TSTP Solution File: LCL146-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL146-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.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 11:29:30 EDT 2023
% Result : Unsatisfiable 2.71s 1.63s
% Output : Refutation 2.71s
% 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 : 122 ( 6 ~; 4 |; 0 &; 112 @)
% ( 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(not_type,type,
not: $i > $i ).
thf(big_hat_type,type,
big_hat: $i > $i > $i ).
thf(x_type,type,
x: $i ).
thf(y_type,type,
y: $i ).
thf(big_V_type,type,
big_V: $i > $i > $i ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(truth_type,type,
truth: $i ).
thf(ordered_type,type,
ordered: $i > $i > $o ).
thf(1,negated_conjecture,
( ( not @ ( big_hat @ x @ y ) )
!= ( big_V @ ( not @ x ) @ ( not @ y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).
thf(10,plain,
( ( not @ ( big_hat @ x @ y ) )
!= ( big_V @ ( not @ x ) @ ( not @ y ) ) ),
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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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(31,plain,
$false,
inference(e,[status(thm)],[10,25,13,17,23,19,15,28,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL146-1 : TPTP v8.1.2. Released v1.0.0.
% 0.15/0.16 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n001.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 16:35:35 EDT 2023
% 0.21/0.36 % CPUTime :
% 0.91/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.98 % [INFO] Parsing done (119ms).
% 1.22/0.99 % [INFO] Running in sequential loop mode.
% 1.62/1.20 % [INFO] eprover registered as external prover.
% 1.62/1.21 % [INFO] cvc4 registered as external prover.
% 1.62/1.21 % [INFO] Scanning for conjecture ...
% 1.79/1.26 % [INFO] Found a conjecture and 8 axioms. Running axiom selection ...
% 1.79/1.28 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.79/1.30 % [INFO] Problem is propositional (TPTP CNF).
% 1.79/1.30 % [INFO] Type checking passed.
% 1.79/1.30 % [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 ...
% 2.71/1.62 % External prover 'e' found a proof!
% 2.71/1.62 % [INFO] Killing All external provers ...
% 2.71/1.63 % Time passed: 1107ms (effective reasoning time: 638ms)
% 2.71/1.63 % 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)>
% 2.71/1.63 % 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
% 2.71/1.63 % No. of inferences in proof: 19
% 2.71/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1107 ms resp. 638 ms w/o parsing
% 2.71/1.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.71/1.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------