%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV255-2 : 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 : n006.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 08:58:34 AM UTC 2026
% Result : Unsatisfiable 3.36s 7.60s
% Output : Refutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 146 ( 12 ~; 10 |; 0 &; 124 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_xb_decl,type,
v_xb: $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
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_Message_Oparts_decl,type,
c_Message_Oparts: $i > $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(v_msg1_decl,type,
v_msg1: $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(tc_Message_Omsg_decl,type,
tc_Message_Omsg: $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(v_msg2_decl,type,
v_msg2: $i ).
thf(v_xa_decl,type,
v_xa: $i ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(4,negated_conjecture,
! [A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( v_msg1 @ c_insert ) ) @ c_Message_Oparts @ ( A @ v_xb @ c_Message_Omsg_ONonce @ c_in ) ) )
| ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( v_msg2 @ c_insert ) ) @ c_Message_Oparts @ ( A @ v_xb @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(10,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( v_msg1 @ c_insert ) ) @ c_Message_Oparts @ ( A @ v_xb @ c_Message_Omsg_ONonce @ c_in ) ) )
| ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( v_msg2 @ c_insert ) ) @ c_Message_Oparts @ ( A @ v_xb @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__leE_0) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( v_xa @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( v_msg2 @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(9,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( v_xa @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( v_msg2 @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
! [A: $i] : ( tc_nat @ ( A @ v_xb @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(7,plain,
! [A: $i] : ( tc_nat @ ( A @ v_xb @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__leE_1) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( v_x @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( v_msg1 @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(8,plain,
! [A: $i] :
( ~ ( tc_nat @ ( A @ ( v_x @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( c_emptyset @ ( v_msg1 @ c_insert ) ) @ c_Message_Oparts @ ( A @ c_Message_Omsg_ONonce @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[10,14,9,7,16,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV255-2 : 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
% 0.15/5.44 % Computer : n006.cluster.edu
% 0.15/5.44 % Model : x86_64 x86_64
% 0.15/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.44 % Memory : 8046.5625MB
% 0.15/5.44 % OS : Linux 6.8.0-71-generic
% 0.15/5.44 % CPULimit : 300
% 0.15/5.44 % WCLimit : 300
% 0.15/5.44 % DateTime : Sat Sep 26 13:23:16 UTC 2026
% 0.15/5.45 % CPUTime :
% 0.15/5.45 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
% 0.95/6.22 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.11/6.42 % [INFO] Parsing done (200ms).
% 1.11/6.43 % [INFO] Running in sequential loop mode.
% 1.76/6.87 % [INFO] eprover registered as external prover.
% 1.76/6.87 % [INFO] Scanning for conjecture ...
% 1.92/6.97 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.92/7.02 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.92/7.02 % [INFO] Problem is propositional (TPTP CNF).
% 1.92/7.02 % [INFO] Type checking passed.
% 1.92/7.03 % [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 ...
% 3.17/7.60 % External prover 'e' found a proof!
% 3.36/7.60 % [INFO] Killing All external provers ...
% 3.36/7.60 % Time passed: 1891ms (effective reasoning time: 1166ms)
% 3.36/7.60 % Axioms used in derivation (2): cls_Nat_Oadd__leE_0, cls_Nat_Oadd__leE_1
% 3.36/7.60 % No. of inferences in proof: 13
% 3.36/7.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1891 ms resp. 1166 ms w/o parsing
% 3.36/7.63 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.36/7.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------