%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL445-2 : 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 : n008.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 07:51:51 AM UTC 2026
% Result : Unsatisfiable 3.11s 13.02s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 194 ( 8 ~; 6 |; 0 &; 180 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 24 ( 0 ^; 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_q_decl,type,
v_q: $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(v_p_decl,type,
v_p: $i ).
thf(v_H_decl,type,
v_H: $i ).
thf(tc_PropLog_Opl_decl,type,
tc_PropLog_Opl: $i > $i ).
thf(t_a_decl,type,
t_a: $i ).
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_Ofalse_decl,type,
c_PropLog_Opl_Ofalse: $i ).
thf(3,negated_conjecture,
~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_q @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(9,plain,
~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_q @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( C @ ( D @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
thf(13,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( C @ ( D @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,negated_conjecture,
t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ ( v_H @ ( v_p @ c_insert ) ) @ c_PropLog_Othms ) @ ( v_q @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(7,plain,
t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ ( v_H @ ( v_p @ c_insert ) ) @ c_PropLog_Othms ) @ ( v_q @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_PropLog_Opl @ ( D @ ( C @ c_PropLog_Othms ) @ ( D @ ( A @ ( B @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( D @ tc_PropLog_Opl @ ( D @ ( D @ tc_PropLog_Opl @ ( C @ ( B @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Odeduction_0) ).
thf(11,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_PropLog_Opl @ ( D @ ( C @ c_PropLog_Othms ) @ ( D @ ( A @ ( B @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
| ~ ( D @ tc_PropLog_Opl @ ( D @ ( D @ tc_PropLog_Opl @ ( C @ ( B @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,negated_conjecture,
t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ ( v_H @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) @ c_PropLog_Othms ) @ ( v_q @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(8,plain,
t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ ( v_H @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) @ c_PropLog_Othms ) @ ( v_q @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ tc_PropLog_Opl @ ( C @ ( D @ c_PropLog_Othms ) @ ( C @ ( C @ ( B @ ( C @ ( B @ ( C @ ( c_PropLog_Opl_Ofalse @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ ( C @ ( B @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms__excluded__middle_0) ).
thf(15,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ tc_PropLog_Opl @ ( C @ ( D @ c_PropLog_Othms ) @ ( C @ ( C @ ( B @ ( C @ ( B @ ( C @ ( c_PropLog_Opl_Ofalse @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ ( C @ ( B @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,plain,
$false,
inference(e,[status(thm)],[9,13,7,11,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL445-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.21/11.13 % Computer : n008.cluster.edu
% 0.21/11.13 % Model : x86_64 x86_64
% 0.21/11.13 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/11.13 % Memory : 8046.5625MB
% 0.21/11.13 % OS : Linux 6.8.0-71-generic
% 0.21/11.13 % CPULimit : 300
% 0.21/11.13 % WCLimit : 300
% 0.21/11.13 % DateTime : Fri Sep 25 22:35:21 UTC 2026
% 0.21/11.13 % CPUTime :
% 0.21/11.13 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
% 0.26/11.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.26/11.91 % [INFO] Parsing done (187ms).
% 0.26/11.93 % [INFO] Running in sequential loop mode.
% 1.93/12.32 % [INFO] eprover registered as external prover.
% 1.93/12.33 % [INFO] Scanning for conjecture ...
% 2.11/12.43 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.11/12.47 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.11/12.48 % [INFO] Problem is propositional (TPTP CNF).
% 2.11/12.48 % [INFO] Type checking passed.
% 2.11/12.49 % [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 ...
% 3.11/13.02 % External prover 'e' found a proof!
% 3.11/13.02 % [INFO] Killing All external provers ...
% 3.11/13.02 % Time passed: 1742ms (effective reasoning time: 1088ms)
% 3.11/13.02 % Axioms used in derivation (3): cls_PropLog_Othms_OMP_0, cls_PropLog_Odeduction_0, cls_PropLog_Othms__excluded__middle_0
% 3.11/13.02 % No. of inferences in proof: 13
% 3.11/13.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1742 ms resp. 1088 ms w/o parsing
% 3.44/13.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.44/13.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------