
| ~ neq(s0,s1)
| p(s0,s0,s0,s2,s2)
| ~ neq(s0,s2)
| ~ p(s0,s0,s0,s1,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(195,plain,
( ( ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| p(s0,s0,s0,s2,s2)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ p(s0,s0,s0,s1,s2) )
<=> ( ~ neq(s0,s1)
| p(s0,s0,s0,s2,s2)
| ~ neq(s0,s2)
| ~ p(s0,s0,s0,s1,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(196,plain,
( ( ~ ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| p(s0,s0,s0,s2,s2)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ p(s0,s0,s0,s1,s2) )
<=> ( ~ ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
| ~ neq(s0,s1)
| p(s0,s0,s0,s2,s2)
| ~ neq(s0,s2)
| ~ p(s0,s0,s0,s1,s2) ) ),
inference(monotonicity,[status(thm)],[195]) ).
tff(197,plain,
( ( ~ ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| p(s0,s0,s0,s2,s2)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ p(s0,s0,s0,s1,s2) )
<=> ( ~ ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
| ~ neq(s0,s1)
| p(s0,s0,s0,s2,s2)
| ~ neq(s0,s2)
| ~ p(s0,s0,s0,s1,s2) ) ),
inference(transitivity,[status(thm)],[196,194]) ).
tff(198,plain,
( ~ ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| p(s0,s0,s0,s2,s2)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ p(s0,s0,s0,s1,s2) ),
inference(quant_inst,[status(thm)],]) ).
tff(199,plain,
( ~ ! [T2: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| p(T0,T1,T2,J,T4)
| ~ neq(T2,J)
| ~ neq(T2,I)
| ~ p(T0,T1,T2,I,T4) )
| ~ neq(s0,s1)
| p(s0,s0,s0,s2,s2)
| ~ neq(s0,s2)
| ~ p(s0,s0,s0,s1,s2) ),
inference(modus_ponens,[status(thm)],[198,197]) ).
tff(200,plain,
p(s0,s0,s0,s2,s2),
inference(unit_resolution,[status(thm)],[199,95,74,71,193]) ).
tff(201,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s0,s0,s2,s2)
| p(s2,s0,s0,s2,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s0,s0,s2,s2)
| p(s2,s0,s0,s2,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(202,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s0,s0,s2,s2)
| p(s2,s0,s0,s2,s2) ),
inference(quant_inst,[status(thm)],]) ).
tff(203,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s0,s0,s2,s2)
| p(s2,s0,s0,s2,s2) ),
inference(modus_ponens,[status(thm)],[202,201]) ).
tff(204,plain,
p(s2,s0,s0,s2,s2),
inference(unit_resolution,[status(thm)],[203,10,200]) ).
tff(205,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s2,s2)
| p(s2,s1,s0,s2,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s2,s2)
| p(s2,s1,s0,s2,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(206,plain,
( ( p(s2,s1,s0,s2,s2)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s2,s2) )
<=> ( ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s2,s2)
| p(s2,s1,s0,s2,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(207,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s2,s1,s0,s2,s2)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s2,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s2,s2)
| p(s2,s1,s0,s2,s2) ) ),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s2,s1,s0,s2,s2)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s2,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s2,s2)
| p(s2,s1,s0,s2,s2) ) ),
inference(transitivity,[status(thm)],[207,205]) ).
tff(209,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s2,s1,s0,s2,s2)
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s2,s2) ),
inference(quant_inst,[status(thm)],]) ).
tff(210,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s2,s1)
| ~ neq(s2,s0)
| ~ p(s2,s0,s0,s2,s2)
| p(s2,s1,s0,s2,s2) ),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
p(s2,s1,s0,s2,s2),
inference(unit_resolution,[status(thm)],[210,30,20,17,204]) ).
tff(212,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s1,s0,s2,s2)
| p(s1,s1,s0,s2,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s1,s0,s2,s2)
| p(s1,s1,s0,s2,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(213,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s1,s0,s2,s2)
| p(s1,s1,s0,s2,s2) ),
inference(quant_inst,[status(thm)],]) ).
tff(214,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s2,s1,s0,s2,s2)
| p(s1,s1,s0,s2,s2) ),
inference(modus_ponens,[status(thm)],[213,212]) ).
tff(215,plain,
p(s1,s1,s0,s2,s2),
inference(unit_resolution,[status(thm)],[214,10,211]) ).
tff(216,plain,
( ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s1,s2,s2,s2)
| ~ p(s1,s1,s0,s2,s2) )
<=> ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s1,s2,s2,s2)
| ~ p(s1,s1,s0,s2,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(217,plain,
( ( p(s1,s1,s2,s2,s2)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ p(s1,s1,s0,s2,s2) )
<=> ( ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s1,s2,s2,s2)
| ~ p(s1,s1,s0,s2,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(218,plain,
( ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| p(s1,s1,s2,s2,s2)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ p(s1,s1,s0,s2,s2) )
<=> ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s1,s2,s2,s2)
| ~ p(s1,s1,s0,s2,s2) ) ),
inference(monotonicity,[status(thm)],[217]) ).
tff(219,plain,
( ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| p(s1,s1,s2,s2,s2)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ p(s1,s1,s0,s2,s2) )
<=> ( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s1,s2,s2,s2)
| ~ p(s1,s1,s0,s2,s2) ) ),
inference(transitivity,[status(thm)],[218,216]) ).
tff(220,plain,
( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| p(s1,s1,s2,s2,s2)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| ~ neq(s1,s0)
| ~ p(s1,s1,s0,s2,s2) ),
inference(quant_inst,[status(thm)],]) ).
tff(221,plain,
( ~ ! [T3: $i,I: $i,T4: $i,J: $i,T1: $i,T0: $i] :
( p(T0,T1,J,T3,T4)
| ~ neq(T1,J)
| ~ neq(T1,I)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,T1,I,T3,T4) )
| ~ neq(s1,s0)
| ~ neq(s1,s2)
| p(s1,s1,s2,s2,s2)
| ~ p(s1,s1,s0,s2,s2) ),
inference(modus_ponens,[status(thm)],[220,219]) ).
tff(222,plain,
p(s1,s1,s2,s2,s2),
inference(unit_resolution,[status(thm)],[221,57,47,44,215]) ).
tff(223,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s1,s2,s2,s2)
| p(s0,s1,s2,s2,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s1,s2,s2,s2)
| p(s0,s1,s2,s2,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(224,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s1,s2,s2,s2)
| p(s0,s1,s2,s2,s2) ),
inference(quant_inst,[status(thm)],]) ).
tff(225,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s1,s1,s2,s2,s2)
| p(s0,s1,s2,s2,s2) ),
inference(modus_ponens,[status(thm)],[224,223]) ).
tff(226,plain,
p(s0,s1,s2,s2,s2),
inference(unit_resolution,[status(thm)],[225,10,222]) ).
tff(227,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ p(s0,s1,s2,s2,s2)
| p(s0,s2,s2,s2,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ p(s0,s1,s2,s2,s2)
| p(s0,s2,s2,s2,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(228,plain,
( ( p(s0,s2,s2,s2,s2)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ p(s0,s1,s2,s2,s2) )
<=> ( ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ p(s0,s1,s2,s2,s2)
| p(s0,s2,s2,s2,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(229,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s0,s2,s2,s2,s2)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ p(s0,s1,s2,s2,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ p(s0,s1,s2,s2,s2)
| p(s0,s2,s2,s2,s2) ) ),
inference(monotonicity,[status(thm)],[228]) ).
tff(230,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s0,s2,s2,s2,s2)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ p(s0,s1,s2,s2,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ p(s0,s1,s2,s2,s2)
| p(s0,s2,s2,s2,s2) ) ),
inference(transitivity,[status(thm)],[229,227]) ).
tff(231,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| p(s0,s2,s2,s2,s2)
| ~ neq(s0,s2)
| ~ neq(s0,s1)
| ~ p(s0,s1,s2,s2,s2) ),
inference(quant_inst,[status(thm)],]) ).
tff(232,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T0: $i] :
( p(T0,J,T2,T3,T4)
| ~ neq(T0,J)
| ~ neq(T0,I)
| ~ p(T0,I,T2,T3,T4) )
| ~ neq(s0,s1)
| ~ neq(s0,s2)
| ~ p(s0,s1,s2,s2,s2)
| p(s0,s2,s2,s2,s2) ),
inference(modus_ponens,[status(thm)],[231,230]) ).
tff(233,plain,
p(s0,s2,s2,s2,s2),
inference(unit_resolution,[status(thm)],[232,30,74,71,226]) ).
tff(234,plain,
( ~ p(s2,s2,s2,s2,s2)
<=> ~ p(s2,s2,s2,s2,s2) ),
inference(rewrite,[status(thm)],]) ).
tff(235,axiom,
~ p(s2,s2,s2,s2,s2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
tff(236,plain,
~ p(s2,s2,s2,s2,s2),
inference(modus_ponens,[status(thm)],[235,234]) ).
tff(237,plain,
( ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s2,s2,s2,s2)
| p(s2,s2,s2,s2,s2) )
<=> ( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s2,s2,s2,s2)
| p(s2,s2,s2,s2,s2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(238,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s2,s2,s2,s2)
| p(s2,s2,s2,s2,s2) ),
inference(quant_inst,[status(thm)],]) ).
tff(239,plain,
( ~ ! [T3: $i,T2: $i,I: $i,T4: $i,J: $i,T1: $i] :
( ~ p(I,T1,T2,T3,T4)
| p(J,T1,T2,T3,T4) )
| ~ p(s0,s2,s2,s2,s2)
| p(s2,s2,s2,s2,s2) ),
inference(modus_ponens,[status(thm)],[238,237]) ).
tff(240,plain,
$false,
inference(unit_resolution,[status(thm)],[239,10,236,233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ056-2.005 : TPTP v8.1.0. Released v3.5.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 18:48:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 2.48/1.84 % SZS status Unsatisfiable
% 2.48/1.84 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------