TSTP Solution File: LCL109-10 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL109-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 11:29:23 EDT 2023
% Result : Unsatisfiable 3.57s 1.92s
% Output : Refutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 22
% Syntax : Number of formulae : 39 ( 33 unt; 6 typ; 0 def)
% Number of atoms : 33 ( 32 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 198 ( 2 ~; 0 |; 0 &; 196 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 60 ( 0 ^; 60 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(implies_type,type,
implies: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(truth_type,type,
truth: $i ).
thf(not_type,type,
not: $i > $i ).
thf(ifeq_type,type,
ifeq: $i > $i > $i > $i > $i ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( implies @ ( implies @ ( not @ A ) @ ( not @ B ) ) @ ( implies @ B @ A ) )
= truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_4) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ ( not @ A ) @ ( not @ B ) ) @ ( implies @ B @ A ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: $i] :
( ( implies @ A @ ( not @ truth ) )
= ( not @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_8) ).
thf(42,plain,
! [A: $i] :
( ( implies @ A @ ( not @ truth ) )
= ( not @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) )
= truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_2) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [A: $i] :
( ( not @ ( not @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_9) ).
thf(20,plain,
! [A: $i] :
( ( not @ ( not @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( implies @ ( implies @ A @ B ) @ B )
= ( implies @ ( implies @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_3) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ A @ B ) @ B )
= ( implies @ ( implies @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ C ) )
= ( implies @ B @ ( implies @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_7) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ C ) )
= ( implies @ B @ ( implies @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
= truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_4) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,negated_conjecture,
( ( implies @ ( implies @ ( implies @ a @ b ) @ ( implies @ b @ a ) ) @ ( implies @ b @ a ) )
!= truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_mv_4) ).
thf(17,plain,
( ( implies @ ( implies @ ( implies @ a @ b ) @ ( implies @ b @ a ) ) @ ( implies @ b @ a ) )
!= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] :
( ( implies @ A @ truth )
= truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3) ).
thf(32,plain,
! [A: $i] :
( ( implies @ A @ truth )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( implies @ A @ B ) @ ( implies @ B @ C ) @ ( implies @ A @ C ) @ truth )
= truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_5) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( implies @ A @ B ) @ ( implies @ B @ C ) @ ( implies @ A @ C ) @ truth )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [A: $i] :
( ( implies @ truth @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_1) ).
thf(44,plain,
! [A: $i] :
( ( implies @ truth @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [A: $i] :
( ( implies @ A @ A )
= truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1) ).
thf(40,plain,
! [A: $i] :
( ( implies @ A @ A )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ C @ A ) @ ( implies @ C @ B ) ) )
= truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_6) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ C @ A ) @ ( implies @ C @ B ) ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( implies @ ( not @ A ) @ ( not @ B ) )
= ( implies @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_10) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( implies @ ( not @ A ) @ ( not @ B ) )
= ( implies @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( implies @ A @ B ) @ ( implies @ B @ A ) @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_2) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( implies @ A @ B ) @ ( implies @ B @ A ) @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(118,plain,
$false,
inference(e,[status(thm)],[48,42,24,20,46,28,38,17,32,34,22,44,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL109-10 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 15:53:25 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.93/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/1.03 % [INFO] Parsing done (125ms).
% 1.19/1.03 % [INFO] Running in sequential loop mode.
% 1.70/1.23 % [INFO] eprover registered as external prover.
% 1.70/1.23 % [INFO] cvc4 registered as external prover.
% 1.70/1.24 % [INFO] Scanning for conjecture ...
% 1.80/1.28 % [INFO] Found a conjecture and 15 axioms. Running axiom selection ...
% 1.80/1.32 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 1.80/1.33 % [INFO] Problem is propositional (TPTP CNF).
% 2.03/1.34 % [INFO] Type checking passed.
% 2.03/1.34 % [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 ...
% 3.57/1.92 % External prover 'e' found a proof!
% 3.57/1.92 % [INFO] Killing All external provers ...
% 3.57/1.92 % Time passed: 1393ms (effective reasoning time: 884ms)
% 3.57/1.92 % 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)>
% 3.57/1.92 % Axioms used in derivation (15): wajsberg_3, wajsberg_4, lemma_1, lemma_6, wajsberg_2, lemma_8, lemma_3, lemma_7, lemma_10, lemma_4, ifeq_axiom, lemma_5, wajsberg_1, lemma_9, lemma_2
% 3.57/1.92 % No. of inferences in proof: 33
% 3.57/1.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1393 ms resp. 884 ms w/o parsing
% 3.88/1.96 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.88/1.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------