%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ANA042-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 04:59:16 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 18 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 15 ~; 2 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 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 : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 30 ( 27 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(t_c_type,type,
t_c: $i ).
tff(c_times_type,type,
c_times: ( $i * $i * $i ) > $i ).
tff(v_h_type,type,
v_h: ( $i * $i ) > $i ).
tff(v_xb_type,type,
v_xb: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_xa_type,type,
v_xa: $i > $i ).
tff(c_HOL_Oabs_type,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(v_f_type,type,
v_f: ( $i * $i ) > $i ).
tff(1,plain,
^ [V_U: $i] :
refl(( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U),v_xb(V_U)),t_c),c_times(V_U,v_h(v_xa(V_U),v_xb(V_U)),t_c),t_c)
<=> ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U),v_xb(V_U)),t_c),c_times(V_U,v_h(v_xa(V_U),v_xb(V_U)),t_c),t_c) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U),v_xb(V_U)),t_c),c_times(V_U,v_h(v_xa(V_U),v_xb(V_U)),t_c),t_c)
<=> ! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U),v_xb(V_U)),t_c),c_times(V_U,v_h(v_xa(V_U),v_xb(V_U)),t_c),t_c) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U),v_xb(V_U)),t_c),c_times(V_U,v_h(v_xa(V_U),v_xb(V_U)),t_c),t_c)
<=> ! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U),v_xb(V_U)),t_c),c_times(V_U,v_h(v_xa(V_U),v_xb(V_U)),t_c),t_c) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U),v_xb(V_U)),t_c),c_times(V_U,v_h(v_xa(V_U),v_xb(V_U)),t_c),t_c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(5,plain,
! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U),v_xb(V_U)),t_c),c_times(V_U,v_h(v_xa(V_U),v_xb(V_U)),t_c),t_c),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U),v_xb(V_U)),t_c),c_times(V_U,v_h(v_xa(V_U),v_xb(V_U)),t_c),t_c),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U),v_xb(V_U)),t_c),c_times(V_U,v_h(v_xa(V_U),v_xb(V_U)),t_c),t_c),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U),v_xb(V_U)),t_c),c_times(V_U,v_h(v_xa(V_U),v_xb(V_U)),t_c),t_c)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x),v_xb(v_x)),t_c),c_times(v_x,v_h(v_xa(v_x),v_xb(v_x)),t_c),t_c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x),v_xb(v_x)),t_c),c_times(v_x,v_h(v_xa(v_x),v_xb(v_x)),t_c),t_c),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V_V: $i,V_U: $i] :
refl(( c_lessequals(c_HOL_Oabs(v_f(V_U,V_V),t_c),c_times(v_x,v_h(V_U,V_V),t_c),t_c)
<=> c_lessequals(c_HOL_Oabs(v_f(V_U,V_V),t_c),c_times(v_x,v_h(V_U,V_V),t_c),t_c) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V_V: $i,V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U,V_V),t_c),c_times(v_x,v_h(V_U,V_V),t_c),t_c)
<=> ! [V_V: $i,V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U,V_V),t_c),c_times(v_x,v_h(V_U,V_V),t_c),t_c) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V_V: $i,V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U,V_V),t_c),c_times(v_x,v_h(V_U,V_V),t_c),t_c)
<=> ! [V_V: $i,V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U,V_V),t_c),c_times(v_x,v_h(V_U,V_V),t_c),t_c) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [V_V: $i,V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U,V_V),t_c),c_times(v_x,v_h(V_U,V_V),t_c),t_c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(14,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U,V_V),t_c),c_times(v_x,v_h(V_U,V_V),t_c),t_c),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U,V_V),t_c),c_times(v_x,v_h(V_U,V_V),t_c),t_c),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V_V: $i,V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U,V_V),t_c),c_times(v_x,v_h(V_U,V_V),t_c),t_c),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [V_V: $i,V_U: $i] : c_lessequals(c_HOL_Oabs(v_f(V_U,V_V),t_c),c_times(v_x,v_h(V_U,V_V),t_c),t_c)
| c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x),v_xb(v_x)),t_c),c_times(v_x,v_h(v_xa(v_x),v_xb(v_x)),t_c),t_c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
$false,
inference(unit_resolution,[status(thm)],[17,16,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA042-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 11:23:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% See solution above
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------