TSTP Solution File: LCL109-4 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL109-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 11:29:24 EDT 2023
% Result : Unsatisfiable 7.41s 2.62s
% Output : Refutation 7.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 17
% Syntax : Number of formulae : 27 ( 15 unt; 8 typ; 0 def)
% Number of atoms : 23 ( 18 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 120 ( 6 ~; 4 |; 0 &; 110 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(big_V_type,type,
big_V: $i > $i > $i ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(x_type,type,
x: $i ).
thf(y_type,type,
y: $i ).
thf(truth_type,type,
truth: $i ).
thf(not_type,type,
not: $i > $i ).
thf(big_hat_type,type,
big_hat: $i > $i > $i ).
thf(ordered_type,type,
ordered: $i > $i > $o ).
thf(1,negated_conjecture,
( ( big_V @ ( implies @ x @ y ) @ ( implies @ y @ x ) )
!= truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_mv_4) ).
thf(10,plain,
( ( big_V @ ( implies @ x @ y ) @ ( implies @ y @ x ) )
!= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( ordered @ A @ B )
| ( ( implies @ A @ B )
= truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partial_order_definition1) ).
thf(25,plain,
! [B: $i,A: $i] :
( ~ ( ordered @ A @ B )
| ( ( implies @ A @ B )
= truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [A: $i] :
( ( implies @ truth @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_1) ).
thf(13,plain,
! [A: $i] :
( ( implies @ truth @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,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(17,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ A @ B ) @ B )
= ( implies @ ( implies @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( big_hat @ A @ B )
= ( not @ ( big_V @ ( not @ A ) @ ( not @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big_hat_definition) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( big_hat @ A @ B )
= ( not @ ( big_V @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,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(19,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ ( not @ A ) @ ( not @ B ) ) @ ( implies @ B @ A ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,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(15,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)],[3]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
!= truth )
| ( ordered @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partial_order_definition2) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
!= truth )
| ( ordered @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( big_V @ A @ B )
= ( implies @ ( implies @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big_V_definition) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( big_V @ A @ B )
= ( implies @ ( implies @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(640,plain,
$false,
inference(e,[status(thm)],[10,25,13,17,23,19,15,28,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL109-4 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.14 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n025.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 16:40:34 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.91/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.09/1.03 % [INFO] Parsing done (121ms).
% 1.09/1.04 % [INFO] Running in sequential loop mode.
% 1.71/1.26 % [INFO] eprover registered as external prover.
% 1.71/1.26 % [INFO] cvc4 registered as external prover.
% 1.71/1.26 % [INFO] Scanning for conjecture ...
% 1.71/1.32 % [INFO] Found a conjecture and 8 axioms. Running axiom selection ...
% 1.87/1.34 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.87/1.35 % [INFO] Problem is propositional (TPTP CNF).
% 1.87/1.36 % [INFO] Type checking passed.
% 1.87/1.36 % [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 ...
% 7.41/2.62 % External prover 'e' found a proof!
% 7.41/2.62 % [INFO] Killing All external provers ...
% 7.41/2.62 % Time passed: 2083ms (effective reasoning time: 1576ms)
% 7.41/2.62 % 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)>
% 7.41/2.62 % Axioms used in derivation (8): partial_order_definition1, wajsberg_3, big_V_definition, wajsberg_1, big_hat_definition, wajsberg_2, partial_order_definition2, wajsberg_4
% 7.41/2.62 % No. of inferences in proof: 19
% 7.41/2.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2083 ms resp. 1576 ms w/o parsing
% 7.41/2.64 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.41/2.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------