TSTP Solution File: LCL429-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL429-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:30:21 EDT 2023
% Result : Unsatisfiable 2.71s 1.59s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 25
% Syntax : Number of formulae : 34 ( 11 unt; 17 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 : 24 ( 24 >; 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_type,type,
c_in: $i > $i > $i > $o ).
thf(v_p_type,type,
v_p: $i ).
thf(c_PropLog_Othms_type,type,
c_PropLog_Othms: $i > $i > $i ).
thf(c_minus_type,type,
c_minus: $i > $i > $i > $i ).
thf(c_PropLog_Ohyps_type,type,
c_PropLog_Ohyps: $i > $i > $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(v_F_type,type,
v_F: $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(tc_PropLog_Opl_type,type,
tc_PropLog_Opl: $i > $i ).
thf(v_t_type,type,
v_t: $i ).
thf(c_insert_type,type,
c_insert: $i > $i > $i > $i ).
thf(c_PropLog_Opl_Ovar_type,type,
c_PropLog_Opl_Ovar: $i > $i > $i ).
thf(v_v_type,type,
v_v: $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(c_PropLog_Opl_Oop_A_N_62_type,type,
c_PropLog_Opl_Oop_A_N_62: $i > $i > $i > $i ).
thf(c_PropLog_Opl_Ofalse_type,type,
c_PropLog_Opl_Ofalse: $i ).
thf(2,negated_conjecture,
~ ( c_in @ v_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ v_p @ v_t @ t_a ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ v_v @ t_a ) @ v_F @ ( tc_PropLog_Opl @ t_a ) ) @ ( tc_set @ ( tc_PropLog_Opl @ t_a ) ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(10,plain,
~ ( c_in @ v_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ v_p @ v_t @ t_a ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ v_v @ t_a ) @ v_F @ ( tc_PropLog_Opl @ t_a ) ) @ ( tc_set @ ( tc_PropLog_Opl @ t_a ) ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_PropLog_Ohyps @ A @ ( c_minus @ B @ ( c_insert @ C @ c_emptyset @ D ) @ ( tc_set @ D ) ) @ D ) @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Ovar @ C @ D ) @ c_PropLog_Opl_Ofalse @ D ) @ ( c_minus @ ( c_PropLog_Ohyps @ A @ B @ D ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ C @ D ) @ c_emptyset @ ( tc_PropLog_Opl @ D ) ) @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) ) @ ( tc_PropLog_Opl @ D ) ) @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Ohyps__Diff_0) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_PropLog_Ohyps @ A @ ( c_minus @ B @ ( c_insert @ C @ c_emptyset @ D ) @ ( tc_set @ D ) ) @ D ) @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Ovar @ C @ D ) @ c_PropLog_Opl_Ofalse @ D ) @ ( c_minus @ ( c_PropLog_Ohyps @ A @ B @ D ) @ ( c_insert @ ( c_PropLog_Opl_Ovar @ C @ D ) @ c_emptyset @ ( tc_PropLog_Opl @ D ) ) @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) ) @ ( tc_PropLog_Opl @ D ) ) @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
! [A: $i] : ( c_in @ v_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ v_p @ A @ t_a ) @ v_F @ ( tc_set @ ( tc_PropLog_Opl @ t_a ) ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(9,plain,
! [A: $i] : ( c_in @ v_p @ ( c_PropLog_Othms @ ( c_minus @ ( c_PropLog_Ohyps @ v_p @ A @ t_a ) @ v_F @ ( tc_set @ ( tc_PropLog_Opl @ t_a ) ) ) @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_PropLog_Othms @ ( c_insert @ B @ C @ ( tc_PropLog_Opl @ D ) ) @ D ) @ ( tc_PropLog_Opl @ D ) )
| ~ ( c_in @ A @ ( c_PropLog_Othms @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ B @ c_PropLog_Opl_Ofalse @ D ) @ C @ ( tc_PropLog_Opl @ D ) ) @ D ) @ ( tc_PropLog_Opl @ D ) )
| ( c_in @ A @ ( c_PropLog_Othms @ C @ D ) @ ( tc_PropLog_Opl @ D ) ) ),
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] :
( ~ ( c_in @ A @ ( c_PropLog_Othms @ ( c_insert @ B @ C @ ( tc_PropLog_Opl @ D ) ) @ D ) @ ( tc_PropLog_Opl @ D ) )
| ~ ( c_in @ A @ ( c_PropLog_Othms @ ( c_insert @ ( c_PropLog_Opl_Oop_A_N_62 @ B @ c_PropLog_Opl_Ofalse @ D ) @ C @ ( tc_PropLog_Opl @ D ) ) @ D ) @ ( tc_PropLog_Opl @ D ) )
| ( c_in @ A @ ( c_PropLog_Othms @ C @ D ) @ ( tc_PropLog_Opl @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_PropLog_Othms @ ( c_minus @ B @ C @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) ) @ D ) @ ( tc_PropLog_Opl @ D ) )
| ~ ( c_lessequals @ B @ E @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) )
| ( c_in @ A @ ( c_PropLog_Othms @ ( c_minus @ E @ C @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) ) @ D ) @ ( tc_PropLog_Opl @ D ) ) ),
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] :
( ~ ( c_in @ A @ ( c_PropLog_Othms @ ( c_minus @ B @ C @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) ) @ D ) @ ( tc_PropLog_Opl @ D ) )
| ~ ( c_lessequals @ B @ E @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) )
| ( c_in @ A @ ( c_PropLog_Othms @ ( c_minus @ E @ C @ ( tc_set @ ( tc_PropLog_Opl @ D ) ) ) @ D ) @ ( tc_PropLog_Opl @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_minus @ ( c_insert @ A @ ( c_minus @ B @ ( c_insert @ C @ c_emptyset @ D ) @ ( tc_set @ D ) ) @ D ) @ E @ ( tc_set @ D ) ) @ ( c_insert @ A @ ( c_minus @ B @ ( c_insert @ C @ E @ D ) @ ( tc_set @ D ) ) @ D ) @ ( tc_set @ D ) ),
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] : ( c_lessequals @ ( c_minus @ ( c_insert @ A @ ( c_minus @ B @ ( c_insert @ C @ c_emptyset @ D ) @ ( tc_set @ D ) ) @ D ) @ E @ ( tc_set @ D ) ) @ ( c_insert @ A @ ( c_minus @ B @ ( c_insert @ C @ E @ D ) @ ( tc_set @ D ) ) @ D ) @ ( tc_set @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ ( tc_PropLog_Opl @ C ) ) )
| ( c_in @ A @ ( c_PropLog_Othms @ D @ C ) @ ( tc_PropLog_Opl @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left_0) ).
thf(19,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_PropLog_Othms @ B @ C ) @ ( tc_PropLog_Opl @ C ) )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ ( tc_PropLog_Opl @ C ) ) )
| ( c_in @ A @ ( c_PropLog_Othms @ D @ C ) @ ( tc_PropLog_Opl @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ ( c_insert @ D @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ C ) @ ( tc_set @ C ) ),
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_lessequals @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ ( c_insert @ D @ ( c_minus @ A @ ( c_insert @ D @ B @ C ) @ ( tc_set @ C ) ) @ C ) @ ( tc_set @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[10,14,9,17,12,16,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL429-2 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 15:06:31 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.94/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.95 % [INFO] Parsing done (117ms).
% 1.22/0.96 % [INFO] Running in sequential loop mode.
% 1.64/1.15 % [INFO] eprover registered as external prover.
% 1.64/1.15 % [INFO] cvc4 registered as external prover.
% 1.64/1.16 % [INFO] Scanning for conjecture ...
% 1.73/1.22 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 1.86/1.24 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.94/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.94/1.27 % [INFO] Type checking passed.
% 1.94/1.27 % [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 ...
% 2.71/1.59 % External prover 'e' found a proof!
% 2.71/1.59 % [INFO] Killing All external provers ...
% 2.71/1.59 % Time passed: 1078ms (effective reasoning time: 631ms)
% 2.71/1.59 % Solved by 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)>
% 2.71/1.59 % 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
% 2.71/1.59 % No. of inferences in proof: 17
% 2.71/1.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1078 ms resp. 631 ms w/o parsing
% 2.71/1.63 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.71/1.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------