TSTP Solution File: LCL172-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL172-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 04:55:11 EDT 2022
% Result : Unsatisfiable 0.17s 0.37s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 18
% Syntax : Number of formulae : 30 ( 10 unt; 7 typ; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 58 ( 27 ~; 23 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 4 >; 1 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 39 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
tff(axiom_type,type,
axiom: $i > $o ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(r_type,type,
r: $i ).
tff(not_type,type,
not: $i > $i ).
tff(p_type,type,
p: $i ).
tff(q_type,type,
q: $i ).
tff(theorem_type,type,
theorem: $i > $o ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
<=> axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
<=> ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
<=> ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
file('/export/starexec/sandbox/benchmark/Axioms/LCL003-0.ax',axiom_1_5) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
| axiom(or(not(or(not(p),or(not(q),r))),or(not(q),or(not(p),r)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
axiom(or(not(or(not(p),or(not(q),r))),or(not(q),or(not(p),r)))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ theorem(or(not(or(not(p),or(not(q),r))),or(not(q),or(not(p),r))))
<=> ~ theorem(or(not(or(not(p),or(not(q),r))),or(not(q),or(not(p),r)))) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
~ theorem(or(not(or(not(p),or(not(q),r))),or(not(q),or(not(p),r)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(12,plain,
~ theorem(or(not(or(not(p),or(not(q),r))),or(not(q),or(not(p),r)))),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [X: $i] :
refl(
( ( theorem(X)
| ~ axiom(X) )
<=> ( theorem(X)
| ~ axiom(X) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL003-0.ax',rule_1) ).
tff(17,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(or(not(p),or(not(q),r))),or(not(q),or(not(p),r))))
| ~ axiom(or(not(or(not(p),or(not(q),r))),or(not(q),or(not(p),r)))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(or(not(p),or(not(q),r))),or(not(q),or(not(p),r))))
| ~ axiom(or(not(or(not(p),or(not(q),r))),or(not(q),or(not(p),r)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(or(not(p),or(not(q),r))),or(not(q),or(not(p),r))))
| ~ axiom(or(not(or(not(p),or(not(q),r))),or(not(q),or(not(p),r)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(or(not(p),or(not(q),r))),or(not(q),or(not(p),r))))
| ~ axiom(or(not(or(not(p),or(not(q),r))),or(not(q),or(not(p),r)))) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,19,12,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL172-1 : TPTP v8.1.0. Released v1.1.0.
% 0.00/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n012.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Sep 1 18:27:19 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.17/0.37 % SZS status Unsatisfiable
% 0.17/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------