TSTP Solution File: SYN248-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN248-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 23:54:22 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 29
% Syntax : Number of formulae : 49 ( 14 unt; 8 typ; 0 def)
% Number of atoms : 210 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 291 ( 137 ~; 133 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 68 ( 62 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
tff(k1_type,type,
k1: $i > $o ).
tff(a_type,type,
a: $i ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(d_type,type,
d: $i ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(1,plain,
^ [I: $i,J: $i] :
refl(
( ( k1(I)
| ~ n0(J,I) )
<=> ( k1(I)
| ~ n0(J,I) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_001) ).
tff(5,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( n0(b,a)
<=> n0(b,a) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
n0(b,a),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_37) ).
tff(10,plain,
n0(b,a),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(a)
| ~ n0(b,a) )
<=> ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(a)
| ~ n0(b,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(a)
| ~ n0(b,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(a)
| ~ n0(b,a) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
k1(a),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
( ~ m1(d,c,c)
<=> ~ m1(d,c,c) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
~ m1(d,c,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(17,plain,
~ m1(d,c,c),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( n0(d,c)
<=> n0(d,c) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
n0(d,c),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_26) ).
tff(20,plain,
n0(d,c),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) )
<=> ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
k1(c),
inference(unit_resolution,[status(thm)],[23,20,7]) ).
tff(25,plain,
^ [B: $i,A: $i] :
refl(
( ( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) )
<=> ( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) )
<=> ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) )
<=> ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
^ [B: $i,A: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( m1(A,B,B)
| ~ k1(a) )
<=> ( ~ k1(a)
| m1(A,B,B) ) )),
( ( m1(A,B,B)
| ~ k1(a)
| ~ k1(B) )
<=> ( ~ k1(a)
| m1(A,B,B)
| ~ k1(B) ) )),
rewrite(
( ( ~ k1(a)
| m1(A,B,B)
| ~ k1(B) )
<=> ( ~ k1(a)
| ~ k1(B)
| m1(A,B,B) ) )),
( ( m1(A,B,B)
| ~ k1(a)
| ~ k1(B) )
<=> ( ~ k1(a)
| ~ k1(B)
| m1(A,B,B) ) )),
( ( m1(A,B,B)
| ~ k1(a)
| ~ k1(B)
| ~ q0(A,A) )
<=> ( ~ k1(a)
| ~ k1(B)
| m1(A,B,B)
| ~ q0(A,A) ) )),
rewrite(
( ( ~ k1(a)
| ~ k1(B)
| m1(A,B,B)
| ~ q0(A,A) )
<=> ( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ) )),
( ( m1(A,B,B)
| ~ k1(a)
| ~ k1(B)
| ~ q0(A,A) )
<=> ( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [B: $i,A: $i] :
( m1(A,B,B)
| ~ k1(a)
| ~ k1(B)
| ~ q0(A,A) )
<=> ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,axiom,
! [B: $i,A: $i] :
( m1(A,B,B)
| ~ k1(a)
| ~ k1(B)
| ~ q0(A,A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_034) ).
tff(31,plain,
! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) ),
inference(modus_ponens,[status(thm)],[33,26]) ).
tff(35,plain,
( q0(d,d)
<=> q0(d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
q0(d,d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_25) ).
tff(37,plain,
q0(d,d),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) )
| ~ k1(a)
| ~ q0(d,d)
| ~ k1(c)
| m1(d,c,c) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) )
| ~ k1(a)
| ~ q0(d,d)
| ~ k1(c)
| m1(d,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) )
| ~ k1(a)
| ~ q0(d,d)
| ~ k1(c)
| m1(d,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [B: $i,A: $i] :
( ~ k1(a)
| ~ q0(A,A)
| ~ k1(B)
| m1(A,B,B) )
| ~ k1(a)
| ~ q0(d,d)
| ~ k1(c)
| m1(d,c,c) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
$false,
inference(unit_resolution,[status(thm)],[40,37,34,24,17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN248-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 02:39:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------