TSTP Solution File: SYN107-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN107-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 23:53:46 EDT 2022
% Result : Unsatisfiable 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 25
% Syntax : Number of formulae : 52 ( 13 unt; 6 typ; 0 def)
% Number of atoms : 134 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 160 ( 75 ~; 60 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 44 ( 39 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
tff(k2_type,type,
k2: ( $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(q1_type,type,
q1: ( $i * $i * $i ) > $o ).
tff(k0_type,type,
k0: $i > $o ).
tff(e_type,type,
e: $i ).
tff(s0_type,type,
s0: $i > $o ).
tff(1,plain,
^ [A: $i,J: $i] :
refl(
( ( ~ q1(A,J,J)
| k2(J,J) )
<=> ( ~ q1(A,J,J)
| k2(J,J) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
<=> ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
<=> ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [A: $i,J: $i] :
rewrite(
( ( k2(J,J)
| ~ q1(A,J,J) )
<=> ( ~ q1(A,J,J)
| k2(J,J) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [A: $i,J: $i] :
( k2(J,J)
| ~ q1(A,J,J) )
<=> ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [A: $i,J: $i] :
( k2(J,J)
| ~ q1(A,J,J) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_129) ).
tff(7,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( q1(d,d,d)
<=> q1(d,d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ( $false
| $false
| q1(d,d,d) )
<=> q1(d,d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
k0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(15,plain,
( k0(e)
<=> $true ),
inference(iff_true,[status(thm)],[14]) ).
tff(16,plain,
( ~ k0(e)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ~ k0(e)
<=> $false ),
inference(transitivity,[status(thm)],[16,13]) ).
tff(18,axiom,
s0(d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_1) ).
tff(19,plain,
( s0(d)
<=> $true ),
inference(iff_true,[status(thm)],[18]) ).
tff(20,plain,
( ~ s0(d)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
( ~ s0(d)
<=> $false ),
inference(transitivity,[status(thm)],[20,13]) ).
tff(22,plain,
( ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) )
<=> ( $false
| $false
| q1(d,d,d) ) ),
inference(monotonicity,[status(thm)],[21,17]) ).
tff(23,plain,
( ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) )
<=> q1(d,d,d) ),
inference(transitivity,[status(thm)],[22,12]) ).
tff(24,plain,
( ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ k0(e)
| q1(d,d,d)
| ~ s0(d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ( q1(d,d,d)
| ~ k0(e) )
<=> ( ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) )
<=> ( ~ k0(e)
| q1(d,d,d)
| ~ s0(d) ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(transitivity,[status(thm)],[27,25]) ).
tff(29,axiom,
( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_117) ).
tff(30,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[30,24]) ).
tff(32,plain,
q1(d,d,d),
inference(modus_ponens,[status(thm)],[31,23]) ).
tff(33,plain,
q1(d,d,d),
inference(modus_ponens,[status(thm)],[32,11]) ).
tff(34,plain,
( ( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(d,d,d)
| k2(d,d) )
<=> ( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(d,d,d)
| k2(d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(d,d,d)
| k2(d,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(d,d,d)
| k2(d,d) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
k2(d,d),
inference(unit_resolution,[status(thm)],[36,33,10]) ).
tff(38,plain,
^ [X: $i] :
refl(
( ~ k2(X,d)
<=> ~ k2(X,d) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [X: $i] : ~ k2(X,d)
<=> ! [X: $i] : ~ k2(X,d) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X: $i] : ~ k2(X,d)
<=> ! [X: $i] : ~ k2(X,d) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
! [X: $i] : ~ k2(X,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(42,plain,
! [X: $i] : ~ k2(X,d),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X: $i] : ~ k2(X,d),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [X: $i] : ~ k2(X,d),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [X: $i] : ~ k2(X,d)
| ~ k2(d,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
$false,
inference(unit_resolution,[status(thm)],[45,44,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN107-1 : TPTP v8.1.0. Released v1.1.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 01:12:40 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -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
%------------------------------------------------------------------------------