TSTP Solution File: LCL190-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL190-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 04:55:19 EDT 2022
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 29
% Syntax : Number of formulae : 56 ( 19 unt; 7 typ; 0 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 221 ( 103 ~; 98 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 4 >; 1 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 105 ( 95 !; 0 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
tff(axiom_type,type,
axiom: $i > $o ).
tff(or_type,type,
or: ( $i * $i ) > $i ).
tff(q_type,type,
q: $i ).
tff(r_type,type,
r: $i ).
tff(not_type,type,
not: $i > $i ).
tff(theorem_type,type,
theorem: $i > $o ).
tff(p_type,type,
p: $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(
( axiom(or(not(or(A,B)),or(B,A)))
<=> axiom(or(not(or(A,B)),or(B,A))) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A)))
<=> ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A)))
<=> ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL003-0.ax',axiom_1_4) ).
tff(5,plain,
! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A))),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : axiom(or(not(or(A,B)),or(B,A)))
| axiom(or(not(or(q,r)),or(r,q))) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
axiom(or(not(or(q,r)),or(r,q))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))
<=> axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [B: $i,A: $i,C: $i] : axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))
<=> ! [B: $i,A: $i,C: $i] : axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))
<=> ! [B: $i,A: $i,C: $i] : axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [B: $i,A: $i,C: $i] : axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL003-0.ax',axiom_1_6) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] : axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i,C: $i] : axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))
| axiom(or(not(or(not(or(q,r)),or(r,q))),or(not(or(p,or(q,r))),or(p,or(r,q))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
axiom(or(not(or(not(or(q,r)),or(r,q))),or(not(or(p,or(q,r))),or(p,or(r,q))))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ theorem(or(not(or(p,or(q,r))),or(p,or(r,q))))
<=> ~ theorem(or(not(or(p,or(q,r))),or(p,or(r,q)))) ),
inference(rewrite,[status(thm)],]) ).
tff(20,axiom,
~ theorem(or(not(or(p,or(q,r))),or(p,or(r,q)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(21,plain,
~ theorem(or(not(or(p,or(q,r))),or(p,or(r,q)))),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
^ [Y: $i,X: $i] :
refl(
( ( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
<=> ( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
<=> ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
<=> ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
^ [Y: $i,X: $i] :
rewrite(
( ( theorem(X)
| ~ axiom(or(not(Y),X))
| ~ theorem(Y) )
<=> ( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [Y: $i,X: $i] :
( theorem(X)
| ~ axiom(or(not(Y),X))
| ~ theorem(Y) )
<=> ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [Y: $i,X: $i] :
( theorem(X)
| ~ axiom(or(not(Y),X))
| ~ theorem(Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL003-0.ax',rule_2) ).
tff(28,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| theorem(or(not(or(p,or(q,r))),or(p,or(r,q))))
| ~ axiom(or(not(or(not(or(q,r)),or(r,q))),or(not(or(p,or(q,r))),or(p,or(r,q)))))
| ~ theorem(or(not(or(q,r)),or(r,q))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| theorem(or(not(or(p,or(q,r))),or(p,or(r,q))))
| ~ axiom(or(not(or(not(or(q,r)),or(r,q))),or(not(or(p,or(q,r))),or(p,or(r,q)))))
| ~ theorem(or(not(or(q,r)),or(r,q))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( theorem(or(not(or(p,or(q,r))),or(p,or(r,q))))
| ~ theorem(or(not(or(q,r)),or(r,q)))
| ~ axiom(or(not(or(not(or(q,r)),or(r,q))),or(not(or(p,or(q,r))),or(p,or(r,q))))) )
<=> ( theorem(or(not(or(p,or(q,r))),or(p,or(r,q))))
| ~ axiom(or(not(or(not(or(q,r)),or(r,q))),or(not(or(p,or(q,r))),or(p,or(r,q)))))
| ~ theorem(or(not(or(q,r)),or(r,q))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| theorem(or(not(or(p,or(q,r))),or(p,or(r,q))))
| ~ theorem(or(not(or(q,r)),or(r,q)))
| ~ axiom(or(not(or(not(or(q,r)),or(r,q))),or(not(or(p,or(q,r))),or(p,or(r,q))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| theorem(or(not(or(p,or(q,r))),or(p,or(r,q))))
| ~ axiom(or(not(or(not(or(q,r)),or(r,q))),or(not(or(p,or(q,r))),or(p,or(r,q)))))
| ~ theorem(or(not(or(q,r)),or(r,q))) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| theorem(or(not(or(p,or(q,r))),or(p,or(r,q))))
| ~ theorem(or(not(or(q,r)),or(r,q)))
| ~ axiom(or(not(or(not(or(q,r)),or(r,q))),or(not(or(p,or(q,r))),or(p,or(r,q))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| theorem(or(not(or(p,or(q,r))),or(p,or(r,q))))
| ~ axiom(or(not(or(not(or(q,r)),or(r,q))),or(not(or(p,or(q,r))),or(p,or(r,q)))))
| ~ theorem(or(not(or(q,r)),or(r,q))) ) ),
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| theorem(or(not(or(p,or(q,r))),or(p,or(r,q))))
| ~ theorem(or(not(or(q,r)),or(r,q)))
| ~ axiom(or(not(or(not(or(q,r)),or(r,q))),or(not(or(p,or(q,r))),or(p,or(r,q))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
( ~ ! [Y: $i,X: $i] :
( theorem(X)
| ~ theorem(Y)
| ~ axiom(or(not(Y),X)) )
| theorem(or(not(or(p,or(q,r))),or(p,or(r,q))))
| ~ axiom(or(not(or(not(or(q,r)),or(r,q))),or(not(or(p,or(q,r))),or(p,or(r,q)))))
| ~ theorem(or(not(or(q,r)),or(r,q))) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
~ theorem(or(not(or(q,r)),or(r,q))),
inference(unit_resolution,[status(thm)],[37,31,21,18]) ).
tff(39,plain,
^ [X: $i] :
refl(
( ( theorem(X)
| ~ axiom(X) )
<=> ( theorem(X)
| ~ axiom(X) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
<=> ! [X: $i] :
( theorem(X)
| ~ axiom(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL003-0.ax',rule_1) ).
tff(43,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X: $i] :
( theorem(X)
| ~ axiom(X) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(or(q,r)),or(r,q)))
| ~ axiom(or(not(or(q,r)),or(r,q))) )
<=> ( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(or(q,r)),or(r,q)))
| ~ axiom(or(not(or(q,r)),or(r,q))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(or(q,r)),or(r,q)))
| ~ axiom(or(not(or(q,r)),or(r,q))) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [X: $i] :
( theorem(X)
| ~ axiom(X) )
| theorem(or(not(or(q,r)),or(r,q)))
| ~ axiom(or(not(or(q,r)),or(r,q))) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[48,45,38,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL190-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Sep 1 18:49:53 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------