TSTP Solution File: SYN312-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN312-1 : TPTP v8.1.0. Bugfixed v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:54:38 EDT 2022
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 59
% Syntax : Number of formulae : 118 ( 27 unt; 7 typ; 0 def)
% Number of atoms : 463 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 643 ( 305 ~; 292 |; 0 &)
% ( 46 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 372 ( 346 !; 0 ?; 372 :)
% Comments :
%------------------------------------------------------------------------------
tff(p_type,type,
p: ( $i * $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(c_type,type,
c: $i ).
tff(g_type,type,
g: $i > $i ).
tff(d_type,type,
d: $i ).
tff(f_type,type,
f: $i > $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
( ~ p(f(g(a)),f(g(d)),f(g(c)))
<=> ~ p(f(g(a)),f(g(d)),f(g(c))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ p(f(g(a)),f(g(d)),f(g(c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
tff(3,plain,
~ p(f(g(a)),f(g(d)),f(g(c))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i,X2: $i,X1: $i] :
refl(
( ( ~ p(X,X1,X2)
| p(X,X1,f(X2)) )
<=> ( ~ p(X,X1,X2)
| p(X,X1,f(X2)) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) )
<=> ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) )
<=> ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [X: $i,X2: $i,X1: $i] :
rewrite(
( ( p(X,X1,f(X2))
| ~ p(X,X1,X2) )
<=> ( ~ p(X,X1,X2)
| p(X,X1,f(X2)) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [X: $i,X2: $i,X1: $i] :
( p(X,X1,f(X2))
| ~ p(X,X1,X2) )
<=> ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [X: $i,X2: $i,X1: $i] :
( p(X,X1,f(X2))
| ~ p(X,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
tff(10,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) )
| ~ p(f(g(a)),f(g(d)),g(c))
| p(f(g(a)),f(g(d)),f(g(c))) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) )
| ~ p(f(g(a)),f(g(d)),g(c))
| p(f(g(a)),f(g(d)),f(g(c))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) )
| ~ p(f(g(a)),f(g(d)),g(c))
| p(f(g(a)),f(g(d)),f(g(c))) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) )
| ~ p(f(g(a)),f(g(d)),g(c))
| p(f(g(a)),f(g(d)),f(g(c))) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ p(f(g(a)),f(g(d)),g(c)),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [X: $i,X2: $i,X1: $i] :
refl(
( ( p(X2,X1,X)
| ~ p(X,X1,X2) )
<=> ( p(X2,X1,X)
| ~ p(X,X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
<=> ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
<=> ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
tff(22,plain,
! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
| p(f(g(a)),f(g(d)),g(c))
| ~ p(g(c),f(g(d)),f(g(a))) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
| p(f(g(a)),f(g(d)),g(c))
| ~ p(g(c),f(g(d)),f(g(a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
| p(f(g(a)),f(g(d)),g(c))
| ~ p(g(c),f(g(d)),f(g(a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
| p(f(g(a)),f(g(d)),g(c))
| ~ p(g(c),f(g(d)),f(g(a))) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
~ p(g(c),f(g(d)),f(g(a))),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
^ [X: $i,X2: $i,X1: $i] :
refl(
( ( ~ p(X,X1,X2)
| p(g(X),X1,X2) )
<=> ( ~ p(X,X1,X2)
| p(g(X),X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) )
<=> ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) )
<=> ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
^ [X: $i,X2: $i,X1: $i] :
rewrite(
( ( p(g(X),X1,X2)
| ~ p(X,X1,X2) )
<=> ( ~ p(X,X1,X2)
| p(g(X),X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X: $i,X2: $i,X1: $i] :
( p(g(X),X1,X2)
| ~ p(X,X1,X2) )
<=> ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [X: $i,X2: $i,X1: $i] :
( p(g(X),X1,X2)
| ~ p(X,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
tff(35,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) )
| ~ p(c,f(g(d)),f(g(a)))
| p(g(c),f(g(d)),f(g(a))) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) )
| ~ p(c,f(g(d)),f(g(a)))
| p(g(c),f(g(d)),f(g(a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) )
| ~ p(c,f(g(d)),f(g(a)))
| p(g(c),f(g(d)),f(g(a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) )
| ~ p(c,f(g(d)),f(g(a)))
| p(g(c),f(g(d)),f(g(a))) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
~ p(c,f(g(d)),f(g(a))),
inference(unit_resolution,[status(thm)],[41,38,28]) ).
tff(43,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) )
| ~ p(c,f(g(d)),g(a))
| p(c,f(g(d)),f(g(a))) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) )
| ~ p(c,f(g(d)),g(a))
| p(c,f(g(d)),f(g(a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) )
| ~ p(c,f(g(d)),g(a))
| p(c,f(g(d)),f(g(a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) )
| ~ p(c,f(g(d)),g(a))
| p(c,f(g(d)),f(g(a))) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
~ p(c,f(g(d)),g(a)),
inference(unit_resolution,[status(thm)],[45,13,42]) ).
tff(47,plain,
^ [X: $i,X2: $i,X1: $i] :
refl(
( ( p(X1,X,X2)
| ~ p(X,X1,X2) )
<=> ( p(X1,X,X2)
| ~ p(X,X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) )
<=> ! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) )
<=> ! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,axiom,
! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
tff(51,plain,
! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) )
| p(c,f(g(d)),g(a))
| ~ p(f(g(d)),c,g(a)) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) )
| p(c,f(g(d)),g(a))
| ~ p(f(g(d)),c,g(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) )
| p(c,f(g(d)),g(a))
| ~ p(f(g(d)),c,g(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) )
| p(c,f(g(d)),g(a))
| ~ p(f(g(d)),c,g(a)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
~ p(f(g(d)),c,g(a)),
inference(unit_resolution,[status(thm)],[56,53,46]) ).
tff(58,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
| p(f(g(d)),c,g(a))
| ~ p(g(a),c,f(g(d))) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
| p(f(g(d)),c,g(a))
| ~ p(g(a),c,f(g(d))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
| p(f(g(d)),c,g(a))
| ~ p(g(a),c,f(g(d))) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
| p(f(g(d)),c,g(a))
| ~ p(g(a),c,f(g(d))) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
~ p(g(a),c,f(g(d))),
inference(unit_resolution,[status(thm)],[60,24,57]) ).
tff(62,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) )
| ~ p(a,c,f(g(d)))
| p(g(a),c,f(g(d))) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) )
| ~ p(a,c,f(g(d)))
| p(g(a),c,f(g(d))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) )
| ~ p(a,c,f(g(d)))
| p(g(a),c,f(g(d))) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) )
| ~ p(a,c,f(g(d)))
| p(g(a),c,f(g(d))) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
~ p(a,c,f(g(d))),
inference(unit_resolution,[status(thm)],[64,38,61]) ).
tff(66,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) )
| ~ p(a,c,g(d))
| p(a,c,f(g(d))) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) )
| ~ p(a,c,g(d))
| p(a,c,f(g(d))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) )
| ~ p(a,c,g(d))
| p(a,c,f(g(d))) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(X,X1,f(X2)) )
| ~ p(a,c,g(d))
| p(a,c,f(g(d))) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
~ p(a,c,g(d)),
inference(unit_resolution,[status(thm)],[68,13,65]) ).
tff(70,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
| p(a,c,g(d))
| ~ p(g(d),c,a) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
| p(a,c,g(d))
| ~ p(g(d),c,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
| p(a,c,g(d))
| ~ p(g(d),c,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
| p(a,c,g(d))
| ~ p(g(d),c,a) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
~ p(g(d),c,a),
inference(unit_resolution,[status(thm)],[72,24,69]) ).
tff(74,plain,
( p(f(b),d,c)
<=> p(f(b),d,c) ),
inference(rewrite,[status(thm)],]) ).
tff(75,axiom,
p(f(b),d,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause7) ).
tff(76,plain,
p(f(b),d,c),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
( p(a,f(b),c)
<=> p(a,f(b),c) ),
inference(rewrite,[status(thm)],]) ).
tff(78,axiom,
p(a,f(b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
tff(79,plain,
p(a,f(b),c),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
^ [X3: $i,X: $i,X2: $i,X1: $i] :
refl(
( ( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) )
<=> ( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) ) )),
inference(bind,[status(th)],]) ).
tff(81,plain,
( ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) )
<=> ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) )
<=> ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
^ [X3: $i,X: $i,X2: $i,X1: $i] :
trans(
monotonicity(
rewrite(
( ( p(X,X3,X2)
| ~ p(X,X1,X2) )
<=> ( ~ p(X,X1,X2)
| p(X,X3,X2) ) )),
( ( p(X,X3,X2)
| ~ p(X,X1,X2)
| ~ p(X1,X3,X2) )
<=> ( ~ p(X,X1,X2)
| p(X,X3,X2)
| ~ p(X1,X3,X2) ) )),
rewrite(
( ( ~ p(X,X1,X2)
| p(X,X3,X2)
| ~ p(X1,X3,X2) )
<=> ( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) ) )),
( ( p(X,X3,X2)
| ~ p(X,X1,X2)
| ~ p(X1,X3,X2) )
<=> ( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [X3: $i,X: $i,X2: $i,X1: $i] :
( p(X,X3,X2)
| ~ p(X,X1,X2)
| ~ p(X1,X3,X2) )
<=> ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,axiom,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( p(X,X3,X2)
| ~ p(X,X1,X2)
| ~ p(X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
tff(86,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) ),
inference(modus_ponens,[status(thm)],[88,81]) ).
tff(90,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) )
| ~ p(a,f(b),c)
| ~ p(f(b),d,c)
| p(a,d,c) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) )
| ~ p(a,f(b),c)
| ~ p(f(b),d,c)
| p(a,d,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ( ~ p(f(b),d,c)
| ~ p(a,f(b),c)
| p(a,d,c) )
<=> ( ~ p(a,f(b),c)
| ~ p(f(b),d,c)
| p(a,d,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) )
| ~ p(f(b),d,c)
| ~ p(a,f(b),c)
| p(a,d,c) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) )
| ~ p(a,f(b),c)
| ~ p(f(b),d,c)
| p(a,d,c) ) ),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) )
| ~ p(f(b),d,c)
| ~ p(a,f(b),c)
| p(a,d,c) )
<=> ( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) )
| ~ p(a,f(b),c)
| ~ p(f(b),d,c)
| p(a,d,c) ) ),
inference(transitivity,[status(thm)],[92,90]) ).
tff(94,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) )
| ~ p(f(b),d,c)
| ~ p(a,f(b),c)
| p(a,d,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
( ~ ! [X3: $i,X: $i,X2: $i,X1: $i] :
( ~ p(X1,X3,X2)
| ~ p(X,X1,X2)
| p(X,X3,X2) )
| ~ p(a,f(b),c)
| ~ p(f(b),d,c)
| p(a,d,c) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
p(a,d,c),
inference(unit_resolution,[status(thm)],[95,89,79,76]) ).
tff(97,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
| p(c,d,a)
| ~ p(a,d,c) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
| p(c,d,a)
| ~ p(a,d,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
| p(c,d,a)
| ~ p(a,d,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X2,X1,X)
| ~ p(X,X1,X2) )
| p(c,d,a)
| ~ p(a,d,c) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
p(c,d,a),
inference(unit_resolution,[status(thm)],[99,24,96]) ).
tff(101,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) )
| ~ p(c,d,a)
| p(d,c,a) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) )
| ~ p(c,d,a)
| p(d,c,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ( p(d,c,a)
| ~ p(c,d,a) )
<=> ( ~ p(c,d,a)
| p(d,c,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) )
| p(d,c,a)
| ~ p(c,d,a) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) )
| ~ p(c,d,a)
| p(d,c,a) ) ),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) )
| p(d,c,a)
| ~ p(c,d,a) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) )
| ~ p(c,d,a)
| p(d,c,a) ) ),
inference(transitivity,[status(thm)],[103,101]) ).
tff(105,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) )
| p(d,c,a)
| ~ p(c,d,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( p(X1,X,X2)
| ~ p(X,X1,X2) )
| ~ p(c,d,a)
| p(d,c,a) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
p(d,c,a),
inference(unit_resolution,[status(thm)],[106,53,100]) ).
tff(108,plain,
( ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) )
| ~ p(d,c,a)
| p(g(d),c,a) )
<=> ( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) )
| ~ p(d,c,a)
| p(g(d),c,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) )
| ~ p(d,c,a)
| p(g(d),c,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
( ~ ! [X: $i,X2: $i,X1: $i] :
( ~ p(X,X1,X2)
| p(g(X),X1,X2) )
| ~ p(d,c,a)
| p(g(d),c,a) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
$false,
inference(unit_resolution,[status(thm)],[110,38,107,73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN312-1 : TPTP v8.1.0. Bugfixed v2.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 02:24:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------