TSTP Solution File: SWV888-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV888-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:19:09 EDT 2023
% Result : Unsatisfiable 3.94s 1.92s
% Output : Refutation 4.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 83
% Syntax : Number of formulae : 139 ( 41 unt; 28 typ; 0 def)
% Number of atoms : 191 ( 84 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 798 ( 96 ~; 80 |; 0 &; 622 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 8 con; 0-5 aty)
% Number of variables : 276 ( 0 ^; 276 !; 0 ?; 276 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Natural_Oevalc_type,type,
c_Natural_Oevalc: $i > $i > $i > $o ).
thf(c_Option_Othe_type,type,
c_Option_Othe: $i > $i > $i ).
thf(c_Com_Obody_type,type,
c_Com_Obody: $i > $i ).
thf(v_pn_type,type,
v_pn: $i ).
thf(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
thf(v_x_type,type,
v_x: $i ).
thf(v_xa_type,type,
v_xa: $i ).
thf(c_Com_Ocom_OBODY_type,type,
c_Com_Ocom_OBODY: $i > $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(c_Option_Ooption_OSome_type,type,
c_Option_Ooption_OSome: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Option__Xoption__Xexhaust__1__1_type,type,
c_ATP__Linkup_Osko__Option__Xoption__Xexhaust__1__1: $i > $i > $i ).
thf(c_Option_Ooption_ONone_type,type,
c_Option_Ooption_ONone: $i > $i ).
thf(c_Natural_Oevaln_type,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(c_Natural_Osko__Natural__Xevaln__elim__cases__4__1_type,type,
c_Natural_Osko__Natural__Xevaln__elim__cases__4__1: $i > $i > $i > $i > $i > $i ).
thf(c_Com_Ocom_OSemi_type,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Option__Xnot__Some__eq__1__1_type,type,
c_ATP__Linkup_Osko__Option__Xnot__Some__eq__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Option__Xoption__Xnchotomy__1__1_type,type,
c_ATP__Linkup_Osko__Option__Xoption__Xnchotomy__1__1: $i > $i > $i ).
thf(c_Com_OWT_type,type,
c_Com_OWT: $i > $o ).
thf(c_ATP__Linkup_Osko__Option__Xnot__None__eq__1__1_type,type,
c_ATP__Linkup_Osko__Option__Xnot__None__eq__1__1: $i > $i > $i ).
thf(c_Com_Ocom_OSKIP_type,type,
c_Com_Ocom_OSKIP: $i ).
thf(c_Fun_Oid_type,type,
c_Fun_Oid: $i > $i > $i ).
thf(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1_type,type,
c_Natural_Osko__Natural__Xevaln__elim__cases__6__1: $i > $i > $i > $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(c_Natural_Osko__Natural__Xevalc__elim__cases__4__1_type,type,
c_Natural_Osko__Natural__Xevalc__elim__cases__4__1: $i > $i > $i > $i > $i ).
thf(c_Com_OWT__bodies_type,type,
c_Com_OWT__bodies: $o ).
thf(c_Com_Osko__Com__XWTs__elim__cases__7__1_type,type,
c_Com_Osko__Com__XWTs__elim__cases__7__1: $i > $i ).
thf(c_Natural_Osko__Natural__Xeval__eq__1__1_type,type,
c_Natural_Osko__Natural__Xeval__eq__1__1: $i > $i > $i > $i ).
thf(c_Natural_Osko__Natural__Xevalc__evaln__1__1_type,type,
c_Natural_Osko__Natural__Xevalc__evaln__1__1: $i > $i > $i > $i ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xoption__Xnchotomy__1__1 @ A @ B ) @ B ) )
| ( A
= ( c_Option_Ooption_ONone @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Onchotomy_0) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xoption__Xnchotomy__1__1 @ A @ B ) @ B ) )
| ( A
= ( c_Option_Ooption_ONone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( c_Option_Ooption_ONone @ A )
!= ( c_Option_Ooption_OSome @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( c_Option_Ooption_ONone @ A )
!= ( c_Option_Ooption_OSome @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(14,axiom,
c_Com_OWT @ c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OSkip_0) ).
thf(92,plain,
c_Com_OWT @ c_Com_Ocom_OSKIP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ A ) @ tc_Com_Ocom ) @ B @ C )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ A ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I6_J_0) ).
thf(188,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ A ) @ tc_Com_Ocom ) @ B @ C )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ A ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ A @ B @ C ) @ C )
| ~ ( c_Natural_Oevalc @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__eq_0) ).
thf(173,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ A @ B @ C ) @ C )
| ~ ( c_Natural_Oevalc @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( c_Option_Ooption_OSome @ A @ B )
!= ( c_Option_Ooption_ONone @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( c_Option_Ooption_OSome @ A @ B )
!= ( c_Option_Ooption_ONone @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(47,axiom,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
thf(175,plain,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ ( c_Suc @ C ) @ D )
| ~ ( c_Natural_Oevaln @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__Suc_0) ).
thf(82,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ ( c_Suc @ C ) @ D )
| ~ ( c_Natural_Oevaln @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(45,axiom,
! [A: $i] :
( ( ( c_Com_Obody @ A )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ A ) @ tc_Com_Ocom ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I7_J_0) ).
thf(170,plain,
! [A: $i] :
( ( ( c_Com_Obody @ A )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ A ) @ tc_Com_Ocom ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1,negated_conjecture,
c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ v_pn ) @ tc_Com_Ocom ) @ v_x @ v_xa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(56,plain,
c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ v_pn ) @ tc_Com_Ocom ) @ v_x @ v_xa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ B @ A @ C @ D ) ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ B ) @ C @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_0) ).
thf(142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ B @ A @ C @ D ) ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ B ) @ C @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ A @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ B @ A @ C @ D ) @ D )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ B @ A ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I4_J_1) ).
thf(153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ A @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ B @ A @ C @ D ) @ D )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ B @ A ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( c_Option_Othe @ ( c_Option_Ooption_OSome @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the_Osimps_0) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( c_Option_Othe @ ( c_Option_Ooption_OSome @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_1) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( c_Fun_Oid @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( c_Fun_Oid @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(2,negated_conjecture,
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ v_pn ) @ v_x @ v_xa ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(57,plain,
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ v_pn ) @ v_x @ v_xa ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Option_Ooption_OSome @ A @ B )
!= ( c_Option_Ooption_OSome @ C @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Oinject_0) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Option_Ooption_OSome @ A @ B )
!= ( c_Option_Ooption_OSome @ C @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OBODY @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OBODY @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xnot__None__eq__1__1 @ A @ B ) @ B ) )
| ( A
= ( c_Option_Ooption_ONone @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__None__eq_0) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xnot__None__eq__1__1 @ A @ B ) @ B ) )
| ( A
= ( c_Option_Ooption_ONone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
thf(74,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ A ) @ tc_Com_Ocom ) @ B @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ A @ C @ B @ D ) @ D )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ A ) @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_1) ).
thf(160,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ A ) @ tc_Com_Ocom ) @ B @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ A @ C @ B @ D ) @ D )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ A ) @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ A ) @ B @ ( c_Suc @ C ) @ D )
| ~ ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ A ) @ tc_Com_Ocom ) @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OBody_0) ).
thf(137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ A ) @ B @ ( c_Suc @ C ) @ D )
| ~ ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ A ) @ tc_Com_Ocom ) @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(43,axiom,
! [A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).
thf(165,plain,
! [A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
thf(124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ A ) @ B @ C )
| ~ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ A ) @ tc_Com_Ocom ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OBody_0) ).
thf(193,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ A ) @ B @ C )
| ~ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ A ) @ tc_Com_Ocom ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(17,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ B @ A @ C @ D @ E ) @ C @ E )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ B @ A ) @ D @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I4_J_1) ).
thf(96,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ B @ A @ C @ D @ E ) @ C @ E )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ B @ A ) @ D @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_0) ).
thf(134,plain,
! [B: $i,A: $i] :
( ( c_Com_OWT @ A )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( c_Option_Ooption_ONone @ A )
!= ( c_Option_Ooption_OSome @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( c_Option_Ooption_ONone @ A )
!= ( c_Option_Ooption_OSome @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(7,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(71,plain,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OSemi @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).
thf(181,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= ( c_Com_Ocom_OSemi @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(5,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ C @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ A @ D @ C @ B @ E ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ A @ D ) @ B @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I4_J_0) ).
thf(66,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ C @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ A @ D @ C @ B @ E ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ A @ D ) @ B @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ( ( c_Com_Obody @ A )
!= ( c_Option_Ooption_OSome @ B @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__bodiesD_0) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( ( c_Com_Obody @ A )
!= ( c_Option_Ooption_OSome @ B @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OBODY @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OBODY @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(23,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ A @ B ) @ C @ D @ E )
| ~ ( c_Natural_Oevaln @ B @ F @ D @ E )
| ~ ( c_Natural_Oevaln @ A @ C @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OSemi_0) ).
thf(112,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ A @ B ) @ C @ D @ E )
| ~ ( c_Natural_Oevaln @ B @ F @ D @ E )
| ~ ( c_Natural_Oevaln @ A @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(35,axiom,
( ( c_Fun_Oid @ v_x @ t_a )
= v_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__def_0) ).
thf(145,plain,
( ( c_Fun_Oid @ v_x @ t_a )
= v_x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xoption__Xexhaust__1__1 @ A @ B ) @ B ) )
| ( A
= ( c_Option_Ooption_ONone @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Oexhaust_0) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xoption__Xexhaust__1__1 @ A @ B ) @ B ) )
| ( A
= ( c_Option_Ooption_ONone @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
! [B: $i,A: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ A @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OSkip_0) ).
thf(95,plain,
! [B: $i,A: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ A @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ A @ B ) )
| ~ ( c_Com_OWT @ B )
| ~ ( c_Com_OWT @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OSemi_0) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ A @ B ) )
| ~ ( c_Com_OWT @ B )
| ~ ( c_Com_OWT @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
thf(104,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(40,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ A @ B ) @ C @ D )
| ~ ( c_Natural_Oevalc @ B @ E @ D )
| ~ ( c_Natural_Oevalc @ A @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).
thf(158,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ A @ B ) @ C @ D )
| ~ ( c_Natural_Oevalc @ B @ E @ D )
| ~ ( c_Natural_Oevalc @ A @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ A @ B @ C ) @ C )
| ~ ( c_Natural_Oevalc @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__evaln_0) ).
thf(186,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Natural_Oevaln @ A @ B @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ A @ B @ C ) @ C )
| ~ ( c_Natural_Oevalc @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(24,axiom,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(114,plain,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).
thf(139,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ A @ B @ C )
| ~ ( c_Natural_Oevaln @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__eq_1) ).
thf(151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ A @ B @ C )
| ~ ( c_Natural_Oevaln @ A @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ A @ B @ C )
| ~ ( c_Natural_Oevaln @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__evalc_0) ).
thf(168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ A @ B @ C )
| ~ ( c_Natural_Oevaln @ A @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Natural_Oevalc @ C @ D @ A )
| ~ ( c_Natural_Oevalc @ C @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com__det_0) ).
thf(190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Natural_Oevalc @ C @ D @ A )
| ~ ( c_Natural_Oevalc @ C @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(31,axiom,
! [A: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).
thf(136,plain,
! [A: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ A @ B @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ A @ C @ B @ D ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ A @ C ) @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I4_J_0) ).
thf(195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Natural_Oevalc @ A @ B @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ A @ C @ B @ D ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ A @ C ) @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( c_Option_Ooption_OSome @ A @ B )
!= ( c_Option_Ooption_ONone @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__None__eq_1) ).
thf(131,plain,
! [B: $i,A: $i] :
( ( c_Option_Ooption_OSome @ A @ B )
!= ( c_Option_Ooption_ONone @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Option_Ooption_ONone @ B ) )
| ( A
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xnot__Some__eq__1__1 @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Some__eq_0) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Option_Ooption_ONone @ B ) )
| ( A
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xnot__Some__eq__1__1 @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(48,axiom,
! [A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) )
| ( ( c_Com_Obody @ A )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OBody_0) ).
thf(178,plain,
! [A: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) )
| ( ( c_Com_Obody @ A )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(197,plain,
$false,
inference(e,[status(thm)],[101,84,117,92,188,173,59,98,175,82,170,120,56,142,153,184,110,93,57,78,147,89,74,160,137,165,124,193,96,134,128,71,181,66,155,162,112,145,63,95,87,104,158,186,114,139,151,168,190,107,136,195,131,68,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV888-1 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 02:20:52 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.99/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.39/1.04 % [INFO] Parsing done (143ms).
% 1.39/1.04 % [INFO] Running in sequential loop mode.
% 1.80/1.23 % [INFO] eprover registered as external prover.
% 1.80/1.23 % [INFO] cvc4 registered as external prover.
% 1.80/1.24 % [INFO] Scanning for conjecture ...
% 2.05/1.30 % [INFO] Found a conjecture and 53 axioms. Running axiom selection ...
% 2.05/1.35 % [INFO] Axiom selection finished. Selected 53 axioms (removed 0 axioms).
% 2.39/1.39 % [INFO] Problem is propositional (TPTP CNF).
% 2.39/1.39 % [INFO] Type checking passed.
% 2.39/1.40 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.55/1.87 % External prover 'e' found a proof!
% 3.55/1.87 % [INFO] Killing All external provers ...
% 3.55/1.87 % Time passed: 1347ms (effective reasoning time: 826ms)
% 3.55/1.87 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.94/1.91 % Axioms used in derivation (53): cls_Suc__n__not__n_0, cls_id__apply_0, cls_evalc_OBody_0, cls_option_Oexhaust_0, cls_not__Some__eq_1, cls_evaln__evalc_0, cls_evaln__elim__cases_I1_J_0, cls_evalc__elim__cases_I4_J_1, cls_evaln__elim__cases_I4_J_0, cls_not__None__eq_0, cls_option_Oinject_0, cls_com_Osimps_I18_J_0, cls_com_Osimps_I3_J_0, cls_Suc__inject_0, cls_WT_OSemi_0, cls_WTs__elim__cases_I4_J_1, cls_WT_OSkip_0, cls_evalc_OSemi_0, cls_WTs__elim__cases_I7_J_0, cls_option_Osimps_I2_J_0, cls_evaln_OSkip_0, cls_option_Onchotomy_0, cls_evalc__elim__cases_I1_J_0, cls_evalc__elim__cases_I6_J_0, cls_evalc__evaln_0, cls_not__Some__eq_0, cls_WTs__elim__cases_I4_J_0, cls_WT__bodiesD_0, cls_com_Osimps_I6_J_0, cls_not__None__eq_1, cls_com_Osimps_I48_J_0, cls_evalc_OSkip_0, cls_evalc__elim__cases_I4_J_0, cls_evaln_OBody_0, cls_the_Osimps_0, cls_evaln__elim__cases_I6_J_0, cls_evaln_OSemi_0, cls_com__det_0, cls_com_Osimps_I19_J_0, cls_com_Osimps_I3_J_1, cls_eval__eq_0, cls_WT_OBody_0, cls_eval__eq_1, cls_id__def_0, cls_com_Osimps_I13_J_0, cls_evaln__elim__cases_I4_J_1, cls_nat_Oinject_0, cls_com_Osimps_I49_J_0, cls_evaln__Suc_0, cls_com_Osimps_I12_J_0, cls_evaln__elim__cases_I6_J_1, cls_n__not__Suc__n_0, cls_option_Osimps_I3_J_0
% 3.94/1.91 % No. of inferences in proof: 111
% 3.94/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1347 ms resp. 826 ms w/o parsing
% 4.30/1.99 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.30/1.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------