TSTP Solution File: LCL096-10 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : LCL096-10 : TPTP v8.2.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n032.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 : Mon Jun 24 11:12:47 EDT 2024
% Result : Unsatisfiable 12.73s 4.18s
% Output : Refutation 13.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 164 ( 2 ~; 0 |; 0 &; 162 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 38 ( 0 ^ 38 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_type,type,
is_a_theorem: $i > $i ).
thf(equivalent_type,type,
equivalent: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(true_type,type,
true: $i ).
thf(ifeq_type,type,
ifeq: $i > $i > $i > $i > $i ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ A @ B ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ B @ C ) ) @ D ) @ D ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_2) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ A @ B ) @ ( equivalent @ A @ C ) ) @ ( equivalent @ B @ C ) ) @ D ) @ D ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( is_a_theorem @ ( equivalent @ A @ B ) ) @ true @ ( ifeq @ ( is_a_theorem @ A ) @ true @ ( is_a_theorem @ B ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( is_a_theorem @ ( equivalent @ A @ B ) ) @ true @ ( ifeq @ ( is_a_theorem @ A ) @ true @ ( is_a_theorem @ B ) @ true ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ b ) @ a ) ) @ c ) @ c ) )
!= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lg_1) ).
thf(7,plain,
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ b ) @ a ) ) @ c ) @ c ) )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ A @ B ) @ C ) @ D ) @ ( equivalent @ ( equivalent @ ( equivalent @ A @ E ) @ C ) @ ( equivalent @ ( equivalent @ B @ E ) @ D ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_4) ).
thf(18,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ A @ B ) @ C ) @ D ) @ ( equivalent @ ( equivalent @ ( equivalent @ A @ E ) @ C ) @ ( equivalent @ ( equivalent @ B @ E ) @ D ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ A @ B ) @ ( equivalent @ A @ C ) ) @ D ) @ ( equivalent @ ( equivalent @ B @ C ) @ D ) ) @ E ) @ E ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_3) ).
thf(16,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ A @ B ) @ ( equivalent @ A @ C ) ) @ D ) @ ( equivalent @ ( equivalent @ B @ C ) @ D ) ) @ E ) @ E ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(445,plain,
$false,
inference(e,[status(thm)],[10,14,12,7,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LCL096-10 : TPTP v8.2.0. Released v7.3.0.
% 0.10/0.11 % Command : run_Leo-III %s %d THM
% 0.10/0.31 % Computer : n032.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.32 % DateTime : Sat Jun 22 16:22:40 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.99/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/1.15 % [INFO] Parsing done (158ms).
% 1.20/1.17 % [INFO] Running in sequential loop mode.
% 1.94/1.53 % [INFO] eprover registered as external prover.
% 1.94/1.54 % [INFO] Scanning for conjecture ...
% 2.10/1.64 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.10/1.68 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.22/1.70 % [INFO] Problem is propositional (TPTP CNF).
% 2.22/1.70 % [INFO] Type checking passed.
% 2.22/1.71 % [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 ...
% 12.73/4.18 % External prover 'e' found a proof!
% 12.73/4.18 % [INFO] Killing All external provers ...
% 12.73/4.18 % Time passed: 3683ms (effective reasoning time: 3006ms)
% 12.73/4.18 % Axioms used in derivation (5): ifeq_axiom, condensed_detachment, lg_2, lg_3, lg_4
% 12.73/4.18 % No. of inferences in proof: 13
% 12.73/4.18 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3683 ms resp. 3006 ms w/o parsing
% 13.11/4.22 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.11/4.22 % [INFO] Killing All external provers ...
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