%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV281-2 : TPTP v9.3.1. Released v3.2.0.
% 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 : n019.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 3.51s 2.30s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 10 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 90 ( 8 ~; 8 |; 0 &; 74 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% 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_decl,type,
v_evs_H: $i ).
thf(tc_Message_Omsg_decl,type,
tc_Message_Omsg: $i ).
thf(v_evs_decl,type,
v_evs: $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_0_decl,type,
c_0: $i ).
thf(v_sko__urX_decl,type,
v_sko__urX: $i > $i ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1_0) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add2_0) ).
thf(13,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_plus ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
thf(17,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( c_0 @ c_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,negated_conjecture,
! [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 @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(7,plain,
! [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 @ ( B @ c_Message_Omsg_ONonce @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,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/sandbox/benchmark/theBenchmark.p',cls_Public_ONonce__supply__lemma_0) ).
thf(19,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)],[6]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[10,14,13,17,7,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV281-2 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.13/0.41 % Computer : n019.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sat Sep 26 13:27:18 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.17 % [INFO] Parsing done (184ms).
% 1.24/1.18 % [INFO] Running in sequential loop mode.
% 1.78/1.59 % [INFO] eprover registered as external prover.
% 1.97/1.60 % [INFO] Scanning for conjecture ...
% 1.97/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.16/1.74 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.16/1.75 % [INFO] Problem is propositional (TPTP CNF).
% 2.16/1.75 % [INFO] Type checking passed.
% 2.16/1.75 % [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 ...
% 3.51/2.30 % External prover 'e' found a proof!
% 3.51/2.30 % [INFO] Killing All external provers ...
% 3.51/2.30 % Time passed: 1757ms (effective reasoning time: 1109ms)
% 3.51/2.30 % Axioms used in derivation (5): cls_Nat_Onat__add__right__cancel_0, cls_Nat_Ole__add2_0, cls_List_Olist_Odistinct__1_0, cls_Nat_Oop_A_L_Oadd__0_0, cls_Public_ONonce__supply__lemma_0
% 3.51/2.30 % No. of inferences in proof: 13
% 3.51/2.30 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1757 ms resp. 1109 ms w/o parsing
% 3.51/2.34 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.51/2.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------