TSTP Solution File: SYN065-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN065-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 23:53:29 EDT 2022
% Result : Unsatisfiable 1.34s 1.10s
% Output : Proof 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 25
% Syntax : Number of formulae : 50 ( 21 unt; 6 typ; 0 def)
% Number of atoms : 163 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 209 ( 101 ~; 87 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 93 ( 84 !; 0 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
tff(big_h_type,type,
big_h: ( $i * $i ) > $o ).
tff(f_type,type,
f: $i > $i ).
tff(g_type,type,
g: $i > $i ).
tff(a_type,type,
a: $i ).
tff(big_f_type,type,
big_f: ( $i * $i ) > $o ).
tff(big_g_type,type,
big_g: ( $i * $i ) > $o ).
tff(1,plain,
^ [X: $i] :
refl(
( big_f(X,f(X))
<=> big_f(X,f(X)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : big_f(X,f(X))
<=> ! [X: $i] : big_f(X,f(X)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : big_f(X,f(X))
<=> ! [X: $i] : big_f(X,f(X)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : big_f(X,f(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
tff(5,plain,
! [X: $i] : big_f(X,f(X)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : big_f(X,f(X)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : big_f(X,f(X)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : big_f(X,f(X))
| big_f(g(a),f(g(a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
big_f(g(a),f(g(a))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(
( big_g(X,g(X))
<=> big_g(X,g(X)) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] : big_g(X,g(X))
<=> ! [X: $i] : big_g(X,g(X)) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : big_g(X,g(X))
<=> ! [X: $i] : big_g(X,g(X)) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X: $i] : big_g(X,g(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
tff(14,plain,
! [X: $i] : big_g(X,g(X)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : big_g(X,g(X)),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : big_g(X,g(X)),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : big_g(X,g(X))
| big_g(a,g(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
big_g(a,g(a)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) )
<=> ( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ big_g(X,Y)
| ~ big_f(Y,Z) )
<=> ( ~ big_f(Y,Z)
| ~ big_g(X,Y) ) )),
( ( ~ big_g(X,Y)
| ~ big_f(Y,Z)
| big_h(X,Z) )
<=> ( ~ big_f(Y,Z)
| ~ big_g(X,Y)
| big_h(X,Z) ) )),
rewrite(
( ( ~ big_f(Y,Z)
| ~ big_g(X,Y)
| big_h(X,Z) )
<=> ( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) ) )),
( ( ~ big_g(X,Y)
| ~ big_f(Y,Z)
| big_h(X,Z) )
<=> ( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ big_g(X,Y)
| ~ big_f(Y,Z)
| big_h(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ big_g(X,Y)
| ~ big_f(Y,Z)
| big_h(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) )
| ~ big_f(g(a),f(g(a)))
| big_h(a,f(g(a)))
| ~ big_g(a,g(a)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) )
| ~ big_f(g(a),f(g(a)))
| big_h(a,f(g(a)))
| ~ big_g(a,g(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( big_h(a,f(g(a)))
| ~ big_f(g(a),f(g(a)))
| ~ big_g(a,g(a)) )
<=> ( ~ big_f(g(a),f(g(a)))
| big_h(a,f(g(a)))
| ~ big_g(a,g(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) )
| big_h(a,f(g(a)))
| ~ big_f(g(a),f(g(a)))
| ~ big_g(a,g(a)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) )
| ~ big_f(g(a),f(g(a)))
| big_h(a,f(g(a)))
| ~ big_g(a,g(a)) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) )
| big_h(a,f(g(a)))
| ~ big_f(g(a),f(g(a)))
| ~ big_g(a,g(a)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) )
| ~ big_f(g(a),f(g(a)))
| big_h(a,f(g(a)))
| ~ big_g(a,g(a)) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) )
| big_h(a,f(g(a)))
| ~ big_f(g(a),f(g(a)))
| ~ big_g(a,g(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( big_h(X,Z)
| ~ big_f(Y,Z)
| ~ big_g(X,Y) )
| ~ big_f(g(a),f(g(a)))
| big_h(a,f(g(a)))
| ~ big_g(a,g(a)) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
big_h(a,f(g(a))),
inference(unit_resolution,[status(thm)],[34,28,18,9]) ).
tff(36,plain,
^ [X: $i] :
refl(
( ~ big_h(a,X)
<=> ~ big_h(a,X) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X: $i] : ~ big_h(a,X)
<=> ! [X: $i] : ~ big_h(a,X) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X: $i] : ~ big_h(a,X)
<=> ! [X: $i] : ~ big_h(a,X) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
! [X: $i] : ~ big_h(a,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
tff(40,plain,
! [X: $i] : ~ big_h(a,X),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [X: $i] : ~ big_h(a,X),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [X: $i] : ~ big_h(a,X),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [X: $i] : ~ big_h(a,X)
| ~ big_h(a,f(g(a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
$false,
inference(unit_resolution,[status(thm)],[43,42,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN065-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.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 00:54:55 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.
% 1.34/1.10 % SZS status Unsatisfiable
% 1.34/1.10 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------