TSTP Solution File: LCL355-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL355-1 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 04:56:00 EDT 2022
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 19
% Syntax : Number of formulae : 34 ( 12 unt; 6 typ; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 143 ( 68 ~; 62 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 60 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
tff(is_a_theorem_type,type,
is_a_theorem: $i > $o ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(u_type,type,
u: $i ).
tff(x_type,type,
x: $i ).
tff(z_type,type,
z: $i ).
tff(y_type,type,
y: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
<=> is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
<=> ! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
<=> ! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(implies(z,x),implies(implies(x,y),implies(z,y))),implies(implies(implies(implies(x,y),implies(z,y)),u),implies(implies(z,x),u)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
is_a_theorem(implies(implies(implies(z,x),implies(implies(x,y),implies(z,y))),implies(implies(implies(implies(x,y),implies(z,y)),u),implies(implies(z,x),u)))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| is_a_theorem(implies(implies(z,x),implies(implies(x,y),implies(z,y)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(11,plain,
is_a_theorem(implies(implies(z,x),implies(implies(x,y),implies(z,y)))),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
( ~ is_a_theorem(implies(implies(implies(implies(x,y),implies(z,y)),u),implies(implies(z,x),u)))
<=> ~ is_a_theorem(implies(implies(implies(implies(x,y),implies(z,y)),u),implies(implies(z,x),u))) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
~ is_a_theorem(implies(implies(implies(implies(x,y),implies(z,y)),u),implies(implies(z,x),u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_04) ).
tff(14,plain,
~ is_a_theorem(implies(implies(implies(implies(x,y),implies(z,y)),u),implies(implies(z,x),u))),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
^ [Y: $i,X: $i] :
refl(
( ( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
<=> ( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
<=> ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
<=> ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
^ [Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) )
<=> ( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) )),
( ( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) )
<=> ( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) ) )),
rewrite(
( ( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y))
| is_a_theorem(Y) )
<=> ( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) )),
( ( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) )
<=> ( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [Y: $i,X: $i] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) )
<=> ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [Y: $i,X: $i] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
tff(21,plain,
! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(implies(implies(implies(x,y),implies(z,y)),u),implies(implies(z,x),u)))
| ~ is_a_theorem(implies(implies(z,x),implies(implies(x,y),implies(z,y))))
| ~ is_a_theorem(implies(implies(implies(z,x),implies(implies(x,y),implies(z,y))),implies(implies(implies(implies(x,y),implies(z,y)),u),implies(implies(z,x),u)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(implies(implies(implies(x,y),implies(z,y)),u),implies(implies(z,x),u)))
| ~ is_a_theorem(implies(implies(z,x),implies(implies(x,y),implies(z,y))))
| ~ is_a_theorem(implies(implies(implies(z,x),implies(implies(x,y),implies(z,y))),implies(implies(implies(implies(x,y),implies(z,y)),u),implies(implies(z,x),u)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(implies(implies(implies(x,y),implies(z,y)),u),implies(implies(z,x),u)))
| ~ is_a_theorem(implies(implies(z,x),implies(implies(x,y),implies(z,y))))
| ~ is_a_theorem(implies(implies(implies(z,x),implies(implies(x,y),implies(z,y))),implies(implies(implies(implies(x,y),implies(z,y)),u),implies(implies(z,x),u)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) )
| is_a_theorem(implies(implies(implies(implies(x,y),implies(z,y)),u),implies(implies(z,x),u)))
| ~ is_a_theorem(implies(implies(z,x),implies(implies(x,y),implies(z,y))))
| ~ is_a_theorem(implies(implies(implies(z,x),implies(implies(x,y),implies(z,y))),implies(implies(implies(implies(x,y),implies(z,y)),u),implies(implies(z,x),u)))) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
$false,
inference(unit_resolution,[status(thm)],[27,24,14,11,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL355-1 : TPTP v8.1.0. Released v2.3.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n014.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 : Thu Sep 1 20:40:16 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.
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------