TSTP Solution File: LDA007-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LDA007-2 : TPTP v8.1.0. Bugfixed v2.6.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 05:06:28 EDT 2022
% Result : Unsatisfiable 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 28 ( 15 unt; 7 typ; 0 def)
% Number of atoms : 29 ( 27 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 2 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 33 ( 30 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: ( $i * $i ) > $i ).
tff(critical_point_type,type,
critical_point: $i > $i ).
tff(t_type,type,
t: $i ).
tff(s_type,type,
s: $i ).
tff(tk_type,type,
tk: $i ).
tff(tt_ts_type,type,
tt_ts: $i ).
tff(tsk_type,type,
tsk: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
<=> ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(t,f(t,s)) = f(f(t,t),f(t,s)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
f(t,f(t,s)) = f(f(t,t),f(t,s)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
f(f(t,t),f(t,s)) = f(t,f(t,s)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
f(f(f(t,t),f(t,s)),f(t,critical_point(t))) = f(f(t,f(t,s)),f(t,critical_point(t))),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
f(f(t,f(t,s)),f(t,critical_point(t))) = f(f(f(t,t),f(t,s)),f(t,critical_point(t))),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(t,f(f(t,s),critical_point(t))) = f(f(t,f(t,s)),f(t,critical_point(t))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(14,plain,
f(t,f(f(t,s),critical_point(t))) = f(f(t,f(t,s)),f(t,critical_point(t))),
inference(unit_resolution,[status(thm)],[13,7]) ).
tff(15,plain,
f(t,f(f(t,s),critical_point(t))) = f(f(f(t,t),f(t,s)),f(t,critical_point(t))),
inference(transitivity,[status(thm)],[14,12]) ).
tff(16,plain,
( ( f(t,tsk) != f(tt_ts,tk) )
<=> ( f(t,f(f(t,s),critical_point(t))) != f(f(f(t,t),f(t,s)),f(t,critical_point(t))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( ( f(t,tsk) != f(tt_ts,tk) )
<=> ( f(t,tsk) != f(tt_ts,tk) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
f(t,tsk) != f(tt_ts,tk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
tff(19,plain,
f(t,tsk) != f(tt_ts,tk),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
f(t,f(f(t,s),critical_point(t))) != f(f(f(t,t),f(t,s)),f(t,critical_point(t))),
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
$false,
inference(unit_resolution,[status(thm)],[20,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LDA007-2 : TPTP v8.1.0. Bugfixed v2.6.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n028.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 : Fri Sep 2 02:11:06 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------