%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV888-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n003.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 : Sun Sep 27 09:00:55 AM UTC 2026
% Result : Unsatisfiable 5.06s 2.72s
% Output : Refutation 5.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 55
% Syntax : Number of formulae : 111 ( 41 unt; 0 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 : 0 ( 0 >; 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_decl,type,
c_Natural_Oevalc: $i > $i > $i > $o ).
thf(c_Option_Othe_decl,type,
c_Option_Othe: $i > $i > $i ).
thf(c_Com_Obody_decl,type,
c_Com_Obody: $i > $i ).
thf(v_pn_decl,type,
v_pn: $i ).
thf(tc_Com_Ocom_decl,type,
tc_Com_Ocom: $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(v_xa_decl,type,
v_xa: $i ).
thf(c_Com_Ocom_OBODY_decl,type,
c_Com_Ocom_OBODY: $i > $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(c_Option_Ooption_OSome_decl,type,
c_Option_Ooption_OSome: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Option__Xoption__Xexhaust__1__1_decl,type,
c_ATP__Linkup_Osko__Option__Xoption__Xexhaust__1__1: $i > $i > $i ).
thf(c_Option_Ooption_ONone_decl,type,
c_Option_Ooption_ONone: $i > $i ).
thf(c_Natural_Oevaln_decl,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(c_Natural_Osko__Natural__Xevaln__elim__cases__4__1_decl,type,
c_Natural_Osko__Natural__Xevaln__elim__cases__4__1: $i > $i > $i > $i > $i > $i ).
thf(c_Com_Ocom_OSemi_decl,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Option__Xnot__Some__eq__1__1_decl,type,
c_ATP__Linkup_Osko__Option__Xnot__Some__eq__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Option__Xoption__Xnchotomy__1__1_decl,type,
c_ATP__Linkup_Osko__Option__Xoption__Xnchotomy__1__1: $i > $i > $i ).
thf(c_Com_OWT_decl,type,
c_Com_OWT: $i > $o ).
thf(c_ATP__Linkup_Osko__Option__Xnot__None__eq__1__1_decl,type,
c_ATP__Linkup_Osko__Option__Xnot__None__eq__1__1: $i > $i > $i ).
thf(c_Com_Ocom_OSKIP_decl,type,
c_Com_Ocom_OSKIP: $i ).
thf(c_Fun_Oid_decl,type,
c_Fun_Oid: $i > $i > $i ).
thf(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1_decl,type,
c_Natural_Osko__Natural__Xevaln__elim__cases__6__1: $i > $i > $i > $i > $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_Natural_Osko__Natural__Xevalc__elim__cases__4__1_decl,type,
c_Natural_Osko__Natural__Xevalc__elim__cases__4__1: $i > $i > $i > $i > $i ).
thf(c_Com_OWT__bodies_decl,type,
c_Com_OWT__bodies: $o ).
thf(c_Com_Osko__Com__XWTs__elim__cases__7__1_decl,type,
c_Com_Osko__Com__XWTs__elim__cases__7__1: $i > $i ).
thf(c_Natural_Osko__Natural__Xeval__eq__1__1_decl,type,
c_Natural_Osko__Natural__Xeval__eq__1__1: $i > $i > $i > $i ).
thf(c_Natural_Osko__Natural__Xevalc__evaln__1__1_decl,type,
c_Natural_Osko__Natural__Xevalc__evaln__1__1: $i > $i > $i > $i ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__evalc_0) ).
thf(174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) )
| ( C @ ( C @ ( B @ ( A @ c_Natural_Osko__Natural__Xevalc__evaln__1__1 ) ) @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__evaln_0) ).
thf(192,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) )
| ( C @ ( C @ ( B @ ( A @ c_Natural_Osko__Natural__Xevalc__evaln__1__1 ) ) @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_Option_Ooption_ONone ) )
| ( A
= ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Option__Xnot__None__eq__1__1 ) @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__None__eq_0) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_Option_Ooption_ONone ) )
| ( A
= ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Option__Xnot__None__eq__1__1 ) @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(31,axiom,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).
thf(141,plain,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Fun_Oid ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Fun_Oid ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
thf(128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ ( C @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Oinject_0) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ ( C @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(72,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
thf(75,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( A @ c_Com_OWT )
| ~ ( B @ c_Com_OWT )
| ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OSemi_0) ).
thf(90,plain,
! [B: $i,A: $i] :
( ~ ( A @ c_Com_OWT )
| ~ ( B @ c_Com_OWT )
| ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Option__Xnot__Some__eq__1__1 ) @ c_Option_Ooption_OSome ) ) )
| ( A
= ( B @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Some__eq_0) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Option__Xnot__Some__eq__1__1 ) @ c_Option_Ooption_OSome ) ) )
| ( A
= ( B @ c_Option_Ooption_ONone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ c_Option_Ooption_ONone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ c_Option_Ooption_ONone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(23,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( A @ c_Natural_Oevaln ) ) ) )
| ~ ( E @ ( D @ ( F @ ( B @ c_Natural_Oevaln ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OSemi_0) ).
thf(115,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( A @ c_Natural_Oevaln ) ) ) )
| ~ ( E @ ( D @ ( F @ ( B @ c_Natural_Oevaln ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( A @ ( B @ c_Option_Ooption_OSome ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( A @ ( B @ c_Option_Ooption_OSome ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1,negated_conjecture,
v_xa @ ( v_x @ ( tc_Com_Ocom @ ( v_pn @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevalc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(56,plain,
v_xa @ ( v_x @ ( tc_Com_Ocom @ ( v_pn @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevalc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ c_Suc @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OBody_0) ).
thf(142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ c_Suc @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(48,axiom,
! [A: $i] :
( ( ( A @ c_Com_Obody )
= ( tc_Com_Ocom @ c_Option_Ooption_ONone ) )
| ( A @ c_Com_Ocom_OBODY @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OBody_0) ).
thf(184,plain,
! [A: $i] :
( ( ( A @ c_Com_Obody )
= ( tc_Com_Ocom @ c_Option_Ooption_ONone ) )
| ( A @ c_Com_Ocom_OBODY @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_Natural_Oevalc ) ) )
| ~ ( A @ ( D @ ( C @ c_Natural_Oevalc ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com__det_0) ).
thf(196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_Natural_Oevalc ) ) )
| ~ ( A @ ( D @ ( C @ c_Natural_Oevalc ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__eq_1) ).
thf(157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Com_Ocom_OBODY )
!= ( B @ c_Com_Ocom_OBODY ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
thf(152,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Com_Ocom_OBODY )
!= ( B @ c_Com_Ocom_OBODY ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(2,negated_conjecture,
~ ( v_xa @ ( v_x @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(57,plain,
~ ( v_xa @ ( v_x @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(40,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ c_Natural_Oevalc ) ) )
| ~ ( D @ ( E @ ( B @ c_Natural_Oevalc ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).
thf(164,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ c_Natural_Oevalc ) ) )
| ~ ( D @ ( E @ ( B @ c_Natural_Oevalc ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) )
| ( C @ ( C @ ( B @ ( A @ c_Natural_Osko__Natural__Xeval__eq__1__1 ) ) @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__eq_0) ).
thf(179,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Natural_Oevalc ) ) )
| ( C @ ( C @ ( B @ ( A @ c_Natural_Osko__Natural__Xeval__eq__1__1 ) ) @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ ( B @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
| ( A
= ( D @ ( C @ ( A @ ( B @ c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 ) ) ) @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_0) ).
thf(147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ ( B @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
| ( A
= ( D @ ( C @ ( A @ ( B @ c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 ) ) ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( A @ ( B @ c_Option_Ooption_OSome ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( A @ c_Option_Ooption_ONone )
!= ( A @ ( B @ c_Option_Ooption_OSome ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(24,axiom,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(117,plain,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ c_Suc @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__Suc_0) ).
thf(85,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) )
| ( D @ ( C @ c_Suc @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) )
| ( D @ ( B @ ( C @ ( A @ c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 ) ) ) @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I4_J_0) ).
thf(201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) )
| ( D @ ( B @ ( C @ ( A @ c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 ) ) ) @ ( B @ ( A @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
| ( D @ ( D @ ( B @ ( C @ ( A @ c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 ) ) ) @ ( B @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_1) ).
thf(166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
| ( D @ ( D @ ( B @ ( C @ ( A @ c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 ) ) ) @ ( B @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ( B @ c_Com_OWT )
| ~ c_Com_OWT__bodies
| ( ( A @ c_Com_Obody )
!= ( tc_Com_Ocom @ ( B @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT__bodiesD_0) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( B @ c_Com_OWT )
| ~ c_Com_OWT__bodies
| ( ( A @ c_Com_Obody )
!= ( tc_Com_Ocom @ ( B @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_Option_Ooption_ONone ) )
| ( A
= ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Option__Xoption__Xexhaust__1__1 ) @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Oexhaust_0) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_Option_Ooption_ONone ) )
| ( A
= ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Option__Xoption__Xexhaust__1__1 ) @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(45,axiom,
! [A: $i] :
( ~ ( A @ c_Com_Ocom_OBODY @ c_Com_OWT )
| ( ( A @ c_Com_Obody )
= ( tc_Com_Ocom @ ( A @ c_Com_Osko__Com__XWTs__elim__cases__7__1 @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I7_J_0) ).
thf(176,plain,
! [A: $i] :
( ~ ( A @ c_Com_Ocom_OBODY @ c_Com_OWT )
| ( ( A @ c_Com_Obody )
= ( tc_Com_Ocom @ ( A @ c_Com_Osko__Com__XWTs__elim__cases__7__1 @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).
thf(144,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(47,axiom,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
thf(181,plain,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) )
| ( D @ ( D @ ( C @ ( A @ ( B @ c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 ) ) ) @ ( A @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I4_J_1) ).
thf(159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) )
| ( D @ ( D @ ( C @ ( A @ ( B @ c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 ) ) ) @ ( A @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).
thf(187,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Com_Ocom_OSemi ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_1) ).
thf(113,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Com_Ocom_OSemi ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(16,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OSkip_0) ).
thf(98,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(123,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) )
| ( C @ ( B @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I6_J_0) ).
thf(194,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) )
| ( C @ ( B @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(35,axiom,
( ( t_a @ ( v_x @ c_Fun_Oid ) )
= v_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__def_0) ).
thf(150,plain,
( ( t_a @ ( v_x @ c_Fun_Oid ) )
= v_x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(14,axiom,
c_Com_Ocom_OSKIP @ c_Com_OWT,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OSkip_0) ).
thf(95,plain,
c_Com_Ocom_OSKIP @ c_Com_OWT,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( D @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) )
| ( E @ ( B @ ( C @ ( D @ ( A @ c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 ) ) ) ) @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I4_J_0) ).
thf(67,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( B @ ( D @ ( A @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) )
| ( E @ ( B @ ( C @ ( D @ ( A @ c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 ) ) ) ) @ ( C @ ( B @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevalc ) ) )
| ( C @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OBody_0) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_Com_Ocom @ ( A @ c_Com_Obody @ c_Option_Othe ) @ c_Natural_Oevalc ) ) )
| ( C @ ( B @ ( A @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(17,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( D @ ( A @ ( B @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) )
| ( E @ ( C @ ( E @ ( D @ ( C @ ( A @ ( B @ c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 ) ) ) ) @ ( A @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I4_J_1) ).
thf(99,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( D @ ( A @ ( B @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) )
| ( E @ ( C @ ( E @ ( D @ ( C @ ( A @ ( B @ c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 ) ) ) ) @ ( A @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ c_Option_Ooption_ONone ) )
| ( A
= ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Option__Xoption__Xnchotomy__1__1 ) @ c_Option_Ooption_OSome ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Onchotomy_0) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ c_Option_Ooption_ONone ) )
| ( A
= ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Option__Xoption__Xnchotomy__1__1 ) @ c_Option_Ooption_OSome ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).
thf(171,plain,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_0) ).
thf(139,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Com_Ocom_OSemi ) @ c_Com_OWT )
| ( A @ c_Com_OWT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
thf(168,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Option_Ooption_OSome ) @ c_Option_Othe ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the_Osimps_0) ).
thf(190,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Option_Ooption_OSome ) @ c_Option_Othe ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
thf(107,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ c_Option_Ooption_ONone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__None__eq_1) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Option_Ooption_OSome ) )
!= ( B @ c_Option_Ooption_ONone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(203,plain,
$false,
inference(e,[status(thm)],[174,192,92,141,96,128,80,72,75,90,69,101,115,120,56,142,184,110,196,157,152,57,164,179,147,133,117,85,201,166,161,64,176,59,144,181,159,187,113,98,123,194,150,95,67,199,99,87,104,171,139,168,190,107,136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV888-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.16/0.41 % Computer : n003.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 15:09:25 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.20 % [INFO] Parsing done (209ms).
% 1.49/1.21 % [INFO] Running in sequential loop mode.
% 2.32/1.60 % [INFO] eprover registered as external prover.
% 2.32/1.61 % [INFO] Scanning for conjecture ...
% 2.53/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 53 axioms. Running axiom selection ...
% 2.71/1.80 % [INFO] Axiom selection finished. Selected 53 axioms (removed 0 axioms).
% 2.71/1.86 % [INFO] Problem is propositional (TPTP CNF).
% 2.71/1.87 % [INFO] Type checking passed.
% 2.71/1.88 % [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 ...
% 5.06/2.72 % External prover 'e' found a proof!
% 5.06/2.72 % [INFO] Killing All external provers ...
% 5.06/2.72 % Time passed: 2164ms (effective reasoning time: 1502ms)
% 5.06/2.72 % 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
% 5.06/2.72 % No. of inferences in proof: 111
% 5.06/2.72 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2164 ms resp. 1502 ms w/o parsing
% 5.33/2.82 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.33/2.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------