TSTP Solution File: SYN062-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN062-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 23:53:27 EDT 2022
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 31
% Syntax : Number of formulae : 62 ( 14 unt; 6 typ; 0 def)
% Number of atoms : 267 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 379 ( 179 ~; 172 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 55 ( 50 !; 0 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
tff(big_h_type,type,
big_h: $i > $o ).
tff(a_type,type,
a: $i ).
tff(big_k_type,type,
big_k: $i > $o ).
tff(big_i_type,type,
big_i: $i > $o ).
tff(big_f_type,type,
big_f: $i > $o ).
tff(big_j_type,type,
big_j: $i > $o ).
tff(1,plain,
( big_k(a)
<=> big_k(a) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
big_k(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
tff(3,plain,
big_k(a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i] :
refl(
( ( ~ big_k(X)
| big_h(X) )
<=> ( ~ big_k(X)
| big_h(X) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X: $i] :
( ~ big_k(X)
| big_h(X) )
<=> ! [X: $i] :
( ~ big_k(X)
| big_h(X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i] :
( ~ big_k(X)
| big_h(X) )
<=> ! [X: $i] :
( ~ big_k(X)
| big_h(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [X: $i] :
( ~ big_k(X)
| big_h(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
tff(8,plain,
! [X: $i] :
( ~ big_k(X)
| big_h(X) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [X: $i] :
( ~ big_k(X)
| big_h(X) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] :
( ~ big_k(X)
| big_h(X) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [X: $i] :
( ~ big_k(X)
| big_h(X) )
| big_h(a)
| ~ big_k(a) )
<=> ( ~ ! [X: $i] :
( ~ big_k(X)
| big_h(X) )
| big_h(a)
| ~ big_k(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ( ~ big_k(a)
| big_h(a) )
<=> ( big_h(a)
| ~ big_k(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ( ~ ! [X: $i] :
( ~ big_k(X)
| big_h(X) )
| ~ big_k(a)
| big_h(a) )
<=> ( ~ ! [X: $i] :
( ~ big_k(X)
| big_h(X) )
| big_h(a)
| ~ big_k(a) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( ~ ! [X: $i] :
( ~ big_k(X)
| big_h(X) )
| ~ big_k(a)
| big_h(a) )
<=> ( ~ ! [X: $i] :
( ~ big_k(X)
| big_h(X) )
| big_h(a)
| ~ big_k(a) ) ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
( ~ ! [X: $i] :
( ~ big_k(X)
| big_h(X) )
| ~ big_k(a)
| big_h(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [X: $i] :
( ~ big_k(X)
| big_h(X) )
| big_h(a)
| ~ big_k(a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
big_h(a),
inference(unit_resolution,[status(thm)],[16,10,3]) ).
tff(18,plain,
( big_f(a)
<=> big_f(a) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
big_f(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
tff(20,plain,
big_f(a),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [X: $i] :
refl(
( ( big_i(X)
| ~ big_f(X)
| ~ big_h(X) )
<=> ( big_i(X)
| ~ big_f(X)
| ~ big_h(X) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [X: $i] :
( big_i(X)
| ~ big_f(X)
| ~ big_h(X) )
<=> ! [X: $i] :
( big_i(X)
| ~ big_f(X)
| ~ big_h(X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] :
( big_i(X)
| ~ big_f(X)
| ~ big_h(X) )
<=> ! [X: $i] :
( big_i(X)
| ~ big_f(X)
| ~ big_h(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
^ [X: $i] :
rewrite(
( ( ~ big_f(X)
| ~ big_h(X)
| big_i(X) )
<=> ( big_i(X)
| ~ big_f(X)
| ~ big_h(X) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [X: $i] :
( ~ big_f(X)
| ~ big_h(X)
| big_i(X) )
<=> ! [X: $i] :
( big_i(X)
| ~ big_f(X)
| ~ big_h(X) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [X: $i] :
( ~ big_f(X)
| ~ big_h(X)
| big_i(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
tff(27,plain,
! [X: $i] :
( big_i(X)
| ~ big_f(X)
| ~ big_h(X) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [X: $i] :
( big_i(X)
| ~ big_f(X)
| ~ big_h(X) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [X: $i] :
( big_i(X)
| ~ big_f(X)
| ~ big_h(X) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [X: $i] :
( big_i(X)
| ~ big_f(X)
| ~ big_h(X) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [X: $i] :
( big_i(X)
| ~ big_f(X)
| ~ big_h(X) )
| big_i(a)
| ~ big_f(a)
| ~ big_h(a) )
<=> ( ~ ! [X: $i] :
( big_i(X)
| ~ big_f(X)
| ~ big_h(X) )
| big_i(a)
| ~ big_f(a)
| ~ big_h(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ! [X: $i] :
( big_i(X)
| ~ big_f(X)
| ~ big_h(X) )
| big_i(a)
| ~ big_f(a)
| ~ big_h(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [X: $i] :
( big_i(X)
| ~ big_f(X)
| ~ big_h(X) )
| big_i(a)
| ~ big_f(a)
| ~ big_h(a) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
( big_i(a)
| ~ big_h(a) ),
inference(unit_resolution,[status(thm)],[33,30,20]) ).
tff(35,plain,
big_i(a),
inference(unit_resolution,[status(thm)],[34,17]) ).
tff(36,plain,
( ~ big_j(a)
<=> ~ big_j(a) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
~ big_j(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
tff(38,plain,
~ big_j(a),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
^ [X: $i] :
refl(
( ( ~ big_h(X)
| big_j(X)
| ~ big_i(X) )
<=> ( ~ big_h(X)
| big_j(X)
| ~ big_i(X) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) )
<=> ! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) )
<=> ! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ big_i(X)
| ~ big_h(X) )
<=> ( ~ big_h(X)
| ~ big_i(X) ) )),
( ( ~ big_i(X)
| ~ big_h(X)
| big_j(X) )
<=> ( ~ big_h(X)
| ~ big_i(X)
| big_j(X) ) )),
rewrite(
( ( ~ big_h(X)
| ~ big_i(X)
| big_j(X) )
<=> ( ~ big_h(X)
| big_j(X)
| ~ big_i(X) ) )),
( ( ~ big_i(X)
| ~ big_h(X)
| big_j(X) )
<=> ( ~ big_h(X)
| big_j(X)
| ~ big_i(X) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [X: $i] :
( ~ big_i(X)
| ~ big_h(X)
| big_j(X) )
<=> ! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [X: $i] :
( ~ big_i(X)
| ~ big_h(X)
| big_j(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
tff(45,plain,
! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ( ~ ! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) )
| big_j(a)
| ~ big_h(a)
| ~ big_i(a) )
<=> ( ~ ! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) )
| big_j(a)
| ~ big_h(a)
| ~ big_i(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ( ~ big_h(a)
| big_j(a)
| ~ big_i(a) )
<=> ( big_j(a)
| ~ big_h(a)
| ~ big_i(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( ~ ! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) )
| ~ big_h(a)
| big_j(a)
| ~ big_i(a) )
<=> ( ~ ! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) )
| big_j(a)
| ~ big_h(a)
| ~ big_i(a) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ~ ! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) )
| ~ big_h(a)
| big_j(a)
| ~ big_i(a) )
<=> ( ~ ! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) )
| big_j(a)
| ~ big_h(a)
| ~ big_i(a) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
( ~ ! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) )
| ~ big_h(a)
| big_j(a)
| ~ big_i(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
( ~ ! [X: $i] :
( ~ big_h(X)
| big_j(X)
| ~ big_i(X) )
| big_j(a)
| ~ big_h(a)
| ~ big_i(a) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ big_h(a)
| ~ big_i(a) ),
inference(unit_resolution,[status(thm)],[54,48,38]) ).
tff(56,plain,
$false,
inference(unit_resolution,[status(thm)],[55,35,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN062-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n015.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 01:41:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------