TSTP Solution File: SYN721-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN721-1 : TPTP v8.1.0. Released v2.5.0.
% 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 : Thu Sep 29 23:57:04 EDT 2022
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 46 ( 10 unt; 4 typ; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 188 ( 95 ~; 76 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 98 ( 87 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
tff(r_type,type,
r: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(q_type,type,
q: ( $i * $i ) > $o ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(
( ( ~ r(A,B)
| q(A,A) )
<=> ( ~ r(A,B)
| q(A,A) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i] :
( ~ r(A,B)
| q(A,A) )
<=> ! [B: $i,A: $i] :
( ~ r(A,B)
| q(A,A) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] :
( ~ r(A,B)
| q(A,A) )
<=> ! [B: $i,A: $i] :
( ~ r(A,B)
| q(A,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [B: $i,A: $i] :
rewrite(
( ( q(A,A)
| ~ r(A,B) )
<=> ( ~ r(A,B)
| q(A,A) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [B: $i,A: $i] :
( q(A,A)
| ~ r(A,B) )
<=> ! [B: $i,A: $i] :
( ~ r(A,B)
| q(A,A) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [B: $i,A: $i] :
( q(A,A)
| ~ r(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lx1_2) ).
tff(7,plain,
! [B: $i,A: $i] :
( ~ r(A,B)
| q(A,A) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [B: $i,A: $i] :
( ~ r(A,B)
| q(A,A) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [B: $i,A: $i] :
( ~ r(A,B)
| q(A,A) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,A: $i] :
( ~ r(A,B)
| q(A,A) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( r(a,b)
<=> r(a,b) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
r(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lx1_1) ).
tff(13,plain,
r(a,b),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ r(A,B)
| q(A,A) )
| ~ r(a,b)
| q(a,a) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ r(A,B)
| q(A,A) )
| ~ r(a,b)
| q(a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [B: $i,A: $i] :
( ~ r(A,B)
| q(A,A) )
| ~ r(a,b)
| q(a,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [B: $i,A: $i] :
( ~ r(A,B)
| q(A,A) )
| ~ r(a,b)
| q(a,a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
q(a,a),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [A: $i] :
refl(
( ( ~ q(A,a)
| ~ r(b,A) )
<=> ( ~ q(A,a)
| ~ r(b,A) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [A: $i] :
( ~ q(A,a)
| ~ r(b,A) )
<=> ! [A: $i] :
( ~ q(A,a)
| ~ r(b,A) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [A: $i] :
( ~ q(A,a)
| ~ r(b,A) )
<=> ! [A: $i] :
( ~ q(A,a)
| ~ r(b,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [A: $i] :
( ~ q(A,a)
| ~ r(b,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lx1_4) ).
tff(22,plain,
! [A: $i] :
( ~ q(A,a)
| ~ r(b,A) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [A: $i] :
( ~ q(A,a)
| ~ r(b,A) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [A: $i] :
( ~ q(A,a)
| ~ r(b,A) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [A: $i] :
( ~ q(A,a)
| ~ r(b,A) )
| ~ q(a,a)
| ~ r(b,a) )
<=> ( ~ ! [A: $i] :
( ~ q(A,a)
| ~ r(b,A) )
| ~ q(a,a)
| ~ r(b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [A: $i] :
( ~ q(A,a)
| ~ r(b,A) )
| ~ q(a,a)
| ~ r(b,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [A: $i] :
( ~ q(A,a)
| ~ r(b,A) )
| ~ q(a,a)
| ~ r(b,a) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
~ r(b,a),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ q(A,B)
| r(C,B) )
<=> ( ~ q(A,B)
| r(C,B) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ q(A,B)
| r(C,B) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ q(A,B)
| r(C,B) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ q(A,B)
| r(C,B) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ q(A,B)
| r(C,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
^ [B: $i,A: $i,C: $i] :
rewrite(
( ( r(C,B)
| ~ q(A,B) )
<=> ( ~ q(A,B)
| r(C,B) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [B: $i,A: $i,C: $i] :
( r(C,B)
| ~ q(A,B) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ q(A,B)
| r(C,B) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [B: $i,A: $i,C: $i] :
( r(C,B)
| ~ q(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lx1_3) ).
tff(35,plain,
! [B: $i,A: $i,C: $i] :
( ~ q(A,B)
| r(C,B) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [B: $i,A: $i,C: $i] :
( ~ q(A,B)
| r(C,B) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [B: $i,A: $i,C: $i] :
( ~ q(A,B)
| r(C,B) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [B: $i,A: $i,C: $i] :
( ~ q(A,B)
| r(C,B) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ q(A,B)
| r(C,B) )
| ~ q(a,a)
| r(b,a) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ q(A,B)
| r(C,B) )
| ~ q(a,a)
| r(b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ q(A,B)
| r(C,B) )
| ~ q(a,a)
| r(b,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ q(A,B)
| r(C,B) )
| ~ q(a,a)
| r(b,a) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
$false,
inference(unit_resolution,[status(thm)],[41,38,17,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN721-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 06:53:56 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
%------------------------------------------------------------------------------