%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV898-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 : Sat Jun 21 05:36:18 AM UTC 2025
% Result : Unsatisfiable 0.41s 0.61s
% Output : Proof 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 20 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 66 ( 31 ~; 27 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-5 aty)
% Number of variables : 68 ( 60 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
tff(tc_Com_Ostate_type,type,
tc_Com_Ostate: $i ).
tff(c_Set_Oimage_type,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
tff(c_Map_Odom_type,type,
c_Map_Odom: ( $i * $i * $i ) > $i ).
tff(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
tff(c_Com_Obody_type,type,
c_Com_Obody: $i ).
tff(c_COMBB_type,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(tc_Option_Ooption_type,type,
tc_Option_Ooption: $i > $i ).
tff(c_Option_Othe_type,type,
c_Option_Othe: $i > $i ).
tff(c_Hoare__Mirabelle_OMGT_type,type,
c_Hoare__Mirabelle_OMGT: $i ).
tff(1,plain,
( ~ c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate))
<=> ~ c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(3,plain,
~ c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
refl(( ( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
<=> ( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
<=> ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
<=> ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
rewrite(( ( c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b)
| ~ c_Finite__Set_Ofinite(V_F,T_a) )
<=> ( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b)
| ~ c_Finite__Set_Ofinite(V_F,T_a) )
<=> ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b)
| ~ c_Finite__Set_Ofinite(V_F,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
tff(10,plain,
! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
<=> c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__dom__body_0) ).
tff(16,plain,
c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
| ~ c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
| c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)) )
<=> ( ~ ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
| ~ c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
| c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
| ~ c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
| c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [V_F: $i,T_b: $i,T_a: $i,V_h: $i] :
( ~ c_Finite__Set_Ofinite(V_F,T_a)
| c_Finite__Set_Ofinite(c_Set_Oimage(V_h,V_F,T_a,T_b),T_b) )
| ~ c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)
| c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
$false,
inference(unit_resolution,[status(thm)],[19,16,13,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.15 % Problem : SWV898-1 : TPTP v9.0.0. Released v4.1.0.
% 0.10/0.15 % Command : run_E %s %d THM
% 0.14/0.37 % Computer : n002.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri Jun 20 11:02:16 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.41/0.61 % SZS status Unsatisfiable
% 0.41/0.61 % SZS output start Proof
% See solution above
% 0.47/0.66 % E exiting
%------------------------------------------------------------------------------