TSTP Solution File: ANA041-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA041-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 : Tue Sep 6 16:23:38 EDT 2022
% Result : Unsatisfiable 1.02s 1.04s
% Output : Proof 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 17
% Syntax : Number of formulae : 26 ( 11 unt; 9 typ; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 1 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 3 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 28 ( 24 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(t_c_type,type,
t_c: $i ).
tff(v_h_type,type,
v_h: ( $i * $i ) > $i ).
tff(v_xb_type,type,
v_xb: $i ).
tff(v_xa_type,type,
v_xa: $i ).
tff(c_Nat_Osize_type,type,
c_Nat_Osize: ( $i * $i ) > $i ).
tff(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
tff(c_Product__Type_OUnity_type,type,
c_Product__Type_OUnity: $i ).
tff(c_0_type,type,
c_0: $i ).
tff(1,plain,
( ~ c_lessequals(c_0,v_h(v_xa,v_xb),t_c)
<=> ~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(v_xa,v_xb),t_c) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ c_lessequals(c_0,v_h(v_xa,v_xb),t_c)
<=> ~ c_lessequals(c_0,v_h(v_xa,v_xb),t_c) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ c_lessequals(c_0,v_h(v_xa,v_xb),t_c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(4,plain,
~ c_lessequals(c_0,v_h(v_xa,v_xb),t_c),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(v_xa,v_xb),t_c),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [V_V: $i,V_U: $i] :
refl(
( c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c)
<=> c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c)
<=> ! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [V_V: $i,V_U: $i] :
rewrite(
( c_lessequals(c_0,v_h(V_U,V_V),t_c)
<=> c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_h(V_U,V_V),t_c)
<=> ! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_h(V_U,V_V),t_c)
<=> ! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_h(V_U,V_V),t_c) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_h(V_U,V_V),t_c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(12,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_0,v_h(V_U,V_V),t_c),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c),
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
( ~ ! [V_V: $i,V_U: $i] : c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(V_U,V_V),t_c)
| c_lessequals(c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),v_h(v_xa,v_xb),t_c) ),
inference(quant_inst,[status(thm)],]) ).
tff(17,plain,
$false,
inference(unit_resolution,[status(thm)],[16,15,5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ANA041-1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n007.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 Aug 29 19:30:30 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.
% 1.02/1.04 % SZS status Unsatisfiable
% 1.02/1.04 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------