TSTP Solution File: FLD071-1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : FLD071-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 : Fri Sep 16 14:56:08 EDT 2022
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 31 ( 9 unt; 5 typ; 0 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 187 ( 88 ~; 84 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 38 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_or_equal_type,type,
less_or_equal: ( $i * $i ) > $o ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(1,plain,
( ~ less_or_equal(additive_identity,multiply(a,b))
<=> ~ less_or_equal(additive_identity,multiply(a,b)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ less_or_equal(additive_identity,multiply(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_5) ).
tff(3,plain,
~ less_or_equal(additive_identity,multiply(a,b)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( less_or_equal(additive_identity,b)
<=> less_or_equal(additive_identity,b) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).
tff(6,plain,
less_or_equal(additive_identity,b),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( less_or_equal(additive_identity,a)
<=> less_or_equal(additive_identity,a) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
tff(9,plain,
less_or_equal(additive_identity,a),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z: $i,Y: $i] :
refl(
( ( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
<=> ( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [Z: $i,Y: $i] :
trans(
monotonicity(
rewrite(
( ( less_or_equal(additive_identity,multiply(Y,Z))
| ~ less_or_equal(additive_identity,Y) )
<=> ( ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ) )),
( ( less_or_equal(additive_identity,multiply(Y,Z))
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,Z) )
<=> ( ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z))
| ~ less_or_equal(additive_identity,Z) ) )),
rewrite(
( ( ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z))
| ~ less_or_equal(additive_identity,Z) )
<=> ( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ) )),
( ( less_or_equal(additive_identity,multiply(Y,Z))
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,Z) )
<=> ( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [Z: $i,Y: $i] :
( less_or_equal(additive_identity,multiply(Y,Z))
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,Z) )
<=> ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [Z: $i,Y: $i] :
( less_or_equal(additive_identity,multiply(Y,Z))
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_multiplication) ).
tff(16,plain,
! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
| less_or_equal(additive_identity,multiply(a,b))
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) )
<=> ( ~ ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
| less_or_equal(additive_identity,multiply(a,b))
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ( ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(additive_identity,multiply(a,b)) )
<=> ( less_or_equal(additive_identity,multiply(a,b))
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ~ ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(additive_identity,multiply(a,b)) )
<=> ( ~ ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
| less_or_equal(additive_identity,multiply(a,b))
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(additive_identity,multiply(a,b)) )
<=> ( ~ ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
| less_or_equal(additive_identity,multiply(a,b))
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(additive_identity,multiply(a,b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
| less_or_equal(additive_identity,multiply(a,b))
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,19,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : FLD071-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 03:28:55 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.
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------