TSTP Solution File: LCL266-3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL266-3 : TPTP v8.1.2. Released v2.3.0.
% 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 : Fri May 19 11:29:59 EDT 2023
% Result : Unsatisfiable 6.20s 2.30s
% Output : Refutation 6.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 21
% Syntax : Number of formulae : 33 ( 19 unt; 10 typ; 0 def)
% Number of atoms : 29 ( 6 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 172 ( 8 ~; 6 |; 0 &; 158 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_type,type,
theorem: $i > $o ).
thf(equivalent_type,type,
equivalent: $i > $i > $i ).
thf(and_type,type,
and: $i > $i > $i ).
thf(p_type,type,
p: $i ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(q_type,type,
q: $i ).
thf(r_type,type,
r: $i ).
thf(not_type,type,
not: $i > $i ).
thf(axiom_type,type,
axiom: $i > $o ).
thf(or_type,type,
or: $i > $i > $i ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_defn) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,axiom,
! [A: $i] : ( axiom @ ( implies @ ( or @ A @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
thf(14,plain,
! [A: $i] : ( axiom @ ( implies @ ( or @ A @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i] :
( ( theorem @ A )
| ~ ( axiom @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
thf(21,plain,
! [A: $i] :
( ( theorem @ A )
| ~ ( axiom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( axiom @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] : ( axiom @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( equivalent @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalent_defn) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,negated_conjecture,
~ ( theorem @ ( equivalent @ ( and @ p @ ( implies @ q @ r ) ) @ ( and @ p @ ( implies @ ( not @ r ) @ ( not @ q ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(12,plain,
~ ( theorem @ ( equivalent @ ( and @ p @ ( implies @ q @ r ) ) @ ( and @ p @ ( implies @ ( not @ r ) @ ( not @ q ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] : ( axiom @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] : ( axiom @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( axiom @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
thf(16,plain,
! [B: $i,A: $i] : ( axiom @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( theorem @ A )
| ~ ( theorem @ ( implies @ B @ A ) )
| ~ ( theorem @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( theorem @ A )
| ~ ( theorem @ ( implies @ B @ A ) )
| ~ ( theorem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( axiom @ ( implies @ A @ ( or @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
thf(15,plain,
! [B: $i,A: $i] : ( axiom @ ( implies @ A @ ( or @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(315,plain,
$false,
inference(e,[status(thm)],[25,14,21,17,27,12,18,16,23,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL266-3 : TPTP v8.1.2. Released v2.3.0.
% 0.12/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 16:36:51 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.13/1.00 % [INFO] Parsing done (133ms).
% 1.13/1.01 % [INFO] Running in sequential loop mode.
% 1.77/1.21 % [INFO] eprover registered as external prover.
% 1.77/1.21 % [INFO] cvc4 registered as external prover.
% 1.77/1.21 % [INFO] Scanning for conjecture ...
% 1.83/1.26 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.83/1.28 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.83/1.29 % [INFO] Problem is propositional (TPTP CNF).
% 1.83/1.30 % [INFO] Type checking passed.
% 1.83/1.30 % [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 ...
% 6.20/2.30 % External prover 'e' found a proof!
% 6.20/2.30 % [INFO] Killing All external provers ...
% 6.20/2.30 % Time passed: 1792ms (effective reasoning time: 1284ms)
% 6.20/2.30 % 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)>
% 6.20/2.30 % Axioms used in derivation (10): axiom_1_5, equivalent_defn, and_defn, axiom_1_4, rule_1, axiom_1_3, implies_definition, axiom_1_2, rule_2, axiom_1_6
% 6.20/2.30 % No. of inferences in proof: 23
% 6.20/2.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1792 ms resp. 1284 ms w/o parsing
% 6.20/2.32 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.20/2.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------