TSTP Solution File: SYN175-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN175-1 : 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 23:54:04 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 44 ( 13 unt; 4 typ; 0 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 176 ( 84 ~; 70 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 8 ( 3 >; 5 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 71 ( 63 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
tff(q2_type,type,
q2: ( $i * $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(n1_type,type,
n1: ( $i * $i * $i ) > $o ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(1,plain,
^ [B: $i,D: $i,C: $i] :
refl(
( ( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
<=> ( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [B: $i,D: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( q2(B,B,B)
| ~ q0(C,B) )
<=> ( ~ q0(C,B)
| q2(B,B,B) ) )),
( ( q2(B,B,B)
| ~ q0(C,B)
| ~ n1(C,B,D) )
<=> ( ~ q0(C,B)
| q2(B,B,B)
| ~ n1(C,B,D) ) )),
rewrite(
( ( ~ q0(C,B)
| q2(B,B,B)
| ~ n1(C,B,D) )
<=> ( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) )),
( ( q2(B,B,B)
| ~ q0(C,B)
| ~ n1(C,B,D) )
<=> ( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [B: $i,D: $i,C: $i] :
( q2(B,B,B)
| ~ q0(C,B)
| ~ n1(C,B,D) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [B: $i,D: $i,C: $i] :
( q2(B,B,B)
| ~ q0(C,B)
| ~ n1(C,B,D) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_178) ).
tff(7,plain,
! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( n1(d,d,d)
<=> n1(d,d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ( n1(d,d,d)
| $false )
<=> n1(d,d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
q0(d,d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_25) ).
tff(15,plain,
( q0(d,d)
<=> $true ),
inference(iff_true,[status(thm)],[14]) ).
tff(16,plain,
( ~ q0(d,d)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ~ q0(d,d)
<=> $false ),
inference(transitivity,[status(thm)],[16,13]) ).
tff(18,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> ( n1(d,d,d)
| $false ) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> n1(d,d,d) ),
inference(transitivity,[status(thm)],[18,12]) ).
tff(20,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> ( n1(d,d,d)
| ~ q0(d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
( n1(d,d,d)
| ~ q0(d,d) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_045) ).
tff(22,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[22,20]) ).
tff(24,plain,
n1(d,d,d),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
n1(d,d,d),
inference(modus_ponens,[status(thm)],[24,11]) ).
tff(26,plain,
( q0(d,d)
<=> q0(d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
q0(d,d),
inference(modus_ponens,[status(thm)],[14,26]) ).
tff(28,plain,
( ( ~ ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
| ~ q0(d,d)
| ~ n1(d,d,d)
| q2(d,d,d) )
<=> ( ~ ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
| ~ q0(d,d)
| ~ n1(d,d,d)
| q2(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
| ~ q0(d,d)
| ~ n1(d,d,d)
| q2(d,d,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ q0(C,B)
| ~ n1(C,B,D)
| q2(B,B,B) )
| ~ q0(d,d)
| ~ n1(d,d,d)
| q2(d,d,d) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
q2(d,d,d),
inference(unit_resolution,[status(thm)],[30,27,25,10]) ).
tff(32,plain,
^ [Y: $i,X: $i] :
refl(
( ~ q2(X,d,Y)
<=> ~ q2(X,d,Y) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [Y: $i,X: $i] : ~ q2(X,d,Y)
<=> ! [Y: $i,X: $i] : ~ q2(X,d,Y) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [Y: $i,X: $i] : ~ q2(X,d,Y)
<=> ! [Y: $i,X: $i] : ~ q2(X,d,Y) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [Y: $i,X: $i] : ~ q2(X,d,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(36,plain,
! [Y: $i,X: $i] : ~ q2(X,d,Y),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [Y: $i,X: $i] : ~ q2(X,d,Y),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [Y: $i,X: $i] : ~ q2(X,d,Y),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [Y: $i,X: $i] : ~ q2(X,d,Y)
| ~ q2(d,d,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
$false,
inference(unit_resolution,[status(thm)],[39,38,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN175-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % 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 02:28:09 EDT 2022
% 0.13/0.34 % 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.
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------