%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV904-1 : 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 : n013.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 10:59:46 AM UTC 2026
% Result : Unsatisfiable 0.58s 0.30s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of formulae : 203 ( 156 unt; 0 typ; 0 def)
% Number of atoms : 751 ( 403 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 824 ( 181 ~; 128 |; 0 &; 515 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 11 con; 0-2 aty)
% Number of variables : 364 ( 0 ^; 364 !; 0 ?; 364 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Com_OWT,type,
c_Com_OWT: $i > $o ).
thf(tp_c_Com_OWT__bodies,type,
c_Com_OWT__bodies: $o ).
thf(tp_c_Com_Obody,type,
c_Com_Obody: $i > $i ).
thf(tp_c_Com_Ocom_OBODY,type,
c_Com_Ocom_OBODY: $i > $i ).
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_Com_Osko__Com__XWTs__elim__cases__7__1,type,
c_Com_Osko__Com__XWTs__elim__cases__7__1: $i > $i ).
thf(tp_c_Hoare__Mirabelle_Ostate__not__singleton,type,
c_Hoare__Mirabelle_Ostate__not__singleton: $o ).
thf(tp_c_Option_Ooption_ONone,type,
c_Option_Ooption_ONone: $i > $i ).
thf(tp_c_Option_Ooption_OSome,type,
c_Option_Ooption_OSome: $i > $i > $i ).
thf(tp_tc_Com_Ocom,type,
tc_Com_Ocom: $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(1,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(2,axiom,
c_Com_OWT @ c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OSkip_0) ).
thf(3,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(4,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(5,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(6,axiom,
! [V_c2: $i,V_c1: $i] :
( ( c_Com_OWT @ V_c2 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_1) ).
thf(7,axiom,
! [V_c1: $i,V_c2: $i] :
( ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_0) ).
thf(8,axiom,
! [V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OSemi_0) ).
thf(9,axiom,
! [V_pn: $i,V_b: $i] :
( ( ( c_Com_Obody @ V_pn )
!= ( c_Option_Ooption_OSome @ V_b @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__bodiesD_0) ).
thf(10,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(11,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(12,axiom,
! [V_a: $i,T_a: $i,V_a_H: $i] :
( ( ( c_Option_Ooption_OSome @ V_a @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) )
| ( V_a = V_a_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Oinject_0) ).
thf(13,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(14,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(15,axiom,
! [V_P: $i] :
( ( ( c_Com_Obody @ V_P )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ V_P ) @ tc_Com_Ocom ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I7_J_0) ).
thf(16,axiom,
! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
thf(17,axiom,
! [V_pname: $i,V_pname_H: $i] :
( ( ( c_Com_Ocom_OBODY @ V_pname )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) )
| ( V_pname = V_pname_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
thf(18,axiom,
! [V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
thf(19,axiom,
! [V_pname_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).
thf(20,axiom,
! [V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).
thf(21,axiom,
! [V_pn: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_pn ) )
| ( ( c_Com_Obody @ V_pn )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OBody_0) ).
thf(22,axiom,
! [V_xa: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_xa @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__None__eq_1) ).
thf(23,axiom,
! [V_a_H: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_a_H @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).
thf(24,axiom,
! [T_a: $i,V_y: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).
thf(25,axiom,
! [T_a: $i,V_a_H: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_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,
~ c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(29,negated_conjecture,
c_Com_OWT @ v_c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(30,negated_conjecture,
c_Com_OWT__bodies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(31,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(32,plain,
$false = $false,
inference(unfold_def,[status(thm)],[27]) ).
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)],[1]) ).
thf(34,plain,
( ( c_Com_OWT @ c_Com_Ocom_OSKIP )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
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)],[3]) ).
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)],[4]) ).
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)],[5]) ).
thf(38,plain,
( ( ! [V_c2: $i,V_c1: $i] :
( ( c_Com_OWT @ V_c2 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(39,plain,
( ( ! [V_c1: $i,V_c2: $i] :
( ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(40,plain,
( ( ! [V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(41,plain,
( ( ! [V_pn: $i,V_b: $i] :
( ( ( c_Com_Obody @ V_pn )
!= ( c_Option_Ooption_OSome @ V_b @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(42,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)],[10]) ).
thf(43,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)],[11]) ).
thf(44,plain,
( ( ! [V_a: $i,T_a: $i,V_a_H: $i] :
( ( ( c_Option_Ooption_OSome @ V_a @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(45,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)],[13]) ).
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_com2 = V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(47,plain,
( ( ! [V_P: $i] :
( ( ( c_Com_Obody @ V_P )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ V_P ) @ tc_Com_Ocom ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(48,plain,
( ( ! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(49,plain,
( ( ! [V_pname: $i,V_pname_H: $i] :
( ( ( c_Com_Ocom_OBODY @ V_pname )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) )
| ( V_pname = V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(50,plain,
( ( ! [V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(51,plain,
( ( ! [V_pname_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(52,plain,
( ( ! [V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(53,plain,
( ( ! [V_pn: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_pn ) )
| ( ( c_Com_Obody @ V_pn )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(54,plain,
( ( ! [V_xa: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_xa @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(55,plain,
( ( ! [V_a_H: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_a_H @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(56,plain,
( ( ! [T_a: $i,V_y: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(57,plain,
( ( ! [T_a: $i,V_a_H: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(58,plain,
( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton ) = $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(59,plain,
( ( c_Com_OWT @ v_c )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(60,plain,
c_Com_OWT__bodies = $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,
c_Hoare__Mirabelle_Ostate__not__singleton = $true,
inference(copy,[status(thm)],[61]) ).
thf(64,plain,
c_Com_OWT__bodies = $true,
inference(copy,[status(thm)],[60]) ).
thf(65,plain,
( ( c_Com_OWT @ v_c )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(66,plain,
( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton ) = $true ),
inference(copy,[status(thm)],[58]) ).
thf(67,plain,
( ( ! [T_a: $i,V_a_H: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(68,plain,
( ( ! [T_a: $i,V_y: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(69,plain,
( ( ! [V_a_H: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_a_H @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(70,plain,
( ( ! [V_xa: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_xa @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(71,plain,
( ( ! [V_pn: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_pn ) )
| ( ( c_Com_Obody @ V_pn )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(72,plain,
( ( ! [V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(73,plain,
( ( ! [V_pname_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(74,plain,
( ( ! [V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(75,plain,
( ( ! [V_pname: $i,V_pname_H: $i] :
( ( ( c_Com_Ocom_OBODY @ V_pname )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) )
| ( V_pname = V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(76,plain,
( ( ! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(77,plain,
( ( ! [V_P: $i] :
( ( ( c_Com_Obody @ V_P )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ V_P ) @ tc_Com_Ocom ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_P ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(78,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)],[46]) ).
thf(79,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)],[45]) ).
thf(80,plain,
( ( ! [V_a: $i,T_a: $i,V_a_H: $i] :
( ( ( c_Option_Ooption_OSome @ V_a @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(81,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)],[43]) ).
thf(82,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)],[42]) ).
thf(83,plain,
( ( ! [V_pn: $i,V_b: $i] :
( ( ( c_Com_Obody @ V_pn )
!= ( c_Option_Ooption_OSome @ V_b @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ V_b ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(84,plain,
( ( ! [V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(85,plain,
( ( ! [V_c1: $i,V_c2: $i] :
( ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(86,plain,
( ( ! [V_c2: $i,V_c1: $i] :
( ( c_Com_OWT @ V_c2 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
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(copy,[status(thm)],[37]) ).
thf(88,plain,
( ( ! [V_x: $i,V_xa: $i] :
( c_Hoare__Mirabelle_Ostate__not__singleton
| ( V_x = V_xa ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(89,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(90,plain,
( ( c_Com_OWT @ c_Com_Ocom_OSKIP )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(91,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(92,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[62]) ).
thf(93,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Com_Obody @ SX0 )
!= ( c_Option_Ooption_OSome @ SX1 @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(94,plain,
( ( ! [SX0: $i] :
( ( c_Com_Ocom_OBODY @ SX0 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(95,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)],[91]) ).
thf(96,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Com_Ocom_OBODY @ SX0 )
!= ( c_Com_Ocom_OSemi @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(97,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Com_Ocom_OBODY @ SX0 )
!= ( c_Com_Ocom_OBODY @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(98,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Com_Ocom_OSemi @ SX0 @ SX1 )
!= ( c_Com_Ocom_OBODY @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
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(unfold_def,[status(thm)],[87]) ).
thf(100,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Option_Ooption_ONone @ SX0 )
!= ( c_Option_Ooption_OSome @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(101,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Option_Ooption_ONone @ SX0 )
!= ( c_Option_Ooption_OSome @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(102,plain,
( ( ! [SX0: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(103,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Option_Ooption_OSome @ SX0 @ SX1 )
!= ( c_Option_Ooption_ONone @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(104,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Com_Ocom_OSemi @ SX0 @ SX1 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(105,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)],[78]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Option_Ooption_OSome @ SX0 @ SX1 )
!= ( c_Option_Ooption_ONone @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(107,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)],[79]) ).
thf(108,plain,
( ( ! [SX0: $i] :
( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ SX0 )
!= SX0 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(109,plain,
( ( ! [SX0: $i,SX1: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Option_Ooption_OSome @ SX0 @ SX1 )
!= ( c_Option_Ooption_OSome @ SX2 @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(111,plain,
c_Hoare__Mirabelle_Ostate__not__singleton = $false,
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(112,plain,
! [SV1: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ SV1 ) )
| ( ( c_Com_Obody @ SV1 )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(113,plain,
! [SV2: $i] :
( ( ( ( c_Com_Obody @ SV2 )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ SV2 ) @ tc_Com_Ocom ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(114,plain,
! [SV3: $i] :
( ( ! [SY46: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV3 @ SY46 ) )
| ~ ( c_Com_OWT @ SY46 )
| ~ ( c_Com_OWT @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(115,plain,
! [SV4: $i] :
( ( ! [SY47: $i] :
( ( c_Com_OWT @ SV4 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV4 @ SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(116,plain,
! [SV5: $i] :
( ( ! [SY48: $i] :
( ( c_Com_OWT @ SV5 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SY48 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(117,plain,
! [SV6: $i] :
( ( ! [SY49: $i] :
( c_Hoare__Mirabelle_Ostate__not__singleton
| ( SV6 = SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(118,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(119,plain,
! [SV7: $i] :
( ( ! [SY50: $i] :
( ( ( c_Com_Obody @ SV7 )
!= ( c_Option_Ooption_OSome @ SY50 @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(120,plain,
! [SV8: $i] :
( ( ( c_Com_Ocom_OBODY @ SV8 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(121,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)],[95]) ).
thf(122,plain,
! [SV9: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ( c_Com_Ocom_OBODY @ SV9 )
!= ( c_Com_Ocom_OSemi @ SY51 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(123,plain,
! [SV10: $i] :
( ( ! [SY53: $i] :
( ( ( c_Com_Ocom_OBODY @ SV10 )
!= ( c_Com_Ocom_OBODY @ SY53 ) )
| ( SV10 = SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(124,plain,
! [SV11: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ( c_Com_Ocom_OSemi @ SV11 @ SY54 )
!= ( c_Com_Ocom_OBODY @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(125,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(126,plain,
! [SV12: $i] :
( ( ! [SY56: $i] :
( ( c_Option_Ooption_ONone @ SV12 )
!= ( c_Option_Ooption_OSome @ SY56 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(127,plain,
! [SV13: $i] :
( ( ! [SY57: $i] :
( ( c_Option_Ooption_ONone @ SV13 )
!= ( c_Option_Ooption_OSome @ SY57 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(128,plain,
! [SV14: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(129,plain,
! [SV15: $i] :
( ( ! [SY58: $i] :
( ( c_Option_Ooption_OSome @ SV15 @ SY58 )
!= ( c_Option_Ooption_ONone @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(130,plain,
! [SV16: $i] :
( ( ! [SY59: $i] :
( ( c_Com_Ocom_OSemi @ SV16 @ SY59 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(131,plain,
! [SV17: $i] :
( ( ! [SY60: $i,SY61: $i,SY62: $i] :
( ( ( c_Com_Ocom_OSemi @ SV17 @ SY60 )
!= ( c_Com_Ocom_OSemi @ SY61 @ SY62 ) )
| ( SY60 = SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(132,plain,
! [SV18: $i] :
( ( ! [SY63: $i] :
( ( c_Option_Ooption_OSome @ SV18 @ SY63 )
!= ( c_Option_Ooption_ONone @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(133,plain,
! [SV19: $i] :
( ( ! [SY64: $i,SY65: $i,SY66: $i] :
( ( ( c_Com_Ocom_OSemi @ SV19 @ SY64 )
!= ( c_Com_Ocom_OSemi @ SY65 @ SY66 ) )
| ( SV19 = SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(134,plain,
! [SV20: $i] :
( ( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ SV20 )
!= SV20 )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(135,plain,
! [SV21: $i] :
( ( ! [SY67: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SV21 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(136,plain,
! [SV22: $i] :
( ( ! [SY68: $i,SY69: $i] :
( ( ( c_Option_Ooption_OSome @ SV22 @ SY68 )
!= ( c_Option_Ooption_OSome @ SY69 @ SY68 ) )
| ( SV22 = SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(137,plain,
! [SV1: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ SV1 ) )
= $true )
| ( ( ( c_Com_Obody @ SV1 )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(138,plain,
! [SV2: $i] :
( ( ( ( c_Com_Obody @ SV2 )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ SV2 ) @ tc_Com_Ocom ) )
= $true )
| ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(139,plain,
! [SV23: $i,SV3: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV3 @ SV23 ) )
| ~ ( c_Com_OWT @ SV23 )
| ~ ( c_Com_OWT @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(140,plain,
! [SV24: $i,SV4: $i] :
( ( ( c_Com_OWT @ SV4 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV4 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(141,plain,
! [SV25: $i,SV5: $i] :
( ( ( c_Com_OWT @ SV5 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV25 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(142,plain,
! [SV26: $i,SV6: $i] :
( ( c_Hoare__Mirabelle_Ostate__not__singleton
| ( SV6 = SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(143,plain,
! [SV27: $i,SV7: $i] :
( ( ( ( c_Com_Obody @ SV7 )
!= ( c_Option_Ooption_OSome @ SV27 @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(144,plain,
! [SV8: $i] :
( ( ( c_Com_Ocom_OBODY @ SV8 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(145,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)],[121]) ).
thf(146,plain,
! [SV28: $i,SV9: $i] :
( ( ! [SY70: $i] :
( ( c_Com_Ocom_OBODY @ SV9 )
!= ( c_Com_Ocom_OSemi @ SV28 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(147,plain,
! [SV29: $i,SV10: $i] :
( ( ( ( c_Com_Ocom_OBODY @ SV10 )
!= ( c_Com_Ocom_OBODY @ SV29 ) )
| ( SV10 = SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(148,plain,
! [SV30: $i,SV11: $i] :
( ( ! [SY71: $i] :
( ( c_Com_Ocom_OSemi @ SV11 @ SV30 )
!= ( c_Com_Ocom_OBODY @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(149,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)],[125]) ).
thf(150,plain,
! [SV31: $i,SV12: $i] :
( ( ( c_Option_Ooption_ONone @ SV12 )
!= ( c_Option_Ooption_OSome @ SV31 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(151,plain,
! [SV32: $i,SV13: $i] :
( ( ( c_Option_Ooption_ONone @ SV13 )
!= ( c_Option_Ooption_OSome @ SV32 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(152,plain,
! [SV14: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OBODY @ SV14 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(153,plain,
! [SV33: $i,SV15: $i] :
( ( ( c_Option_Ooption_OSome @ SV15 @ SV33 )
!= ( c_Option_Ooption_ONone @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(154,plain,
! [SV34: $i,SV16: $i] :
( ( ( c_Com_Ocom_OSemi @ SV16 @ SV34 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(155,plain,
! [SV35: $i,SV17: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ( ( c_Com_Ocom_OSemi @ SV17 @ SV35 )
!= ( c_Com_Ocom_OSemi @ SY72 @ SY73 ) )
| ( SV35 = SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(156,plain,
! [SV36: $i,SV18: $i] :
( ( ( c_Option_Ooption_OSome @ SV18 @ SV36 )
!= ( c_Option_Ooption_ONone @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(157,plain,
! [SV37: $i,SV19: $i] :
( ( ! [SY74: $i,SY75: $i] :
( ( ( c_Com_Ocom_OSemi @ SV19 @ SV37 )
!= ( c_Com_Ocom_OSemi @ SY74 @ SY75 ) )
| ( SV19 = SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(158,plain,
! [SV20: $i] :
( ( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ SV20 )
!= SV20 )
= $true )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(159,plain,
! [SV38: $i,SV21: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SV21 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(160,plain,
! [SV39: $i,SV22: $i] :
( ( ! [SY76: $i] :
( ( ( c_Option_Ooption_OSome @ SV22 @ SV39 )
!= ( c_Option_Ooption_OSome @ SY76 @ SV39 ) )
| ( SV22 = SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(161,plain,
! [SV2: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ SV2 ) )
= $false )
| ( ( ( c_Com_Obody @ SV2 )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ SV2 ) @ tc_Com_Ocom ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(162,plain,
! [SV23: $i,SV3: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV3 @ SV23 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ SV23 )
| ~ ( c_Com_OWT @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(163,plain,
! [SV24: $i,SV4: $i] :
( ( ( c_Com_OWT @ SV4 )
= $true )
| ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV4 @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(164,plain,
! [SV25: $i,SV5: $i] :
( ( ( c_Com_OWT @ SV5 )
= $true )
| ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV25 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(165,plain,
! [SV26: $i,SV6: $i] :
( ( c_Hoare__Mirabelle_Ostate__not__singleton = $true )
| ( ( SV6 = SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(166,plain,
! [SV27: $i,SV7: $i] :
( ( ( ( c_Com_Obody @ SV7 )
!= ( c_Option_Ooption_OSome @ SV27 @ tc_Com_Ocom ) )
= $true )
| ( ( ~ c_Com_OWT__bodies
| ( c_Com_OWT @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(167,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)],[145]) ).
thf(168,plain,
! [SV40: $i,SV28: $i,SV9: $i] :
( ( ( c_Com_Ocom_OBODY @ SV9 )
!= ( c_Com_Ocom_OSemi @ SV28 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(169,plain,
! [SV29: $i,SV10: $i] :
( ( ( ( c_Com_Ocom_OBODY @ SV10 )
!= ( c_Com_Ocom_OBODY @ SV29 ) )
= $true )
| ( ( SV10 = SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(170,plain,
! [SV41: $i,SV30: $i,SV11: $i] :
( ( ( c_Com_Ocom_OSemi @ SV11 @ SV30 )
!= ( c_Com_Ocom_OBODY @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(171,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)],[149]) ).
thf(172,plain,
! [SV31: $i,SV12: $i] :
( ( ( c_Option_Ooption_ONone @ SV12 )
= ( c_Option_Ooption_OSome @ SV31 @ SV12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(173,plain,
! [SV32: $i,SV13: $i] :
( ( ( c_Option_Ooption_ONone @ SV13 )
= ( c_Option_Ooption_OSome @ SV32 @ SV13 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(174,plain,
! [SV33: $i,SV15: $i] :
( ( ( c_Option_Ooption_OSome @ SV15 @ SV33 )
= ( c_Option_Ooption_ONone @ SV33 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(175,plain,
! [SV34: $i,SV16: $i] :
( ( ( c_Com_Ocom_OSemi @ SV16 @ SV34 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(176,plain,
! [SV42: $i,SV35: $i,SV17: $i] :
( ( ! [SY77: $i] :
( ( ( c_Com_Ocom_OSemi @ SV17 @ SV35 )
!= ( c_Com_Ocom_OSemi @ SV42 @ SY77 ) )
| ( SV35 = SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(177,plain,
! [SV36: $i,SV18: $i] :
( ( ( c_Option_Ooption_OSome @ SV18 @ SV36 )
= ( c_Option_Ooption_ONone @ SV36 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(178,plain,
! [SV43: $i,SV37: $i,SV19: $i] :
( ( ! [SY78: $i] :
( ( ( c_Com_Ocom_OSemi @ SV19 @ SV37 )
!= ( c_Com_Ocom_OSemi @ SV43 @ SY78 ) )
| ( SV19 = SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(179,plain,
! [SV20: $i] :
( ( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ SV20 )
= SV20 )
= $false )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(180,plain,
! [SV38: $i,SV21: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OSemi @ SV21 @ SV38 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(181,plain,
! [SV44: $i,SV39: $i,SV22: $i] :
( ( ( ( c_Option_Ooption_OSome @ SV22 @ SV39 )
!= ( c_Option_Ooption_OSome @ SV44 @ SV39 ) )
| ( SV22 = SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(182,plain,
! [SV3: $i,SV23: $i] :
( ( ( ~ ( c_Com_OWT @ SV23 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ SV3 ) )
= $true )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV3 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(183,plain,
! [SV24: $i,SV4: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV4 @ SV24 ) )
= $false )
| ( ( c_Com_OWT @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(184,plain,
! [SV5: $i,SV25: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV25 @ SV5 ) )
= $false )
| ( ( c_Com_OWT @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(185,plain,
! [SV27: $i,SV7: $i] :
( ( ( ( c_Com_Obody @ SV7 )
= ( c_Option_Ooption_OSome @ SV27 @ tc_Com_Ocom ) )
= $false )
| ( ( ~ c_Com_OWT__bodies
| ( c_Com_OWT @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(186,plain,
! [SV40: $i,SV28: $i,SV9: $i] :
( ( ( c_Com_Ocom_OBODY @ SV9 )
= ( c_Com_Ocom_OSemi @ SV28 @ SV40 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(187,plain,
! [SV29: $i,SV10: $i] :
( ( ( ( c_Com_Ocom_OBODY @ SV10 )
= ( c_Com_Ocom_OBODY @ SV29 ) )
= $false )
| ( ( SV10 = SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(188,plain,
! [SV41: $i,SV30: $i,SV11: $i] :
( ( ( c_Com_Ocom_OSemi @ SV11 @ SV30 )
= ( c_Com_Ocom_OBODY @ SV41 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(189,plain,
! [SV45: $i,SV42: $i,SV35: $i,SV17: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV17 @ SV35 )
!= ( c_Com_Ocom_OSemi @ SV42 @ SV45 ) )
| ( SV35 = SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(190,plain,
! [SV46: $i,SV43: $i,SV37: $i,SV19: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV19 @ SV37 )
!= ( c_Com_Ocom_OSemi @ SV43 @ SV46 ) )
| ( SV19 = SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(191,plain,
! [SV20: $i] :
( ( c_Hoare__Mirabelle_Ostate__not__singleton = $false )
| ( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ SV20 )
= SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(192,plain,
! [SV44: $i,SV39: $i,SV22: $i] :
( ( ( ( c_Option_Ooption_OSome @ SV22 @ SV39 )
!= ( c_Option_Ooption_OSome @ SV44 @ SV39 ) )
= $true )
| ( ( SV22 = SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(193,plain,
! [SV3: $i,SV23: $i] :
( ( ( c_Com_OWT @ SV23 )
= $false )
| ( ( ~ ( c_Com_OWT @ SV3 ) )
= $true )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV3 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(194,plain,
! [SV7: $i,SV27: $i] :
( ( ( ~ c_Com_OWT__bodies ) = $true )
| ( ( c_Com_OWT @ SV27 )
= $true )
| ( ( ( c_Com_Obody @ SV7 )
= ( c_Option_Ooption_OSome @ SV27 @ tc_Com_Ocom ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(195,plain,
! [SV45: $i,SV42: $i,SV35: $i,SV17: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV17 @ SV35 )
!= ( c_Com_Ocom_OSemi @ SV42 @ SV45 ) )
= $true )
| ( ( SV35 = SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(196,plain,
! [SV46: $i,SV43: $i,SV37: $i,SV19: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV19 @ SV37 )
!= ( c_Com_Ocom_OSemi @ SV43 @ SV46 ) )
= $true )
| ( ( SV19 = SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(197,plain,
! [SV44: $i,SV39: $i,SV22: $i] :
( ( ( ( c_Option_Ooption_OSome @ SV22 @ SV39 )
= ( c_Option_Ooption_OSome @ SV44 @ SV39 ) )
= $false )
| ( ( SV22 = SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(198,plain,
! [SV23: $i,SV3: $i] :
( ( ( c_Com_OWT @ SV3 )
= $false )
| ( ( c_Com_OWT @ SV23 )
= $false )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV3 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(199,plain,
! [SV7: $i,SV27: $i] :
( ( c_Com_OWT__bodies = $false )
| ( ( c_Com_OWT @ SV27 )
= $true )
| ( ( ( c_Com_Obody @ SV7 )
= ( c_Option_Ooption_OSome @ SV27 @ tc_Com_Ocom ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(200,plain,
! [SV45: $i,SV42: $i,SV35: $i,SV17: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV17 @ SV35 )
= ( c_Com_Ocom_OSemi @ SV42 @ SV45 ) )
= $false )
| ( ( SV35 = SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(201,plain,
! [SV46: $i,SV43: $i,SV37: $i,SV19: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV19 @ SV37 )
= ( c_Com_Ocom_OSemi @ SV43 @ SV46 ) )
= $false )
| ( ( SV19 = SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(202,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[63,201,200,199,198,197,191,188,187,186,184,183,180,177,175,174,173,172,171,167,165,161,152,144,137,118,111,90,65,64]) ).
thf(203,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV904-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n013.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 16:46:21 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.58/0.30
% 0.58/0.30 No.of.Axioms: 29
% 0.58/0.30
% 0.58/0.30 Length.of.Defs: 0
% 0.58/0.30
% 0.58/0.30 Contains.Choice.Funs: false
% 0.58/0.30 ....
% 0.58/0.30
% 0.58/0.30 ********************************
% 0.58/0.30 * All subproblems solved! *
% 0.58/0.30 ********************************
% 0.58/0.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:29,ps:0,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:202,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.58/0.30
% 0.58/0.30 %**** Beginning of derivation protocol ****
% 0.58/0.30 % SZS output start CNFRefutation
% See solution above
% 0.58/0.30
% 0.58/0.30 %**** End of derivation protocol ****
% 0.58/0.30 %**** no. of clauses in derivation: 203 ****
% 0.58/0.30 %**** clause counter: 202 ****
% 0.58/0.30
% 0.58/0.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:29,ps:0,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:202,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------