%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ANA020-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 04:59:11 AM UTC 2025
% Result : Unsatisfiable 0.14s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 51
% Syntax : Number of formulae : 122 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 503 ( 32 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 683 ( 318 ~; 312 |; 0 &)
% ( 53 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 204 ( 185 !; 0 ?; 204 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(t_a_type,type,
t_a: $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_h_type,type,
v_h: $i > $i ).
tff(v_x_type,type,
v_x: $i ).
tff(v_c_type,type,
v_c: $i ).
tff(v_f_type,type,
v_f: $i > $i ).
tff(c_0_type,type,
c_0: $i ).
tff(class_OrderedGroup_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
tff(c_less_type,type,
c_less: ( $i * $i * $i ) > $o ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,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)],[4]) ).
tff(6,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(7,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( class_Ring__and__Field_Oordered__idom(t_a)
<=> class_Ring__and__Field_Oordered__idom(t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tff(13,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) )
<=> ( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [T: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) )
| class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [T_a: $i] :
refl(( ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(c_0,T_a) = c_0 ) )
<=> ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(c_0,T_a) = c_0 ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(c_0,T_a) = c_0 ) )
<=> ! [T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(c_0,T_a) = c_0 ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(c_0,T_a) = c_0 ) )
<=> ! [T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(c_0,T_a) = c_0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(c_0,T_a) = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
tff(22,plain,
! [T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(c_0,T_a) = c_0 ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(c_0,T_a) = c_0 ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(c_0,T_a) = c_0 ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(c_0,T_a) = c_0 ) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ( c_HOL_Oabs(c_0,t_a) = c_0 ) )
<=> ( ~ ! [T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(c_0,T_a) = c_0 ) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ( c_HOL_Oabs(c_0,t_a) = c_0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(c_0,T_a) = c_0 ) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ( c_HOL_Oabs(c_0,t_a) = c_0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(c_0,T_a) = c_0 ) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ( c_HOL_Oabs(c_0,t_a) = c_0 ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ( c_HOL_Oabs(c_0,t_a) = c_0 ) ),
inference(unit_resolution,[status(thm)],[27,24]) ).
tff(29,plain,
c_HOL_Oabs(c_0,t_a) = c_0,
inference(unit_resolution,[status(thm)],[28,17]) ).
tff(30,plain,
( ( v_f(c_0) = c_0 )
<=> ( v_f(c_0) = c_0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
v_f(c_0) = c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(32,plain,
v_f(c_0) = c_0,
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( ( v_x = c_0 )
<=> ( v_x = c_0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
v_x = c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
tff(35,plain,
v_x = c_0,
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
v_f(v_x) = v_f(c_0),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
v_f(v_x) = c_0,
inference(transitivity,[status(thm)],[36,32]) ).
tff(38,plain,
c_HOL_Oabs(v_f(v_x),t_a) = c_HOL_Oabs(c_0,t_a),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
c_HOL_Oabs(v_f(v_x),t_a) = c_0,
inference(transitivity,[status(thm)],[38,29]) ).
tff(40,plain,
( c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a)
<=> c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a)
<=> c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a) ),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
^ [T: $i] :
refl(( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
<=> ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
tff(46,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
| class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
| class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Ring__and__Field_Opordered__cancel__semiring(t_a) )
<=> ( class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Ring__and__Field_Opordered__cancel__semiring(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
| class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Ring__and__Field_Opordered__cancel__semiring(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
| class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) )
| class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_a),
inference(unit_resolution,[status(thm)],[54,13,48]) ).
tff(56,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(57,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)],[56]) ).
tff(58,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(59,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(60,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)],[59,58]) ).
tff(61,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)],[60]) ).
tff(62,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)],[61,57]) ).
tff(63,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_a)
| c_lessequals(c_0,c_HOL_Oabs(v_h(v_x),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) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_lessequals(c_0,c_HOL_Oabs(v_h(v_x),t_a),t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,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_a)
| c_lessequals(c_0,c_HOL_Oabs(v_h(v_x),t_a),t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,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_a)
| c_lessequals(c_0,c_HOL_Oabs(v_h(v_x),t_a),t_a) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| c_lessequals(c_0,c_HOL_Oabs(v_h(v_x),t_a),t_a) ),
inference(unit_resolution,[status(thm)],[65,62]) ).
tff(67,plain,
c_lessequals(c_0,c_HOL_Oabs(v_h(v_x),t_a),t_a),
inference(unit_resolution,[status(thm)],[66,17]) ).
tff(68,plain,
^ [T: $i] :
refl(( ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
<=> ( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
tff(72,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| class_Orderings_Oorder(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| class_Orderings_Oorder(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
( ( ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Orderings_Oorder(t_a) )
<=> ( class_Orderings_Oorder(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Orderings_Oorder(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| class_Orderings_Oorder(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Orderings_Oorder(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| class_Orderings_Oorder(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ) ),
inference(transitivity,[status(thm)],[77,75]) ).
tff(79,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| class_Orderings_Oorder(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) )
| class_Orderings_Oorder(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
class_Orderings_Oorder(t_a),
inference(unit_resolution,[status(thm)],[80,13,74]) ).
tff(82,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
refl(( ( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
<=> ( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
^ [V_x: $i,T_a: $i,V_y: $i] :
rewrite(( ( ~ class_Orderings_Oorder(T_a)
| ~ c_less(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_less(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a) )
<=> ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_less(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
tff(88,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(modus_ponens,[status(thm)],[90,83]) ).
tff(92,plain,
( c_less(c_0,v_c,t_a)
<=> c_less(c_0,v_c,t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,axiom,
c_less(c_0,v_c,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(94,plain,
c_less(c_0,v_c,t_a),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_0,v_c,t_a)
| ~ c_less(c_0,v_c,t_a) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_0,v_c,t_a)
| ~ c_less(c_0,v_c,t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ( c_lessequals(c_0,v_c,t_a)
| ~ c_less(c_0,v_c,t_a)
| ~ class_Orderings_Oorder(t_a) )
<=> ( ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_0,v_c,t_a)
| ~ c_less(c_0,v_c,t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_0,v_c,t_a)
| ~ c_less(c_0,v_c,t_a)
| ~ class_Orderings_Oorder(t_a) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_0,v_c,t_a)
| ~ c_less(c_0,v_c,t_a) ) ),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
( ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_0,v_c,t_a)
| ~ c_less(c_0,v_c,t_a)
| ~ class_Orderings_Oorder(t_a) )
<=> ( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_0,v_c,t_a)
| ~ c_less(c_0,v_c,t_a) ) ),
inference(transitivity,[status(thm)],[97,95]) ).
tff(99,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
| c_lessequals(c_0,v_c,t_a)
| ~ c_less(c_0,v_c,t_a)
| ~ class_Orderings_Oorder(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [V_x: $i,T_a: $i,V_y: $i] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) )
| ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_0,v_c,t_a)
| ~ c_less(c_0,v_c,t_a) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
( ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_0,v_c,t_a) ),
inference(unit_resolution,[status(thm)],[100,94,91]) ).
tff(102,plain,
c_lessequals(c_0,v_c,t_a),
inference(unit_resolution,[status(thm)],[101,81]) ).
tff(103,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
refl(( ( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) )
<=> ( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(104,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
^ [V_b: $i,V_a: $i,T_a: $i] :
trans(monotonicity(rewrite(( ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a) )
<=> ( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ) )),
( ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ) )),
rewrite(( ( ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ) )),
( ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(107,plain,
( ! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) )
<=> ! [V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
tff(109,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
inference(modus_ponens,[status(thm)],[109,105]) ).
tff(111,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
inference(skolemize,[status(sab)],[110]) ).
tff(112,plain,
! [V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
inference(modus_ponens,[status(thm)],[111,104]) ).
tff(113,plain,
( ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) )
| c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_0,v_c,t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a) )
<=> ( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) )
| c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_0,v_c,t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) )
| c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_0,v_c,t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
( ~ ! [V_b: $i,V_a: $i,T_a: $i] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) )
| c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_0,v_c,t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
( c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a)
| ~ c_lessequals(c_0,v_c,t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_h(v_x),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
inference(unit_resolution,[status(thm)],[115,112]) ).
tff(117,plain,
c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[116,102,67,55]) ).
tff(118,plain,
c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(modus_ponens,[status(thm)],[117,41]) ).
tff(119,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a)
<=> ~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,axiom,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
tff(121,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
$false,
inference(unit_resolution,[status(thm)],[121,118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : ANA020-2 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 11:21:24 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.39 % SZS status Unsatisfiable
% 0.14/0.39 % SZS output start Proof
% See solution above
% 0.22/0.41 % E exiting
%------------------------------------------------------------------------------