TSTP Solution File: LCL080-2 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL080-2 : 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 11:29:19 EDT 2023
% Result : Unsatisfiable 7.72s 2.63s
% Output : Refutation 7.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 78 ( 47 unt; 6 typ; 0 def)
% Number of atoms : 143 ( 62 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 669 ( 85 ~; 33 |; 0 &; 551 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 102 ( 0 ^; 102 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_type,type,
is_a_theorem: $i > $o ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(e_type,type,
e: $i ).
thf(3,axiom,
! [A: $i] : ( is_a_theorem @ ( implies @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ic_1) ).
thf(11,plain,
! [A: $i] : ( is_a_theorem @ ( implies @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ic_2) ).
thf(12,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( implies @ A @ B ) )
| ~ ( is_a_theorem @ A )
| ( is_a_theorem @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
thf(9,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( implies @ A @ B ) )
| ~ ( is_a_theorem @ A )
| ( is_a_theorem @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ ( implies @ A @ B ) )
| ~ ( is_a_theorem @ A )
| ( is_a_theorem @ B ) ),
inference(cnf,[status(esa)],[9]) ).
thf(35,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( is_a_theorem @ C )
| ( is_a_theorem @ D )
| ( ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) )
!= ( is_a_theorem @ ( implies @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,10]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ B )
| ( is_a_theorem @ ( implies @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[35:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( implies @ E @ F ))]]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ B )
| ( is_a_theorem @ ( implies @ A @ B ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(1,negated_conjecture,
~ ( is_a_theorem @ ( implies @ ( implies @ ( implies @ a @ b ) @ c ) @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ic_JLukasiewicz) ).
thf(7,plain,
~ ( is_a_theorem @ ( implies @ ( implies @ ( implies @ a @ b ) @ c ) @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,plain,
~ ( is_a_theorem @ ( implies @ ( implies @ ( implies @ a @ b ) @ c ) @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ B )
| ( ( is_a_theorem @ ( implies @ A @ B ) )
!= ( is_a_theorem @ ( implies @ ( implies @ ( implies @ a @ b ) @ c ) @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[48,8]) ).
thf(68,plain,
~ ( is_a_theorem @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( implies @ ( implies @ a @ b ) @ c )),bind(B,$thf( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ))]]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ B )
| ( ( is_a_theorem @ ( implies @ A @ B ) )
!= ( is_a_theorem @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[48,68]) ).
thf(88,plain,
~ ( is_a_theorem @ ( implies @ e @ a ) ),
inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( implies @ c @ a )),bind(B,$thf( implies @ e @ a ))]]) ).
thf(95,plain,
! [A: $i] :
( ( is_a_theorem @ ( implies @ A @ A ) )
!= ( is_a_theorem @ ( implies @ e @ a ) ) ),
inference(paramod_ordered,[status(thm)],[11,88]) ).
thf(101,plain,
! [A: $i] :
( ( implies @ A @ A )
!= ( implies @ e @ a ) ),
inference(simp,[status(thm)],[95]) ).
thf(114,plain,
! [A: $i] :
( ( A != e )
| ( A != a ) ),
inference(simp,[status(thm)],[101]) ).
thf(115,plain,
e != a,
inference(simp,[status(thm)],[114]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ic_4) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] : ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) )
!= ( is_a_theorem @ ( implies @ ( implies @ ( implies @ a @ b ) @ c ) @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,8]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) )
!= ( implies @ ( implies @ ( implies @ a @ b ) @ c ) @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( implies @ B @ C ) )
| ( ( is_a_theorem @ ( implies @ A @ A ) )
!= ( is_a_theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11,48]) ).
thf(66,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ B ) ) ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( implies @ E @ E ))]]) ).
thf(78,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ B ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( implies @ A @ ( implies @ B @ B ) ) )
!= ( is_a_theorem @ ( implies @ e @ a ) ) ),
inference(paramod_ordered,[status(thm)],[78,88]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ B ) )
!= ( implies @ e @ a ) ),
inference(simp,[status(thm)],[123]) ).
thf(85,plain,
! [A: $i] :
( ( is_a_theorem @ ( implies @ A @ A ) )
!= ( is_a_theorem @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,68]) ).
thf(90,plain,
! [A: $i] :
( ( implies @ A @ A )
!= ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(116,plain,
! [A: $i] :
( ( A
!= ( implies @ c @ a ) )
| ( A
!= ( implies @ e @ a ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(117,plain,
( ( implies @ e @ a )
!= ( implies @ c @ a ) ),
inference(simp,[status(thm)],[116]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ B )
| ( ( is_a_theorem @ ( implies @ A @ B ) )
!= ( is_a_theorem @ ( implies @ e @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[48,88]) ).
thf(98,plain,
~ ( is_a_theorem @ a ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( e )),bind(B,$thf( a ))]]) ).
thf(106,plain,
! [A: $i] :
( ( is_a_theorem @ ( implies @ A @ A ) )
!= ( is_a_theorem @ a ) ),
inference(paramod_ordered,[status(thm)],[11,98]) ).
thf(109,plain,
! [A: $i] :
( ( implies @ A @ A )
!= a ),
inference(simp,[status(thm)],[106]) ).
thf(5,axiom,
! [B: $i,A: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ A @ B ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ic_3) ).
thf(13,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( implies @ A @ B ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,plain,
! [A: $i] :
( ( is_a_theorem @ ( implies @ A @ A ) )
!= ( is_a_theorem @ ( implies @ ( implies @ ( implies @ a @ b ) @ c ) @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,8]) ).
thf(17,plain,
! [A: $i] :
( ( implies @ A @ A )
!= ( implies @ ( implies @ ( implies @ a @ b ) @ c ) @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( implies @ A @ ( implies @ B @ B ) ) )
!= ( is_a_theorem @ a ) ),
inference(paramod_ordered,[status(thm)],[78,98]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ B ) )
!= a ),
inference(simp,[status(thm)],[120]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) )
!= ( is_a_theorem @ ( implies @ e @ a ) ) ),
inference(paramod_ordered,[status(thm)],[12,88]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
!= ( implies @ e @ a ) ),
inference(simp,[status(thm)],[96]) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( A != e )
| ( ( implies @ B @ A )
!= a ) ),
inference(simp,[status(thm)],[100]) ).
thf(194,plain,
! [A: $i] :
( ( implies @ A @ e )
!= a ),
inference(simp,[status(thm)],[193]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) )
!= ( is_a_theorem @ ( implies @ ( implies @ ( implies @ a @ b ) @ c ) @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,8]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
!= ( implies @ ( implies @ ( implies @ a @ b ) @ c ) @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( A
!= ( implies @ ( implies @ a @ b ) @ c ) )
| ( ( implies @ B @ A )
!= ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(54,plain,
! [A: $i] :
( ( implies @ A @ ( implies @ ( implies @ a @ b ) @ c ) )
!= ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(55,plain,
! [A: $i] :
( ( A
!= ( implies @ c @ a ) )
| ( ( implies @ ( implies @ a @ b ) @ c )
!= ( implies @ e @ a ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(56,plain,
( ( implies @ ( implies @ a @ b ) @ c )
!= ( implies @ e @ a ) ),
inference(simp,[status(thm)],[55]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( implies @ ( implies @ ( implies @ A @ B ) @ A ) @ A ) )
!= ( is_a_theorem @ ( implies @ ( implies @ ( implies @ a @ b ) @ c ) @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,8]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( implies @ ( implies @ ( implies @ A @ B ) @ A ) @ A )
!= ( implies @ ( implies @ ( implies @ a @ b ) @ c ) @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(57,plain,
( ( ( implies @ a @ b )
!= e )
| ( c != a ) ),
inference(simp,[status(thm)],[56]) ).
thf(21,plain,
! [A: $i] :
( ( A
!= ( implies @ ( implies @ a @ b ) @ c ) )
| ( A
!= ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(22,plain,
( ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) )
!= ( implies @ ( implies @ a @ b ) @ c ) ),
inference(simp,[status(thm)],[21]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ A )
| ( is_a_theorem @ B )
| ( ( is_a_theorem @ ( implies @ A @ B ) )
!= ( is_a_theorem @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[10]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ B )
| ~ ( is_a_theorem @ A )
| ( ( is_a_theorem @ ( implies @ A @ B ) )
!= ( is_a_theorem @ A ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( ( implies @ ( implies @ A @ B ) @ A )
!= ( implies @ ( implies @ a @ b ) @ c ) )
| ( A
!= ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(59,plain,
! [A: $i] :
( ( implies @ ( implies @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) @ A ) @ ( implies @ ( implies @ c @ a ) @ ( implies @ e @ a ) ) )
!= ( implies @ ( implies @ a @ b ) @ c ) ),
inference(simp,[status(thm)],[58]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) )
!= ( is_a_theorem @ a ) ),
inference(paramod_ordered,[status(thm)],[12,98]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( implies @ A @ ( implies @ B @ A ) )
!= a ),
inference(simp,[status(thm)],[107]) ).
thf(23,plain,
( ( ( implies @ c @ a )
!= ( implies @ a @ b ) )
| ( ( implies @ e @ a )
!= c ) ),
inference(simp,[status(thm)],[22]) ).
thf(26,plain,
( ( c != a )
| ( b != a )
| ( ( implies @ e @ a )
!= c ) ),
inference(simp,[status(thm)],[23]) ).
thf(118,plain,
( ( e != c )
| ( a != a ) ),
inference(simp,[status(thm)],[117]) ).
thf(119,plain,
e != c,
inference(simp,[status(thm)],[118]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ B )
| ( ( is_a_theorem @ ( implies @ A @ B ) )
!= ( is_a_theorem @ a ) ) ),
inference(paramod_ordered,[status(thm)],[48,98]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ~ ( is_a_theorem @ B )
| ( ( implies @ A @ B )
!= a ) ),
inference(simp,[status(thm)],[108]) ).
thf(273,plain,
$false,
inference(e,[status(thm)],[115,25,14,132,117,9,109,13,17,130,194,11,68,101,88,10,56,20,57,78,22,44,59,12,54,113,7,98,48,18,26,23,8,119,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL080-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n001.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 16:11:50 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.88/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/1.01 % [INFO] Parsing done (116ms).
% 1.19/1.02 % [INFO] Running in sequential loop mode.
% 1.63/1.26 % [INFO] eprover registered as external prover.
% 1.63/1.27 % [INFO] cvc4 registered as external prover.
% 1.63/1.27 % [INFO] Scanning for conjecture ...
% 1.73/1.33 % [INFO] Found a conjecture and 5 axioms. Running axiom selection ...
% 1.87/1.35 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.87/1.36 % [INFO] Problem is propositional (TPTP CNF).
% 1.87/1.36 % [INFO] Type checking passed.
% 1.87/1.36 % [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 ...
% 7.72/2.63 % External prover 'e' found a proof!
% 7.72/2.63 % [INFO] Killing All external provers ...
% 7.72/2.63 % Time passed: 2103ms (effective reasoning time: 1606ms)
% 7.72/2.63 % 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)>
% 7.72/2.63 % Axioms used in derivation (5): ic_1, condensed_detachment, ic_2, ic_3, ic_4
% 7.72/2.63 % No. of inferences in proof: 72
% 7.72/2.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2103 ms resp. 1606 ms w/o parsing
% 7.72/2.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.72/2.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------