%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ANA045-2 : 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 04:59:17 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 53 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 151 ( 19 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 : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 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_HOL_Oabs_type,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(v_g_type,type,
v_g: $i > $i ).
tff(v_x_type,type,
v_x: $i > $i ).
tff(c_1_type,type,
c_1: $i ).
tff(c_0_type,type,
c_0: $i ).
tff(c_times_type,type,
c_times: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(class_OrderedGroup_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $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/sandbox2/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/sandbox2/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_g(v_x(c_1)),t_b) = c_times(c_1,c_HOL_Oabs(v_g(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_g(v_x(c_1)),t_b) = c_times(c_1,c_HOL_Oabs(v_g(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_g(v_x(c_1)),t_b) = c_times(c_1,c_HOL_Oabs(v_g(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_g(v_x(c_1)),t_b) = c_times(c_1,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
c_HOL_Oabs(v_g(v_x(c_1)),t_b) = c_times(c_1,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
( c_lessequals(c_0,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b)
<=> c_lessequals(c_0,c_times(c_1,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b),t_b) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( c_lessequals(c_0,c_times(c_1,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b),t_b)
<=> c_lessequals(c_0,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b) ),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
( ~ c_lessequals(c_0,c_times(c_1,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b),t_b)
<=> ~ c_lessequals(c_0,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
^ [V_U: $i] :
refl(( ~ c_lessequals(c_0,c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b)
<=> ~ c_lessequals(c_0,c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_U: $i] : ~ c_lessequals(c_0,c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b)
<=> ! [V_U: $i] : ~ c_lessequals(c_0,c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_U: $i] : ~ c_lessequals(c_0,c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b)
<=> ! [V_U: $i] : ~ c_lessequals(c_0,c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [V_U: $i] : ~ c_lessequals(c_0,c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(22,plain,
! [V_U: $i] : ~ c_lessequals(c_0,c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_U: $i] : ~ c_lessequals(c_0,c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_U: $i] : ~ c_lessequals(c_0,c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [V_U: $i] : ~ c_lessequals(c_0,c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(c_1,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b),t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
~ c_lessequals(c_0,c_times(c_1,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b),t_b),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
~ c_lessequals(c_0,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b),
inference(modus_ponens,[status(thm)],[26,17]) ).
tff(28,plain,
^ [T: $i] :
refl(( ( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
^ [T: $i] :
rewrite(( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
<=> ( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
<=> ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
tff(34,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
( ( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
<=> ( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(unit_resolution,[status(thm)],[40,10,37]) ).
tff(42,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
<=> ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
tff(46,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
c_lessequals(c_0,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b),
inference(unit_resolution,[status(thm)],[51,48,41]) ).
tff(53,plain,
$false,
inference(unit_resolution,[status(thm)],[52,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA045-2 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.12 % 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 11:23:21 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------