TSTP Solution File: SYN070-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN070-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 56
% Syntax : Number of formulae : 120 ( 25 unt; 7 typ; 0 def)
% Number of atoms : 858 ( 0 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 1193 ( 504 ~; 615 |; 0 &)
% ( 74 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 56 ( 56 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 5 >; 2 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 173 ( 155 !; 0 ?; 173 :)
% Comments :
%------------------------------------------------------------------------------
tff(big_j_type,type,
big_j: ( $i * $i ) > $o ).
tff(f_type,type,
f: $i > $i ).
tff(a_type,type,
a: $i ).
tff(big_h_type,type,
big_h: ( $i * $i ) > $o ).
tff(big_f_type,type,
big_f: $i > $o ).
tff(big_g_type,type,
big_g: $i > $o ).
tff(b_type,type,
b: $i ).
tff(1,plain,
( ~ big_g(b)
<=> ~ big_g(b) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ big_g(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
tff(3,plain,
~ big_g(b),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( big_f(b)
<=> big_f(b) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
big_f(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
tff(6,plain,
big_f(b),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [X: $i] :
refl(
( ( big_f(a)
| big_g(X)
| ~ big_f(X) )
<=> ( big_f(a)
| big_g(X)
| ~ big_f(X) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [X: $i] :
( big_f(a)
| big_g(X)
| ~ big_f(X) )
<=> ! [X: $i] :
( big_f(a)
| big_g(X)
| ~ big_f(X) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [X: $i] :
( big_f(a)
| big_g(X)
| ~ big_f(X) )
<=> ! [X: $i] :
( big_f(a)
| big_g(X)
| ~ big_f(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ big_f(X)
| big_g(X) )
<=> ( big_g(X)
| ~ big_f(X) ) )),
( ( ~ big_f(X)
| big_g(X)
| big_f(a) )
<=> ( big_g(X)
| ~ big_f(X)
| big_f(a) ) )),
rewrite(
( ( big_g(X)
| ~ big_f(X)
| big_f(a) )
<=> ( big_f(a)
| big_g(X)
| ~ big_f(X) ) )),
( ( ~ big_f(X)
| big_g(X)
| big_f(a) )
<=> ( big_f(a)
| big_g(X)
| ~ big_f(X) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] :
( ~ big_f(X)
| big_g(X)
| big_f(a) )
<=> ! [X: $i] :
( big_f(a)
| big_g(X)
| ~ big_f(X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [X: $i] :
( ~ big_f(X)
| big_g(X)
| big_f(a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
tff(13,plain,
! [X: $i] :
( big_f(a)
| big_g(X)
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X: $i] :
( big_f(a)
| big_g(X)
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [X: $i] :
( big_f(a)
| big_g(X)
| ~ big_f(X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] :
( big_f(a)
| big_g(X)
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
( big_f(a)
| big_g(X)
| ~ big_f(X) )
| big_f(a)
| big_g(b)
| ~ big_f(b) )
<=> ( ~ ! [X: $i] :
( big_f(a)
| big_g(X)
| ~ big_f(X) )
| big_f(a)
| big_g(b)
| ~ big_f(b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [X: $i] :
( big_f(a)
| big_g(X)
| ~ big_f(X) )
| big_f(a)
| big_g(b)
| ~ big_f(b) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [X: $i] :
( big_f(a)
| big_g(X)
| ~ big_f(X) )
| big_f(a)
| big_g(b)
| ~ big_f(b) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
big_f(a),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
^ [X: $i] :
refl(
( ( ~ big_g(a)
| big_g(X)
| ~ big_f(X) )
<=> ( ~ big_g(a)
| big_g(X)
| ~ big_f(X) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) )
<=> ! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) )
<=> ! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ big_f(X)
| big_g(X) )
<=> ( big_g(X)
| ~ big_f(X) ) )),
( ( ~ big_f(X)
| big_g(X)
| ~ big_g(a) )
<=> ( big_g(X)
| ~ big_f(X)
| ~ big_g(a) ) )),
rewrite(
( ( big_g(X)
| ~ big_f(X)
| ~ big_g(a) )
<=> ( ~ big_g(a)
| big_g(X)
| ~ big_f(X) ) )),
( ( ~ big_f(X)
| big_g(X)
| ~ big_g(a) )
<=> ( ~ big_g(a)
| big_g(X)
| ~ big_f(X) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [X: $i] :
( ~ big_f(X)
| big_g(X)
| ~ big_g(a) )
<=> ! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [X: $i] :
( ~ big_f(X)
| big_g(X)
| ~ big_g(a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
tff(27,plain,
! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) )
| big_g(b)
| ~ big_g(a)
| ~ big_f(b) )
<=> ( ~ ! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) )
| big_g(b)
| ~ big_g(a)
| ~ big_f(b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( ~ big_g(a)
| big_g(b)
| ~ big_f(b) )
<=> ( big_g(b)
| ~ big_g(a)
| ~ big_f(b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( ~ ! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) )
| ~ big_g(a)
| big_g(b)
| ~ big_f(b) )
<=> ( ~ ! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) )
| big_g(b)
| ~ big_g(a)
| ~ big_f(b) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) )
| ~ big_g(a)
| big_g(b)
| ~ big_f(b) )
<=> ( ~ ! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) )
| big_g(b)
| ~ big_g(a)
| ~ big_f(b) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) )
| ~ big_g(a)
| big_g(b)
| ~ big_f(b) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [X: $i] :
( ~ big_g(a)
| big_g(X)
| ~ big_f(X) )
| big_g(b)
| ~ big_g(a)
| ~ big_f(b) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
~ big_g(a),
inference(unit_resolution,[status(thm)],[36,30,6,3]) ).
tff(38,plain,
^ [X: $i] :
refl(
( ( big_g(X)
| ~ big_f(X)
| big_h(f(X),X) )
<=> ( big_g(X)
| ~ big_f(X)
| big_h(f(X),X) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| big_h(f(X),X) )
<=> ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| big_h(f(X),X) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| big_h(f(X),X) )
<=> ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| big_h(f(X),X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
^ [X: $i] :
rewrite(
( ( ~ big_f(X)
| big_h(f(X),X)
| big_g(X) )
<=> ( big_g(X)
| ~ big_f(X)
| big_h(f(X),X) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [X: $i] :
( ~ big_f(X)
| big_h(f(X),X)
| big_g(X) )
<=> ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| big_h(f(X),X) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [X: $i] :
( ~ big_f(X)
| big_h(f(X),X)
| big_g(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
tff(44,plain,
! [X: $i] :
( big_g(X)
| ~ big_f(X)
| big_h(f(X),X) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [X: $i] :
( big_g(X)
| ~ big_f(X)
| big_h(f(X),X) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [X: $i] :
( big_g(X)
| ~ big_f(X)
| big_h(f(X),X) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [X: $i] :
( big_g(X)
| ~ big_f(X)
| big_h(f(X),X) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| big_h(f(X),X) )
| big_g(a)
| ~ big_f(a)
| big_h(f(a),a) )
<=> ( ~ ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| big_h(f(X),X) )
| big_g(a)
| ~ big_f(a)
| big_h(f(a),a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ~ ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| big_h(f(X),X) )
| big_g(a)
| ~ big_f(a)
| big_h(f(a),a) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
( ~ ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| big_h(f(X),X) )
| big_g(a)
| ~ big_f(a)
| big_h(f(a),a) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
big_h(f(a),a),
inference(unit_resolution,[status(thm)],[50,47,37,20]) ).
tff(52,plain,
^ [X: $i] :
refl(
( ( big_g(X)
| big_f(f(X))
| ~ big_f(X) )
<=> ( big_g(X)
| big_f(f(X))
| ~ big_f(X) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [X: $i] :
( big_g(X)
| big_f(f(X))
| ~ big_f(X) )
<=> ! [X: $i] :
( big_g(X)
| big_f(f(X))
| ~ big_f(X) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [X: $i] :
( big_g(X)
| big_f(f(X))
| ~ big_f(X) )
<=> ! [X: $i] :
( big_g(X)
| big_f(f(X))
| ~ big_f(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ big_f(X)
| big_f(f(X)) )
<=> ( big_f(f(X))
| ~ big_f(X) ) )),
( ( ~ big_f(X)
| big_f(f(X))
| big_g(X) )
<=> ( big_f(f(X))
| ~ big_f(X)
| big_g(X) ) )),
rewrite(
( ( big_f(f(X))
| ~ big_f(X)
| big_g(X) )
<=> ( big_g(X)
| big_f(f(X))
| ~ big_f(X) ) )),
( ( ~ big_f(X)
| big_f(f(X))
| big_g(X) )
<=> ( big_g(X)
| big_f(f(X))
| ~ big_f(X) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [X: $i] :
( ~ big_f(X)
| big_f(f(X))
| big_g(X) )
<=> ! [X: $i] :
( big_g(X)
| big_f(f(X))
| ~ big_f(X) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [X: $i] :
( ~ big_f(X)
| big_f(f(X))
| big_g(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
tff(58,plain,
! [X: $i] :
( big_g(X)
| big_f(f(X))
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [X: $i] :
( big_g(X)
| big_f(f(X))
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [X: $i] :
( big_g(X)
| big_f(f(X))
| ~ big_f(X) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [X: $i] :
( big_g(X)
| big_f(f(X))
| ~ big_f(X) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ( ~ ! [X: $i] :
( big_g(X)
| big_f(f(X))
| ~ big_f(X) )
| big_g(a)
| big_f(f(a))
| ~ big_f(a) )
<=> ( ~ ! [X: $i] :
( big_g(X)
| big_f(f(X))
| ~ big_f(X) )
| big_g(a)
| big_f(f(a))
| ~ big_f(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ~ ! [X: $i] :
( big_g(X)
| big_f(f(X))
| ~ big_f(X) )
| big_g(a)
| big_f(f(a))
| ~ big_f(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
( ~ ! [X: $i] :
( big_g(X)
| big_f(f(X))
| ~ big_f(X) )
| big_g(a)
| big_f(f(a))
| ~ big_f(a) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
big_f(f(a)),
inference(unit_resolution,[status(thm)],[64,61,37,20]) ).
tff(66,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) )
<=> ( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
^ [Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ big_f(X)
| ~ big_f(Y)
| ~ big_h(X,Y) )
<=> ( ~ big_f(X)
| ~ big_f(Y)
| ~ big_h(X,Y) ) )),
( ( ~ big_f(X)
| ~ big_f(Y)
| ~ big_h(X,Y)
| ~ big_j(Y,X) )
<=> ( ~ big_f(X)
| ~ big_f(Y)
| ~ big_h(X,Y)
| ~ big_j(Y,X) ) )),
rewrite(
( ( ~ big_f(X)
| ~ big_f(Y)
| ~ big_h(X,Y)
| ~ big_j(Y,X) )
<=> ( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) ) )),
( ( ~ big_f(X)
| ~ big_f(Y)
| ~ big_h(X,Y)
| ~ big_j(Y,X) )
<=> ( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_h(X,Y)
| ~ big_j(Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,axiom,
! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_h(X,Y)
| ~ big_j(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
tff(72,plain,
! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) )
| ~ big_f(a)
| ~ big_f(f(a))
| ~ big_j(a,f(a))
| ~ big_h(f(a),a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) )
| ~ big_f(a)
| ~ big_f(f(a))
| ~ big_j(a,f(a))
| ~ big_h(f(a),a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ( ~ big_f(f(a))
| ~ big_f(a)
| ~ big_j(a,f(a))
| ~ big_h(f(a),a) )
<=> ( ~ big_f(a)
| ~ big_f(f(a))
| ~ big_j(a,f(a))
| ~ big_h(f(a),a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) )
| ~ big_f(f(a))
| ~ big_f(a)
| ~ big_j(a,f(a))
| ~ big_h(f(a),a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) )
| ~ big_f(a)
| ~ big_f(f(a))
| ~ big_j(a,f(a))
| ~ big_h(f(a),a) ) ),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) )
| ~ big_f(f(a))
| ~ big_f(a)
| ~ big_j(a,f(a))
| ~ big_h(f(a),a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) )
| ~ big_f(a)
| ~ big_f(f(a))
| ~ big_j(a,f(a))
| ~ big_h(f(a),a) ) ),
inference(transitivity,[status(thm)],[78,76]) ).
tff(80,plain,
( ~ ! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) )
| ~ big_f(f(a))
| ~ big_f(a)
| ~ big_j(a,f(a))
| ~ big_h(f(a),a) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
( ~ ! [Y: $i,X: $i] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_j(Y,X)
| ~ big_h(X,Y) )
| ~ big_f(a)
| ~ big_f(f(a))
| ~ big_j(a,f(a))
| ~ big_h(f(a),a) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
~ big_j(a,f(a)),
inference(unit_resolution,[status(thm)],[81,75,20,65,51]) ).
tff(83,plain,
^ [X: $i] :
refl(
( ( big_g(X)
| ~ big_f(X)
| ~ big_g(f(X)) )
<=> ( big_g(X)
| ~ big_f(X)
| ~ big_g(f(X)) ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| ~ big_g(f(X)) )
<=> ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| ~ big_g(f(X)) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| ~ big_g(f(X)) )
<=> ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| ~ big_g(f(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
^ [X: $i] :
rewrite(
( ( ~ big_f(X)
| ~ big_g(f(X))
| big_g(X) )
<=> ( big_g(X)
| ~ big_f(X)
| ~ big_g(f(X)) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [X: $i] :
( ~ big_f(X)
| ~ big_g(f(X))
| big_g(X) )
<=> ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| ~ big_g(f(X)) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,axiom,
! [X: $i] :
( ~ big_f(X)
| ~ big_g(f(X))
| big_g(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
tff(89,plain,
! [X: $i] :
( big_g(X)
| ~ big_f(X)
| ~ big_g(f(X)) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [X: $i] :
( big_g(X)
| ~ big_f(X)
| ~ big_g(f(X)) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [X: $i] :
( big_g(X)
| ~ big_f(X)
| ~ big_g(f(X)) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [X: $i] :
( big_g(X)
| ~ big_f(X)
| ~ big_g(f(X)) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
( ( ~ ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| ~ big_g(f(X)) )
| big_g(a)
| ~ big_f(a)
| ~ big_g(f(a)) )
<=> ( ~ ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| ~ big_g(f(X)) )
| big_g(a)
| ~ big_f(a)
| ~ big_g(f(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ~ ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| ~ big_g(f(X)) )
| big_g(a)
| ~ big_f(a)
| ~ big_g(f(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
( ~ ! [X: $i] :
( big_g(X)
| ~ big_f(X)
| ~ big_g(f(X)) )
| big_g(a)
| ~ big_f(a)
| ~ big_g(f(a)) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
~ big_g(f(a)),
inference(unit_resolution,[status(thm)],[95,92,37,20]) ).
tff(97,plain,
^ [Y: $i,X: $i] :
refl(
( ( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) )
<=> ( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) )
<=> ! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
( ! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) )
<=> ! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
^ [Y: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ big_f(X)
| big_g(X) )
<=> ( big_g(X)
| ~ big_f(X) ) )),
( ( ~ big_f(X)
| big_g(X)
| ~ big_f(Y) )
<=> ( big_g(X)
| ~ big_f(X)
| ~ big_f(Y) ) )),
rewrite(
( ( big_g(X)
| ~ big_f(X)
| ~ big_f(Y) )
<=> ( big_g(X)
| ~ big_f(X)
| ~ big_f(Y) ) )),
( ( ~ big_f(X)
| big_g(X)
| ~ big_f(Y) )
<=> ( big_g(X)
| ~ big_f(X)
| ~ big_f(Y) ) )),
( ( ~ big_f(X)
| big_g(X)
| ~ big_f(Y)
| big_g(Y) )
<=> ( big_g(X)
| ~ big_f(X)
| ~ big_f(Y)
| big_g(Y) ) )),
rewrite(
( ( big_g(X)
| ~ big_f(X)
| ~ big_f(Y)
| big_g(Y) )
<=> ( big_g(X)
| ~ big_f(X)
| big_g(Y)
| ~ big_f(Y) ) )),
( ( ~ big_f(X)
| big_g(X)
| ~ big_f(Y)
| big_g(Y) )
<=> ( big_g(X)
| ~ big_f(X)
| big_g(Y)
| ~ big_f(Y) ) )),
( ( ~ big_f(X)
| big_g(X)
| ~ big_f(Y)
| big_g(Y)
| big_j(a,Y) )
<=> ( big_g(X)
| ~ big_f(X)
| big_g(Y)
| ~ big_f(Y)
| big_j(a,Y) ) )),
rewrite(
( ( big_g(X)
| ~ big_f(X)
| big_g(Y)
| ~ big_f(Y)
| big_j(a,Y) )
<=> ( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) ) )),
( ( ~ big_f(X)
| big_g(X)
| ~ big_f(Y)
| big_g(Y)
| big_j(a,Y) )
<=> ( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) ) )),
inference(bind,[status(th)],]) ).
tff(101,plain,
( ! [Y: $i,X: $i] :
( ~ big_f(X)
| big_g(X)
| ~ big_f(Y)
| big_g(Y)
| big_j(a,Y) )
<=> ! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,axiom,
! [Y: $i,X: $i] :
( ~ big_f(X)
| big_g(X)
| ~ big_f(Y)
| big_g(Y)
| big_j(a,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
tff(103,plain,
! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) ),
inference(modus_ponens,[status(thm)],[103,99]) ).
tff(105,plain,
! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) ),
inference(skolemize,[status(sab)],[104]) ).
tff(106,plain,
! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) ),
inference(modus_ponens,[status(thm)],[105,98]) ).
tff(107,plain,
( ( ~ ! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) )
| big_g(b)
| ~ big_f(b)
| big_g(f(a))
| ~ big_f(f(a))
| big_j(a,f(a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) )
| big_g(b)
| ~ big_f(b)
| big_g(f(a))
| ~ big_f(f(a))
| big_j(a,f(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ( big_g(b)
| ~ big_f(b)
| big_j(a,f(a))
| big_g(f(a))
| ~ big_f(f(a)) )
<=> ( big_g(b)
| ~ big_f(b)
| big_g(f(a))
| ~ big_f(f(a))
| big_j(a,f(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ( ~ ! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) )
| big_g(b)
| ~ big_f(b)
| big_j(a,f(a))
| big_g(f(a))
| ~ big_f(f(a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) )
| big_g(b)
| ~ big_f(b)
| big_g(f(a))
| ~ big_f(f(a))
| big_j(a,f(a)) ) ),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( ( ~ ! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) )
| big_g(b)
| ~ big_f(b)
| big_j(a,f(a))
| big_g(f(a))
| ~ big_f(f(a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) )
| big_g(b)
| ~ big_f(b)
| big_g(f(a))
| ~ big_f(f(a))
| big_j(a,f(a)) ) ),
inference(transitivity,[status(thm)],[109,107]) ).
tff(111,plain,
( ~ ! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) )
| big_g(b)
| ~ big_f(b)
| big_j(a,f(a))
| big_g(f(a))
| ~ big_f(f(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
( ~ ! [Y: $i,X: $i] :
( big_g(X)
| ~ big_f(X)
| big_j(a,Y)
| big_g(Y)
| ~ big_f(Y) )
| big_g(b)
| ~ big_f(b)
| big_g(f(a))
| ~ big_f(f(a))
| big_j(a,f(a)) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
$false,
inference(unit_resolution,[status(thm)],[112,106,6,3,65,96,82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN070-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 01:54:47 EDT 2022
% 0.13/0.35 % 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.
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------