%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV866-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:59:34 AM UTC 2026
% Result : Unsatisfiable 0.35s 0.33s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 27
% Syntax : Number of formulae : 214 ( 149 unt; 0 typ; 0 def)
% Number of atoms : 903 ( 353 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1816 ( 211 ~; 207 |; 0 &;1398 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 11 con; 0-5 aty)
% Number of variables : 663 ( 0 ^; 663 !; 0 ?; 663 :)
% 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_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_v_Z,type,
v_Z: $i ).
thf(tp_v_c,type,
v_c: $i ).
thf(tp_v_s_H,type,
v_s_H: $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(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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_state__not__singleton__def__raw_0) ).
thf(9,axiom,
! [V_s: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_s ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',cls_com__det_0) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',cls_evalc__evaln_0) ).
thf(13,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/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
thf(14,axiom,
! [V_s: $i,V_n: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OSkip_0) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I4_J_0) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I4_J_1) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
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_com2 = V_com2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',cls_eval__eq_0) ).
thf(20,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/sandbox2/benchmark/theBenchmark.p',cls_evaln_OSemi_0) ).
thf(21,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/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I4_J_0) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I4_J_1) ).
thf(23,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/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).
thf(24,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(25,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[24]) ).
thf(26,negated_conjecture,
! [V_x: $i] :
~ ( c_Natural_Oevalc @ v_c @ v_Z @ V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(27,negated_conjecture,
! [V_Z_H: $i] : ( V_Z_H = v_s_H ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(28,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(29,plain,
$false = $false,
inference(unfold_def,[status(thm)],[25]) ).
thf(30,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(31,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(32,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(33,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(34,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(35,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(36,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(37,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(38,plain,
( ( ! [V_s: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_s ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(39,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)],[10]) ).
thf(40,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)],[11]) ).
thf(41,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)],[12]) ).
thf(42,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)],[13]) ).
thf(43,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)],[14]) ).
thf(44,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)],[15]) ).
thf(45,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)],[16]) ).
thf(46,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)],[17]) ).
thf(47,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)],[18]) ).
thf(48,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)],[19]) ).
thf(49,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)],[20]) ).
thf(50,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)],[21]) ).
thf(51,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)],[22]) ).
thf(52,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)],[23]) ).
thf(53,plain,
( ( ! [V_x: $i] :
~ ( c_Natural_Oevalc @ v_c @ v_Z @ V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(54,plain,
( ( ! [V_Z_H: $i] : ( V_Z_H = v_s_H ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(55,plain,
c_Hoare__Mirabelle_Ostate__not__singleton = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(56,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[29]) ).
thf(57,plain,
c_Hoare__Mirabelle_Ostate__not__singleton = $true,
inference(copy,[status(thm)],[55]) ).
thf(58,plain,
( ( ! [V_Z_H: $i] : ( V_Z_H = v_s_H ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(59,plain,
( ( ! [V_x: $i] :
~ ( c_Natural_Oevalc @ v_c @ v_Z @ V_x ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(60,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(copy,[status(thm)],[52]) ).
thf(61,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)],[51]) ).
thf(62,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)],[50]) ).
thf(63,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(copy,[status(thm)],[49]) ).
thf(64,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)],[48]) ).
thf(65,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)],[47]) ).
thf(66,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)],[46]) ).
thf(67,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)],[45]) ).
thf(68,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)],[44]) ).
thf(69,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)],[43]) ).
thf(70,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)],[42]) ).
thf(71,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)],[41]) ).
thf(72,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)],[40]) ).
thf(73,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(copy,[status(thm)],[39]) ).
thf(74,plain,
( ( ! [V_s: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_s ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(75,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)],[37]) ).
thf(76,plain,
( ( ! [V_x: $i,V_xa: $i] :
( c_Hoare__Mirabelle_Ostate__not__singleton
| ( V_x = V_xa ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(77,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)],[35]) ).
thf(78,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(copy,[status(thm)],[34]) ).
thf(79,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)],[33]) ).
thf(80,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)],[32]) ).
thf(81,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(copy,[status(thm)],[31]) ).
thf(82,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(copy,[status(thm)],[30]) ).
thf(83,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[56]) ).
thf(84,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Com_Ocom_OSemi @ SX0 @ SX1 )
!= ( c_Com_Ocom_OSemi @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(85,plain,
( ( ! [SX0: $i,SX1: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(86,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Com_Ocom_OSemi @ SX0 @ SX1 )
!= ( c_Com_Ocom_OSemi @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(87,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)],[75]) ).
thf(88,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Com_Ocom_OSemi @ SX0 @ SX1 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(89,plain,
( ( ! [SX0: $i] :
( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ SX0 )
!= SX0 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(90,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)],[79]) ).
thf(91,plain,
! [SV1: $i] :
( ( SV1 = v_s_H )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(92,plain,
! [SV2: $i] :
( ( ~ ( c_Natural_Oevalc @ v_c @ v_Z @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(93,plain,
! [SV3: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ( SV3 = SY72 )
| ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY72 @ SY73 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(94,plain,
! [SV4: $i] :
( ( ! [SY74: $i,SY75: $i,SY76: $i] :
( ( c_Natural_Oevalc @ SV4 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SY74 @ SV4 @ SY75 @ SY76 ) @ SY76 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY74 @ SV4 ) @ SY75 @ SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(95,plain,
! [SV5: $i] :
( ( ! [SY77: $i,SY78: $i,SY79: $i] :
( ( c_Natural_Oevalc @ SV5 @ SY77 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV5 @ SY78 @ SY77 @ SY79 ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV5 @ SY78 ) @ SY77 @ SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(96,plain,
! [SV6: $i] :
( ( ! [SY80: $i,SY81: $i,SY82: $i,SY83: $i,SY84: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV6 @ SY80 ) @ SY81 @ SY82 @ SY83 )
| ~ ( c_Natural_Oevaln @ SY80 @ SY84 @ SY82 @ SY83 )
| ~ ( c_Natural_Oevaln @ SV6 @ SY81 @ SY82 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(97,plain,
! [SV7: $i] :
( ( ! [SY85: $i,SY86: $i] :
( ( c_Natural_Oevaln @ SV7 @ SY85 @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ SV7 @ SY85 @ SY86 ) @ SY86 )
| ~ ( c_Natural_Oevalc @ SV7 @ SY85 @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(98,plain,
! [SV8: $i] :
( ( ! [SY87: $i,SY88: $i,SY89: $i,SY90: $i] :
( ( c_Natural_Oevaln @ SV8 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SY87 @ SV8 @ SY88 @ SY89 @ SY90 ) @ SY88 @ SY90 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY87 @ SV8 ) @ SY89 @ SY88 @ SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(99,plain,
! [SV9: $i] :
( ( ! [SY91: $i,SY92: $i,SY93: $i,SY94: $i] :
( ( c_Natural_Oevaln @ SV9 @ SY91 @ SY92 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV9 @ SY93 @ SY92 @ SY91 @ SY94 ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV9 @ SY93 ) @ SY91 @ SY92 @ SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(100,plain,
! [SV10: $i] :
( ( ! [SY95: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV10 @ SY95 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(101,plain,
! [SV11: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ( c_Natural_Oevaln @ SV11 @ SY96 @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ SV11 @ SY96 @ SY97 ) @ SY97 )
| ~ ( c_Natural_Oevalc @ SV11 @ SY96 @ SY97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(102,plain,
! [SV12: $i] :
( ( ! [SY98: $i,SY99: $i,SY100: $i] :
( ( SV12 = SY98 )
| ~ ( c_Natural_Oevalc @ SY99 @ SY100 @ SV12 )
| ~ ( c_Natural_Oevalc @ SY99 @ SY100 @ SY98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(103,plain,
! [SV13: $i] :
( ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SV13 @ SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(104,plain,
! [SV14: $i] :
( ( ! [SY101: $i] :
( c_Hoare__Mirabelle_Ostate__not__singleton
| ( SV14 = SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(105,plain,
! [SV15: $i] :
( ( ! [SY102: $i,SY103: $i,SY104: $i,SY105: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV15 @ SY102 ) @ SY103 @ SY104 )
| ~ ( c_Natural_Oevalc @ SY102 @ SY105 @ SY104 )
| ~ ( c_Natural_Oevalc @ SV15 @ SY103 @ SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(106,plain,
! [SV16: $i] :
( ( ! [SY106: $i] :
( ( SV16 = SY106 )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SY106 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(107,plain,
! [SV17: $i] :
( ( ! [SY107: $i,SY108: $i,SY109: $i] :
( ( c_Natural_Oevalc @ SV17 @ SY107 @ SY108 )
| ~ ( c_Natural_Oevaln @ SV17 @ SY107 @ SY109 @ SY108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(108,plain,
! [SV18: $i] :
( ( ! [SY110: $i,SY111: $i,SY112: $i] :
( ( c_Natural_Oevalc @ SV18 @ SY110 @ SY111 )
| ~ ( c_Natural_Oevaln @ SV18 @ SY110 @ SY112 @ SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(109,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(110,plain,
! [SV19: $i] :
( ( ! [SY113: $i,SY114: $i,SY115: $i] :
( ( ( c_Com_Ocom_OSemi @ SV19 @ SY113 )
!= ( c_Com_Ocom_OSemi @ SY114 @ SY115 ) )
| ( SV19 = SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(111,plain,
! [SV20: $i] :
( ( ! [SY116: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SV20 @ SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(112,plain,
! [SV21: $i] :
( ( ! [SY117: $i,SY118: $i,SY119: $i] :
( ( ( c_Com_Ocom_OSemi @ SV21 @ SY117 )
!= ( c_Com_Ocom_OSemi @ SY118 @ SY119 ) )
| ( SY117 = SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(113,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)],[87]) ).
thf(114,plain,
! [SV22: $i] :
( ( ! [SY120: $i] :
( ( c_Com_Ocom_OSemi @ SV22 @ SY120 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(115,plain,
! [SV23: $i] :
( ( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ SV23 )
!= SV23 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(116,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)],[90]) ).
thf(117,plain,
! [SV2: $i] :
( ( c_Natural_Oevalc @ v_c @ v_Z @ SV2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(118,plain,
! [SV24: $i,SV3: $i] :
( ( ! [SY121: $i] :
( ( SV3 = SV24 )
| ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV24 @ SY121 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(119,plain,
! [SV25: $i,SV4: $i] :
( ( ! [SY122: $i,SY123: $i] :
( ( c_Natural_Oevalc @ SV4 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV25 @ SV4 @ SY122 @ SY123 ) @ SY123 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV25 @ SV4 ) @ SY122 @ SY123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(120,plain,
! [SV26: $i,SV5: $i] :
( ( ! [SY124: $i,SY125: $i] :
( ( c_Natural_Oevalc @ SV5 @ SV26 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV5 @ SY124 @ SV26 @ SY125 ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV5 @ SY124 ) @ SV26 @ SY125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(121,plain,
! [SV27: $i,SV6: $i] :
( ( ! [SY126: $i,SY127: $i,SY128: $i,SY129: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV6 @ SV27 ) @ SY126 @ SY127 @ SY128 )
| ~ ( c_Natural_Oevaln @ SV27 @ SY129 @ SY127 @ SY128 )
| ~ ( c_Natural_Oevaln @ SV6 @ SY126 @ SY127 @ SY129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(122,plain,
! [SV28: $i,SV7: $i] :
( ( ! [SY130: $i] :
( ( c_Natural_Oevaln @ SV7 @ SV28 @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ SV7 @ SV28 @ SY130 ) @ SY130 )
| ~ ( c_Natural_Oevalc @ SV7 @ SV28 @ SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(123,plain,
! [SV29: $i,SV8: $i] :
( ( ! [SY131: $i,SY132: $i,SY133: $i] :
( ( c_Natural_Oevaln @ SV8 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV29 @ SV8 @ SY131 @ SY132 @ SY133 ) @ SY131 @ SY133 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV29 @ SV8 ) @ SY132 @ SY131 @ SY133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(124,plain,
! [SV30: $i,SV9: $i] :
( ( ! [SY134: $i,SY135: $i,SY136: $i] :
( ( c_Natural_Oevaln @ SV9 @ SV30 @ SY134 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV9 @ SY135 @ SY134 @ SV30 @ SY136 ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV9 @ SY135 ) @ SV30 @ SY134 @ SY136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(125,plain,
! [SV31: $i,SV10: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV10 @ SV31 @ SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(126,plain,
! [SV32: $i,SV11: $i] :
( ( ! [SY137: $i] :
( ( c_Natural_Oevaln @ SV11 @ SV32 @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ SV11 @ SV32 @ SY137 ) @ SY137 )
| ~ ( c_Natural_Oevalc @ SV11 @ SV32 @ SY137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(127,plain,
! [SV33: $i,SV12: $i] :
( ( ! [SY138: $i,SY139: $i] :
( ( SV12 = SV33 )
| ~ ( c_Natural_Oevalc @ SY138 @ SY139 @ SV12 )
| ~ ( c_Natural_Oevalc @ SY138 @ SY139 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(128,plain,
! [SV34: $i,SV14: $i] :
( ( c_Hoare__Mirabelle_Ostate__not__singleton
| ( SV14 = SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(129,plain,
! [SV35: $i,SV15: $i] :
( ( ! [SY140: $i,SY141: $i,SY142: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV15 @ SV35 ) @ SY140 @ SY141 )
| ~ ( c_Natural_Oevalc @ SV35 @ SY142 @ SY141 )
| ~ ( c_Natural_Oevalc @ SV15 @ SY140 @ SY142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(130,plain,
! [SV36: $i,SV16: $i] :
( ( ( SV16 = SV36 )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SV36 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(131,plain,
! [SV37: $i,SV17: $i] :
( ( ! [SY143: $i,SY144: $i] :
( ( c_Natural_Oevalc @ SV17 @ SV37 @ SY143 )
| ~ ( c_Natural_Oevaln @ SV17 @ SV37 @ SY144 @ SY143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(132,plain,
! [SV38: $i,SV18: $i] :
( ( ! [SY145: $i,SY146: $i] :
( ( c_Natural_Oevalc @ SV18 @ SV38 @ SY145 )
| ~ ( c_Natural_Oevaln @ SV18 @ SV38 @ SY146 @ SY145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(133,plain,
! [SV39: $i,SV19: $i] :
( ( ! [SY147: $i,SY148: $i] :
( ( ( c_Com_Ocom_OSemi @ SV19 @ SV39 )
!= ( c_Com_Ocom_OSemi @ SY147 @ SY148 ) )
| ( SV19 = SY147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(134,plain,
! [SV40: $i,SV20: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SV20 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(135,plain,
! [SV41: $i,SV21: $i] :
( ( ! [SY149: $i,SY150: $i] :
( ( ( c_Com_Ocom_OSemi @ SV21 @ SV41 )
!= ( c_Com_Ocom_OSemi @ SY149 @ SY150 ) )
| ( SV41 = SY150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(136,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)],[113]) ).
thf(137,plain,
! [SV42: $i,SV22: $i] :
( ( ( c_Com_Ocom_OSemi @ SV22 @ SV42 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(138,plain,
! [SV23: $i] :
( ( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ SV23 )
!= SV23 )
= $true )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(139,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)],[116]) ).
thf(140,plain,
! [SV43: $i,SV24: $i,SV3: $i] :
( ( ( SV3 = SV24 )
| ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV24 @ SV43 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(141,plain,
! [SV44: $i,SV25: $i,SV4: $i] :
( ( ! [SY151: $i] :
( ( c_Natural_Oevalc @ SV4 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV25 @ SV4 @ SV44 @ SY151 ) @ SY151 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV25 @ SV4 ) @ SV44 @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(142,plain,
! [SV45: $i,SV26: $i,SV5: $i] :
( ( ! [SY152: $i] :
( ( c_Natural_Oevalc @ SV5 @ SV26 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV5 @ SV45 @ SV26 @ SY152 ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV5 @ SV45 ) @ SV26 @ SY152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(143,plain,
! [SV46: $i,SV27: $i,SV6: $i] :
( ( ! [SY153: $i,SY154: $i,SY155: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV6 @ SV27 ) @ SV46 @ SY153 @ SY154 )
| ~ ( c_Natural_Oevaln @ SV27 @ SY155 @ SY153 @ SY154 )
| ~ ( c_Natural_Oevaln @ SV6 @ SV46 @ SY153 @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(144,plain,
! [SV47: $i,SV28: $i,SV7: $i] :
( ( ( c_Natural_Oevaln @ SV7 @ SV28 @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ SV7 @ SV28 @ SV47 ) @ SV47 )
| ~ ( c_Natural_Oevalc @ SV7 @ SV28 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(145,plain,
! [SV48: $i,SV29: $i,SV8: $i] :
( ( ! [SY156: $i,SY157: $i] :
( ( c_Natural_Oevaln @ SV8 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV29 @ SV8 @ SV48 @ SY156 @ SY157 ) @ SV48 @ SY157 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV29 @ SV8 ) @ SY156 @ SV48 @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(146,plain,
! [SV49: $i,SV30: $i,SV9: $i] :
( ( ! [SY158: $i,SY159: $i] :
( ( c_Natural_Oevaln @ SV9 @ SV30 @ SV49 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV9 @ SY158 @ SV49 @ SV30 @ SY159 ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV9 @ SY158 ) @ SV30 @ SV49 @ SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(147,plain,
! [SV50: $i,SV32: $i,SV11: $i] :
( ( ( c_Natural_Oevaln @ SV11 @ SV32 @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ SV11 @ SV32 @ SV50 ) @ SV50 )
| ~ ( c_Natural_Oevalc @ SV11 @ SV32 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(148,plain,
! [SV51: $i,SV33: $i,SV12: $i] :
( ( ! [SY160: $i] :
( ( SV12 = SV33 )
| ~ ( c_Natural_Oevalc @ SV51 @ SY160 @ SV12 )
| ~ ( c_Natural_Oevalc @ SV51 @ SY160 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(149,plain,
! [SV34: $i,SV14: $i] :
( ( c_Hoare__Mirabelle_Ostate__not__singleton = $true )
| ( ( SV14 = SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(150,plain,
! [SV52: $i,SV35: $i,SV15: $i] :
( ( ! [SY161: $i,SY162: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV15 @ SV35 ) @ SV52 @ SY161 )
| ~ ( c_Natural_Oevalc @ SV35 @ SY162 @ SY161 )
| ~ ( c_Natural_Oevalc @ SV15 @ SV52 @ SY162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(151,plain,
! [SV36: $i,SV16: $i] :
( ( ( SV16 = SV36 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SV36 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(152,plain,
! [SV53: $i,SV37: $i,SV17: $i] :
( ( ! [SY163: $i] :
( ( c_Natural_Oevalc @ SV17 @ SV37 @ SV53 )
| ~ ( c_Natural_Oevaln @ SV17 @ SV37 @ SY163 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(153,plain,
! [SV54: $i,SV38: $i,SV18: $i] :
( ( ! [SY164: $i] :
( ( c_Natural_Oevalc @ SV18 @ SV38 @ SV54 )
| ~ ( c_Natural_Oevaln @ SV18 @ SV38 @ SY164 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(154,plain,
! [SV55: $i,SV39: $i,SV19: $i] :
( ( ! [SY165: $i] :
( ( ( c_Com_Ocom_OSemi @ SV19 @ SV39 )
!= ( c_Com_Ocom_OSemi @ SV55 @ SY165 ) )
| ( SV19 = SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(155,plain,
! [SV40: $i,SV20: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OSemi @ SV20 @ SV40 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(156,plain,
! [SV56: $i,SV41: $i,SV21: $i] :
( ( ! [SY166: $i] :
( ( ( c_Com_Ocom_OSemi @ SV21 @ SV41 )
!= ( c_Com_Ocom_OSemi @ SV56 @ SY166 ) )
| ( SV41 = SY166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(157,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)],[136]) ).
thf(158,plain,
! [SV42: $i,SV22: $i] :
( ( ( c_Com_Ocom_OSemi @ SV22 @ SV42 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(159,plain,
! [SV23: $i] :
( ( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ SV23 )
= SV23 )
= $false )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(160,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)],[139]) ).
thf(161,plain,
! [SV43: $i,SV24: $i,SV3: $i] :
( ( ( SV3 = SV24 )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV24 @ SV43 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(162,plain,
! [SV57: $i,SV44: $i,SV25: $i,SV4: $i] :
( ( ( c_Natural_Oevalc @ SV4 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV25 @ SV4 @ SV44 @ SV57 ) @ SV57 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV25 @ SV4 ) @ SV44 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(163,plain,
! [SV58: $i,SV45: $i,SV26: $i,SV5: $i] :
( ( ( c_Natural_Oevalc @ SV5 @ SV26 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV5 @ SV45 @ SV26 @ SV58 ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV5 @ SV45 ) @ SV26 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(164,plain,
! [SV59: $i,SV46: $i,SV27: $i,SV6: $i] :
( ( ! [SY167: $i,SY168: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV6 @ SV27 ) @ SV46 @ SV59 @ SY167 )
| ~ ( c_Natural_Oevaln @ SV27 @ SY168 @ SV59 @ SY167 )
| ~ ( c_Natural_Oevaln @ SV6 @ SV46 @ SV59 @ SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(165,plain,
! [SV47: $i,SV28: $i,SV7: $i] :
( ( ( c_Natural_Oevaln @ SV7 @ SV28 @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ SV7 @ SV28 @ SV47 ) @ SV47 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV7 @ SV28 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(166,plain,
! [SV60: $i,SV48: $i,SV29: $i,SV8: $i] :
( ( ! [SY169: $i] :
( ( c_Natural_Oevaln @ SV8 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV29 @ SV8 @ SV48 @ SV60 @ SY169 ) @ SV48 @ SY169 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV29 @ SV8 ) @ SV60 @ SV48 @ SY169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(167,plain,
! [SV61: $i,SV49: $i,SV30: $i,SV9: $i] :
( ( ! [SY170: $i] :
( ( c_Natural_Oevaln @ SV9 @ SV30 @ SV49 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV9 @ SV61 @ SV49 @ SV30 @ SY170 ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV9 @ SV61 ) @ SV30 @ SV49 @ SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(168,plain,
! [SV50: $i,SV32: $i,SV11: $i] :
( ( ( c_Natural_Oevaln @ SV11 @ SV32 @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ SV11 @ SV32 @ SV50 ) @ SV50 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV11 @ SV32 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(169,plain,
! [SV62: $i,SV51: $i,SV33: $i,SV12: $i] :
( ( ( SV12 = SV33 )
| ~ ( c_Natural_Oevalc @ SV51 @ SV62 @ SV12 )
| ~ ( c_Natural_Oevalc @ SV51 @ SV62 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(170,plain,
! [SV63: $i,SV52: $i,SV35: $i,SV15: $i] :
( ( ! [SY171: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV15 @ SV35 ) @ SV52 @ SV63 )
| ~ ( c_Natural_Oevalc @ SV35 @ SY171 @ SV63 )
| ~ ( c_Natural_Oevalc @ SV15 @ SV52 @ SY171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(171,plain,
! [SV16: $i,SV36: $i] :
( ( ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SV36 @ SV16 )
= $false )
| ( ( SV16 = SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(172,plain,
! [SV64: $i,SV53: $i,SV37: $i,SV17: $i] :
( ( ( c_Natural_Oevalc @ SV17 @ SV37 @ SV53 )
| ~ ( c_Natural_Oevaln @ SV17 @ SV37 @ SV64 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(173,plain,
! [SV65: $i,SV54: $i,SV38: $i,SV18: $i] :
( ( ( c_Natural_Oevalc @ SV18 @ SV38 @ SV54 )
| ~ ( c_Natural_Oevaln @ SV18 @ SV38 @ SV65 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(174,plain,
! [SV66: $i,SV55: $i,SV39: $i,SV19: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV19 @ SV39 )
!= ( c_Com_Ocom_OSemi @ SV55 @ SV66 ) )
| ( SV19 = SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(175,plain,
! [SV67: $i,SV56: $i,SV41: $i,SV21: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV21 @ SV41 )
!= ( c_Com_Ocom_OSemi @ SV56 @ SV67 ) )
| ( SV41 = SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(176,plain,
! [SV23: $i] :
( ( c_Hoare__Mirabelle_Ostate__not__singleton = $false )
| ( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ SV23 )
= SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(177,plain,
! [SV3: $i,SV43: $i,SV24: $i] :
( ( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV24 @ SV43 @ SV3 )
= $false )
| ( ( SV3 = SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(178,plain,
! [SV57: $i,SV44: $i,SV25: $i,SV4: $i] :
( ( ( c_Natural_Oevalc @ SV4 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV25 @ SV4 @ SV44 @ SV57 ) @ SV57 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV25 @ SV4 ) @ SV44 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(179,plain,
! [SV58: $i,SV45: $i,SV26: $i,SV5: $i] :
( ( ( c_Natural_Oevalc @ SV5 @ SV26 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV5 @ SV45 @ SV26 @ SV58 ) )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV5 @ SV45 ) @ SV26 @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(180,plain,
! [SV68: $i,SV59: $i,SV46: $i,SV27: $i,SV6: $i] :
( ( ! [SY172: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV6 @ SV27 ) @ SV46 @ SV59 @ SV68 )
| ~ ( c_Natural_Oevaln @ SV27 @ SY172 @ SV59 @ SV68 )
| ~ ( c_Natural_Oevaln @ SV6 @ SV46 @ SV59 @ SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(181,plain,
! [SV47: $i,SV28: $i,SV7: $i] :
( ( ( c_Natural_Oevalc @ SV7 @ SV28 @ SV47 )
= $false )
| ( ( c_Natural_Oevaln @ SV7 @ SV28 @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ SV7 @ SV28 @ SV47 ) @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(182,plain,
! [SV69: $i,SV60: $i,SV48: $i,SV29: $i,SV8: $i] :
( ( ( c_Natural_Oevaln @ SV8 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV29 @ SV8 @ SV48 @ SV60 @ SV69 ) @ SV48 @ SV69 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV29 @ SV8 ) @ SV60 @ SV48 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(183,plain,
! [SV70: $i,SV61: $i,SV49: $i,SV30: $i,SV9: $i] :
( ( ( c_Natural_Oevaln @ SV9 @ SV30 @ SV49 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV9 @ SV61 @ SV49 @ SV30 @ SV70 ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV9 @ SV61 ) @ SV30 @ SV49 @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(184,plain,
! [SV50: $i,SV32: $i,SV11: $i] :
( ( ( c_Natural_Oevalc @ SV11 @ SV32 @ SV50 )
= $false )
| ( ( c_Natural_Oevaln @ SV11 @ SV32 @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ SV11 @ SV32 @ SV50 ) @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(185,plain,
! [SV62: $i,SV51: $i,SV33: $i,SV12: $i] :
( ( ( SV12 = SV33 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV51 @ SV62 @ SV12 )
| ~ ( c_Natural_Oevalc @ SV51 @ SV62 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(186,plain,
! [SV71: $i,SV63: $i,SV52: $i,SV35: $i,SV15: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV15 @ SV35 ) @ SV52 @ SV63 )
| ~ ( c_Natural_Oevalc @ SV35 @ SV71 @ SV63 )
| ~ ( c_Natural_Oevalc @ SV15 @ SV52 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(187,plain,
! [SV64: $i,SV53: $i,SV37: $i,SV17: $i] :
( ( ( c_Natural_Oevalc @ SV17 @ SV37 @ SV53 )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV17 @ SV37 @ SV64 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(188,plain,
! [SV65: $i,SV54: $i,SV38: $i,SV18: $i] :
( ( ( c_Natural_Oevalc @ SV18 @ SV38 @ SV54 )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV18 @ SV38 @ SV65 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(189,plain,
! [SV66: $i,SV55: $i,SV39: $i,SV19: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV19 @ SV39 )
!= ( c_Com_Ocom_OSemi @ SV55 @ SV66 ) )
= $true )
| ( ( SV19 = SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(190,plain,
! [SV67: $i,SV56: $i,SV41: $i,SV21: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV21 @ SV41 )
!= ( c_Com_Ocom_OSemi @ SV56 @ SV67 ) )
= $true )
| ( ( SV41 = SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(191,plain,
! [SV57: $i,SV44: $i,SV4: $i,SV25: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV25 @ SV4 ) @ SV44 @ SV57 )
= $false )
| ( ( c_Natural_Oevalc @ SV4 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV25 @ SV4 @ SV44 @ SV57 ) @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(192,plain,
! [SV58: $i,SV26: $i,SV45: $i,SV5: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV5 @ SV45 ) @ SV26 @ SV58 )
= $false )
| ( ( c_Natural_Oevalc @ SV5 @ SV26 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV5 @ SV45 @ SV26 @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(193,plain,
! [SV72: $i,SV68: $i,SV59: $i,SV46: $i,SV27: $i,SV6: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV6 @ SV27 ) @ SV46 @ SV59 @ SV68 )
| ~ ( c_Natural_Oevaln @ SV27 @ SV72 @ SV59 @ SV68 )
| ~ ( c_Natural_Oevaln @ SV6 @ SV46 @ SV59 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(194,plain,
! [SV69: $i,SV60: $i,SV48: $i,SV29: $i,SV8: $i] :
( ( ( c_Natural_Oevaln @ SV8 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV29 @ SV8 @ SV48 @ SV60 @ SV69 ) @ SV48 @ SV69 )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV29 @ SV8 ) @ SV60 @ SV48 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(195,plain,
! [SV70: $i,SV61: $i,SV49: $i,SV30: $i,SV9: $i] :
( ( ( c_Natural_Oevaln @ SV9 @ SV30 @ SV49 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV9 @ SV61 @ SV49 @ SV30 @ SV70 ) )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV9 @ SV61 ) @ SV30 @ SV49 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(196,plain,
! [SV33: $i,SV12: $i,SV62: $i,SV51: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV51 @ SV62 @ SV12 ) )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV51 @ SV62 @ SV33 ) )
= $true )
| ( ( SV12 = SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(197,plain,
! [SV71: $i,SV63: $i,SV52: $i,SV35: $i,SV15: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV15 @ SV35 ) @ SV52 @ SV63 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV35 @ SV71 @ SV63 )
| ~ ( c_Natural_Oevalc @ SV15 @ SV52 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(198,plain,
! [SV53: $i,SV64: $i,SV37: $i,SV17: $i] :
( ( ( c_Natural_Oevaln @ SV17 @ SV37 @ SV64 @ SV53 )
= $false )
| ( ( c_Natural_Oevalc @ SV17 @ SV37 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(199,plain,
! [SV54: $i,SV65: $i,SV38: $i,SV18: $i] :
( ( ( c_Natural_Oevaln @ SV18 @ SV38 @ SV65 @ SV54 )
= $false )
| ( ( c_Natural_Oevalc @ SV18 @ SV38 @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(200,plain,
! [SV66: $i,SV55: $i,SV39: $i,SV19: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV19 @ SV39 )
= ( c_Com_Ocom_OSemi @ SV55 @ SV66 ) )
= $false )
| ( ( SV19 = SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(201,plain,
! [SV67: $i,SV56: $i,SV41: $i,SV21: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV21 @ SV41 )
= ( c_Com_Ocom_OSemi @ SV56 @ SV67 ) )
= $false )
| ( ( SV41 = SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(202,plain,
! [SV72: $i,SV68: $i,SV59: $i,SV46: $i,SV27: $i,SV6: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV6 @ SV27 ) @ SV46 @ SV59 @ SV68 )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV27 @ SV72 @ SV59 @ SV68 )
| ~ ( c_Natural_Oevaln @ SV6 @ SV46 @ SV59 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(203,plain,
! [SV69: $i,SV48: $i,SV60: $i,SV8: $i,SV29: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV29 @ SV8 ) @ SV60 @ SV48 @ SV69 )
= $false )
| ( ( c_Natural_Oevaln @ SV8 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV29 @ SV8 @ SV48 @ SV60 @ SV69 ) @ SV48 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(204,plain,
! [SV70: $i,SV49: $i,SV30: $i,SV61: $i,SV9: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV9 @ SV61 ) @ SV30 @ SV49 @ SV70 )
= $false )
| ( ( c_Natural_Oevaln @ SV9 @ SV30 @ SV49 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV9 @ SV61 @ SV49 @ SV30 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(205,plain,
! [SV33: $i,SV12: $i,SV62: $i,SV51: $i] :
( ( ( c_Natural_Oevalc @ SV51 @ SV62 @ SV12 )
= $false )
| ( ( ~ ( c_Natural_Oevalc @ SV51 @ SV62 @ SV33 ) )
= $true )
| ( ( SV12 = SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(206,plain,
! [SV52: $i,SV15: $i,SV63: $i,SV71: $i,SV35: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV35 @ SV71 @ SV63 ) )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV15 @ SV52 @ SV71 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV15 @ SV35 ) @ SV52 @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(207,plain,
! [SV46: $i,SV6: $i,SV68: $i,SV59: $i,SV72: $i,SV27: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV27 @ SV72 @ SV59 @ SV68 ) )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV6 @ SV46 @ SV59 @ SV72 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV6 @ SV27 ) @ SV46 @ SV59 @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(208,plain,
! [SV12: $i,SV33: $i,SV62: $i,SV51: $i] :
( ( ( c_Natural_Oevalc @ SV51 @ SV62 @ SV33 )
= $false )
| ( ( c_Natural_Oevalc @ SV51 @ SV62 @ SV12 )
= $false )
| ( ( SV12 = SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(209,plain,
! [SV52: $i,SV15: $i,SV63: $i,SV71: $i,SV35: $i] :
( ( ( c_Natural_Oevalc @ SV35 @ SV71 @ SV63 )
= $false )
| ( ( ~ ( c_Natural_Oevalc @ SV15 @ SV52 @ SV71 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV15 @ SV35 ) @ SV52 @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(210,plain,
! [SV46: $i,SV6: $i,SV68: $i,SV59: $i,SV72: $i,SV27: $i] :
( ( ( c_Natural_Oevaln @ SV27 @ SV72 @ SV59 @ SV68 )
= $false )
| ( ( ~ ( c_Natural_Oevaln @ SV6 @ SV46 @ SV59 @ SV72 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV6 @ SV27 ) @ SV46 @ SV59 @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(211,plain,
! [SV63: $i,SV35: $i,SV71: $i,SV52: $i,SV15: $i] :
( ( ( c_Natural_Oevalc @ SV15 @ SV52 @ SV71 )
= $false )
| ( ( c_Natural_Oevalc @ SV35 @ SV71 @ SV63 )
= $false )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV15 @ SV35 ) @ SV52 @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(212,plain,
! [SV68: $i,SV27: $i,SV72: $i,SV59: $i,SV46: $i,SV6: $i] :
( ( ( c_Natural_Oevaln @ SV6 @ SV46 @ SV59 @ SV72 )
= $false )
| ( ( c_Natural_Oevaln @ SV27 @ SV72 @ SV59 @ SV68 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV6 @ SV27 ) @ SV46 @ SV59 @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(213,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[57,212,211,208,204,203,201,200,199,198,192,191,184,181,177,176,171,160,158,157,155,149,125,117,109,103,91]) ).
thf(214,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV866-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.20 % Computer : n017.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Oct 6 16:42:01 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.35/0.33
% 0.35/0.33 No.of.Axioms: 26
% 0.35/0.33
% 0.35/0.33 Length.of.Defs: 0
% 0.35/0.33
% 0.35/0.33 Contains.Choice.Funs: false
% 0.35/0.33 .....
% 0.35/0.33
% 0.35/0.33 ********************************
% 0.35/0.33 * All subproblems solved! *
% 0.35/0.33 ********************************
% 0.35/0.33 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:26,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:213,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.35/0.33
% 0.35/0.33 %**** Beginning of derivation protocol ****
% 0.35/0.33 % SZS output start CNFRefutation
% See solution above
% 0.35/0.33
% 0.35/0.33 %**** End of derivation protocol ****
% 0.35/0.33 %**** no. of clauses in derivation: 214 ****
% 0.35/0.33 %**** clause counter: 213 ****
% 0.35/0.33
% 0.35/0.33 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:26,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:213,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------