%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV282-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:58:42 AM UTC 2026
% Result : Unsatisfiable 24.65s 17.12s
% Output : Refutation 25.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 20 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 212 ( 12 ~; 18 |; 0 &; 182 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 8 con; 0-3 aty)
% Number of variables : 46 ( 0 ^; 46 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_Message_Omsg_ONonce_decl,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(c_Event_Oused_decl,type,
c_Event_Oused: $i > $i ).
thf(v_evs_H_H_decl,type,
v_evs_H_H: $i ).
thf(tc_Message_Omsg_decl,type,
tc_Message_Omsg: $i ).
thf(v_evs_H_decl,type,
v_evs_H: $i ).
thf(v_evs_decl,type,
v_evs: $i ).
thf(c_Binomial_Obinomial_decl,type,
c_Binomial_Obinomial: $i > $i > $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_1_decl,type,
c_1: $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(v_sko__urX_decl,type,
v_sko__urX: $i > $i ).
thf(c_Finite__Set_Ocard_decl,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(c_SetInterval_OatMost_decl,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__Suc__eq__le_1) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Suc @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_Finite__Set_Ocard ) )
= ( A @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
thf(41,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_Finite__Set_Ocard ) )
= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(32,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: $i] :
( ( c_0 @ ( A @ c_Binomial_Obinomial ) )
= c_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).
thf(22,plain,
! [A: $i] :
( ( c_0 @ ( A @ c_Binomial_Obinomial ) )
= c_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ v_sko__urX @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_ONonce__supply__lemma_0) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ v_sko__urX @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,axiom,
! [A: $i] :
( ( c_0 @ c_Suc @ ( A @ c_Binomial_Obinomial ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).
thf(18,plain,
! [A: $i] :
( ( c_0 @ c_Suc @ ( A @ c_Binomial_Obinomial ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add1_0) ).
thf(31,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_minus ) ) )
!= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_minus ) ) )
!= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( v_evs @ c_Event_Oused @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
| ( tc_Message_Omsg @ ( v_evs_H @ c_Event_Oused @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) )
| ( tc_Message_Omsg @ ( v_evs_H_H @ c_Event_Oused @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) )
| ( A = C )
| ( C = B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( v_evs @ c_Event_Oused @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) )
| ( tc_Message_Omsg @ ( v_evs_H @ c_Event_Oused @ ( C @ c_Message_Omsg_ONonce @ c_in ) ) )
| ( tc_Message_Omsg @ ( v_evs_H_H @ c_Event_Oused @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) )
| ( A = C )
| ( C = B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
( c_1
= ( c_0 @ c_Suc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
thf(24,plain,
( c_1
= ( c_0 @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
thf(37,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ c_Suc @ ( A @ c_Suc @ c_Binomial_Obinomial ) )
= ( tc_nat @ ( B @ c_Suc @ ( A @ c_Binomial_Obinomial ) @ ( B @ ( A @ c_Binomial_Obinomial ) @ c_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__Suc_0) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ c_Suc @ ( A @ c_Suc @ c_Binomial_Obinomial ) )
= ( tc_nat @ ( B @ c_Suc @ ( A @ c_Binomial_Obinomial ) @ ( B @ ( A @ c_Binomial_Obinomial ) @ c_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_minus ) ) )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
thf(29,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_minus ) ) )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2003,plain,
$false,
inference(e,[status(thm)],[33,41,32,22,39,35,18,31,26,15,24,37,20,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV282-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.16/10.44 % Computer : n017.cluster.edu
% 0.16/10.44 % Model : x86_64 x86_64
% 0.16/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.44 % Memory : 8046.5625MB
% 0.16/10.44 % OS : Linux 6.8.0-71-generic
% 0.16/10.44 % CPULimit : 300
% 0.16/10.44 % WCLimit : 300
% 0.16/10.44 % DateTime : Sat Sep 26 13:22:30 UTC 2026
% 0.16/10.44 % CPUTime :
% 0.16/10.44 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.31/11.25 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/11.52 % [INFO] Parsing done (268ms).
% 1.85/11.55 % [INFO] Running in sequential loop mode.
% 2.75/12.15 % [INFO] eprover registered as external prover.
% 2.98/12.16 % [INFO] Scanning for conjecture ...
% 3.23/12.30 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 3.23/12.36 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 3.23/12.39 % [INFO] Problem is propositional (TPTP CNF).
% 3.23/12.39 % [INFO] Type checking passed.
% 3.44/12.40 % [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 ...
% 24.65/17.12 % External prover 'e' found a proof!
% 24.65/17.12 % [INFO] Killing All external provers ...
% 24.65/17.12 % Time passed: 6491ms (effective reasoning time: 5565ms)
% 24.65/17.12 % Axioms used in derivation (13): cls_Nat_Odiff__is__0__eq_0, cls_Nat_Onat__add__left__cancel__le_0, cls_Nat_Odiff__self__eq__0_0, cls_Nat_Ole__add1_0, cls_Nat_OOne__nat__def_0, cls_Binomial_Obinomial__1_0, cls_SetInterval_Ocard__atMost_0, cls_Nat_OlessI_0, cls_Public_ONonce__supply__lemma_0, cls_Binomial_Obinomial__Suc__Suc_0, cls_Nat_Oless__Suc__eq__le_1, cls_Binomial_Obinomial__n__0_0, cls_Nat_Onot__add__less2_0
% 24.65/17.12 % No. of inferences in proof: 29
% 24.65/17.12 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6491 ms resp. 5565 ms w/o parsing
% 25.11/17.18 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.11/17.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------