%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% 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 : n015.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 3.86s 7.47s
% Output : Refutation 4.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of formulae : 19 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 248 ( 2 ~; 0 |; 0 &; 246 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $i ).
thf(v_p_decl,type,
v_p: $i ).
thf(c_PropLog_Othms_decl,type,
c_PropLog_Othms: $i > $i > $i ).
thf(v_H_decl,type,
v_H: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(tc_PropLog_Opl_decl,type,
tc_PropLog_Opl: $i > $i ).
thf(true_decl,type,
true: $i ).
thf(c_PropLog_Opl_Oop_A_N_62_decl,type,
c_PropLog_Opl_Oop_A_N_62: $i > $i > $i > $i ).
thf(v_q_decl,type,
v_q: $i ).
thf(c_PropLog_Opl_Ofalse_decl,type,
c_PropLog_Opl_Ofalse: $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(1,negated_conjecture,
( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(10,plain,
( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( C @ tc_PropLog_Opl @ ( C @ ( C @ tc_PropLog_Opl @ ( B @ ( D @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) @ ( true @ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left__insert_0) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( C @ tc_PropLog_Opl @ ( C @ ( C @ tc_PropLog_Opl @ ( B @ ( D @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) @ ( true @ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( D @ tc_PropLog_Opl @ ( D @ ( C @ c_PropLog_Othms ) @ ( D @ ( A @ ( B @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) @ ( true @ ( D @ tc_PropLog_Opl @ ( D @ ( D @ tc_PropLog_Opl @ ( C @ ( B @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Odeduction_0) ).
thf(21,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( D @ tc_PropLog_Opl @ ( D @ ( C @ c_PropLog_Othms ) @ ( D @ ( A @ ( B @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) @ ( true @ ( D @ tc_PropLog_Opl @ ( D @ ( D @ tc_PropLog_Opl @ ( C @ ( B @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,negated_conjecture,
( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(12,plain,
( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( t_a @ ( v_q @ ( v_p @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,negated_conjecture,
( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(11,plain,
( ( t_a @ tc_PropLog_Opl @ ( t_a @ ( v_H @ c_PropLog_Othms ) @ ( t_a @ ( c_PropLog_Opl_Ofalse @ ( v_q @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) @ ( true @ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) @ ( true @ ( C @ tc_PropLog_Opl @ ( B @ ( A @ c_in ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( C @ tc_PropLog_Opl @ ( C @ ( D @ c_PropLog_Othms ) @ ( B @ c_in ) ) @ ( true @ ( C @ tc_PropLog_Opl @ ( C @ ( D @ c_PropLog_Othms ) @ ( A @ c_in ) ) @ ifeq ) ) ) @ ( true @ ( C @ tc_PropLog_Opl @ ( C @ ( D @ c_PropLog_Othms ) @ ( C @ ( B @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
thf(19,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( C @ tc_PropLog_Opl @ ( C @ ( D @ c_PropLog_Othms ) @ ( B @ c_in ) ) @ ( true @ ( C @ tc_PropLog_Opl @ ( C @ ( D @ c_PropLog_Othms ) @ ( A @ c_in ) ) @ ifeq ) ) ) @ ( true @ ( C @ tc_PropLog_Opl @ ( C @ ( D @ c_PropLog_Othms ) @ ( C @ ( B @ ( A @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_in ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(43,plain,
$false,
inference(e,[status(thm)],[10,25,21,17,27,12,11,23,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL443-10 : TPTP v9.3.1. Released v7.3.0.
% 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
% 0.07/5.40 % Computer : n015.cluster.edu
% 0.07/5.40 % Model : x86_64 x86_64
% 0.07/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.40 % Memory : 8046.5625MB
% 0.07/5.40 % OS : Linux 6.8.0-71-generic
% 0.07/5.40 % CPULimit : 300
% 0.07/5.40 % WCLimit : 300
% 0.07/5.40 % DateTime : Fri Sep 25 22:37:18 UTC 2026
% 0.07/5.40 % CPUTime :
% 0.07/5.40 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
% 0.17/5.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/6.17 % [INFO] Parsing done (188ms).
% 1.27/6.19 % [INFO] Running in sequential loop mode.
% 2.04/6.60 % [INFO] eprover registered as external prover.
% 2.04/6.61 % [INFO] Scanning for conjecture ...
% 2.22/6.71 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.22/6.74 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.22/6.76 % [INFO] Problem is propositional (TPTP CNF).
% 2.22/6.77 % [INFO] Type checking passed.
% 2.22/6.78 % [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 ...
% 3.86/7.47 % External prover 'e' found a proof!
% 3.86/7.47 % [INFO] Killing All external provers ...
% 3.86/7.47 % Time passed: 1931ms (effective reasoning time: 1276ms)
% 3.86/7.47 % Axioms used in derivation (6): cls_PropLog_Oweaken__left__insert_0, ifeq_axiom, cls_PropLog_Othms_OMP_0, cls_PropLog_Odeduction_0, cls_PropLog_Othms_OH_0, cls_Set_OinsertCI_1
% 3.86/7.47 % No. of inferences in proof: 19
% 3.86/7.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1931 ms resp. 1276 ms w/o parsing
% 4.31/7.52 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.31/7.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------