TSTP Solution File: SWV864-1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV864-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n008.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 : 600s
% DateTime : Wed Jul 20 20:14:45 EDT 2022
% Result : Unsatisfiable 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 50
% Syntax : Number of formulae : 256 ( 155 unt; 20 typ; 0 def)
% Number of atoms : 1013 ( 412 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1941 ( 225 ~; 229 |; 0 &;1487 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 12 con; 0-5 aty)
% Number of variables : 704 ( 0 ^ 704 !; 0 ?; 704 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Com_Ocom_OSKIP,type,
c_Com_Ocom_OSKIP: $i ).
thf(tp_c_Com_Ocom_OSemi,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(tp_c_Fun_Oid,type,
c_Fun_Oid: $i > $i > $i ).
thf(tp_c_Hoare__Mirabelle_Ostate__not__singleton,type,
c_Hoare__Mirabelle_Ostate__not__singleton: $o ).
thf(tp_c_Natural_Oevalc,type,
c_Natural_Oevalc: $i > $i > $i > $o ).
thf(tp_c_Natural_Oevaln,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(tp_c_Natural_Osko__Natural__Xeval__eq__1__1,type,
c_Natural_Osko__Natural__Xeval__eq__1__1: $i > $i > $i > $i ).
thf(tp_c_Natural_Osko__Natural__Xevalc__elim__cases__4__1,type,
c_Natural_Osko__Natural__Xevalc__elim__cases__4__1: $i > $i > $i > $i > $i ).
thf(tp_c_Natural_Osko__Natural__Xevalc__evaln__1__1,type,
c_Natural_Osko__Natural__Xevalc__evaln__1__1: $i > $i > $i > $i ).
thf(tp_c_Natural_Osko__Natural__Xevaln__elim__cases__4__1,type,
c_Natural_Osko__Natural__Xevaln__elim__cases__4__1: $i > $i > $i > $i > $i > $i ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_v_c,type,
v_c: $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xsingle__stateE__1,type,
v_sko__Hoare__Mirabelle__Xsingle__stateE__1: $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1,type,
v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1: $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2,type,
v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2: $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1,type,
v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1: $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2,type,
v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2: $i ).
thf(tp_v_x,type,
v_x: $i ).
thf(tp_v_xa,type,
v_xa: $i ).
thf(tp_v_xb,type,
v_xb: $i > $i ).
thf(1,axiom,
! [V_c: $i,V_s: $i,V_t: $i,V_x: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_x @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__eq_1) ).
thf(2,axiom,
! [V_c: $i,V_s: $i,V_t: $i,V_n: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__evalc_0) ).
thf(3,axiom,
! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).
thf(4,axiom,
( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_state__not__singleton__def_0) ).
thf(5,axiom,
! [V_c0: $i,V_c1: $i,V_s0: $i,V_s2: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c1 @ V_s1 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c0 @ V_s0 @ V_s1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).
thf(6,axiom,
! [V_t: $i] :
( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ V_t )
!= V_t )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__stateE_0) ).
thf(7,axiom,
! [V_x: $i,V_xa: $i] :
( c_Hoare__Mirabelle_Ostate__not__singleton
| ( V_x = V_xa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_state__not__singleton__def_1) ).
thf(8,axiom,
( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_state__not__singleton__def__raw_0) ).
thf(9,axiom,
( ( c_Fun_Oid @ v_x @ t_a )
= v_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__def_0) ).
thf(10,axiom,
! [V_s: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).
thf(11,axiom,
! [V_u: $i,V_t: $i,V_c: $i,V_s: $i] :
( ( V_u = V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_u )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com__det_0) ).
thf(12,axiom,
! [V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
thf(13,axiom,
! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ V_c @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__evaln_0) ).
thf(14,axiom,
! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
thf(15,axiom,
! [V_s: $i,V_n: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OSkip_0) ).
thf(16,axiom,
! [V_c1: $i,V_s: $i,V_n: $i,V_c2: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ V_c1 @ V_c2 @ V_n @ V_s @ V_t ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I4_J_0) ).
thf(17,axiom,
! [V_c2: $i,V_c1: $i,V_n: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c2 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ V_c1 @ V_c2 @ V_n @ V_s @ V_t ) @ V_n @ V_t )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I4_J_1) ).
thf(18,axiom,
! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
thf(19,axiom,
! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
thf(20,axiom,
! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ V_c @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__eq_0) ).
thf(21,axiom,
! [V_c0: $i,V_c1: $i,V_s0: $i,V_n: $i,V_s2: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OSemi_0) ).
thf(22,axiom,
! [V_c1: $i,V_s: $i,V_c2: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c1 @ V_s @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ V_c1 @ V_c2 @ V_s @ V_t ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I4_J_0) ).
thf(23,axiom,
! [V_c2: $i,V_c1: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c2 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ V_c1 @ V_c2 @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I4_J_1) ).
thf(24,axiom,
! [V_t: $i,V_s: $i,V_n: $i] :
( ( V_t = V_s )
| ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).
thf(25,axiom,
! [V_x: $i,T_a: $i] :
( ( c_Fun_Oid @ V_x @ T_a )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(26,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(27,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[26]) ).
thf(28,negated_conjecture,
! [V_Z_H: $i] :
( ( V_Z_H
!= ( v_xb @ V_Z_H ) )
| ( V_Z_H = v_xa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(29,negated_conjecture,
! [V_Z_H: $i] :
( ( V_Z_H = v_xa )
| ( c_Natural_Oevalc @ v_c @ v_x @ ( v_xb @ V_Z_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(30,negated_conjecture,
~ ( c_Natural_Oevalc @ v_c @ v_x @ v_xa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(31,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(32,plain,
$false = $false,
inference(unfold_def,[status(thm)],[27]) ).
thf(33,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i,V_x: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_x @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(34,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i,V_n: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(35,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(36,plain,
( ( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(37,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_s2: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c1 @ V_s1 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c0 @ V_s0 @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(38,plain,
( ( ! [V_t: $i] :
( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ V_t )
!= V_t )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(39,plain,
( ( ! [V_x: $i,V_xa: $i] :
( c_Hoare__Mirabelle_Ostate__not__singleton
| ( V_x = V_xa ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(40,plain,
( ( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(41,plain,
( ( ( c_Fun_Oid @ v_x @ t_a )
= v_x )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(42,plain,
( ( ! [V_s: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_s ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(43,plain,
( ( ! [V_u: $i,V_t: $i,V_c: $i,V_s: $i] :
( ( V_u = V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_u )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(44,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(45,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ V_c @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(46,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(47,plain,
( ( ! [V_s: $i,V_n: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(48,plain,
( ( ! [V_c1: $i,V_s: $i,V_n: $i,V_c2: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ V_c1 @ V_c2 @ V_n @ V_s @ V_t ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(49,plain,
( ( ! [V_c2: $i,V_c1: $i,V_n: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c2 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ V_c1 @ V_c2 @ V_n @ V_s @ V_t ) @ V_n @ V_t )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(50,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(51,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(52,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ V_c @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(53,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_n: $i,V_s2: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(54,plain,
( ( ! [V_c1: $i,V_s: $i,V_c2: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c1 @ V_s @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ V_c1 @ V_c2 @ V_s @ V_t ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(55,plain,
( ( ! [V_c2: $i,V_c1: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c2 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ V_c1 @ V_c2 @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(56,plain,
( ( ! [V_t: $i,V_s: $i,V_n: $i] :
( ( V_t = V_s )
| ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(57,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_Fun_Oid @ V_x @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(58,plain,
( ( ! [V_Z_H: $i] :
( ( V_Z_H
!= ( v_xb @ V_Z_H ) )
| ( V_Z_H = v_xa ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(59,plain,
( ( ! [V_Z_H: $i] :
( ( V_Z_H = v_xa )
| ( c_Natural_Oevalc @ v_c @ v_x @ ( v_xb @ V_Z_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(60,plain,
( ( ~ ( c_Natural_Oevalc @ v_c @ v_x @ v_xa ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(61,plain,
c_Hoare__Mirabelle_Ostate__not__singleton = $true,
inference(unfold_def,[status(thm)],[31]) ).
thf(62,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(63,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ! [V_x: $i] :
~ ( c_Natural_Oevaln @ V_c @ V_s @ V_x @ V_t ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(64,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ! [V_n: $i] :
~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(65,plain,
( ( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(66,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_s2: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_s2 )
| ! [V_s1: $i] :
( ~ ( c_Natural_Oevalc @ V_c1 @ V_s1 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c0 @ V_s0 @ V_s1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(67,plain,
( ( ! [V_t: $i] :
( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ V_t )
!= V_t )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(68,plain,
( ( ! [V_x: $i,V_xa: $i] : ( V_x = V_xa )
| c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(69,plain,
( ( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(70,plain,
( ( ! [V_u: $i,V_t: $i] :
( ( V_u = V_t )
| ! [V_c: $i,V_s: $i] :
( ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_u )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(71,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(72,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(73,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i] :
( ! [V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(74,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(75,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_n: $i,V_s2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 )
| ! [V_s1: $i] :
( ~ ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(76,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ! [V_n: $i] :
~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(77,plain,
( ( ! [V_Z_H: $i] :
( ( V_Z_H
!= ( v_xb @ V_Z_H ) )
| ( V_Z_H = v_xa ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(78,plain,
c_Hoare__Mirabelle_Ostate__not__singleton = $true,
inference(copy,[status(thm)],[61]) ).
thf(79,plain,
( ( ~ ( c_Natural_Oevalc @ v_c @ v_x @ v_xa ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(80,plain,
( ( ! [V_Z_H: $i] :
( ( V_Z_H = v_xa )
| ( c_Natural_Oevalc @ v_c @ v_x @ ( v_xb @ V_Z_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(81,plain,
( ( ! [V_Z_H: $i] :
( ( V_Z_H
!= ( v_xb @ V_Z_H ) )
| ( V_Z_H = v_xa ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(82,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_Fun_Oid @ V_x @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(83,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ! [V_n: $i] :
~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(84,plain,
( ( ! [V_c2: $i,V_c1: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c2 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ V_c1 @ V_c2 @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(85,plain,
( ( ! [V_c1: $i,V_s: $i,V_c2: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c1 @ V_s @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ V_c1 @ V_c2 @ V_s @ V_t ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(86,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_n: $i,V_s2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 )
| ! [V_s1: $i] :
( ~ ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(87,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ V_c @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(88,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(89,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i] :
( ! [V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(90,plain,
( ( ! [V_c2: $i,V_c1: $i,V_n: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c2 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ V_c1 @ V_c2 @ V_n @ V_s @ V_t ) @ V_n @ V_t )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(91,plain,
( ( ! [V_c1: $i,V_s: $i,V_n: $i,V_c2: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ V_c1 @ V_c2 @ V_n @ V_s @ V_t ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(92,plain,
( ( ! [V_s: $i,V_n: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(93,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(94,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ V_c @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(95,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(96,plain,
( ( ! [V_u: $i,V_t: $i] :
( ( V_u = V_t )
| ! [V_c: $i,V_s: $i] :
( ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_u )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(97,plain,
( ( ! [V_s: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_s ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(98,plain,
( ( ( c_Fun_Oid @ v_x @ t_a )
= v_x )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(99,plain,
( ( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(100,plain,
( ( ! [V_x: $i,V_xa: $i] : ( V_x = V_xa )
| c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(101,plain,
( ( ! [V_t: $i] :
( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ V_t )
!= V_t )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(102,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_s2: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_s2 )
| ! [V_s1: $i] :
( ~ ( c_Natural_Oevalc @ V_c1 @ V_s1 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c0 @ V_s0 @ V_s1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(103,plain,
( ( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(104,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(105,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ! [V_n: $i] :
~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(106,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ! [V_x: $i] :
~ ( c_Natural_Oevaln @ V_c @ V_s @ V_x @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(107,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(108,plain,
( ( c_Natural_Oevalc @ v_c @ v_x @ v_xa )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(109,plain,
! [SV1: $i] :
( ( ( SV1 = v_xa )
| ( c_Natural_Oevalc @ v_c @ v_x @ ( v_xb @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(110,plain,
! [SV2: $i] :
( ( ( SV2
!= ( v_xb @ SV2 ) )
| ( SV2 = v_xa ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(111,plain,
! [SV3: $i] :
( ( ! [SY74: $i] :
( ( c_Fun_Oid @ SV3 @ SY74 )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(112,plain,
! [SV4: $i] :
( ( ! [SY75: $i] :
( ( SV4 = SY75 )
| ! [SY76: $i] :
~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY75 @ SY76 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(113,plain,
! [SV5: $i] :
( ( ! [SY77: $i,SY78: $i,SY79: $i] :
( ( c_Natural_Oevalc @ SV5 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SY77 @ SV5 @ SY78 @ SY79 ) @ SY79 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY77 @ SV5 ) @ SY78 @ SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(114,plain,
! [SV6: $i] :
( ( ! [SY80: $i,SY81: $i,SY82: $i] :
( ( c_Natural_Oevalc @ SV6 @ SY80 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV6 @ SY81 @ SY80 @ SY82 ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV6 @ SY81 ) @ SY80 @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(115,plain,
! [SV7: $i] :
( ( ! [SY83: $i,SY84: $i,SY85: $i,SY86: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SY83 ) @ SY84 @ SY85 @ SY86 )
| ! [SY87: $i] :
( ~ ( c_Natural_Oevaln @ SY83 @ SY87 @ SY85 @ SY86 )
| ~ ( c_Natural_Oevaln @ SV7 @ SY84 @ SY85 @ SY87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(116,plain,
! [SV8: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ( c_Natural_Oevaln @ SV8 @ SY88 @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ SV8 @ SY88 @ SY89 ) @ SY89 )
| ~ ( c_Natural_Oevalc @ SV8 @ SY88 @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(117,plain,
! [SV9: $i] :
( ( ! [SY90: $i,SY91: $i,SY92: $i] :
( ( ( c_Com_Ocom_OSemi @ SV9 @ SY90 )
!= ( c_Com_Ocom_OSemi @ SY91 @ SY92 ) )
| ( SY90 = SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(118,plain,
! [SV10: $i] :
( ( ! [SY93: $i,SY94: $i] :
( ! [SY95: $i] :
( ( c_Com_Ocom_OSemi @ SV10 @ SY93 )
!= ( c_Com_Ocom_OSemi @ SY94 @ SY95 ) )
| ( SV10 = SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(119,plain,
! [SV11: $i] :
( ( ! [SY96: $i,SY97: $i,SY98: $i,SY99: $i] :
( ( c_Natural_Oevaln @ SV11 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SY96 @ SV11 @ SY97 @ SY98 @ SY99 ) @ SY97 @ SY99 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY96 @ SV11 ) @ SY98 @ SY97 @ SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(120,plain,
! [SV12: $i] :
( ( ! [SY100: $i,SY101: $i,SY102: $i,SY103: $i] :
( ( c_Natural_Oevaln @ SV12 @ SY100 @ SY101 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV12 @ SY102 @ SY101 @ SY100 @ SY103 ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV12 @ SY102 ) @ SY100 @ SY101 @ SY103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(121,plain,
! [SV13: $i] :
( ( ! [SY104: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV13 @ SY104 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(122,plain,
! [SV14: $i] :
( ( ! [SY105: $i] :
( ( c_Com_Ocom_OSemi @ SV14 @ SY105 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(123,plain,
! [SV15: $i] :
( ( ! [SY106: $i,SY107: $i] :
( ( c_Natural_Oevaln @ SV15 @ SY106 @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ SV15 @ SY106 @ SY107 ) @ SY107 )
| ~ ( c_Natural_Oevalc @ SV15 @ SY106 @ SY107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(124,plain,
! [SV16: $i] :
( ( ! [SY108: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SV16 @ SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(125,plain,
! [SV17: $i] :
( ( ! [SY109: $i] :
( ( SV17 = SY109 )
| ! [SY110: $i,SY111: $i] :
( ~ ( c_Natural_Oevalc @ SY110 @ SY111 @ SV17 )
| ~ ( c_Natural_Oevalc @ SY110 @ SY111 @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(126,plain,
! [SV18: $i] :
( ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SV18 @ SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(127,plain,
( ( ( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 ) )
= $true )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(128,plain,
( ( ( ! [V_x: $i,V_xa: $i] : ( V_x = V_xa ) )
= $true )
| ( c_Hoare__Mirabelle_Ostate__not__singleton = $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(129,plain,
( ( ( ! [V_t: $i] :
( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ V_t )
!= V_t ) )
= $true )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(130,plain,
! [SV19: $i] :
( ( ! [SY112: $i,SY113: $i,SY114: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV19 @ SY112 ) @ SY113 @ SY114 )
| ! [SY115: $i] :
( ~ ( c_Natural_Oevalc @ SY112 @ SY115 @ SY114 )
| ~ ( c_Natural_Oevalc @ SV19 @ SY113 @ SY115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(131,plain,
( ( ( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 != v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2 ) )
= $true )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(132,plain,
! [SV20: $i] :
( ( ! [SY116: $i] :
( ( SV20 = SY116 )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SY116 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(133,plain,
! [SV21: $i] :
( ( ! [SY117: $i,SY118: $i] :
( ( c_Natural_Oevalc @ SV21 @ SY117 @ SY118 )
| ! [SY119: $i] :
~ ( c_Natural_Oevaln @ SV21 @ SY117 @ SY119 @ SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(134,plain,
! [SV22: $i] :
( ( ! [SY120: $i,SY121: $i] :
( ( c_Natural_Oevalc @ SV22 @ SY120 @ SY121 )
| ! [SY122: $i] :
~ ( c_Natural_Oevaln @ SV22 @ SY120 @ SY122 @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(135,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(136,plain,
! [SV1: $i] :
( ( ( SV1 = v_xa )
= $true )
| ( ( c_Natural_Oevalc @ v_c @ v_x @ ( v_xb @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(137,plain,
! [SV2: $i] :
( ( ( ( SV2
!= ( v_xb @ SV2 ) ) )
= $true )
| ( ( SV2 = v_xa )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(138,plain,
! [SV23: $i,SV3: $i] :
( ( ( c_Fun_Oid @ SV3 @ SV23 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(139,plain,
! [SV24: $i,SV4: $i] :
( ( ( SV4 = SV24 )
| ! [SY123: $i] :
~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV24 @ SY123 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(140,plain,
! [SV25: $i,SV5: $i] :
( ( ! [SY124: $i,SY125: $i] :
( ( c_Natural_Oevalc @ SV5 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV25 @ SV5 @ SY124 @ SY125 ) @ SY125 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV25 @ SV5 ) @ SY124 @ SY125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(141,plain,
! [SV26: $i,SV6: $i] :
( ( ! [SY126: $i,SY127: $i] :
( ( c_Natural_Oevalc @ SV6 @ SV26 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV6 @ SY126 @ SV26 @ SY127 ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV6 @ SY126 ) @ SV26 @ SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(142,plain,
! [SV27: $i,SV7: $i] :
( ( ! [SY128: $i,SY129: $i,SY130: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV27 ) @ SY128 @ SY129 @ SY130 )
| ! [SY131: $i] :
( ~ ( c_Natural_Oevaln @ SV27 @ SY131 @ SY129 @ SY130 )
| ~ ( c_Natural_Oevaln @ SV7 @ SY128 @ SY129 @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(143,plain,
! [SV28: $i,SV8: $i] :
( ( ! [SY132: $i] :
( ( c_Natural_Oevaln @ SV8 @ SV28 @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ SV8 @ SV28 @ SY132 ) @ SY132 )
| ~ ( c_Natural_Oevalc @ SV8 @ SV28 @ SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(144,plain,
! [SV29: $i,SV9: $i] :
( ( ! [SY133: $i,SY134: $i] :
( ( ( c_Com_Ocom_OSemi @ SV9 @ SV29 )
!= ( c_Com_Ocom_OSemi @ SY133 @ SY134 ) )
| ( SV29 = SY134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(145,plain,
! [SV30: $i,SV10: $i] :
( ( ! [SY135: $i] :
( ! [SY136: $i] :
( ( c_Com_Ocom_OSemi @ SV10 @ SV30 )
!= ( c_Com_Ocom_OSemi @ SY135 @ SY136 ) )
| ( SV10 = SY135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(146,plain,
! [SV31: $i,SV11: $i] :
( ( ! [SY137: $i,SY138: $i,SY139: $i] :
( ( c_Natural_Oevaln @ SV11 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV31 @ SV11 @ SY137 @ SY138 @ SY139 ) @ SY137 @ SY139 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV31 @ SV11 ) @ SY138 @ SY137 @ SY139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(147,plain,
! [SV32: $i,SV12: $i] :
( ( ! [SY140: $i,SY141: $i,SY142: $i] :
( ( c_Natural_Oevaln @ SV12 @ SV32 @ SY140 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV12 @ SY141 @ SY140 @ SV32 @ SY142 ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV12 @ SY141 ) @ SV32 @ SY140 @ SY142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(148,plain,
! [SV33: $i,SV13: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV13 @ SV33 @ SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(149,plain,
! [SV34: $i,SV14: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV14 @ SV34 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(150,plain,
! [SV35: $i,SV15: $i] :
( ( ! [SY143: $i] :
( ( c_Natural_Oevaln @ SV15 @ SV35 @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ SV15 @ SV35 @ SY143 ) @ SY143 )
| ~ ( c_Natural_Oevalc @ SV15 @ SV35 @ SY143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(151,plain,
! [SV36: $i,SV16: $i] :
( ( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SV16 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(152,plain,
! [SV37: $i,SV17: $i] :
( ( ( SV17 = SV37 )
| ! [SY144: $i,SY145: $i] :
( ~ ( c_Natural_Oevalc @ SY144 @ SY145 @ SV17 )
| ~ ( c_Natural_Oevalc @ SY144 @ SY145 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(153,plain,
( ( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
= $false )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(154,plain,
! [SV38: $i] :
( ( ( ! [SY146: $i] : ( SV38 = SY146 ) )
= $true )
| ( c_Hoare__Mirabelle_Ostate__not__singleton = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(155,plain,
! [SV39: $i] :
( ( ( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ SV39 )
!= SV39 ) )
= $true )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(156,plain,
! [SV40: $i,SV19: $i] :
( ( ! [SY147: $i,SY148: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV19 @ SV40 ) @ SY147 @ SY148 )
| ! [SY149: $i] :
( ~ ( c_Natural_Oevalc @ SV40 @ SY149 @ SY148 )
| ~ ( c_Natural_Oevalc @ SV19 @ SY147 @ SY149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(157,plain,
( ( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2 )
= $false )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(158,plain,
! [SV41: $i,SV20: $i] :
( ( ( SV20 = SV41 )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SV41 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(159,plain,
! [SV42: $i,SV21: $i] :
( ( ! [SY150: $i] :
( ( c_Natural_Oevalc @ SV21 @ SV42 @ SY150 )
| ! [SY151: $i] :
~ ( c_Natural_Oevaln @ SV21 @ SV42 @ SY151 @ SY150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(160,plain,
! [SV43: $i,SV22: $i] :
( ( ! [SY152: $i] :
( ( c_Natural_Oevalc @ SV22 @ SV43 @ SY152 )
| ! [SY153: $i] :
~ ( c_Natural_Oevaln @ SV22 @ SV43 @ SY153 @ SY152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(161,plain,
! [SV2: $i] :
( ( ( SV2
= ( v_xb @ SV2 ) )
= $false )
| ( ( SV2 = v_xa )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(162,plain,
! [SV24: $i,SV4: $i] :
( ( ( SV4 = SV24 )
= $true )
| ( ( ! [SY123: $i] :
~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV24 @ SY123 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(163,plain,
! [SV44: $i,SV25: $i,SV5: $i] :
( ( ! [SY154: $i] :
( ( c_Natural_Oevalc @ SV5 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV25 @ SV5 @ SV44 @ SY154 ) @ SY154 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV25 @ SV5 ) @ SV44 @ SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(164,plain,
! [SV45: $i,SV26: $i,SV6: $i] :
( ( ! [SY155: $i] :
( ( c_Natural_Oevalc @ SV6 @ SV26 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV6 @ SV45 @ SV26 @ SY155 ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV6 @ SV45 ) @ SV26 @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(165,plain,
! [SV46: $i,SV27: $i,SV7: $i] :
( ( ! [SY156: $i,SY157: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV27 ) @ SV46 @ SY156 @ SY157 )
| ! [SY158: $i] :
( ~ ( c_Natural_Oevaln @ SV27 @ SY158 @ SY156 @ SY157 )
| ~ ( c_Natural_Oevaln @ SV7 @ SV46 @ SY156 @ SY158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(166,plain,
! [SV47: $i,SV28: $i,SV8: $i] :
( ( ( c_Natural_Oevaln @ SV8 @ SV28 @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ SV8 @ SV28 @ SV47 ) @ SV47 )
| ~ ( c_Natural_Oevalc @ SV8 @ SV28 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(167,plain,
! [SV48: $i,SV29: $i,SV9: $i] :
( ( ! [SY159: $i] :
( ( ( c_Com_Ocom_OSemi @ SV9 @ SV29 )
!= ( c_Com_Ocom_OSemi @ SV48 @ SY159 ) )
| ( SV29 = SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(168,plain,
! [SV49: $i,SV30: $i,SV10: $i] :
( ( ! [SY160: $i] :
( ( c_Com_Ocom_OSemi @ SV10 @ SV30 )
!= ( c_Com_Ocom_OSemi @ SV49 @ SY160 ) )
| ( SV10 = SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(169,plain,
! [SV50: $i,SV31: $i,SV11: $i] :
( ( ! [SY161: $i,SY162: $i] :
( ( c_Natural_Oevaln @ SV11 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV31 @ SV11 @ SV50 @ SY161 @ SY162 ) @ SV50 @ SY162 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV31 @ SV11 ) @ SY161 @ SV50 @ SY162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(170,plain,
! [SV51: $i,SV32: $i,SV12: $i] :
( ( ! [SY163: $i,SY164: $i] :
( ( c_Natural_Oevaln @ SV12 @ SV32 @ SV51 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV12 @ SY163 @ SV51 @ SV32 @ SY164 ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV12 @ SY163 ) @ SV32 @ SV51 @ SY164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(171,plain,
! [SV34: $i,SV14: $i] :
( ( ( c_Com_Ocom_OSemi @ SV14 @ SV34 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(172,plain,
! [SV52: $i,SV35: $i,SV15: $i] :
( ( ( c_Natural_Oevaln @ SV15 @ SV35 @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ SV15 @ SV35 @ SV52 ) @ SV52 )
| ~ ( c_Natural_Oevalc @ SV15 @ SV35 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(173,plain,
! [SV36: $i,SV16: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OSemi @ SV16 @ SV36 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(174,plain,
! [SV37: $i,SV17: $i] :
( ( ( SV17 = SV37 )
= $true )
| ( ( ! [SY144: $i,SY145: $i] :
( ~ ( c_Natural_Oevalc @ SY144 @ SY145 @ SV17 )
| ~ ( c_Natural_Oevalc @ SY144 @ SY145 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(175,plain,
( ( c_Hoare__Mirabelle_Ostate__not__singleton = $false )
| ( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__raw__2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(176,plain,
! [SV53: $i,SV38: $i] :
( ( ( SV38 = SV53 )
= $true )
| ( c_Hoare__Mirabelle_Ostate__not__singleton = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(177,plain,
! [SV39: $i] :
( ( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ SV39 )
= SV39 )
= $false )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(178,plain,
! [SV54: $i,SV40: $i,SV19: $i] :
( ( ! [SY165: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV19 @ SV40 ) @ SV54 @ SY165 )
| ! [SY166: $i] :
( ~ ( c_Natural_Oevalc @ SV40 @ SY166 @ SY165 )
| ~ ( c_Natural_Oevalc @ SV19 @ SV54 @ SY166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(179,plain,
( ( c_Hoare__Mirabelle_Ostate__not__singleton = $false )
| ( ( v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(180,plain,
! [SV41: $i,SV20: $i] :
( ( ( SV20 = SV41 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SV41 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(181,plain,
! [SV55: $i,SV42: $i,SV21: $i] :
( ( ( c_Natural_Oevalc @ SV21 @ SV42 @ SV55 )
| ! [SY167: $i] :
~ ( c_Natural_Oevaln @ SV21 @ SV42 @ SY167 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(182,plain,
! [SV56: $i,SV43: $i,SV22: $i] :
( ( ( c_Natural_Oevalc @ SV22 @ SV43 @ SV56 )
| ! [SY168: $i] :
~ ( c_Natural_Oevaln @ SV22 @ SV43 @ SY168 @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(183,plain,
! [SV4: $i,SV57: $i,SV24: $i] :
( ( ( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV24 @ SV57 @ SV4 ) )
= $true )
| ( ( SV4 = SV24 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(184,plain,
! [SV58: $i,SV44: $i,SV25: $i,SV5: $i] :
( ( ( c_Natural_Oevalc @ SV5 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV25 @ SV5 @ SV44 @ SV58 ) @ SV58 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV25 @ SV5 ) @ SV44 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(185,plain,
! [SV59: $i,SV45: $i,SV26: $i,SV6: $i] :
( ( ( c_Natural_Oevalc @ SV6 @ SV26 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV6 @ SV45 @ SV26 @ SV59 ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV6 @ SV45 ) @ SV26 @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(186,plain,
! [SV60: $i,SV46: $i,SV27: $i,SV7: $i] :
( ( ! [SY169: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV27 ) @ SV46 @ SV60 @ SY169 )
| ! [SY170: $i] :
( ~ ( c_Natural_Oevaln @ SV27 @ SY170 @ SV60 @ SY169 )
| ~ ( c_Natural_Oevaln @ SV7 @ SV46 @ SV60 @ SY170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(187,plain,
! [SV47: $i,SV28: $i,SV8: $i] :
( ( ( c_Natural_Oevaln @ SV8 @ SV28 @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ SV8 @ SV28 @ SV47 ) @ SV47 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV8 @ SV28 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(188,plain,
! [SV61: $i,SV48: $i,SV29: $i,SV9: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV9 @ SV29 )
!= ( c_Com_Ocom_OSemi @ SV48 @ SV61 ) )
| ( SV29 = SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(189,plain,
! [SV49: $i,SV30: $i,SV10: $i] :
( ( ( ! [SY160: $i] :
( ( c_Com_Ocom_OSemi @ SV10 @ SV30 )
!= ( c_Com_Ocom_OSemi @ SV49 @ SY160 ) ) )
= $true )
| ( ( SV10 = SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(190,plain,
! [SV62: $i,SV50: $i,SV31: $i,SV11: $i] :
( ( ! [SY171: $i] :
( ( c_Natural_Oevaln @ SV11 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV31 @ SV11 @ SV50 @ SV62 @ SY171 ) @ SV50 @ SY171 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV31 @ SV11 ) @ SV62 @ SV50 @ SY171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(191,plain,
! [SV63: $i,SV51: $i,SV32: $i,SV12: $i] :
( ( ! [SY172: $i] :
( ( c_Natural_Oevaln @ SV12 @ SV32 @ SV51 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV12 @ SV63 @ SV51 @ SV32 @ SY172 ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV12 @ SV63 ) @ SV32 @ SV51 @ SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(192,plain,
! [SV52: $i,SV35: $i,SV15: $i] :
( ( ( c_Natural_Oevaln @ SV15 @ SV35 @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ SV15 @ SV35 @ SV52 ) @ SV52 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV15 @ SV35 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(193,plain,
! [SV37: $i,SV17: $i,SV64: $i] :
( ( ( ! [SY173: $i] :
( ~ ( c_Natural_Oevalc @ SV64 @ SY173 @ SV17 )
| ~ ( c_Natural_Oevalc @ SV64 @ SY173 @ SV37 ) ) )
= $true )
| ( ( SV17 = SV37 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(194,plain,
! [SV39: $i] :
( ( c_Hoare__Mirabelle_Ostate__not__singleton = $false )
| ( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ SV39 )
= SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(195,plain,
! [SV65: $i,SV54: $i,SV40: $i,SV19: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV19 @ SV40 ) @ SV54 @ SV65 )
| ! [SY174: $i] :
( ~ ( c_Natural_Oevalc @ SV40 @ SY174 @ SV65 )
| ~ ( c_Natural_Oevalc @ SV19 @ SV54 @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(196,plain,
! [SV20: $i,SV41: $i] :
( ( ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SV41 @ SV20 )
= $false )
| ( ( SV20 = SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(197,plain,
! [SV55: $i,SV42: $i,SV21: $i] :
( ( ( c_Natural_Oevalc @ SV21 @ SV42 @ SV55 )
= $true )
| ( ( ! [SY167: $i] :
~ ( c_Natural_Oevaln @ SV21 @ SV42 @ SY167 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(198,plain,
! [SV56: $i,SV43: $i,SV22: $i] :
( ( ( c_Natural_Oevalc @ SV22 @ SV43 @ SV56 )
= $true )
| ( ( ! [SY168: $i] :
~ ( c_Natural_Oevaln @ SV22 @ SV43 @ SY168 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(199,plain,
! [SV4: $i,SV57: $i,SV24: $i] :
( ( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV24 @ SV57 @ SV4 )
= $false )
| ( ( SV4 = SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(200,plain,
! [SV58: $i,SV44: $i,SV25: $i,SV5: $i] :
( ( ( c_Natural_Oevalc @ SV5 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV25 @ SV5 @ SV44 @ SV58 ) @ SV58 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV25 @ SV5 ) @ SV44 @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(201,plain,
! [SV59: $i,SV45: $i,SV26: $i,SV6: $i] :
( ( ( c_Natural_Oevalc @ SV6 @ SV26 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV6 @ SV45 @ SV26 @ SV59 ) )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV6 @ SV45 ) @ SV26 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(202,plain,
! [SV66: $i,SV60: $i,SV46: $i,SV27: $i,SV7: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV27 ) @ SV46 @ SV60 @ SV66 )
| ! [SY175: $i] :
( ~ ( c_Natural_Oevaln @ SV27 @ SY175 @ SV60 @ SV66 )
| ~ ( c_Natural_Oevaln @ SV7 @ SV46 @ SV60 @ SY175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(203,plain,
! [SV47: $i,SV28: $i,SV8: $i] :
( ( ( c_Natural_Oevalc @ SV8 @ SV28 @ SV47 )
= $false )
| ( ( c_Natural_Oevaln @ SV8 @ SV28 @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ SV8 @ SV28 @ SV47 ) @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(204,plain,
! [SV61: $i,SV48: $i,SV29: $i,SV9: $i] :
( ( ( ( ( c_Com_Ocom_OSemi @ SV9 @ SV29 )
!= ( c_Com_Ocom_OSemi @ SV48 @ SV61 ) ) )
= $true )
| ( ( SV29 = SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(205,plain,
! [SV67: $i,SV49: $i,SV30: $i,SV10: $i] :
( ( ( ( ( c_Com_Ocom_OSemi @ SV10 @ SV30 )
!= ( c_Com_Ocom_OSemi @ SV49 @ SV67 ) ) )
= $true )
| ( ( SV10 = SV49 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(206,plain,
! [SV68: $i,SV62: $i,SV50: $i,SV31: $i,SV11: $i] :
( ( ( c_Natural_Oevaln @ SV11 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV31 @ SV11 @ SV50 @ SV62 @ SV68 ) @ SV50 @ SV68 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV31 @ SV11 ) @ SV62 @ SV50 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(207,plain,
! [SV69: $i,SV63: $i,SV51: $i,SV32: $i,SV12: $i] :
( ( ( c_Natural_Oevaln @ SV12 @ SV32 @ SV51 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV12 @ SV63 @ SV51 @ SV32 @ SV69 ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV12 @ SV63 ) @ SV32 @ SV51 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(208,plain,
! [SV52: $i,SV35: $i,SV15: $i] :
( ( ( c_Natural_Oevalc @ SV15 @ SV35 @ SV52 )
= $false )
| ( ( c_Natural_Oevaln @ SV15 @ SV35 @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ SV15 @ SV35 @ SV52 ) @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(209,plain,
! [SV37: $i,SV17: $i,SV70: $i,SV64: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV64 @ SV70 @ SV17 )
| ~ ( c_Natural_Oevalc @ SV64 @ SV70 @ SV37 ) )
= $true )
| ( ( SV17 = SV37 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(210,plain,
! [SV65: $i,SV54: $i,SV40: $i,SV19: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV19 @ SV40 ) @ SV54 @ SV65 )
= $true )
| ( ( ! [SY174: $i] :
( ~ ( c_Natural_Oevalc @ SV40 @ SY174 @ SV65 )
| ~ ( c_Natural_Oevalc @ SV19 @ SV54 @ SY174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(211,plain,
! [SV55: $i,SV71: $i,SV42: $i,SV21: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV21 @ SV42 @ SV71 @ SV55 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV21 @ SV42 @ SV55 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(212,plain,
! [SV56: $i,SV72: $i,SV43: $i,SV22: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV22 @ SV43 @ SV72 @ SV56 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV22 @ SV43 @ SV56 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(213,plain,
! [SV58: $i,SV44: $i,SV5: $i,SV25: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV25 @ SV5 ) @ SV44 @ SV58 )
= $false )
| ( ( c_Natural_Oevalc @ SV5 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV25 @ SV5 @ SV44 @ SV58 ) @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(214,plain,
! [SV59: $i,SV26: $i,SV45: $i,SV6: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV6 @ SV45 ) @ SV26 @ SV59 )
= $false )
| ( ( c_Natural_Oevalc @ SV6 @ SV26 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV6 @ SV45 @ SV26 @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(215,plain,
! [SV66: $i,SV60: $i,SV46: $i,SV27: $i,SV7: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV27 ) @ SV46 @ SV60 @ SV66 )
= $true )
| ( ( ! [SY175: $i] :
( ~ ( c_Natural_Oevaln @ SV27 @ SY175 @ SV60 @ SV66 )
| ~ ( c_Natural_Oevaln @ SV7 @ SV46 @ SV60 @ SY175 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(216,plain,
! [SV61: $i,SV48: $i,SV29: $i,SV9: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV9 @ SV29 )
= ( c_Com_Ocom_OSemi @ SV48 @ SV61 ) )
= $false )
| ( ( SV29 = SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(217,plain,
! [SV67: $i,SV49: $i,SV30: $i,SV10: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV10 @ SV30 )
= ( c_Com_Ocom_OSemi @ SV49 @ SV67 ) )
= $false )
| ( ( SV10 = SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(218,plain,
! [SV68: $i,SV62: $i,SV50: $i,SV31: $i,SV11: $i] :
( ( ( c_Natural_Oevaln @ SV11 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV31 @ SV11 @ SV50 @ SV62 @ SV68 ) @ SV50 @ SV68 )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV31 @ SV11 ) @ SV62 @ SV50 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(219,plain,
! [SV69: $i,SV63: $i,SV51: $i,SV32: $i,SV12: $i] :
( ( ( c_Natural_Oevaln @ SV12 @ SV32 @ SV51 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV12 @ SV63 @ SV51 @ SV32 @ SV69 ) )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV12 @ SV63 ) @ SV32 @ SV51 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(220,plain,
! [SV37: $i,SV17: $i,SV70: $i,SV64: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV64 @ SV70 @ SV17 ) )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV64 @ SV70 @ SV37 ) )
= $true )
| ( ( SV17 = SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(221,plain,
! [SV54: $i,SV19: $i,SV65: $i,SV73: $i,SV40: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV40 @ SV73 @ SV65 )
| ~ ( c_Natural_Oevalc @ SV19 @ SV54 @ SV73 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV19 @ SV40 ) @ SV54 @ SV65 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(222,plain,
! [SV55: $i,SV71: $i,SV42: $i,SV21: $i] :
( ( ( c_Natural_Oevaln @ SV21 @ SV42 @ SV71 @ SV55 )
= $false )
| ( ( c_Natural_Oevalc @ SV21 @ SV42 @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(223,plain,
! [SV56: $i,SV72: $i,SV43: $i,SV22: $i] :
( ( ( c_Natural_Oevaln @ SV22 @ SV43 @ SV72 @ SV56 )
= $false )
| ( ( c_Natural_Oevalc @ SV22 @ SV43 @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(224,plain,
! [SV46: $i,SV7: $i,SV66: $i,SV60: $i,SV74: $i,SV27: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV27 @ SV74 @ SV60 @ SV66 )
| ~ ( c_Natural_Oevaln @ SV7 @ SV46 @ SV60 @ SV74 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV27 ) @ SV46 @ SV60 @ SV66 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(225,plain,
! [SV68: $i,SV50: $i,SV62: $i,SV11: $i,SV31: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV31 @ SV11 ) @ SV62 @ SV50 @ SV68 )
= $false )
| ( ( c_Natural_Oevaln @ SV11 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV31 @ SV11 @ SV50 @ SV62 @ SV68 ) @ SV50 @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(226,plain,
! [SV69: $i,SV51: $i,SV32: $i,SV63: $i,SV12: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV12 @ SV63 ) @ SV32 @ SV51 @ SV69 )
= $false )
| ( ( c_Natural_Oevaln @ SV12 @ SV32 @ SV51 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV12 @ SV63 @ SV51 @ SV32 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(227,plain,
! [SV37: $i,SV17: $i,SV70: $i,SV64: $i] :
( ( ( c_Natural_Oevalc @ SV64 @ SV70 @ SV17 )
= $false )
| ( ( ~ ( c_Natural_Oevalc @ SV64 @ SV70 @ SV37 ) )
= $true )
| ( ( SV17 = SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(228,plain,
! [SV54: $i,SV19: $i,SV65: $i,SV73: $i,SV40: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV40 @ SV73 @ SV65 ) )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV19 @ SV54 @ SV73 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV19 @ SV40 ) @ SV54 @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(229,plain,
! [SV46: $i,SV7: $i,SV66: $i,SV60: $i,SV74: $i,SV27: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV27 @ SV74 @ SV60 @ SV66 ) )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV7 @ SV46 @ SV60 @ SV74 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV27 ) @ SV46 @ SV60 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(230,plain,
! [SV17: $i,SV37: $i,SV70: $i,SV64: $i] :
( ( ( c_Natural_Oevalc @ SV64 @ SV70 @ SV37 )
= $false )
| ( ( c_Natural_Oevalc @ SV64 @ SV70 @ SV17 )
= $false )
| ( ( SV17 = SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(231,plain,
! [SV54: $i,SV19: $i,SV65: $i,SV73: $i,SV40: $i] :
( ( ( c_Natural_Oevalc @ SV40 @ SV73 @ SV65 )
= $false )
| ( ( ~ ( c_Natural_Oevalc @ SV19 @ SV54 @ SV73 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV19 @ SV40 ) @ SV54 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(232,plain,
! [SV46: $i,SV7: $i,SV66: $i,SV60: $i,SV74: $i,SV27: $i] :
( ( ( c_Natural_Oevaln @ SV27 @ SV74 @ SV60 @ SV66 )
= $false )
| ( ( ~ ( c_Natural_Oevaln @ SV7 @ SV46 @ SV60 @ SV74 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV27 ) @ SV46 @ SV60 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(233,plain,
! [SV65: $i,SV40: $i,SV73: $i,SV54: $i,SV19: $i] :
( ( ( c_Natural_Oevalc @ SV19 @ SV54 @ SV73 )
= $false )
| ( ( c_Natural_Oevalc @ SV40 @ SV73 @ SV65 )
= $false )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV19 @ SV40 ) @ SV54 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(234,plain,
! [SV66: $i,SV27: $i,SV74: $i,SV60: $i,SV46: $i,SV7: $i] :
( ( ( c_Natural_Oevaln @ SV7 @ SV46 @ SV60 @ SV74 )
= $false )
| ( ( c_Natural_Oevaln @ SV27 @ SV74 @ SV60 @ SV66 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV27 ) @ SV46 @ SV60 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(235,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[78,234,233,230,226,225,223,222,217,216,214,213,208,203,199,196,194,179,176,175,173,171,161,148,138,136,135,126,108,98]) ).
thf(236,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWV864-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n008.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 : 600
% 0.12/0.33 % DateTime : Wed Jun 15 10:24:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.36
% 0.18/0.36 No.of.Axioms: 29
% 0.18/0.36
% 0.18/0.36 Length.of.Defs: 0
% 0.18/0.36
% 0.18/0.36 Contains.Choice.Funs: false
% 0.18/0.37 .
% 0.18/0.38 (rf:0,axioms:29,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:31,loop_count:0,foatp_calls:0,translation:fof_full)............
% 0.18/0.52
% 0.18/0.52 ********************************
% 0.18/0.52 * All subproblems solved! *
% 0.18/0.52 ********************************
% 0.18/0.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:29,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:235,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.54
% 0.18/0.54 %**** Beginning of derivation protocol ****
% 0.18/0.54 % SZS output start CNFRefutation
% See solution above
% 0.18/0.54
% 0.18/0.54 %**** End of derivation protocol ****
% 0.18/0.54 %**** no. of clauses in derivation: 236 ****
% 0.18/0.54 %**** clause counter: 235 ****
% 0.18/0.54
% 0.18/0.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:29,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:235,loop_count:0,foatp_calls:1,translation:fof_full)
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