TSTP Solution File: SYN256-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN256-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 23:54:24 EDT 2022
% Result : Unsatisfiable 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 24
% Syntax : Number of formulae : 41 ( 11 unt; 7 typ; 0 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 184 ( 86 ~; 82 |; 0 &)
% ( 16 <=>; 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 : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 90 ( 81 !; 0 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
tff(n2_type,type,
n2: $i > $o ).
tff(c_type,type,
c: $i ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(b_type,type,
b: $i ).
tff(e_type,type,
e: $i ).
tff(1,plain,
( ~ n2(c)
<=> ~ n2(c) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ n2(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(3,plain,
~ n2(c),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( n2(A)
| ~ p1(B,C,A) )
<=> ( n2(A)
| ~ p1(B,C,A) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
<=> ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
<=> ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_137) ).
tff(8,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
^ [I: $i,A: $i,J: $i] :
refl(
( ( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
<=> ( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
^ [I: $i,A: $i,J: $i] :
trans(
monotonicity(
rewrite(
( ( p1(I,I,I)
| ~ l0(I) )
<=> ( ~ l0(I)
| p1(I,I,I) ) )),
( ( p1(I,I,I)
| ~ l0(I)
| ~ m0(J,A,I) )
<=> ( ~ l0(I)
| p1(I,I,I)
| ~ m0(J,A,I) ) )),
rewrite(
( ( ~ l0(I)
| p1(I,I,I)
| ~ m0(J,A,I) )
<=> ( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) )),
( ( p1(I,I,I)
| ~ l0(I)
| ~ m0(J,A,I) )
<=> ( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [I: $i,A: $i,J: $i] :
( p1(I,I,I)
| ~ l0(I)
| ~ m0(J,A,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,axiom,
! [I: $i,A: $i,J: $i] :
( p1(I,I,I)
| ~ l0(I)
| ~ m0(J,A,I) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_086) ).
tff(17,plain,
! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
( m0(e,b,c)
<=> m0(e,b,c) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
m0(e,b,c),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_27) ).
tff(23,plain,
m0(e,b,c),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( l0(c)
<=> l0(c) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
l0(c),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_24) ).
tff(26,plain,
l0(c),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
( ( ~ ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
| ~ l0(c)
| ~ m0(e,b,c)
| p1(c,c,c) )
<=> ( ~ ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
| ~ l0(c)
| ~ m0(e,b,c)
| p1(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ~ ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
| ~ l0(c)
| ~ m0(e,b,c)
| p1(c,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
( ~ ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
| ~ l0(c)
| ~ m0(e,b,c)
| p1(c,c,c) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
p1(c,c,c),
inference(unit_resolution,[status(thm)],[29,26,23,20]) ).
tff(31,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(c)
| ~ p1(c,c,c) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(c)
| ~ p1(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(c)
| ~ p1(c,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(c)
| ~ p1(c,c,c) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,30,10,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN256-1 : 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 : n018.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 02:22:46 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.
% 0.20/0.50 % SZS status Unsatisfiable
% 0.20/0.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------