TSTP Solution File: LCL341-3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL341-3 : TPTP v8.1.2. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 11:30:08 EDT 2023
% Result : Unsatisfiable 9.05s 2.67s
% Output : Refutation 9.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of formulae : 77 ( 48 unt; 9 typ; 0 def)
% Number of atoms : 104 ( 25 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 538 ( 28 ~; 26 |; 0 &; 484 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 140 ( 0 ^; 140 !; 0 ?; 140 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_type,type,
theorem: $i > $o ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(p_type,type,
p: $i ).
thf(equivalent_type,type,
equivalent: $i > $i > $i ).
thf(q_type,type,
q: $i ).
thf(axiom_type,type,
axiom: $i > $o ).
thf(or_type,type,
or: $i > $i > $i ).
thf(not_type,type,
not: $i > $i ).
thf(and_type,type,
and: $i > $i > $i ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ),
file('/export/starexec/sandbox2/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(20,plain,
! [B: $i,A: $i] :
( ( or @ ( not @ A ) @ B )
= ( implies @ A @ B ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( axiom @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ),
file('/export/starexec/sandbox2/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(61,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ C @ D ) @ ( implies @ A @ B ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,16]) ).
thf(62,plain,
! [B: $i,A: $i] : ( axiom @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[61:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( not @ E ))]]) ).
thf(69,plain,
! [B: $i,A: $i] : ( axiom @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
file('/export/starexec/sandbox2/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(26,plain,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ( and @ A @ B )
= ( not @ ( implies @ A @ ( not @ B ) ) ) ),
inference(rewrite,[status(thm)],[26,20]) ).
thf(2,axiom,
! [A: $i] : ( axiom @ ( implies @ ( or @ A @ A ) @ A ) ),
file('/export/starexec/sandbox2/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(1,negated_conjecture,
~ ( theorem @ ( implies @ p @ ( equivalent @ ( implies @ p @ q ) @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(12,plain,
~ ( theorem @ ( implies @ p @ ( equivalent @ ( implies @ p @ q ) @ q ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( equivalent @ A @ B )
= ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ),
file('/export/starexec/sandbox2/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(28,plain,
! [B: $i,A: $i] :
( ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) )
= ( equivalent @ A @ B ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( equivalent @ A @ B )
= ( not @ ( implies @ ( implies @ A @ B ) @ ( not @ ( implies @ B @ A ) ) ) ) ),
inference(rewrite,[status(thm)],[28,153]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] : ( axiom @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/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(9,axiom,
! [B: $i,A: $i] :
( ( theorem @ A )
| ~ ( theorem @ ( implies @ B @ A ) )
| ~ ( theorem @ B ) ),
file('/export/starexec/sandbox2/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(24,plain,
! [B: $i,A: $i] :
( ( theorem @ A )
| ~ ( theorem @ ( implies @ B @ A ) )
| ~ ( theorem @ B ) ),
inference(cnf,[status(esa)],[23]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( theorem @ A )
| ~ ( theorem @ B )
| ( ( theorem @ ( implies @ B @ A ) )
!= ( theorem @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[24]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( theorem @ A )
| ~ ( theorem @ B )
| ( ( implies @ B @ A )
!= B ) ),
inference(simp,[status(thm)],[35]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( axiom @ ( implies @ A @ ( or @ B @ A ) ) ),
file('/export/starexec/sandbox2/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(8,axiom,
! [A: $i] :
( ( theorem @ A )
| ~ ( axiom @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
thf(21,plain,
! [A: $i] :
( ( theorem @ A )
| ~ ( axiom @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(22,plain,
! [A: $i] :
( ( theorem @ A )
| ~ ( axiom @ A ) ),
inference(cnf,[status(esa)],[21]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ C )
| ( ( axiom @ ( implies @ A @ ( or @ B @ A ) ) )
!= ( axiom @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,22]) ).
thf(43,plain,
! [B: $i,A: $i] : ( theorem @ ( implies @ B @ ( or @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( implies @ G @ ( or @ F @ G ) ))]]) ).
thf(46,plain,
! [B: $i,A: $i] : ( theorem @ ( implies @ B @ ( or @ A @ B ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( theorem @ B )
| ( ( axiom @ ( implies @ ( or @ A @ A ) @ A ) )
!= ( axiom @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14,22]) ).
thf(39,plain,
! [A: $i] : ( theorem @ ( implies @ ( or @ A @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( D )),bind(B,$thf( implies @ ( or @ D @ D ) @ D ))]]) ).
thf(44,plain,
! [A: $i] : ( theorem @ ( implies @ ( or @ A @ A ) @ A ) ),
inference(simp,[status(thm)],[39]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ ( implies @ A @ B ) @ C ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,44]) ).
thf(48,plain,
! [A: $i] : ( theorem @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) ),
inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( E )),bind(B,$thf( not @ E )),bind(C,$thf( not @ E ))]]) ).
thf(57,plain,
! [A: $i] : ( theorem @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ C @ ( implies @ A @ B ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,15]) ).
thf(32,plain,
! [B: $i,A: $i] : ( axiom @ ( implies @ A @ ( implies @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( not @ E ))]]) ).
thf(33,plain,
! [B: $i,A: $i] : ( axiom @ ( implies @ A @ ( implies @ B @ A ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ B ) @ C ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,14]) ).
thf(30,plain,
! [A: $i] : ( axiom @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( E )),bind(B,$thf( not @ E )),bind(C,$thf( not @ E ))]]) ).
thf(34,plain,
! [A: $i] : ( axiom @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ C )
| ( ( axiom @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) )
!= ( axiom @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16,22]) ).
thf(66,plain,
! [B: $i,A: $i] : ( theorem @ ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( implies @ ( or @ I @ H ) @ ( or @ H @ I ) ))]]) ).
thf(68,plain,
! [B: $i,A: $i] : ( theorem @ ( implies @ ( or @ B @ A ) @ ( or @ A @ B ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ ( implies @ A @ B ) @ ( or @ C @ D ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,68]) ).
thf(144,plain,
! [B: $i,A: $i] : ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( not @ E ))]]) ).
thf(148,plain,
! [B: $i,A: $i] : ( theorem @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) ),
inference(simp,[status(thm)],[144]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( theorem @ C )
| ( ( axiom @ ( implies @ A @ ( implies @ B @ A ) ) )
!= ( axiom @ C ) ) ),
inference(paramod_ordered,[status(thm)],[33,22]) ).
thf(41,plain,
! [B: $i,A: $i] : ( theorem @ ( implies @ B @ ( implies @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( implies @ G @ ( implies @ F @ G ) ))]]) ).
thf(45,plain,
! [B: $i,A: $i] : ( theorem @ ( implies @ B @ ( implies @ A @ B ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( axiom @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/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(145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( theorem @ ( implies @ ( or @ D @ C ) @ ( implies @ A @ B ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[20,68]) ).
thf(146,plain,
! [B: $i,A: $i] : ( theorem @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[145:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(149,plain,
! [B: $i,A: $i] : ( theorem @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) ),
inference(simp,[status(thm)],[146]) ).
thf(63,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ B ) @ ( or @ D @ C ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[20,16]) ).
thf(64,plain,
! [B: $i,A: $i] : ( axiom @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(67,plain,
! [B: $i,A: $i] : ( axiom @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ D @ C ) @ ( implies @ A @ B ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,67]) ).
thf(155,plain,
! [B: $i,A: $i] : ( axiom @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[154:[bind(A,$thf( E )),bind(B,$thf( not @ F )),bind(C,$thf( not @ E )),bind(D,$thf( F ))]]) ).
thf(158,plain,
! [B: $i,A: $i] : ( axiom @ ( implies @ ( implies @ B @ ( not @ A ) ) @ ( implies @ A @ ( not @ B ) ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(466,plain,
$false,
inference(e,[status(thm)],[69,153,14,12,226,18,19,24,37,25,20,46,57,21,33,34,148,45,17,149,22,44,27,67,16,158,23,15,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL341-3 : TPTP v8.1.2. Released v2.3.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n017.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 15:35:46 EDT 2023
% 0.15/0.37 % CPUTime :
% 1.01/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.98 % [INFO] Parsing done (118ms).
% 1.39/0.99 % [INFO] Running in sequential loop mode.
% 1.76/1.19 % [INFO] eprover registered as external prover.
% 1.76/1.19 % [INFO] cvc4 registered as external prover.
% 1.76/1.20 % [INFO] Scanning for conjecture ...
% 1.92/1.25 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.99/1.27 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.99/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 1.99/1.29 % [INFO] Type checking passed.
% 1.99/1.29 % [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 ...
% 9.05/2.67 % External prover 'e' found a proof!
% 9.05/2.67 % [INFO] Killing All external provers ...
% 9.05/2.67 % Time passed: 2138ms (effective reasoning time: 1682ms)
% 9.05/2.67 % 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)>
% 9.05/2.67 % 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
% 9.05/2.67 % No. of inferences in proof: 68
% 9.05/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2138 ms resp. 1682 ms w/o parsing
% 9.05/2.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.05/2.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------