%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL429-2 : 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 : n005.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 3.62s 2.44s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of formulae : 17 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 408 ( 14 ~; 12 |; 0 &; 382 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 17 usr; 8 con; 0-3 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_p_decl,type,
v_p: $i ).
thf(c_PropLog_Othms_decl,type,
c_PropLog_Othms: $i > $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(t_a_decl,type,
t_a: $i ).
thf(v_F_decl,type,
v_F: $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(tc_PropLog_Opl_decl,type,
tc_PropLog_Opl: $i > $i ).
thf(v_t_decl,type,
v_t: $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(c_PropLog_Opl_Ovar_decl,type,
c_PropLog_Opl_Ovar: $i > $i > $i ).
thf(v_v_decl,type,
v_v: $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_emptyset_decl,type,
c_emptyset: $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(2,negated_conjecture,
~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ tc_set @ ( t_a @ tc_PropLog_Opl @ ( v_F @ ( t_a @ ( v_v @ c_PropLog_Opl_Ovar ) @ c_insert ) ) @ ( t_a @ ( v_t @ ( v_p @ c_PropLog_Ohyps ) ) @ c_minus ) ) @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(10,plain,
~ ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ tc_set @ ( t_a @ tc_PropLog_Opl @ ( v_F @ ( t_a @ ( v_v @ c_PropLog_Opl_Ovar ) @ c_insert ) ) @ ( t_a @ ( v_t @ ( v_p @ c_PropLog_Ohyps ) ) @ c_minus ) ) @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ tc_PropLog_Opl @ tc_set @ ( D @ tc_PropLog_Opl @ ( D @ tc_PropLog_Opl @ tc_set @ ( D @ tc_PropLog_Opl @ ( c_emptyset @ ( D @ ( C @ c_PropLog_Opl_Ovar ) @ c_insert ) ) @ ( D @ ( B @ ( A @ c_PropLog_Ohyps ) ) @ c_minus ) ) @ ( D @ ( c_PropLog_Opl_Ofalse @ ( D @ ( C @ c_PropLog_Opl_Ovar ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) @ ( D @ ( D @ tc_set @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_minus ) ) @ ( A @ c_PropLog_Ohyps ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Ohyps__Diff_0) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ tc_PropLog_Opl @ tc_set @ ( D @ tc_PropLog_Opl @ ( D @ tc_PropLog_Opl @ tc_set @ ( D @ tc_PropLog_Opl @ ( c_emptyset @ ( D @ ( C @ c_PropLog_Opl_Ovar ) @ c_insert ) ) @ ( D @ ( B @ ( A @ c_PropLog_Ohyps ) ) @ c_minus ) ) @ ( D @ ( c_PropLog_Opl_Ofalse @ ( D @ ( C @ c_PropLog_Opl_Ovar ) @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) @ ( D @ ( D @ tc_set @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_minus ) ) @ ( A @ c_PropLog_Ohyps ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
! [A: $i] : ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ tc_set @ ( v_F @ ( t_a @ ( A @ ( v_p @ c_PropLog_Ohyps ) ) @ c_minus ) ) @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(9,plain,
! [A: $i] : ( t_a @ tc_PropLog_Opl @ ( t_a @ ( t_a @ tc_PropLog_Opl @ tc_set @ ( v_F @ ( t_a @ ( A @ ( v_p @ c_PropLog_Ohyps ) ) @ c_minus ) ) @ c_PropLog_Othms ) @ ( v_p @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_PropLog_Opl @ ( D @ ( C @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( D @ tc_PropLog_Opl @ ( D @ ( D @ tc_PropLog_Opl @ ( C @ ( D @ ( c_PropLog_Opl_Ofalse @ ( B @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ 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_Othms__excluded__middle__rule_0) ).
thf(17,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_PropLog_Opl @ ( D @ ( C @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( D @ tc_PropLog_Opl @ ( D @ ( D @ tc_PropLog_Opl @ ( C @ ( D @ ( c_PropLog_Opl_Ofalse @ ( B @ c_PropLog_Opl_Oop_A_N_62 ) ) @ c_insert ) ) @ c_PropLog_Othms ) @ ( A @ 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)],[7]) ).
thf(3,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_PropLog_Opl @ ( D @ ( D @ tc_PropLog_Opl @ tc_set @ ( C @ ( E @ c_minus ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( D @ tc_PropLog_Opl @ tc_set @ ( E @ ( B @ c_lessequals ) ) )
| ~ ( D @ tc_PropLog_Opl @ ( D @ ( D @ tc_PropLog_Opl @ tc_set @ ( C @ ( B @ c_minus ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_ODiff__weaken__left_0) ).
thf(12,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_PropLog_Opl @ ( D @ ( D @ tc_PropLog_Opl @ tc_set @ ( C @ ( E @ c_minus ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( D @ tc_PropLog_Opl @ tc_set @ ( E @ ( B @ c_lessequals ) ) )
| ~ ( D @ tc_PropLog_Opl @ ( D @ ( D @ tc_PropLog_Opl @ tc_set @ ( C @ ( B @ c_minus ) ) @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ tc_set @ ( D @ ( D @ tc_set @ ( D @ ( E @ ( C @ c_insert ) ) @ ( B @ c_minus ) ) @ ( A @ c_insert ) ) @ ( D @ tc_set @ ( E @ ( D @ ( D @ tc_set @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_minus ) ) @ ( A @ c_insert ) ) @ c_minus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oinsert__Diff__subset2_0) ).
thf(16,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ tc_set @ ( D @ ( D @ tc_set @ ( D @ ( E @ ( C @ c_insert ) ) @ ( B @ c_minus ) ) @ ( A @ c_insert ) ) @ ( D @ tc_set @ ( E @ ( D @ ( D @ tc_set @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_minus ) ) @ ( A @ c_insert ) ) @ c_minus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( D @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left_0) ).
thf(19,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_PropLog_Opl @ ( C @ ( D @ c_PropLog_Othms ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_PropLog_Opl @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_PropLog_Opl @ ( C @ ( B @ c_PropLog_Othms ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ ( D @ c_insert ) ) @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oinsert__Diff__same_0) ).
thf(15,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ ( D @ c_insert ) ) @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(25,plain,
$false,
inference(e,[status(thm)],[10,14,9,17,12,16,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL429-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % 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
% 0.12/0.39 % Computer : n005.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 22:32:01 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.84/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/1.16 % [INFO] Parsing done (183ms).
% 1.20/1.17 % [INFO] Running in sequential loop mode.
% 1.75/1.59 % [INFO] eprover registered as external prover.
% 1.75/1.59 % [INFO] Scanning for conjecture ...
% 2.08/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.08/1.74 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.08/1.77 % [INFO] Problem is propositional (TPTP CNF).
% 2.08/1.78 % [INFO] Type checking passed.
% 2.08/1.78 % [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 ...
% 3.62/2.44 % External prover 'e' found a proof!
% 3.62/2.44 % [INFO] Killing All external provers ...
% 3.62/2.44 % Time passed: 1900ms (effective reasoning time: 1258ms)
% 3.62/2.44 % Axioms used in derivation (6): cls_PropLog_Oinsert__Diff__subset2_0, cls_PropLog_Oweaken__left_0, cls_PropLog_ODiff__weaken__left_0, cls_PropLog_Othms__excluded__middle__rule_0, cls_PropLog_Oinsert__Diff__same_0, cls_PropLog_Ohyps__Diff_0
% 3.62/2.44 % No. of inferences in proof: 17
% 3.62/2.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1900 ms resp. 1258 ms w/o parsing
% 3.62/2.49 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.62/2.49 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------