TSTP Solution File: NUM020-1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM020-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 13:02:41 EDT 2022
% Result : Unsatisfiable 0.22s 0.44s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 27
% Syntax : Number of formulae : 53 ( 18 unt; 5 typ; 0 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 211 ( 98 ~; 94 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 116 ( 108 !; 0 ?; 116 :)
% Comments :
%------------------------------------------------------------------------------
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(successor_type,type,
successor: $i > $i ).
tff(a_type,type,
a: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(n0_type,type,
n0: $i ).
tff(1,plain,
^ [A: $i] :
refl(
( equalish(add(A,n0),A)
<=> equalish(add(A,n0),A) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i] : equalish(add(A,n0),A)
<=> ! [A: $i] : equalish(add(A,n0),A) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : equalish(add(A,n0),A)
<=> ! [A: $i] : equalish(add(A,n0),A) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [A: $i] : equalish(add(A,n0),A),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-0.ax',adding_zero) ).
tff(5,plain,
! [A: $i] : equalish(add(A,n0),A),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : equalish(add(A,n0),A),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : equalish(add(A,n0),A),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : equalish(add(A,n0),A)
| equalish(add(a,n0),a) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
equalish(add(a,n0),a),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i] :
refl(
( ( ~ equalish(A,B)
| equalish(successor(A),successor(B)) )
<=> ( ~ equalish(A,B)
| equalish(successor(A),successor(B)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [B: $i,A: $i] :
( ~ equalish(A,B)
| equalish(successor(A),successor(B)) )
<=> ! [B: $i,A: $i] :
( ~ equalish(A,B)
| equalish(successor(A),successor(B)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [B: $i,A: $i] :
( ~ equalish(A,B)
| equalish(successor(A),successor(B)) )
<=> ! [B: $i,A: $i] :
( ~ equalish(A,B)
| equalish(successor(A),successor(B)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [B: $i,A: $i] :
( ~ equalish(A,B)
| equalish(successor(A),successor(B)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-0.ax',successor_substitution) ).
tff(14,plain,
! [B: $i,A: $i] :
( ~ equalish(A,B)
| equalish(successor(A),successor(B)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i] :
( ~ equalish(A,B)
| equalish(successor(A),successor(B)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i] :
( ~ equalish(A,B)
| equalish(successor(A),successor(B)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ equalish(A,B)
| equalish(successor(A),successor(B)) )
| ~ equalish(add(a,n0),a)
| equalish(successor(add(a,n0)),successor(a)) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ equalish(A,B)
| equalish(successor(A),successor(B)) )
| ~ equalish(add(a,n0),a)
| equalish(successor(add(a,n0)),successor(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i] :
( ~ equalish(A,B)
| equalish(successor(A),successor(B)) )
| ~ equalish(add(a,n0),a)
| equalish(successor(add(a,n0)),successor(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i] :
( ~ equalish(A,B)
| equalish(successor(A),successor(B)) )
| ~ equalish(add(a,n0),a)
| equalish(successor(add(a,n0)),successor(a)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
equalish(successor(add(a,n0)),successor(a)),
inference(unit_resolution,[status(thm)],[19,16,9]) ).
tff(21,plain,
^ [B: $i,A: $i] :
refl(
( equalish(add(A,successor(B)),successor(add(A,B)))
<=> equalish(add(A,successor(B)),successor(add(A,B))) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [B: $i,A: $i] : equalish(add(A,successor(B)),successor(add(A,B)))
<=> ! [B: $i,A: $i] : equalish(add(A,successor(B)),successor(add(A,B))) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [B: $i,A: $i] : equalish(add(A,successor(B)),successor(add(A,B)))
<=> ! [B: $i,A: $i] : equalish(add(A,successor(B)),successor(add(A,B))) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [B: $i,A: $i] : equalish(add(A,successor(B)),successor(add(A,B))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-0.ax',addition) ).
tff(25,plain,
! [B: $i,A: $i] : equalish(add(A,successor(B)),successor(add(A,B))),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [B: $i,A: $i] : equalish(add(A,successor(B)),successor(add(A,B))),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [B: $i,A: $i] : equalish(add(A,successor(B)),successor(add(A,B))),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [B: $i,A: $i] : equalish(add(A,successor(B)),successor(add(A,B)))
| equalish(add(a,successor(n0)),successor(add(a,n0))) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
equalish(add(a,successor(n0)),successor(add(a,n0))),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ equalish(add(a,successor(n0)),successor(a))
<=> ~ equalish(add(a,successor(n0)),successor(a)) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
~ equalish(add(a,successor(n0)),successor(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',deny_addition_lemma) ).
tff(32,plain,
~ equalish(add(a,successor(n0)),successor(a)),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(
( ( ~ equalish(X,Y)
| ~ equalish(Y,Z)
| equalish(X,Z) )
<=> ( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| ~ equalish(Y,Z)
| equalish(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| ~ equalish(Y,Z)
| equalish(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
tff(38,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
| equalish(add(a,successor(n0)),successor(a))
| ~ equalish(add(a,successor(n0)),successor(add(a,n0)))
| ~ equalish(successor(add(a,n0)),successor(a)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
| equalish(add(a,successor(n0)),successor(a))
| ~ equalish(add(a,successor(n0)),successor(add(a,n0)))
| ~ equalish(successor(add(a,n0)),successor(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( ~ equalish(add(a,successor(n0)),successor(add(a,n0)))
| equalish(add(a,successor(n0)),successor(a))
| ~ equalish(successor(add(a,n0)),successor(a)) )
<=> ( equalish(add(a,successor(n0)),successor(a))
| ~ equalish(add(a,successor(n0)),successor(add(a,n0)))
| ~ equalish(successor(add(a,n0)),successor(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
| ~ equalish(add(a,successor(n0)),successor(add(a,n0)))
| equalish(add(a,successor(n0)),successor(a))
| ~ equalish(successor(add(a,n0)),successor(a)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
| equalish(add(a,successor(n0)),successor(a))
| ~ equalish(add(a,successor(n0)),successor(add(a,n0)))
| ~ equalish(successor(add(a,n0)),successor(a)) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
| ~ equalish(add(a,successor(n0)),successor(add(a,n0)))
| equalish(add(a,successor(n0)),successor(a))
| ~ equalish(successor(add(a,n0)),successor(a)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
| equalish(add(a,successor(n0)),successor(a))
| ~ equalish(add(a,successor(n0)),successor(add(a,n0)))
| ~ equalish(successor(add(a,n0)),successor(a)) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
| ~ equalish(add(a,successor(n0)),successor(add(a,n0)))
| equalish(add(a,successor(n0)),successor(a))
| ~ equalish(successor(add(a,n0)),successor(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
| equalish(add(a,successor(n0)),successor(a))
| ~ equalish(add(a,successor(n0)),successor(add(a,n0)))
| ~ equalish(successor(add(a,n0)),successor(a)) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
$false,
inference(unit_resolution,[status(thm)],[47,41,32,29,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM020-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 06:33:40 EDT 2022
% 0.13/0.35 % 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.
% 0.22/0.44 % SZS status Unsatisfiable
% 0.22/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------