%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL441-2 : 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 07:51:50 AM UTC 2026
% Result : Unsatisfiable 5.05s 3.12s
% Output : Refutation 5.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of formulae : 7 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 11 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 110 ( 6 ~; 4 |; 0 &; 100 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_PropLog_Opl_Oop_A_N_62_decl,type,
c_PropLog_Opl_Oop_A_N_62: $i > $i > $i > $i ).
thf(c_PropLog_Opl_Ovar_decl,type,
c_PropLog_Opl_Ovar: $i > $i > $i ).
thf(v_a_decl,type,
v_a: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_PropLog_Opl_Ofalse_decl,type,
c_PropLog_Opl_Ofalse: $i ).
thf(c_PropLog_Othms_decl,type,
c_PropLog_Othms: $i > $i > $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(tc_PropLog_Opl_decl,type,
tc_PropLog_Opl: $i > $i ).
thf(1,negated_conjecture,
( ~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ ( c_emptyset @ ( t_a @ ( v_a @ c_PropLog_Opl_Ovar ) @ c_insert ) ) @ c_PropLog_Othms ) @ ( t_a @ ( v_a @ c_PropLog_Opl_Ovar ) @ c_in ) ) )
| ~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ ( c_emptyset @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_a @ c_PropLog_Opl_Ovar ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_a @ c_PropLog_Opl_Ovar ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(4,plain,
( ~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ ( c_emptyset @ ( t_a @ ( v_a @ c_PropLog_Opl_Ovar ) @ c_insert ) ) @ c_PropLog_Othms ) @ ( t_a @ ( v_a @ c_PropLog_Opl_Ovar ) @ c_in ) ) )
| ~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ ( c_emptyset @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_a @ c_PropLog_Opl_Ovar ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_a @ c_PropLog_Opl_Ovar ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
thf(6,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
$false,
inference(e,[status(thm)],[4,6,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL441-2 : 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
% 0.13/0.40 % Computer : n007.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Fri Sep 25 22:31:54 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 1.12/1.12 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.58/1.38 % [INFO] Parsing done (260ms).
% 1.77/1.40 % [INFO] Running in sequential loop mode.
% 2.48/2.02 % [INFO] eprover registered as external prover.
% 2.48/2.04 % [INFO] Scanning for conjecture ...
% 2.96/2.18 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 3.03/2.23 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 3.03/2.24 % [INFO] Problem is propositional (TPTP CNF).
% 3.03/2.24 % [INFO] Type checking passed.
% 3.03/2.25 % [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 ...
% 5.05/3.12 % External prover 'e' found a proof!
% 5.05/3.12 % [INFO] Killing All external provers ...
% 5.05/3.12 % Time passed: 2572ms (effective reasoning time: 1708ms)
% 5.05/3.12 % Axioms used in derivation (2): cls_PropLog_Othms_OH_0, cls_Set_OinsertCI_1
% 5.05/3.12 % No. of inferences in proof: 7
% 5.05/3.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2572 ms resp. 1708 ms w/o parsing
% 5.32/3.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.32/3.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------