TSTP Solution File: SYN243-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN243-1 : TPTP v8.1.0. Released v1.1.0.
% 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 23:54:21 EDT 2022
% Result : Unsatisfiable 1.76s 1.38s
% Output : Proof 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 19
% Syntax : Number of formulae : 34 ( 13 unt; 5 typ; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 140 ( 65 ~; 61 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 3 >; 4 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 71 ( 63 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(d_type,type,
d: $i ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(
( m0(X,d,Y)
<=> m0(X,d,Y) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : m0(X,d,Y)
<=> ! [Y: $i,X: $i] : m0(X,d,Y) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : m0(X,d,Y)
<=> ! [Y: $i,X: $i] : m0(X,d,Y) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [Y: $i,X: $i] : m0(X,d,Y),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_19) ).
tff(5,plain,
! [Y: $i,X: $i] : m0(X,d,Y),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : m0(X,d,Y),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : m0(X,d,Y),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : m0(X,d,Y)
| m0(d,d,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
m0(d,d,a),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ m1(a,d,d)
<=> ~ m1(a,d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
~ m1(a,d,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(12,plain,
~ m1(a,d,d),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [B: $i,D: $i,C: $i] :
refl(
( ( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
<=> ( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
^ [B: $i,D: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( m1(B,C,C)
| ~ l0(D) )
<=> ( ~ l0(D)
| m1(B,C,C) ) )),
( ( m1(B,C,C)
| ~ l0(D)
| ~ m0(C,C,B) )
<=> ( ~ l0(D)
| m1(B,C,C)
| ~ m0(C,C,B) ) )),
rewrite(
( ( ~ l0(D)
| m1(B,C,C)
| ~ m0(C,C,B) )
<=> ( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) )),
( ( m1(B,C,C)
| ~ l0(D)
| ~ m0(C,C,B) )
<=> ( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [B: $i,D: $i,C: $i] :
( m1(B,C,C)
| ~ l0(D)
| ~ m0(C,C,B) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [B: $i,D: $i,C: $i] :
( m1(B,C,C)
| ~ l0(D)
| ~ m0(C,C,B) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_015) ).
tff(19,plain,
! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( l0(a)
<=> l0(a) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
l0(a),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_20) ).
tff(25,plain,
l0(a),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ( ~ ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
| ~ l0(a)
| ~ m0(d,d,a)
| m1(a,d,d) )
<=> ( ~ ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
| ~ l0(a)
| ~ m0(d,d,a)
| m1(a,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
| ~ l0(a)
| ~ m0(d,d,a)
| m1(a,d,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ l0(D)
| ~ m0(C,C,B)
| m1(B,C,C) )
| ~ l0(a)
| ~ m0(d,d,a)
| m1(a,d,d) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,25,22,12,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN243-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n028.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 : Mon Sep 5 02:24:40 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.
% 1.76/1.38 % SZS status Unsatisfiable
% 1.76/1.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------