%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV282-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 09:07:15 AM UTC 2026
% Result : Unsatisfiable 6.57s 1.30s
% Output : CNFRefutation 6.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 14
% Syntax : Number of formulae : 112 ( 57 unt; 0 def)
% Number of atoms : 211 ( 129 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 142 ( 43 ~; 99 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 140 ( 24 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(c_Message_Omsg_ONonce(VAR_0),c_Event_Oused(v_evs),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(VAR_2),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(VAR_1),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| VAR_0 = VAR_2
| VAR_2 = VAR_1
| VAR_0 = VAR_1 ),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
( c_in(c_Message_Omsg_ONonce(A),c_Event_Oused(v_evs),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(C),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(B),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| A = C
| C = B
| A = B ),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_Binomial_Obinomial__1_0,axiom,
! [VAR_0] : c_Binomial_Obinomial(VAR_0,c_Suc(c_0)) = VAR_0,
file('theBenchmark.p',cls_Binomial_Obinomial__1_0) ).
cnf(c_2,plain,
c_Binomial_Obinomial(A,c_Suc(c_0)) = A,
inference(clausify,[status(thm)],[cls_Binomial_Obinomial__1_0]) ).
fof(cls_Binomial_Obinomial__Suc__Suc_0,axiom,
! [VAR_0,VAR_1] : c_Binomial_Obinomial(c_Suc(VAR_0),c_Suc(VAR_1)) = c_plus(c_Binomial_Obinomial(VAR_0,VAR_1),c_Binomial_Obinomial(VAR_0,c_Suc(VAR_1)),tc_nat),
file('theBenchmark.p',cls_Binomial_Obinomial__Suc__Suc_0) ).
cnf(c_3,plain,
c_Binomial_Obinomial(c_Suc(A),c_Suc(B)) = c_plus(c_Binomial_Obinomial(A,B),c_Binomial_Obinomial(A,c_Suc(B)),tc_nat),
inference(clausify,[status(thm)],[cls_Binomial_Obinomial__Suc__Suc_0]) ).
cnf(c_4,plain,
c_plus(c_Binomial_Obinomial(A,B),c_Binomial_Obinomial(A,c_Suc(B)),tc_nat) = c_Binomial_Obinomial(c_Suc(A),c_Suc(B)),
inference(copy,[status(thm)],[c_3]) ).
fof(cls_Binomial_Obinomial__n__0_0,axiom,
! [VAR_0] : c_Binomial_Obinomial(VAR_0,c_0) = c_1,
file('theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).
cnf(c_5,plain,
c_Binomial_Obinomial(A,c_0) = c_1,
inference(clausify,[status(thm)],[cls_Binomial_Obinomial__n__0_0]) ).
fof(cls_Nat_OOne__nat__def_0,axiom,
c_1 = c_Suc(c_0),
file('theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
cnf(c_6,plain,
c_1 = c_Suc(c_0),
inference(clausify,[status(thm)],[cls_Nat_OOne__nat__def_0]) ).
cnf(c_7,plain,
c_Suc(c_0) = c_1,
inference(copy,[status(thm)],[c_6]) ).
fof(cls_Nat_Odiff__is__0__eq_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(VAR_0,VAR_1,tc_nat)
| c_minus(VAR_0,VAR_1,tc_nat) != c_0 ),
file('theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
cnf(c_8,plain,
( c_lessequals(A,B,tc_nat)
| c_minus(A,B,tc_nat) != c_0 ),
inference(clausify,[status(thm)],[cls_Nat_Odiff__is__0__eq_0]) ).
fof(cls_Nat_Odiff__self__eq__0_0,axiom,
! [VAR_0] : c_minus(VAR_0,VAR_0,tc_nat) = c_0,
file('theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
cnf(c_9,plain,
c_minus(A,A,tc_nat) = c_0,
inference(clausify,[status(thm)],[cls_Nat_Odiff__self__eq__0_0]) ).
fof(cls_Nat_Ole__add1_0,axiom,
! [VAR_0,VAR_1] : c_lessequals(VAR_0,c_plus(VAR_0,VAR_1,tc_nat),tc_nat),
file('theBenchmark.p',cls_Nat_Ole__add1_0) ).
cnf(c_10,plain,
c_lessequals(A,c_plus(A,B,tc_nat),tc_nat),
inference(clausify,[status(thm)],[cls_Nat_Ole__add1_0]) ).
fof(cls_Nat_OlessI_0,axiom,
! [VAR_0] : c_less(VAR_0,c_Suc(VAR_0),tc_nat),
file('theBenchmark.p',cls_Nat_OlessI_0) ).
cnf(c_11,plain,
c_less(A,c_Suc(A),tc_nat),
inference(clausify,[status(thm)],[cls_Nat_OlessI_0]) ).
fof(cls_Nat_Oless__Suc__eq__le_1,axiom,
! [VAR_0,VAR_1] :
( c_less(VAR_0,c_Suc(VAR_1),tc_nat)
| ~ c_lessequals(VAR_0,VAR_1,tc_nat) ),
file('theBenchmark.p',cls_Nat_Oless__Suc__eq__le_1) ).
cnf(c_12,plain,
( c_less(A,c_Suc(B),tc_nat)
| ~ c_lessequals(A,B,tc_nat) ),
inference(clausify,[status(thm)],[cls_Nat_Oless__Suc__eq__le_1]) ).
fof(cls_Nat_Onat__add__left__cancel__le_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_1,VAR_2,tc_nat)
| ~ c_lessequals(c_plus(VAR_0,VAR_1,tc_nat),c_plus(VAR_0,VAR_2,tc_nat),tc_nat) ),
file('theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
cnf(c_13,plain,
( c_lessequals(B,C,tc_nat)
| ~ c_lessequals(c_plus(A,B,tc_nat),c_plus(A,C,tc_nat),tc_nat) ),
inference(clausify,[status(thm)],[cls_Nat_Onat__add__left__cancel__le_0]) ).
fof(cls_Nat_Onot__add__less2_0,axiom,
! [VAR_0,VAR_1] : ~ c_less(c_plus(VAR_0,VAR_1,tc_nat),VAR_1,tc_nat),
file('theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
cnf(c_14,plain,
~ c_less(c_plus(A,B,tc_nat),B,tc_nat),
inference(clausify,[status(thm)],[cls_Nat_Onot__add__less2_0]) ).
fof(cls_Public_ONonce__supply__lemma_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_lessequals(v_sko__urX(VAR_1),VAR_0,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(VAR_0),c_Event_Oused(VAR_1),tc_Message_Omsg) ),
file('theBenchmark.p',cls_Public_ONonce__supply__lemma_0) ).
cnf(c_15,plain,
( ~ c_lessequals(v_sko__urX(B),A,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(A),c_Event_Oused(B),tc_Message_Omsg) ),
inference(clausify,[status(thm)],[cls_Public_ONonce__supply__lemma_0]) ).
fof(cls_SetInterval_Ocard__atMost_0,axiom,
! [VAR_0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(VAR_0,tc_nat),tc_nat) = c_Suc(VAR_0),
file('theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
cnf(c_16,plain,
c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat) = c_Suc(A),
inference(clausify,[status(thm)],[cls_SetInterval_Ocard__atMost_0]) ).
cnf(c_17,plain,
c_Suc(A) = c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_18,plain,
c_Binomial_Obinomial(A,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)) = A,
inference(paramod,[status(thm)],[c_17,c_2]) ).
cnf(c_19,plain,
( c_less(A,c_Finite__Set_Ocard(c_SetInterval_OatMost(B,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(A,B,tc_nat) ),
inference(paramod,[status(thm)],[c_17,c_12]) ).
cnf(c_20,plain,
c_less(A,c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),tc_nat),
inference(paramod,[status(thm)],[c_17,c_11]) ).
cnf(c_21,plain,
c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = c_1,
inference(paramod,[status(thm)],[c_17,c_7]) ).
cnf(c_1806,plain,
c_plus(c_Binomial_Obinomial(A,B),c_Binomial_Obinomial(A,c_Finite__Set_Ocard(c_SetInterval_OatMost(B,tc_nat),tc_nat)),tc_nat) = c_Binomial_Obinomial(c_Suc(A),c_Suc(B)),
inference(paramod,[status(thm)],[c_17,c_4]) ).
cnf(c_1807,plain,
c_plus(c_Binomial_Obinomial(A,B),c_Binomial_Obinomial(A,c_Finite__Set_Ocard(c_SetInterval_OatMost(B,tc_nat),tc_nat)),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),c_Suc(B)),
inference(paramod,[status(thm)],[c_17,c_1806]) ).
cnf(c_22,plain,
c_plus(c_Binomial_Obinomial(A,B),c_Binomial_Obinomial(A,c_Finite__Set_Ocard(c_SetInterval_OatMost(B,tc_nat),tc_nat)),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(B,tc_nat),tc_nat)),
inference(paramod,[status(thm)],[c_17,c_1807]) ).
cnf(c_23,plain,
c_Binomial_Obinomial(A,c_1) = A,
inference(paramod,[status(thm)],[c_21,c_18]) ).
cnf(c_24,plain,
c_lessequals(A,A,tc_nat),
inference(resolve,[status(thm)],[c_9,c_8]) ).
cnf(c_28,plain,
~ c_in(c_Message_Omsg_ONonce(c_plus(v_sko__urX(A),B,tc_nat)),c_Event_Oused(A),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_15,c_10]) ).
cnf(c_29,plain,
c_less(A,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(A,B,tc_nat),tc_nat),tc_nat),tc_nat),
inference(resolve,[status(thm)],[c_19,c_10]) ).
cnf(c_30,plain,
~ c_lessequals(c_plus(A,c_Finite__Set_Ocard(c_SetInterval_OatMost(B,tc_nat),tc_nat),tc_nat),B,tc_nat),
inference(resolve,[status(thm)],[c_19,c_14]) ).
cnf(c_1808,plain,
c_plus(c_1,c_Binomial_Obinomial(A,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)),
inference(paramod,[status(thm)],[c_5,c_22]) ).
cnf(c_1809,plain,
c_plus(c_1,c_Binomial_Obinomial(A,c_1),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)),
inference(paramod,[status(thm)],[c_21,c_1808]) ).
cnf(c_1810,plain,
c_plus(c_1,A,tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)),
inference(paramod,[status(thm)],[c_23,c_1809]) ).
cnf(c_1811,plain,
c_plus(c_1,A,tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),c_1),
inference(paramod,[status(thm)],[c_21,c_1810]) ).
cnf(c_32,plain,
c_plus(c_1,A,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),
inference(paramod,[status(thm)],[c_23,c_1811]) ).
cnf(c_37,plain,
c_plus(A,c_Binomial_Obinomial(A,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),
inference(paramod,[status(thm)],[c_23,c_22]) ).
cnf(c_38,plain,
~ c_in(c_Message_Omsg_ONonce(v_sko__urX(A)),c_Event_Oused(A),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_15,c_24]) ).
cnf(c_39,plain,
( c_in(c_Message_Omsg_ONonce(B),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(A),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| v_sko__urX(v_evs) = B
| B = A
| v_sko__urX(v_evs) = A ),
inference(resolve,[status(thm)],[c_38,c_1]) ).
cnf(c_47,plain,
~ c_lessequals(c_plus(A,c_1,tc_nat),c_0,tc_nat),
inference(paramod,[status(thm)],[c_21,c_30]) ).
cnf(c_1812,plain,
( c_lessequals(A,B,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),c_plus(c_1,B,tc_nat),tc_nat) ),
inference(paramod,[status(thm)],[c_32,c_13]) ).
cnf(c_51,plain,
( c_lessequals(A,B,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(B,tc_nat),tc_nat),tc_nat) ),
inference(paramod,[status(thm)],[c_32,c_1812]) ).
cnf(c_54,plain,
~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat),c_0,tc_nat),
inference(paramod,[status(thm)],[c_32,c_47]) ).
cnf(c_58,plain,
~ c_lessequals(c_plus(A,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat),tc_nat),c_plus(A,c_0,tc_nat),tc_nat),
inference(resolve,[status(thm)],[c_13,c_54]) ).
cnf(c_75,plain,
~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(A,c_Finite__Set_Ocard(c_SetInterval_OatMost(B,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(B,tc_nat),tc_nat),tc_nat),
inference(resolve,[status(thm)],[c_51,c_30]) ).
cnf(c_92,plain,
( c_lessequals(B,c_Binomial_Obinomial(A,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),tc_nat)
| ~ c_lessequals(c_plus(A,B,tc_nat),c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),tc_nat) ),
inference(paramod,[status(thm)],[c_37,c_13]) ).
cnf(c_1813,plain,
c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Binomial_Obinomial(c_1,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),tc_nat),tc_nat),
inference(paramod,[status(thm)],[c_37,c_32]) ).
cnf(c_93,plain,
c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Binomial_Obinomial(c_1,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),
inference(copy,[status(thm)],[c_1813]) ).
cnf(c_1814,plain,
( c_in(c_Message_Omsg_ONonce(A),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| v_sko__urX(v_evs) = A
| A = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolve,[status(thm)],[c_39,c_38]) ).
cnf(c_1815,plain,
( c_in(c_Message_Omsg_ONonce(A),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| v_sko__urX(v_evs) = A
| A = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs) ),
inference(copy,[status(thm)],[c_1814]) ).
cnf(c_97,plain,
( c_in(c_Message_Omsg_ONonce(A),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| v_sko__urX(v_evs) = A
| v_sko__urX(v_evs_H_H) = A
| v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs) ),
inference(copy,[status(thm)],[c_1815]) ).
cnf(c_1816,plain,
( c_in(c_Message_Omsg_ONonce(A),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = A
| v_sko__urX(v_evs) = A ),
inference(resolve,[status(thm)],[c_39,c_38]) ).
cnf(c_101,plain,
( c_in(c_Message_Omsg_ONonce(A),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs)
| v_sko__urX(v_evs_H) = A
| v_sko__urX(v_evs) = A ),
inference(copy,[status(thm)],[c_1816]) ).
cnf(c_1817,plain,
( c_in(c_Message_Omsg_ONonce(A),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H),B,tc_nat)
| c_plus(v_sko__urX(v_evs_H),B,tc_nat) = A
| v_sko__urX(v_evs) = A ),
inference(resolve,[status(thm)],[c_39,c_28]) ).
cnf(c_102,plain,
( c_in(c_Message_Omsg_ONonce(A),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| c_plus(v_sko__urX(v_evs_H),B,tc_nat) = v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs_H),B,tc_nat) = A
| v_sko__urX(v_evs) = A ),
inference(copy,[status(thm)],[c_1817]) ).
cnf(c_1818,plain,
( v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H),A,tc_nat)
| v_sko__urX(v_evs_H_H) = c_plus(v_sko__urX(v_evs_H),A,tc_nat)
| v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs) ),
inference(resolve,[status(thm)],[c_97,c_28]) ).
cnf(c_1819,plain,
( v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H),A,tc_nat)
| c_plus(v_sko__urX(v_evs_H),A,tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs) ),
inference(copy,[status(thm)],[c_1818]) ).
cnf(c_106,plain,
( c_plus(v_sko__urX(v_evs_H),A,tc_nat) = v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs_H),A,tc_nat) = v_sko__urX(v_evs_H_H)
| v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs) ),
inference(copy,[status(thm)],[c_1819]) ).
cnf(c_122,plain,
~ c_lessequals(c_plus(A,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(B,c_Finite__Set_Ocard(c_SetInterval_OatMost(C,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_plus(A,c_Finite__Set_Ocard(c_SetInterval_OatMost(C,tc_nat),tc_nat),tc_nat),tc_nat),
inference(resolve,[status(thm)],[c_13,c_75]) ).
cnf(c_1820,plain,
( v_sko__urX(v_evs_H) = v_sko__urX(v_evs)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),A,tc_nat)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs_H_H),A,tc_nat) ),
inference(resolve,[status(thm)],[c_101,c_28]) ).
cnf(c_1821,plain,
( v_sko__urX(v_evs_H) = v_sko__urX(v_evs)
| v_sko__urX(v_evs_H) = c_plus(v_sko__urX(v_evs_H_H),A,tc_nat)
| c_plus(v_sko__urX(v_evs_H_H),A,tc_nat) = v_sko__urX(v_evs) ),
inference(copy,[status(thm)],[c_1820]) ).
cnf(c_136,plain,
( v_sko__urX(v_evs_H) = v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs_H_H),A,tc_nat) = v_sko__urX(v_evs_H)
| c_plus(v_sko__urX(v_evs_H_H),A,tc_nat) = v_sko__urX(v_evs) ),
inference(copy,[status(thm)],[c_1821]) ).
cnf(c_151,plain,
( ~ c_less(v_sko__urX(v_evs_H_H),A,tc_nat)
| c_plus(v_sko__urX(v_evs_H),A,tc_nat) = v_sko__urX(v_evs)
| v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs) ),
inference(paramod,[status(thm)],[c_106,c_14]) ).
cnf(c_192,plain,
( c_plus(v_sko__urX(v_evs_H),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(v_sko__urX(v_evs_H_H),A,tc_nat),tc_nat),tc_nat),tc_nat) = v_sko__urX(v_evs)
| v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs) ),
inference(resolve,[status(thm)],[c_151,c_29]) ).
cnf(c_193,plain,
( c_plus(v_sko__urX(v_evs_H),c_Finite__Set_Ocard(c_SetInterval_OatMost(v_sko__urX(v_evs_H_H),tc_nat),tc_nat),tc_nat) = v_sko__urX(v_evs)
| v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs) ),
inference(resolve,[status(thm)],[c_151,c_20]) ).
cnf(c_442,plain,
( ~ c_less(v_sko__urX(v_evs_H),A,tc_nat)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs_H_H),A,tc_nat) = v_sko__urX(v_evs) ),
inference(paramod,[status(thm)],[c_136,c_14]) ).
cnf(c_577,plain,
( v_sko__urX(v_evs_H) = v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs_H_H),c_Finite__Set_Ocard(c_SetInterval_OatMost(v_sko__urX(v_evs_H),tc_nat),tc_nat),tc_nat) = v_sko__urX(v_evs) ),
inference(resolve,[status(thm)],[c_442,c_20]) ).
cnf(c_622,plain,
( c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(v_sko__urX(v_evs_H),tc_nat),tc_nat),A,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs_H_H),A,tc_nat),tc_nat)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs) ),
inference(paramod,[status(thm)],[c_577,c_13]) ).
cnf(c_873,plain,
( ~ c_lessequals(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs_H),c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),tc_nat),tc_nat)
| v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs) ),
inference(paramod,[status(thm)],[c_192,c_122]) ).
cnf(c_944,plain,
~ c_lessequals(c_plus(A,c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),tc_nat),c_Binomial_Obinomial(c_1,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),tc_nat),
inference(paramod,[status(thm)],[c_93,c_30]) ).
cnf(c_991,plain,
~ c_lessequals(c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat),tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),c_Binomial_Obinomial(c_1,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),tc_nat),
inference(paramod,[status(thm)],[c_22,c_944]) ).
cnf(c_1822,plain,
~ c_lessequals(c_plus(c_1,c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat),tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),tc_nat),c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),tc_nat),
inference(resolve,[status(thm)],[c_92,c_991]) ).
cnf(c_994,plain,
~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat),tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),tc_nat),tc_nat),c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),tc_nat),
inference(paramod,[status(thm)],[c_32,c_1822]) ).
cnf(c_1823,plain,
( ~ c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs),tc_nat)
| v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs)
| v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs) ),
inference(paramod,[status(thm)],[c_193,c_873]) ).
cnf(c_1824,plain,
( ~ c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs),tc_nat)
| v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs) ),
inference(copy,[status(thm)],[c_1823]) ).
cnf(c_1000,plain,
v_sko__urX(v_evs_H_H) = v_sko__urX(v_evs),
inference(resolve,[status(thm)],[c_24,c_1824]) ).
cnf(c_1825,plain,
( c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(v_sko__urX(v_evs_H),tc_nat),tc_nat),A,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs),A,tc_nat),tc_nat)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs) ),
inference(paramod,[status(thm)],[c_1000,c_622]) ).
cnf(c_1103,plain,
( c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(v_sko__urX(v_evs_H),tc_nat),tc_nat),A,tc_nat)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs) ),
inference(resolve,[status(thm)],[c_10,c_1825]) ).
cnf(c_1243,plain,
( ~ c_less(v_sko__urX(v_evs_H),A,tc_nat)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs),A,tc_nat) = v_sko__urX(v_evs) ),
inference(paramod,[status(thm)],[c_1000,c_442]) ).
cnf(c_1272,plain,
~ c_in(c_Message_Omsg_ONonce(c_plus(v_sko__urX(v_evs),A,tc_nat)),c_Event_Oused(v_evs_H_H),tc_Message_Omsg),
inference(paramod,[status(thm)],[c_1000,c_28]) ).
cnf(c_1275,plain,
( c_lessequals(v_sko__urX(v_evs_H),A,tc_nat)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs) ),
inference(resolve,[status(thm)],[c_1103,c_51]) ).
cnf(c_1281,plain,
( c_less(v_sko__urX(v_evs_H),c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),tc_nat)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs) ),
inference(resolve,[status(thm)],[c_1275,c_19]) ).
cnf(c_1826,plain,
( c_plus(v_sko__urX(v_evs_H),B,tc_nat) = v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs_H),B,tc_nat) = c_plus(v_sko__urX(v_evs),A,tc_nat)
| v_sko__urX(v_evs) = c_plus(v_sko__urX(v_evs),A,tc_nat) ),
inference(resolve,[status(thm)],[c_102,c_1272]) ).
cnf(c_1827,plain,
( c_plus(v_sko__urX(v_evs_H),B,tc_nat) = v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs_H),B,tc_nat) = c_plus(v_sko__urX(v_evs),A,tc_nat)
| c_plus(v_sko__urX(v_evs),A,tc_nat) = v_sko__urX(v_evs) ),
inference(copy,[status(thm)],[c_1826]) ).
cnf(c_1359,plain,
( c_plus(v_sko__urX(v_evs_H),B,tc_nat) = v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs),A,tc_nat) = c_plus(v_sko__urX(v_evs_H),B,tc_nat)
| c_plus(v_sko__urX(v_evs),A,tc_nat) = v_sko__urX(v_evs) ),
inference(copy,[status(thm)],[c_1827]) ).
cnf(c_1828,plain,
( v_sko__urX(v_evs_H) = v_sko__urX(v_evs)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs),c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),tc_nat) = v_sko__urX(v_evs) ),
inference(resolve,[status(thm)],[c_1243,c_1281]) ).
cnf(c_1367,plain,
( v_sko__urX(v_evs_H) = v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs),c_Finite__Set_Ocard(c_SetInterval_OatMost(A,tc_nat),tc_nat),tc_nat) = v_sko__urX(v_evs) ),
inference(copy,[status(thm)],[c_1828]) ).
cnf(c_1829,plain,
( ~ c_lessequals(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs),c_0,tc_nat),tc_nat)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs) ),
inference(paramod,[status(thm)],[c_1367,c_58]) ).
cnf(c_1398,plain,
v_sko__urX(v_evs_H) = v_sko__urX(v_evs),
inference(resolve,[status(thm)],[c_10,c_1829]) ).
cnf(c_1830,plain,
( c_plus(v_sko__urX(v_evs_H),B,tc_nat) = v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs),A,tc_nat) = c_plus(v_sko__urX(v_evs),B,tc_nat)
| c_plus(v_sko__urX(v_evs),A,tc_nat) = v_sko__urX(v_evs) ),
inference(paramod,[status(thm)],[c_1398,c_1359]) ).
cnf(c_1400,plain,
( c_plus(v_sko__urX(v_evs),B,tc_nat) = v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs),A,tc_nat) = c_plus(v_sko__urX(v_evs),B,tc_nat)
| c_plus(v_sko__urX(v_evs),A,tc_nat) = v_sko__urX(v_evs) ),
inference(paramod,[status(thm)],[c_1398,c_1830]) ).
cnf(c_1473,plain,
( ~ c_less(c_plus(v_sko__urX(v_evs),B,tc_nat),A,tc_nat)
| c_plus(v_sko__urX(v_evs),B,tc_nat) = v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs),A,tc_nat) = v_sko__urX(v_evs) ),
inference(paramod,[status(thm)],[c_1400,c_14]) ).
cnf(c_1790,plain,
( c_plus(v_sko__urX(v_evs),A,tc_nat) = v_sko__urX(v_evs)
| c_plus(v_sko__urX(v_evs),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(v_sko__urX(v_evs),A,tc_nat),tc_nat),tc_nat),tc_nat) = v_sko__urX(v_evs) ),
inference(resolve,[status(thm)],[c_1473,c_20]) ).
cnf(c_1831,plain,
( ~ c_less(v_sko__urX(v_evs),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(v_sko__urX(v_evs),A,tc_nat),tc_nat),tc_nat),tc_nat)
| c_plus(v_sko__urX(v_evs),A,tc_nat) = v_sko__urX(v_evs) ),
inference(paramod,[status(thm)],[c_1790,c_14]) ).
cnf(c_1795,plain,
c_plus(v_sko__urX(v_evs),A,tc_nat) = v_sko__urX(v_evs),
inference(resolve,[status(thm)],[c_29,c_1831]) ).
cnf(c_1798,plain,
~ c_lessequals(c_plus(A,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat),tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),tc_nat),tc_nat),tc_nat),c_plus(A,c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_1,tc_nat),tc_nat)),tc_nat),tc_nat),
inference(resolve,[status(thm)],[c_13,c_994]) ).
cnf(c_1832,plain,
( c_lessequals(B,A,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),c_plus(v_sko__urX(v_evs),A,tc_nat),tc_nat) ),
inference(paramod,[status(thm)],[c_1795,c_13]) ).
cnf(c_1833,plain,
( c_lessequals(B,A,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs),tc_nat) ),
inference(paramod,[status(thm)],[c_1795,c_1832]) ).
cnf(c_1804,plain,
c_lessequals(A,B,tc_nat),
inference(resolve,[status(thm)],[c_24,c_1833]) ).
cnf(c_1805,plain,
$false,
inference(resolve,[status(thm)],[c_1804,c_1798]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV282-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 13:26:48 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 2256966 was started by sandbox on n005,
% 0.13/0.36 % Sat Sep 26 13:26:48 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 6.57/1.30
% 6.57/1.30 % SZS status Unsatisfiable for theBenchmark
% 6.57/1.30
% 6.57/1.30 % Proof 1 at 0.83 (+ 0.08) seconds.
% 6.57/1.30 % Length of proof is 70.
% 6.57/1.30 % Level of proof is 20.
% 6.57/1.30 % Maximum clause weight is 38.000.
% 6.57/1.30 % Given clauses 290.
% 6.57/1.30
% 6.57/1.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------