%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV338-2 : 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 : n007.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 08:59:02 AM UTC 2026
% Result : Unsatisfiable 2.83s 1.55s
% Output : Refutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of formulae : 19 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 186 ( 12 ~; 12 |; 0 &; 162 @)
% ( 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 : 20 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_K_decl,type,
v_K: $i ).
thf(c_Message_OsymKeys_decl,type,
c_Message_OsymKeys: $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(v_X_decl,type,
v_X: $i ).
thf(c_Message_Osynth_decl,type,
c_Message_Osynth: $i > $i ).
thf(c_Message_Oanalz_decl,type,
c_Message_Oanalz: $i > $i ).
thf(c_Event_Oknows_decl,type,
c_Event_Oknows: $i > $i > $i ).
thf(c_Message_Oagent_OSpy_decl,type,
c_Message_Oagent_OSpy: $i ).
thf(v_evsf_decl,type,
v_evsf: $i ).
thf(tc_Message_Omsg_decl,type,
tc_Message_Omsg: $i ).
thf(c_Message_Omsg_OKey_decl,type,
c_Message_Omsg_OKey: $i > $i ).
thf(c_Event_Oused_decl,type,
c_Event_Oused: $i > $i ).
thf(c_Message_OkeysFor_decl,type,
c_Message_OkeysFor: $i > $i ).
thf(c_Message_Oparts_decl,type,
c_Message_Oparts: $i > $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(c_Message_OinvKey_decl,type,
c_Message_OinvKey: $i > $i ).
thf(5,negated_conjecture,
( ( tc_Message_Omsg @ ( v_evsf @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_nat @ ( v_evsf @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(10,plain,
( ( tc_Message_Omsg @ ( v_evsf @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) )
| ~ ( tc_nat @ ( v_evsf @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,negated_conjecture,
tc_nat @ ( tc_Message_Omsg @ ( v_evsf @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(14,plain,
tc_nat @ ( tc_Message_Omsg @ ( v_evsf @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: $i] :
( ( ( A @ c_Message_OinvKey )
= A )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OinvKey__K_0) ).
thf(21,plain,
! [A: $i] :
( ( ( A @ c_Message_OinvKey )
= A )
| ~ ( tc_nat @ ( c_Message_OsymKeys @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,negated_conjecture,
~ ( tc_Message_Omsg @ ( v_evsf @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(13,plain,
~ ( tc_Message_Omsg @ ( v_evsf @ c_Event_Oused @ ( v_K @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Event_Oused @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oparts @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,negated_conjecture,
tc_Message_Omsg @ ( v_evsf @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(12,plain,
tc_Message_Omsg @ ( v_evsf @ ( c_Message_Oagent_OSpy @ c_Event_Oknows ) @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(11,plain,
tc_nat @ ( c_Message_OsymKeys @ ( v_K @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( D @ c_Message_Oparts @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_nat @ ( tc_Message_Omsg @ ( D @ ( C @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( D @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_nat @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OkeysFor__parts__insert__dest_0) ).
thf(19,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ ( D @ c_Message_Oparts @ ( A @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_nat @ ( tc_Message_Omsg @ ( D @ ( C @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( D @ c_Message_Oanalz @ c_Message_Osynth @ ( B @ c_in ) ) )
| ~ ( tc_nat @ ( tc_Message_Omsg @ ( C @ ( B @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(29,plain,
$false,
inference(e,[status(thm)],[10,24,14,21,13,17,12,11,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV338-2 : 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
% 0.14/0.41 % Computer : n007.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 13:32:24 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.71/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.94/0.80 % [INFO] Parsing done (92ms).
% 0.94/0.81 % [INFO] Running in sequential loop mode.
% 1.21/0.99 % [INFO] eprover registered as external prover.
% 1.21/1.00 % [INFO] Scanning for conjecture ...
% 1.51/1.05 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.51/1.06 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.51/1.07 % [INFO] Problem is propositional (TPTP CNF).
% 1.51/1.08 % [INFO] Type checking passed.
% 1.51/1.08 % [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 ...
% 2.83/1.54 % External prover 'e' found a proof!
% 2.83/1.54 % [INFO] Killing All external provers ...
% 2.83/1.55 % Time passed: 1042ms (effective reasoning time: 735ms)
% 2.83/1.55 % Axioms used in derivation (4): cls_Set_OUn__absorb_0, cls_Public_OinvKey__K_0, cls_Event_Oc_A_58_Aparts_A_Iknows_ASpy_Aevs1_J_A_61_61_62_Ac_A_58_Aused_Aevs1_0, cls_Event_OkeysFor__parts__insert__dest_0
% 2.83/1.55 % No. of inferences in proof: 19
% 2.83/1.55 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1042 ms resp. 735 ms w/o parsing
% 2.83/1.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.83/1.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------