TSTP Solution File: LCL156-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL156-1 : 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 11:29:31 EDT 2023
% Result : Unsatisfiable 2.91s 1.63s
% Output : Refutation 3.24s
% 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(and_star_type,type,
and_star: $i > $i > $i ).
thf(x_type,type,
x: $i ).
thf(truth_type,type,
truth: $i ).
thf(and_type,type,
and: $i > $i > $i ).
thf(xor_type,type,
xor: $i > $i > $i ).
thf(not_type,type,
not: $i > $i ).
thf(or_type,type,
or: $i > $i > $i ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(falsehood_type,type,
falsehood: $i ).
thf(6,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(29,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)],[6]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( and_star @ A @ B )
= ( and_star @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_commutativity) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( and_star @ A @ B )
= ( and_star @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i] :
( ( implies @ truth @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_1) ).
thf(45,plain,
! [A: $i] :
( ( implies @ truth @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_definition) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,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(49,plain,
! [B: $i,A: $i] :
( ( and_star @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,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(39,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)],[11]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( or @ A @ B )
= ( implies @ ( not @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_definition) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( or @ A @ B )
= ( implies @ ( not @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
( ( and_star @ x @ truth )
!= x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
thf(18,plain,
( ( and_star @ x @ truth )
!= x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( or @ A @ B )
= ( or @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_commutativity) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( or @ A @ B )
= ( or @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,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(43,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)],[13]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( xor @ A @ B )
= ( xor @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutativity) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( xor @ A @ B )
= ( xor @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
( ( not @ truth )
= falsehood ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_definition) ).
thf(51,plain,
( ( not @ truth )
= falsehood ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,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(47,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ ( not @ A ) @ ( not @ B ) ) @ ( implies @ B @ A ) )
= truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,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(37,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ A @ B ) @ B )
= ( implies @ ( implies @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( and @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_commutativity) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( and @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,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(21,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)],[2]) ).
thf(8,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(33,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)],[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
% 0.07/0.12 % Problem : LCL156-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n001.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 16:30:35 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.88/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.96 % [INFO] Parsing done (115ms).
% 1.20/0.97 % [INFO] Running in sequential loop mode.
% 1.60/1.17 % [INFO] eprover registered as external prover.
% 1.60/1.17 % [INFO] cvc4 registered as external prover.
% 1.60/1.18 % [INFO] Scanning for conjecture ...
% 1.84/1.22 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 1.95/1.26 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 1.95/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 1.95/1.28 % [INFO] Type checking passed.
% 1.95/1.28 % [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 ...
% 2.91/1.63 % External prover 'e' found a proof!
% 2.91/1.63 % [INFO] Killing All external provers ...
% 2.91/1.63 % Time passed: 1107ms (effective reasoning time: 654ms)
% 2.91/1.63 % 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)>
% 2.91/1.63 % 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
% 2.91/1.63 % No. of inferences in proof: 35
% 2.91/1.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1107 ms resp. 654 ms w/o parsing
% 3.24/1.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.24/1.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------