TSTP Solution File: LCL155-1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : LCL155-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 : Tue May 21 00:04:51 EDT 2024
% Result : Unsatisfiable 4.39s 2.70s
% Output : Refutation 4.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 26
% Syntax : Number of formulae : 44 ( 35 unt; 9 typ; 0 def)
% Number of atoms : 35 ( 34 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 202 ( 2 ~; 0 |; 0 &; 200 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 0 ^ 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(xor_type,type,
xor: $i > $i > $i ).
thf(x_type,type,
x: $i ).
thf(falsehood_type,type,
falsehood: $i ).
thf(and_star_type,type,
and_star: $i > $i > $i ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(truth_type,type,
truth: $i ).
thf(or_type,type,
or: $i > $i > $i ).
thf(not_type,type,
not: $i > $i ).
thf(and_type,type,
and: $i > $i > $i ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( or @ A @ B )
= ( implies @ ( not @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_definition) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( or @ A @ B )
= ( implies @ ( not @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,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(41,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ ( not @ A ) @ ( not @ B ) ) @ ( implies @ B @ A ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( and @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_commutativity) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( and @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [A: $i] :
( ( implies @ truth @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_1) ).
thf(27,plain,
! [A: $i] :
( ( implies @ truth @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( xor @ A @ B )
= ( or @ ( and @ A @ ( not @ B ) ) @ ( and @ ( not @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_definition) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( xor @ A @ B )
= ( or @ ( and @ A @ ( not @ B ) ) @ ( and @ ( not @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( and @ ( and @ A @ B ) @ C )
= ( and @ A @ ( and @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_associativity) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( and @ ( and @ A @ B ) @ C )
= ( and @ A @ ( and @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( or @ ( or @ A @ B ) @ C )
= ( or @ A @ ( or @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_associativity) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( or @ ( or @ A @ B ) @ C )
= ( or @ A @ ( or @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
( ( xor @ x @ x )
!= falsehood ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
thf(18,plain,
( ( xor @ x @ x )
!= falsehood ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,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(31,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)],[7]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( and_star @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_definition) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( and_star @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( and_star @ ( and_star @ A @ B ) @ C )
= ( and_star @ A @ ( and_star @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_associativity) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( and_star @ ( and_star @ A @ B ) @ C )
= ( and_star @ A @ ( and_star @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( xor @ A @ B )
= ( xor @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutativity) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( xor @ A @ B )
= ( xor @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
( ( not @ truth )
= falsehood ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_definition) ).
thf(47,plain,
( ( not @ truth )
= falsehood ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( or @ A @ B )
= ( or @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_commutativity) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( or @ A @ B )
= ( or @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
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(25,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(2,axiom,
! [B: $i,A: $i] :
( ( and_star @ A @ B )
= ( and_star @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_commutativity) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( and_star @ A @ B )
= ( and_star @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_definition) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(53,plain,
$false,
inference(e,[status(thm)],[29,41,45,27,49,39,35,18,31,43,23,51,47,37,25,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL155-1 : TPTP v8.2.0. Released v1.0.0.
% 0.13/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n027.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 20 02:19:09 EDT 2024
% 0.15/0.35 % CPUTime :
% 1.30/1.16 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.65/1.36 % [INFO] Parsing done (198ms).
% 1.65/1.38 % [INFO] Running in sequential loop mode.
% 2.49/1.86 % [INFO] eprover registered as external prover.
% 2.49/1.86 % [INFO] cvc4 registered as external prover.
% 2.49/1.87 % [INFO] Scanning for conjecture ...
% 2.72/1.97 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.84/2.03 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.84/2.06 % [INFO] Problem is propositional (TPTP CNF).
% 2.84/2.07 % [INFO] Type checking passed.
% 3.07/2.08 % [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 ...
% 4.14/2.69 % External prover 'e' found a proof!
% 4.39/2.70 % [INFO] Killing All external provers ...
% 4.39/2.70 % Time passed: 2161ms (effective reasoning time: 1311ms)
% 4.39/2.70 % Axioms used in derivation (16): wajsberg_3, or_definition, and_definition, xor_definition, and_commutativity, false_definition, and_associativity, or_associativity, and_star_definition, and_star_commutativity, wajsberg_4, and_star_associativity, or_commutativity, wajsberg_1, wajsberg_2, xor_commutativity
% 4.39/2.70 % No. of inferences in proof: 35
% 4.39/2.70 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2161 ms resp. 1311 ms w/o parsing
% 4.64/2.81 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.64/2.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------