TSTP Solution File: SYN233-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN233-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 23:54:19 EDT 2022
% Result : Unsatisfiable 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 36
% Syntax : Number of formulae : 76 ( 17 unt; 7 typ; 0 def)
% Number of atoms : 256 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 327 ( 150 ~; 137 |; 0 &)
% ( 40 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 6 >; 7 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 2 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 95 ( 86 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
tff(l3_type,type,
l3: ( $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(k0_type,type,
k0: $i > $o ).
tff(1,plain,
^ [D: $i,E: $i] :
refl(
( ( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ( p2(D,E,D)
| ~ m1(E,D,E) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_176) ).
tff(5,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( m1(e,e,e)
<=> m1(e,e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
( ( $false
| m1(e,e,e) )
<=> m1(e,e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
r0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_13) ).
tff(12,plain,
( r0(e)
<=> $true ),
inference(iff_true,[status(thm)],[11]) ).
tff(13,plain,
( ~ r0(e)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ~ r0(e)
<=> $false ),
inference(transitivity,[status(thm)],[13,10]) ).
tff(15,plain,
( ( ~ r0(e)
| m1(e,e,e) )
<=> ( $false
| m1(e,e,e) ) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( ( ~ r0(e)
| m1(e,e,e) )
<=> m1(e,e,e) ),
inference(transitivity,[status(thm)],[15,9]) ).
tff(17,plain,
( ( m1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
( m1(e,e,e)
| ~ r0(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_012) ).
tff(19,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
m1(e,e,e),
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
m1(e,e,e),
inference(modus_ponens,[status(thm)],[20,8]) ).
tff(22,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
p2(e,e,e),
inference(unit_resolution,[status(thm)],[27,21,7]) ).
tff(29,plain,
^ [D: $i,E: $i,F: $i] :
refl(
( ( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
<=> ( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
<=> ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
<=> ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
^ [D: $i,E: $i,F: $i] :
trans(
monotonicity(
rewrite(
( ( l3(D,D)
| ~ p1(D,D,E) )
<=> ( ~ p1(D,D,E)
| l3(D,D) ) )),
( ( l3(D,D)
| ~ p1(D,D,E)
| ~ p2(E,F,D) )
<=> ( ~ p1(D,D,E)
| l3(D,D)
| ~ p2(E,F,D) ) )),
rewrite(
( ( ~ p1(D,D,E)
| l3(D,D)
| ~ p2(E,F,D) )
<=> ( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ) )),
( ( l3(D,D)
| ~ p1(D,D,E)
| ~ p2(E,F,D) )
<=> ( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [D: $i,E: $i,F: $i] :
( l3(D,D)
| ~ p1(D,D,E)
| ~ p2(E,F,D) )
<=> ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [D: $i,E: $i,F: $i] :
( l3(D,D)
| ~ p1(D,D,E)
| ~ p2(E,F,D) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_216) ).
tff(35,plain,
! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( p1(e,e,e)
<=> p1(e,e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( $false
| $false
| p1(e,e,e) )
<=> p1(e,e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
k0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(42,plain,
( k0(e)
<=> $true ),
inference(iff_true,[status(thm)],[41]) ).
tff(43,plain,
( ~ k0(e)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ~ k0(e)
<=> $false ),
inference(transitivity,[status(thm)],[43,10]) ).
tff(45,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> ( $false
| $false
| p1(e,e,e) ) ),
inference(monotonicity,[status(thm)],[14,44]) ).
tff(46,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> p1(e,e,e) ),
inference(transitivity,[status(thm)],[45,40]) ).
tff(47,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ( p1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,axiom,
( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_090) ).
tff(53,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[53,47]) ).
tff(55,plain,
p1(e,e,e),
inference(modus_ponens,[status(thm)],[54,46]) ).
tff(56,plain,
p1(e,e,e),
inference(modus_ponens,[status(thm)],[55,39]) ).
tff(57,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| ~ p2(e,e,e)
| ~ p1(e,e,e)
| l3(e,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| ~ p2(e,e,e)
| ~ p1(e,e,e)
| l3(e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| ~ p2(e,e,e)
| ~ p1(e,e,e)
| l3(e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( ~ p2(E,F,D)
| ~ p1(D,D,E)
| l3(D,D) )
| ~ p2(e,e,e)
| ~ p1(e,e,e)
| l3(e,e) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
l3(e,e),
inference(unit_resolution,[status(thm)],[59,56,38,28]) ).
tff(61,plain,
^ [X: $i] :
refl(
( ~ l3(e,X)
<=> ~ l3(e,X) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [X: $i] : ~ l3(e,X)
<=> ! [X: $i] : ~ l3(e,X) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [X: $i] : ~ l3(e,X)
<=> ! [X: $i] : ~ l3(e,X) ),
inference(rewrite,[status(thm)],]) ).
tff(64,axiom,
! [X: $i] : ~ l3(e,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(65,plain,
! [X: $i] : ~ l3(e,X),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [X: $i] : ~ l3(e,X),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [X: $i] : ~ l3(e,X),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
( ~ ! [X: $i] : ~ l3(e,X)
| ~ l3(e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
$false,
inference(unit_resolution,[status(thm)],[68,67,60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SYN233-1 : TPTP v8.1.0. Released v1.1.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.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 02:12:38 EDT 2022
% 0.13/0.35 % 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.
% 0.21/0.49 % SZS status Unsatisfiable
% 0.21/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------