%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL431-2 : 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 : n011.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 07:51:47 AM UTC 2026
% Result : Unsatisfiable 4.43s 3.04s
% Output : Refutation 4.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of formulae : 9 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 11 ( 2 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 72 ( 4 ~; 2 |; 0 &; 66 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_PropLog_Osat_decl,type,
c_PropLog_Osat: $i > $i > $i > $o ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(v_p_decl,type,
v_p: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_PropLog_Othms_decl,type,
c_PropLog_Othms: $i > $i > $i ).
thf(tc_PropLog_Opl_decl,type,
tc_PropLog_Opl: $i > $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(c_PropLog_Ohyps_decl,type,
c_PropLog_Ohyps: $i > $i > $i > $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(1,negated_conjecture,
t_a @ ( v_p @ ( c_emptyset @ c_PropLog_Osat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(5,plain,
t_a @ ( v_p @ ( c_emptyset @ c_PropLog_Osat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,negated_conjecture,
~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( c_emptyset @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(6,plain,
~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( c_emptyset @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_PropLog_Opl @ ( B @ ( B @ tc_PropLog_Opl @ tc_set @ ( B @ ( D @ ( A @ c_PropLog_Ohyps ) ) @ ( B @ ( C @ ( A @ c_PropLog_Ohyps ) ) @ c_minus ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( B @ ( A @ ( c_emptyset @ c_PropLog_Osat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Ocompleteness__0__lemma__dest_0) ).
thf(8,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_PropLog_Opl @ ( B @ ( B @ tc_PropLog_Opl @ tc_set @ ( B @ ( D @ ( A @ c_PropLog_Ohyps ) ) @ ( B @ ( C @ ( A @ c_PropLog_Ohyps ) ) @ c_minus ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( B @ ( A @ ( c_emptyset @ c_PropLog_Osat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_minus ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_minus ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,plain,
$false,
inference(e,[status(thm)],[5,6,8,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL431-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.21/0.48 % Computer : n011.cluster.edu
% 0.21/0.48 % Model : x86_64 x86_64
% 0.21/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.48 % Memory : 8046.5625MB
% 0.21/0.48 % OS : Linux 6.8.0-71-generic
% 0.21/0.48 % CPULimit : 300
% 0.21/0.48 % WCLimit : 300
% 0.21/0.48 % DateTime : Fri Sep 25 22:32:43 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 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
% 1.44/1.30 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.79/1.55 % [INFO] Parsing done (240ms).
% 1.79/1.57 % [INFO] Running in sequential loop mode.
% 2.85/2.16 % [INFO] eprover registered as external prover.
% 2.85/2.17 % [INFO] Scanning for conjecture ...
% 2.94/2.29 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 3.10/2.34 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 3.10/2.35 % [INFO] Problem is propositional (TPTP CNF).
% 3.10/2.36 % [INFO] Type checking passed.
% 3.10/2.37 % [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 ...
% 4.43/3.03 % External prover 'e' found a proof!
% 4.43/3.03 % [INFO] Killing All external provers ...
% 4.43/3.03 % Time passed: 2342ms (effective reasoning time: 1455ms)
% 4.43/3.03 % Axioms used in derivation (2): cls_PropLog_Ocompleteness__0__lemma__dest_0, cls_Set_ODiff__cancel_0
% 4.43/3.03 % No. of inferences in proof: 9
% 4.43/3.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2342 ms resp. 1455 ms w/o parsing
% 4.89/3.09 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.89/3.09 % [INFO] Killing All external provers ...
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