TSTP Solution File: ANA007-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ANA007-2 : TPTP v8.1.0. Released v3.2.0.
% 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 : Tue Sep 6 16:23:22 EDT 2022
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 31
% Syntax : Number of formulae : 63 ( 18 unt; 9 typ; 0 def)
% Number of atoms : 152 ( 20 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 181 ( 88 ~; 72 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 7 >; 5 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 79 ( 72 !; 0 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(t_b_type,type,
t_b: $i ).
tff(c_times_type,type,
c_times: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oabs_type,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(v_f_type,type,
v_f: $i > $i ).
tff(v_x_type,type,
v_x: $i > $i ).
tff(c_1_type,type,
c_1: $i ).
tff(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
tff(1,plain,
^ [V_c: $i,T_a: $i] :
refl(
( ( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( V_c = c_times(c_1,V_c,T_a) ) )
<=> ( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( V_c = c_times(c_1,V_c,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_c: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( V_c = c_times(c_1,V_c,T_a) ) )
<=> ! [V_c: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( V_c = c_times(c_1,V_c,T_a) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_c: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( V_c = c_times(c_1,V_c,T_a) ) )
<=> ! [V_c: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( V_c = c_times(c_1,V_c,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V_c: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( V_c = c_times(c_1,V_c,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
tff(5,plain,
! [V_c: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( V_c = c_times(c_1,V_c,T_a) ) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_c: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( V_c = c_times(c_1,V_c,T_a) ) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_c: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( V_c = c_times(c_1,V_c,T_a) ) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( class_Ring__and__Field_Oordered__idom(t_b)
<=> class_Ring__and__Field_Oordered__idom(t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
tff(10,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [V_c: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( V_c = c_times(c_1,V_c,T_a) ) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| ( c_HOL_Oabs(v_f(v_x(c_1)),t_b) = c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b) ) )
<=> ( ~ ! [V_c: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( V_c = c_times(c_1,V_c,T_a) ) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| ( c_HOL_Oabs(v_f(v_x(c_1)),t_b) = c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [V_c: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( V_c = c_times(c_1,V_c,T_a) ) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| ( c_HOL_Oabs(v_f(v_x(c_1)),t_b) = c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [V_c: $i,T_a: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( V_c = c_times(c_1,V_c,T_a) ) )
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| ( c_HOL_Oabs(v_f(v_x(c_1)),t_b) = c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_HOL_Oabs(v_f(v_x(c_1)),t_b) = c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b) = c_HOL_Oabs(v_f(v_x(c_1)),t_b),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( c_lessequals(c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),t_b)
<=> c_lessequals(c_HOL_Oabs(v_f(v_x(c_1)),t_b),c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),t_b) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( c_lessequals(c_HOL_Oabs(v_f(v_x(c_1)),t_b),c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),t_b)
<=> c_lessequals(c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),t_b) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_1)),t_b),c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),t_b)
<=> ~ c_lessequals(c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),t_b) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
^ [V_U: $i] :
refl(
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b)
<=> ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b)
<=> ! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b)
<=> ! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(23,plain,
! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [V_U: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_1)),t_b),c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_1)),t_b),c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
~ c_lessequals(c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[27,18]) ).
tff(29,plain,
^ [T: $i] :
refl(
( ( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
^ [T: $i] :
rewrite(
( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
<=> ( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
<=> ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
tff(35,plain,
! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [T: $i] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_Orderings_Oorder(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
class_Orderings_Oorder(t_b),
inference(unit_resolution,[status(thm)],[41,10,38]) ).
tff(43,plain,
^ [V_x: $i,T_a: $i] :
refl(
( ( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) )
<=> ( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) )
<=> ! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
tff(47,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) )
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),t_b) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) )
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),t_b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) )
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),t_b) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) )
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
c_lessequals(c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),c_times(c_1,c_HOL_Oabs(v_f(v_x(c_1)),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[52,49,42]) ).
tff(54,plain,
$false,
inference(unit_resolution,[status(thm)],[53,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ANA007-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 29 18:48:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% See solution above
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