TSTP Solution File: LCL161-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL161-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 11:29:32 EDT 2023
% Result : Unsatisfiable 2.68s 1.61s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 21
% Syntax : Number of formulae : 36 ( 29 unt; 7 typ; 0 def)
% Number of atoms : 29 ( 28 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 134 ( 2 ~; 0 |; 0 &; 132 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 0 ^; 38 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(implies_type,type,
implies: $i > $i > $i ).
thf(truth_type,type,
truth: $i ).
thf(x_type,type,
x: $i ).
thf(not_type,type,
not: $i > $i ).
thf(xor_type,type,
xor: $i > $i > $i ).
thf(falsehood_type,type,
falsehood: $i ).
thf(and_star_type,type,
and_star: $i > $i > $i ).
thf(3,axiom,
! [A: $i] :
( ( xor @ A @ falsehood )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(20,plain,
! [A: $i] :
( ( xor @ A @ falsehood )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i] :
( ( xor @ A @ A )
= falsehood ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(22,plain,
! [A: $i] :
( ( xor @ A @ A )
= falsehood ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [A: $i] :
( ( not @ A )
= ( xor @ A @ truth ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(18,plain,
! [A: $i] :
( ( not @ A )
= ( xor @ A @ truth ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
( ( implies @ truth @ x )
!= x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_axiom) ).
thf(15,plain,
( ( implies @ truth @ x )
!= x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( implies @ A @ B )
= ( xor @ truth @ ( and_star @ A @ ( xor @ truth @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( implies @ A @ B )
= ( xor @ truth @ ( and_star @ A @ ( xor @ truth @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [A: $i] :
( ( and_star @ A @ truth )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(24,plain,
! [A: $i] :
( ( and_star @ A @ truth )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: $i] :
( ( and_star @ ( xor @ truth @ A ) @ A )
= falsehood ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
thf(28,plain,
! [A: $i] :
( ( and_star @ ( xor @ truth @ A ) @ A )
= falsehood ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( and_star @ A @ B )
= ( and_star @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_commutativity) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( and_star @ A @ B )
= ( and_star @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ A ) @ B ) @ truth ) @ B )
= ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ B ) @ A ) @ truth ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ A ) @ B ) @ truth ) @ B )
= ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ B ) @ A ) @ truth ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( xor @ A @ B )
= ( xor @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutativity) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( xor @ A @ B )
= ( xor @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
( ( not @ truth )
= falsehood ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false_definition) ).
thf(40,plain,
( ( not @ truth )
= falsehood ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [A: $i] :
( ( and_star @ A @ falsehood )
= falsehood ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(26,plain,
! [A: $i] :
( ( and_star @ A @ falsehood )
= falsehood ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( and_star @ ( and_star @ A @ B ) @ C )
= ( and_star @ A @ ( and_star @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_associativity) ).
thf(36,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)],[11]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( xor @ A @ ( xor @ truth @ B ) )
= ( xor @ ( xor @ A @ truth ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( xor @ A @ ( xor @ truth @ B ) )
= ( xor @ ( xor @ A @ truth ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44,plain,
$false,
inference(e,[status(thm)],[20,22,18,15,42,24,28,38,32,34,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL161-1 : TPTP v8.1.2. Released v1.0.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n020.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 16:21:18 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.95/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/0.98 % [INFO] Parsing done (118ms).
% 1.28/0.99 % [INFO] Running in sequential loop mode.
% 1.71/1.19 % [INFO] eprover registered as external prover.
% 1.71/1.19 % [INFO] cvc4 registered as external prover.
% 1.71/1.19 % [INFO] Scanning for conjecture ...
% 1.87/1.24 % [INFO] Found a conjecture and 13 axioms. Running axiom selection ...
% 1.93/1.26 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.93/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 1.93/1.28 % [INFO] Type checking passed.
% 1.93/1.28 % [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 ...
% 2.68/1.60 % External prover 'e' found a proof!
% 2.68/1.61 % [INFO] Killing All external provers ...
% 2.68/1.61 % Time passed: 1074ms (effective reasoning time: 617ms)
% 2.68/1.61 % 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)>
% 2.68/1.61 % Axioms used in derivation (13): axiom_7, axiom_6, axiom_3, axiom_1, axiom_8, axiom_5, xor_commutativity, axiom_4, axiom_2, and_star_commutativity, and_star_associativity, false_definition, implies_definition
% 2.68/1.61 % No. of inferences in proof: 29
% 2.68/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1074 ms resp. 617 ms w/o parsing
% 2.68/1.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.68/1.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------