TSTP Solution File: SYN069-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN069-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:53:31 EDT 2022
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 60
% Syntax : Number of formulae : 130 ( 23 unt; 9 typ; 0 def)
% Number of atoms : 966 ( 0 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 1456 ( 666 ~; 714 |; 0 &)
% ( 76 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 55 ( 55 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 8 >; 2 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 203 ( 184 !; 0 ?; 203 :)
% Comments :
%------------------------------------------------------------------------------
tff(big_h_type,type,
big_h: ( $i * $i ) > $o ).
tff(f_type,type,
f: $i > $i ).
tff(a_type,type,
a: $i ).
tff(big_k_type,type,
big_k: $i > $o ).
tff(g_type,type,
g: $i > $i ).
tff(big_l_type,type,
big_l: $i > $o ).
tff(big_f_type,type,
big_f: $i > $o ).
tff(big_g_type,type,
big_g: $i > $o ).
tff(big_j_type,type,
big_j: ( $i * $i ) > $o ).
tff(1,plain,
^ [X: $i] :
refl(
( ( ~ big_f(X)
| big_h(X,g(X)) )
<=> ( ~ big_f(X)
| big_h(X,g(X)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
( ~ big_f(X)
| big_h(X,g(X)) )
<=> ! [X: $i] :
( ~ big_f(X)
| big_h(X,g(X)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] :
( ~ big_f(X)
| big_h(X,g(X)) )
<=> ! [X: $i] :
( ~ big_f(X)
| big_h(X,g(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] :
( ~ big_f(X)
| big_h(X,g(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
tff(5,plain,
! [X: $i] :
( ~ big_f(X)
| big_h(X,g(X)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] :
( ~ big_f(X)
| big_h(X,g(X)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] :
( ~ big_f(X)
| big_h(X,g(X)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( big_f(a)
<=> big_f(a) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
big_f(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
tff(10,plain,
big_f(a),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [X: $i] :
( ~ big_f(X)
| big_h(X,g(X)) )
| ~ big_f(a)
| big_h(a,g(a)) )
<=> ( ~ ! [X: $i] :
( ~ big_f(X)
| big_h(X,g(X)) )
| ~ big_f(a)
| big_h(a,g(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [X: $i] :
( ~ big_f(X)
| big_h(X,g(X)) )
| ~ big_f(a)
| big_h(a,g(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [X: $i] :
( ~ big_f(X)
| big_h(X,g(X)) )
| ~ big_f(a)
| big_h(a,g(a)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
big_h(a,g(a)),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
^ [X: $i] :
refl(
( ( big_l(X)
| ~ big_h(a,X) )
<=> ( big_l(X)
| ~ big_h(a,X) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [X: $i] :
( big_l(X)
| ~ big_h(a,X) )
<=> ! [X: $i] :
( big_l(X)
| ~ big_h(a,X) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X: $i] :
( big_l(X)
| ~ big_h(a,X) )
<=> ! [X: $i] :
( big_l(X)
| ~ big_h(a,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
^ [X: $i] :
rewrite(
( ( ~ big_h(a,X)
| big_l(X) )
<=> ( big_l(X)
| ~ big_h(a,X) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [X: $i] :
( ~ big_h(a,X)
| big_l(X) )
<=> ! [X: $i] :
( big_l(X)
| ~ big_h(a,X) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [X: $i] :
( ~ big_h(a,X)
| big_l(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
tff(21,plain,
! [X: $i] :
( big_l(X)
| ~ big_h(a,X) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [X: $i] :
( big_l(X)
| ~ big_h(a,X) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [X: $i] :
( big_l(X)
| ~ big_h(a,X) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [X: $i] :
( big_l(X)
| ~ big_h(a,X) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
( big_l(X)
| ~ big_h(a,X) )
| big_l(g(a))
| ~ big_h(a,g(a)) )
<=> ( ~ ! [X: $i] :
( big_l(X)
| ~ big_h(a,X) )
| big_l(g(a))
| ~ big_h(a,g(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [X: $i] :
( big_l(X)
| ~ big_h(a,X) )
| big_l(g(a))
| ~ big_h(a,g(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [X: $i] :
( big_l(X)
| ~ big_h(a,X) )
| big_l(g(a))
| ~ big_h(a,g(a)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
big_l(g(a)),
inference(unit_resolution,[status(thm)],[27,24,14]) ).
tff(29,plain,
^ [X: $i] :
refl(
( ( ~ big_l(X)
| ~ big_k(X) )
<=> ( ~ big_l(X)
| ~ big_k(X) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [X: $i] :
( ~ big_l(X)
| ~ big_k(X) )
<=> ! [X: $i] :
( ~ big_l(X)
| ~ big_k(X) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [X: $i] :
( ~ big_l(X)
| ~ big_k(X) )
<=> ! [X: $i] :
( ~ big_l(X)
| ~ big_k(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
! [X: $i] :
( ~ big_l(X)
| ~ big_k(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
tff(33,plain,
! [X: $i] :
( ~ big_l(X)
| ~ big_k(X) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [X: $i] :
( ~ big_l(X)
| ~ big_k(X) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [X: $i] :
( ~ big_l(X)
| ~ big_k(X) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ( ~ ! [X: $i] :
( ~ big_l(X)
| ~ big_k(X) )
| ~ big_l(g(a))
| ~ big_k(g(a)) )
<=> ( ~ ! [X: $i] :
( ~ big_l(X)
| ~ big_k(X) )
| ~ big_l(g(a))
| ~ big_k(g(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ~ ! [X: $i] :
( ~ big_l(X)
| ~ big_k(X) )
| ~ big_l(g(a))
| ~ big_k(g(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
( ~ ! [X: $i] :
( ~ big_l(X)
| ~ big_k(X) )
| ~ big_l(g(a))
| ~ big_k(g(a)) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
~ big_k(g(a)),
inference(unit_resolution,[status(thm)],[38,35,28]) ).
tff(40,plain,
^ [X: $i] :
refl(
( ( ~ big_f(X)
| big_g(g(X)) )
<=> ( ~ big_f(X)
| big_g(g(X)) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [X: $i] :
( ~ big_f(X)
| big_g(g(X)) )
<=> ! [X: $i] :
( ~ big_f(X)
| big_g(g(X)) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [X: $i] :
( ~ big_f(X)
| big_g(g(X)) )
<=> ! [X: $i] :
( ~ big_f(X)
| big_g(g(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
! [X: $i] :
( ~ big_f(X)
| big_g(g(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
tff(44,plain,
! [X: $i] :
( ~ big_f(X)
| big_g(g(X)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [X: $i] :
( ~ big_f(X)
| big_g(g(X)) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [X: $i] :
( ~ big_f(X)
| big_g(g(X)) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ( ~ ! [X: $i] :
( ~ big_f(X)
| big_g(g(X)) )
| ~ big_f(a)
| big_g(g(a)) )
<=> ( ~ ! [X: $i] :
( ~ big_f(X)
| big_g(g(X)) )
| ~ big_f(a)
| big_g(g(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ~ ! [X: $i] :
( ~ big_f(X)
| big_g(g(X)) )
| ~ big_f(a)
| big_g(g(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [X: $i] :
( ~ big_f(X)
| big_g(g(X)) )
| ~ big_f(a)
| big_g(g(a)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
big_g(g(a)),
inference(unit_resolution,[status(thm)],[49,10,46]) ).
tff(51,plain,
^ [Y: $i,X: $i] :
refl(
( ( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) )
<=> ( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) )
<=> ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) )
<=> ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
^ [Y: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ big_f(X)
| big_h(X,f(X))
| ~ big_g(Y) )
<=> ( ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) ) )),
( ( ~ big_f(X)
| big_h(X,f(X))
| ~ big_g(Y)
| ~ big_h(X,Y) )
<=> ( ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X))
| ~ big_h(X,Y) ) )),
rewrite(
( ( ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X))
| ~ big_h(X,Y) )
<=> ( ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) ) )),
( ( ~ big_f(X)
| big_h(X,f(X))
| ~ big_g(Y)
| ~ big_h(X,Y) )
<=> ( ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) ) )),
( ( ~ big_f(X)
| big_h(X,f(X))
| ~ big_g(Y)
| ~ big_h(X,Y)
| big_k(Y) )
<=> ( ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X))
| big_k(Y) ) )),
rewrite(
( ( ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X))
| big_k(Y) )
<=> ( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) ) )),
( ( ~ big_f(X)
| big_h(X,f(X))
| ~ big_g(Y)
| ~ big_h(X,Y)
| big_k(Y) )
<=> ( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [Y: $i,X: $i] :
( ~ big_f(X)
| big_h(X,f(X))
| ~ big_g(Y)
| ~ big_h(X,Y)
| big_k(Y) )
<=> ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [Y: $i,X: $i] :
( ~ big_f(X)
| big_h(X,f(X))
| ~ big_g(Y)
| ~ big_h(X,Y)
| big_k(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
tff(57,plain,
! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
( ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) )
| ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| big_h(a,f(a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) )
| ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| big_h(a,f(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ( big_k(g(a))
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| ~ big_f(a)
| big_h(a,f(a)) )
<=> ( ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| big_h(a,f(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) )
| big_k(g(a))
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| ~ big_f(a)
| big_h(a,f(a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) )
| ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| big_h(a,f(a)) ) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) )
| big_k(g(a))
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| ~ big_f(a)
| big_h(a,f(a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) )
| ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| big_h(a,f(a)) ) ),
inference(transitivity,[status(thm)],[63,61]) ).
tff(65,plain,
( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) )
| big_k(g(a))
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| ~ big_f(a)
| big_h(a,f(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| big_h(X,f(X)) )
| ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| big_h(a,f(a)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
( big_k(g(a))
| big_h(a,f(a)) ),
inference(unit_resolution,[status(thm)],[66,60,10,50,14]) ).
tff(68,plain,
big_h(a,f(a)),
inference(unit_resolution,[status(thm)],[67,39]) ).
tff(69,plain,
^ [Y: $i,X: $i] :
refl(
( ( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) )
<=> ( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) )
<=> ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) )
<=> ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
^ [Y: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ big_f(X)
| big_g(f(X)) )
<=> ( big_g(f(X))
| ~ big_f(X) ) )),
( ( ~ big_f(X)
| big_g(f(X))
| ~ big_g(Y) )
<=> ( big_g(f(X))
| ~ big_f(X)
| ~ big_g(Y) ) )),
rewrite(
( ( big_g(f(X))
| ~ big_f(X)
| ~ big_g(Y) )
<=> ( ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) ) )),
( ( ~ big_f(X)
| big_g(f(X))
| ~ big_g(Y) )
<=> ( ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) ) )),
( ( ~ big_f(X)
| big_g(f(X))
| ~ big_g(Y)
| ~ big_h(X,Y) )
<=> ( ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X)
| ~ big_h(X,Y) ) )),
rewrite(
( ( ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X)
| ~ big_h(X,Y) )
<=> ( ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) ) )),
( ( ~ big_f(X)
| big_g(f(X))
| ~ big_g(Y)
| ~ big_h(X,Y) )
<=> ( ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) ) )),
( ( ~ big_f(X)
| big_g(f(X))
| ~ big_g(Y)
| ~ big_h(X,Y)
| big_k(Y) )
<=> ( ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X)
| big_k(Y) ) )),
rewrite(
( ( ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X)
| big_k(Y) )
<=> ( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) ) )),
( ( ~ big_f(X)
| big_g(f(X))
| ~ big_g(Y)
| ~ big_h(X,Y)
| big_k(Y) )
<=> ( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [Y: $i,X: $i] :
( ~ big_f(X)
| big_g(f(X))
| ~ big_g(Y)
| ~ big_h(X,Y)
| big_k(Y) )
<=> ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,axiom,
! [Y: $i,X: $i] :
( ~ big_f(X)
| big_g(f(X))
| ~ big_g(Y)
| ~ big_h(X,Y)
| big_k(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
tff(75,plain,
! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
( ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) )
| ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| big_g(f(a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) )
| ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| big_g(f(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ( big_k(g(a))
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_g(f(a))
| ~ big_f(a) )
<=> ( ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| big_g(f(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) )
| big_k(g(a))
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_g(f(a))
| ~ big_f(a) )
<=> ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) )
| ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| big_g(f(a)) ) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) )
| big_k(g(a))
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_g(f(a))
| ~ big_f(a) )
<=> ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) )
| ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| big_g(f(a)) ) ),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,plain,
( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) )
| big_k(g(a))
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_g(f(a))
| ~ big_f(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| big_g(f(X))
| ~ big_f(X) )
| ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| big_g(f(a)) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
( big_k(g(a))
| big_g(f(a)) ),
inference(unit_resolution,[status(thm)],[84,78,10,50,14]) ).
tff(86,plain,
big_g(f(a)),
inference(unit_resolution,[status(thm)],[85,39]) ).
tff(87,plain,
^ [Y: $i,X: $i] :
refl(
( ( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) )
<=> ( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) )
<=> ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) )
<=> ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
^ [Y: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ big_f(X)
| ~ big_j(X,f(X))
| ~ big_g(Y) )
<=> ( ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) ) )),
( ( ~ big_f(X)
| ~ big_j(X,f(X))
| ~ big_g(Y)
| ~ big_h(X,Y) )
<=> ( ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X))
| ~ big_h(X,Y) ) )),
rewrite(
( ( ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X))
| ~ big_h(X,Y) )
<=> ( ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) ) )),
( ( ~ big_f(X)
| ~ big_j(X,f(X))
| ~ big_g(Y)
| ~ big_h(X,Y) )
<=> ( ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) ) )),
( ( ~ big_f(X)
| ~ big_j(X,f(X))
| ~ big_g(Y)
| ~ big_h(X,Y)
| big_k(Y) )
<=> ( ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X))
| big_k(Y) ) )),
rewrite(
( ( ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X))
| big_k(Y) )
<=> ( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) ) )),
( ( ~ big_f(X)
| ~ big_j(X,f(X))
| ~ big_g(Y)
| ~ big_h(X,Y)
| big_k(Y) )
<=> ( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) ) )),
inference(bind,[status(th)],]) ).
tff(91,plain,
( ! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_j(X,f(X))
| ~ big_g(Y)
| ~ big_h(X,Y)
| big_k(Y) )
<=> ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,axiom,
! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_j(X,f(X))
| ~ big_g(Y)
| ~ big_h(X,Y)
| big_k(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
tff(93,plain,
! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) ),
inference(skolemize,[status(sab)],[94]) ).
tff(96,plain,
! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) ),
inference(modus_ponens,[status(thm)],[95,88]) ).
tff(97,plain,
( ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) )
| ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| ~ big_j(a,f(a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) )
| ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| ~ big_j(a,f(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ( big_k(g(a))
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| ~ big_f(a)
| ~ big_j(a,f(a)) )
<=> ( ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| ~ big_j(a,f(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) )
| big_k(g(a))
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| ~ big_f(a)
| ~ big_j(a,f(a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) )
| ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| ~ big_j(a,f(a)) ) ),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
( ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) )
| big_k(g(a))
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| ~ big_f(a)
| ~ big_j(a,f(a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) )
| ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| ~ big_j(a,f(a)) ) ),
inference(transitivity,[status(thm)],[99,97]) ).
tff(101,plain,
( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) )
| big_k(g(a))
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| ~ big_f(a)
| ~ big_j(a,f(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
( ~ ! [Y: $i,X: $i] :
( big_k(Y)
| ~ big_h(X,Y)
| ~ big_g(Y)
| ~ big_f(X)
| ~ big_j(X,f(X)) )
| ~ big_f(a)
| ~ big_h(a,g(a))
| ~ big_g(g(a))
| big_k(g(a))
| ~ big_j(a,f(a)) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
( big_k(g(a))
| ~ big_j(a,f(a)) ),
inference(unit_resolution,[status(thm)],[102,96,10,50,14]) ).
tff(104,plain,
~ big_j(a,f(a)),
inference(unit_resolution,[status(thm)],[103,39]) ).
tff(105,plain,
^ [X: $i] :
refl(
( ( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) )
<=> ( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) )
<=> ! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) )
<=> ! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
^ [X: $i] :
rewrite(
( ( ~ big_g(X)
| ~ big_h(a,X)
| big_j(a,X) )
<=> ( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) ) )),
inference(bind,[status(th)],]) ).
tff(109,plain,
( ! [X: $i] :
( ~ big_g(X)
| ~ big_h(a,X)
| big_j(a,X) )
<=> ! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,axiom,
! [X: $i] :
( ~ big_g(X)
| ~ big_h(a,X)
| big_j(a,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
tff(111,plain,
! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) ),
inference(modus_ponens,[status(thm)],[113,106]) ).
tff(115,plain,
( ( ~ ! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) )
| big_j(a,f(a))
| ~ big_h(a,f(a))
| ~ big_g(f(a)) )
<=> ( ~ ! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) )
| big_j(a,f(a))
| ~ big_h(a,f(a))
| ~ big_g(f(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,plain,
( ( ~ big_h(a,f(a))
| big_j(a,f(a))
| ~ big_g(f(a)) )
<=> ( big_j(a,f(a))
| ~ big_h(a,f(a))
| ~ big_g(f(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ( ~ ! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) )
| ~ big_h(a,f(a))
| big_j(a,f(a))
| ~ big_g(f(a)) )
<=> ( ~ ! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) )
| big_j(a,f(a))
| ~ big_h(a,f(a))
| ~ big_g(f(a)) ) ),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
( ( ~ ! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) )
| ~ big_h(a,f(a))
| big_j(a,f(a))
| ~ big_g(f(a)) )
<=> ( ~ ! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) )
| big_j(a,f(a))
| ~ big_h(a,f(a))
| ~ big_g(f(a)) ) ),
inference(transitivity,[status(thm)],[117,115]) ).
tff(119,plain,
( ~ ! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) )
| ~ big_h(a,f(a))
| big_j(a,f(a))
| ~ big_g(f(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
( ~ ! [X: $i] :
( ~ big_h(a,X)
| big_j(a,X)
| ~ big_g(X) )
| big_j(a,f(a))
| ~ big_h(a,f(a))
| ~ big_g(f(a)) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
$false,
inference(unit_resolution,[status(thm)],[120,114,104,86,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN069-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 01:33:54 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------