TSTP Solution File: SYN264-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN264-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 23:54:26 EDT 2022
% Result : Unsatisfiable 0.96s 0.92s
% Output : Proof 0.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 31
% Syntax : Number of formulae : 53 ( 15 unt; 10 typ; 0 def)
% Number of atoms : 278 ( 0 equ)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 369 ( 171 ~; 165 |; 0 &)
% ( 33 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 37 ( 37 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 118 ( 102 !; 0 ?; 118 :)
% Comments :
%------------------------------------------------------------------------------
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(c_type,type,
c: $i ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(k0_type,type,
k0: $i > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(s0_type,type,
s0: $i > $o ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [D: $i,E: $i] :
refl(
( ( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) )
<=> ( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) )
<=> ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) )
<=> ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [D: $i,E: $i] :
trans(
monotonicity(
rewrite(
( ( p1(D,D,E)
| ~ n0(d,D) )
<=> ( ~ n0(d,D)
| p1(D,D,E) ) )),
( ( p1(D,D,E)
| ~ n0(d,D)
| ~ k0(E) )
<=> ( ~ n0(d,D)
| p1(D,D,E)
| ~ k0(E) ) )),
rewrite(
( ( ~ n0(d,D)
| p1(D,D,E)
| ~ k0(E) )
<=> ( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ) )),
( ( p1(D,D,E)
| ~ n0(d,D)
| ~ k0(E) )
<=> ( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [D: $i,E: $i] :
( p1(D,D,E)
| ~ n0(d,D)
| ~ k0(E) )
<=> ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [D: $i,E: $i] :
( p1(D,D,E)
| ~ n0(d,D)
| ~ k0(E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_063) ).
tff(7,plain,
! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( k0(e)
<=> k0(e) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
k0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(13,plain,
k0(e),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( n0(d,c)
<=> n0(d,c) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
n0(d,c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_26) ).
tff(16,plain,
n0(d,c),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) )
| ~ k0(e)
| ~ n0(d,c)
| p1(c,c,e) )
<=> ( ~ ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) )
| ~ k0(e)
| ~ n0(d,c)
| p1(c,c,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) )
| ~ k0(e)
| ~ n0(d,c)
| p1(c,c,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [D: $i,E: $i] :
( ~ k0(E)
| ~ n0(d,D)
| p1(D,D,E) )
| ~ k0(e)
| ~ n0(d,c)
| p1(c,c,e) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
p1(c,c,e),
inference(unit_resolution,[status(thm)],[19,16,13,10]) ).
tff(21,plain,
( ~ p1(e,c,e)
<=> ~ p1(e,c,e) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
~ p1(e,c,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(23,plain,
~ p1(e,c,e),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
refl(
( ( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) )
<=> ( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
trans(
monotonicity(
trans(
monotonicity(
iff_true(asserted(s0(b)),
( s0(b)
<=> $true )),
( ~ s0(b)
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ s0(b)
<=> $false )),
( ( ~ l0(J)
| ~ s0(b)
| ~ p1(I,A,H)
| p1(H,I,H) )
<=> ( ~ l0(J)
| $false
| ~ p1(I,A,H)
| p1(H,I,H) ) )),
rewrite(
( ( ~ l0(J)
| $false
| ~ p1(I,A,H)
| p1(H,I,H) )
<=> ( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) ) )),
( ( ~ l0(J)
| ~ s0(b)
| ~ p1(I,A,H)
| p1(H,I,H) )
<=> ( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ l0(J)
| ~ s0(b)
| ~ p1(I,A,H)
| p1(H,I,H) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p1(H,I,H)
| ~ l0(J) )
<=> ( ~ l0(J)
| p1(H,I,H) ) )),
( ( p1(H,I,H)
| ~ l0(J)
| ~ p1(I,A,H) )
<=> ( ~ l0(J)
| p1(H,I,H)
| ~ p1(I,A,H) ) )),
rewrite(
( ( ~ l0(J)
| p1(H,I,H)
| ~ p1(I,A,H) )
<=> ( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) ) )),
( ( p1(H,I,H)
| ~ l0(J)
| ~ p1(I,A,H) )
<=> ( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) ) )),
( ( p1(H,I,H)
| ~ l0(J)
| ~ p1(I,A,H)
| ~ s0(b) )
<=> ( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H)
| ~ s0(b) ) )),
rewrite(
( ( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H)
| ~ s0(b) )
<=> ( ~ l0(J)
| ~ s0(b)
| ~ p1(I,A,H)
| p1(H,I,H) ) )),
( ( p1(H,I,H)
| ~ l0(J)
| ~ p1(I,A,H)
| ~ s0(b) )
<=> ( ~ l0(J)
| ~ s0(b)
| ~ p1(I,A,H)
| p1(H,I,H) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( p1(H,I,H)
| ~ l0(J)
| ~ p1(I,A,H)
| ~ s0(b) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ l0(J)
| ~ s0(b)
| ~ p1(I,A,H)
| p1(H,I,H) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,axiom,
! [I: $i,A: $i,J: $i,H: $i] :
( p1(H,I,H)
| ~ l0(J)
| ~ p1(I,A,H)
| ~ s0(b) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_071) ).
tff(32,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ l0(J)
| ~ s0(b)
| ~ p1(I,A,H)
| p1(H,I,H) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) ),
inference(modus_ponens,[status(thm)],[33,26]) ).
tff(35,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) ),
inference(modus_ponens,[status(thm)],[35,25]) ).
tff(37,plain,
( l0(a)
<=> l0(a) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
l0(a),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_20) ).
tff(39,plain,
l0(a),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) )
| ~ l0(a)
| ~ p1(c,c,e)
| p1(e,c,e) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) )
| ~ l0(a)
| ~ p1(c,c,e)
| p1(e,c,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) )
| ~ l0(a)
| ~ p1(c,c,e)
| p1(e,c,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ l0(J)
| ~ p1(I,A,H)
| p1(H,I,H) )
| ~ l0(a)
| ~ p1(c,c,e)
| p1(e,c,e) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
$false,
inference(unit_resolution,[status(thm)],[42,39,36,23,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN264-1 : TPTP v8.1.0. Released v1.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 02:20:48 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.
% 0.96/0.92 % SZS status Unsatisfiable
% 0.96/0.92 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------