%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ANA012-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 04:59:09 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 42
% Syntax : Number of formulae : 99 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 387 ( 139 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 504 ( 225 ~; 237 |; 0 &)
% ( 42 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 159 ( 145 !; 0 ?; 159 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(t_a_type,type,
t_a: $i ).
tff(c_1_type,type,
c_1: $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_c_type,type,
v_c: $i ).
tff(c_HOL_Oinverse_type,type,
c_HOL_Oinverse: ( $i * $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__field_type,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(class_Ring__and__Field_Ofield_type,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
tff(1,plain,
^ [T: $i] :
refl(( ( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
<=> ( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).
tff(5,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( class_Ring__and__Field_Oordered__field(t_a)
<=> class_Ring__and__Field_Oordered__field(t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
tff(10,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
| ~ class_Ring__and__Field_Oordered__field(t_a)
| class_OrderedGroup_Olordered__ab__group__abs(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
| ~ class_Ring__and__Field_Oordered__field(t_a)
| class_OrderedGroup_Olordered__ab__group__abs(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
| ~ class_Ring__and__Field_Oordered__field(t_a)
| class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) )
| ~ class_Ring__and__Field_Oordered__field(t_a)
| class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
<=> ( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
^ [V_a: $i,T_a: $i] :
rewrite(( ( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ( V_a = c_0 ) )
<=> ( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ( V_a = c_0 ) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ( V_a = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).
tff(21,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ( v_c != c_0 )
<=> ( v_c != c_0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
v_c != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(27,plain,
v_c != c_0,
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ( v_c = c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ( c_HOL_Oabs(v_c,t_a) != c_0 ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ( v_c = c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ( c_HOL_Oabs(v_c,t_a) != c_0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( ( v_c = c_0 )
| ( c_HOL_Oabs(v_c,t_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a) )
<=> ( ( v_c = c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ( c_HOL_Oabs(v_c,t_a) != c_0 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ( v_c = c_0 )
| ( c_HOL_Oabs(v_c,t_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ( v_c = c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ( c_HOL_Oabs(v_c,t_a) != c_0 ) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ( v_c = c_0 )
| ( c_HOL_Oabs(v_c,t_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ( v_c = c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ( c_HOL_Oabs(v_c,t_a) != c_0 ) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ( v_c = c_0 )
| ( c_HOL_Oabs(v_c,t_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_HOL_Oabs(V_a,T_a) != c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) )
| ( v_c = c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a)
| ( c_HOL_Oabs(v_c,t_a) != c_0 ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
c_HOL_Oabs(v_c,t_a) != c_0,
inference(unit_resolution,[status(thm)],[33,27,24,14]) ).
tff(35,plain,
^ [T: $i] :
refl(( ( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) )
<=> ( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
tff(39,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) )
| ~ class_Ring__and__Field_Oordered__field(t_a)
| class_Ring__and__Field_Ofield(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) )
| ~ class_Ring__and__Field_Oordered__field(t_a)
| class_Ring__and__Field_Ofield(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) )
| ~ class_Ring__and__Field_Oordered__field(t_a)
| class_Ring__and__Field_Ofield(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) )
| ~ class_Ring__and__Field_Oordered__field(t_a)
| class_Ring__and__Field_Ofield(t_a) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
class_Ring__and__Field_Ofield(t_a),
inference(unit_resolution,[status(thm)],[44,10,41]) ).
tff(46,plain,
^ [V_a: $i,T_a: $i] :
refl(( ( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) )
<=> ( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
^ [V_a: $i,T_a: $i] :
rewrite(( ( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 ) )
<=> ( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 ) )
<=> ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
tff(52,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oabs(v_c,t_a) = c_0 )
| ( c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a) = c_1 ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oabs(v_c,t_a) = c_0 )
| ( c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a) = c_1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ( ( c_HOL_Oabs(v_c,t_a) = c_0 )
| ( c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(t_a) )
<=> ( ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oabs(v_c,t_a) = c_0 )
| ( c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a) = c_1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) )
| ( c_HOL_Oabs(v_c,t_a) = c_0 )
| ( c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(t_a) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oabs(v_c,t_a) = c_0 )
| ( c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a) = c_1 ) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) )
| ( c_HOL_Oabs(v_c,t_a) = c_0 )
| ( c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(t_a) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oabs(v_c,t_a) = c_0 )
| ( c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a) = c_1 ) ) ),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) )
| ( c_HOL_Oabs(v_c,t_a) = c_0 )
| ( c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 )
| ~ class_Ring__and__Field_Ofield(T_a) )
| ~ class_Ring__and__Field_Ofield(t_a)
| ( c_HOL_Oabs(v_c,t_a) = c_0 )
| ( c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a) = c_1 ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a) = c_1,
inference(unit_resolution,[status(thm)],[61,55,45,34]) ).
tff(63,plain,
c_1 = c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
( c_lessequals(c_1,c_1,t_a)
<=> c_lessequals(c_1,c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a),t_a) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( c_lessequals(c_1,c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a),t_a)
<=> c_lessequals(c_1,c_1,t_a) ),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( ~ c_lessequals(c_1,c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a),t_a)
<=> ~ c_lessequals(c_1,c_1,t_a) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
^ [V_U: $i] :
refl(( ~ c_lessequals(c_1,c_times(V_U,c_HOL_Oabs(v_c,t_a),t_a),t_a)
<=> ~ c_lessequals(c_1,c_times(V_U,c_HOL_Oabs(v_c,t_a),t_a),t_a) )),
inference(bind,[status(th)],[]) ).
tff(68,plain,
( ! [V_U: $i] : ~ c_lessequals(c_1,c_times(V_U,c_HOL_Oabs(v_c,t_a),t_a),t_a)
<=> ! [V_U: $i] : ~ c_lessequals(c_1,c_times(V_U,c_HOL_Oabs(v_c,t_a),t_a),t_a) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
( ! [V_U: $i] : ~ c_lessequals(c_1,c_times(V_U,c_HOL_Oabs(v_c,t_a),t_a),t_a)
<=> ! [V_U: $i] : ~ c_lessequals(c_1,c_times(V_U,c_HOL_Oabs(v_c,t_a),t_a),t_a) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
! [V_U: $i] : ~ c_lessequals(c_1,c_times(V_U,c_HOL_Oabs(v_c,t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(71,plain,
! [V_U: $i] : ~ c_lessequals(c_1,c_times(V_U,c_HOL_Oabs(v_c,t_a),t_a),t_a),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [V_U: $i] : ~ c_lessequals(c_1,c_times(V_U,c_HOL_Oabs(v_c,t_a),t_a),t_a),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [V_U: $i] : ~ c_lessequals(c_1,c_times(V_U,c_HOL_Oabs(v_c,t_a),t_a),t_a),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
( ~ ! [V_U: $i] : ~ c_lessequals(c_1,c_times(V_U,c_HOL_Oabs(v_c,t_a),t_a),t_a)
| ~ c_lessequals(c_1,c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a),t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
~ c_lessequals(c_1,c_times(c_HOL_Oinverse(c_HOL_Oabs(v_c,t_a),t_a),c_HOL_Oabs(v_c,t_a),t_a),t_a),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
~ c_lessequals(c_1,c_1,t_a),
inference(modus_ponens,[status(thm)],[75,66]) ).
tff(77,plain,
^ [T: $i] :
refl(( ( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) )
<=> ( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
( ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) )
<=> ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,axiom,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).
tff(81,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
( ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__field(t_a)
| class_Orderings_Oorder(t_a) )
<=> ( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__field(t_a)
| class_Orderings_Oorder(t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__field(t_a)
| class_Orderings_Oorder(t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [T: $i] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) )
| ~ class_Ring__and__Field_Oordered__field(t_a)
| class_Orderings_Oorder(t_a) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
class_Orderings_Oorder(t_a),
inference(unit_resolution,[status(thm)],[86,10,83]) ).
tff(88,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(89,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)],[88]) ).
tff(90,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(91,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(92,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)],[91,90]) ).
tff(93,plain,
! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ),
inference(skolemize,[status(sab)],[92]) ).
tff(94,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)],[93,89]) ).
tff(95,plain,
( ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) )
| ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_1,c_1,t_a) )
<=> ( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) )
| ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_1,c_1,t_a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) )
| ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_1,c_1,t_a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
( ~ ! [V_x: $i,T_a: $i] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) )
| ~ class_Orderings_Oorder(t_a)
| c_lessequals(c_1,c_1,t_a) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
c_lessequals(c_1,c_1,t_a),
inference(unit_resolution,[status(thm)],[97,94,87]) ).
tff(99,plain,
$false,
inference(unit_resolution,[status(thm)],[98,76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA012-2 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 11:19:41 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------