TSTP Solution File: NUM021-1 by Leo-III-SAT---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM021-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 : Tue May 7 10:43:38 EDT 2024
% Result : Unsatisfiable 12.57s 3.19s
% Output : Refutation 12.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 50 ( 15 unt; 9 typ; 0 def)
% Number of atoms : 93 ( 7 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 298 ( 47 ~; 38 |; 0 &; 213 @)
% ( 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; 5 con; 0-2 aty)
% Number of variables : 61 ( 0 ^ 61 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(divides_type,type,
divides: $i > $i > $o ).
thf(c_type,type,
c: $i ).
thf(a_type,type,
a: $i ).
thf(equalish_type,type,
equalish: $i > $i > $o ).
thf(successor_type,type,
successor: $i > $i ).
thf(less_type,type,
less: $i > $i > $o ).
thf(b_type,type,
b: $i ).
thf(add_type,type,
add: $i > $i > $i ).
thf(predecessor_of_1st_minus_2nd_type,type,
predecessor_of_1st_minus_2nd: $i > $i > $i ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( less @ A @ B )
| ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ B @ A ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_lemma) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( less @ A @ B )
| ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ B @ A ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( less @ A @ B )
| ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ B @ A ) ) @ A ) @ B ) ),
inference(cnf,[status(esa)],[45]) ).
thf(1,negated_conjecture,
divides @ c @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',impossible_c_divides_a) ).
thf(20,plain,
divides @ c @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( divides @ A @ B )
| ( less @ A @ B )
| ( equalish @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_only_less_or_equal) ).
thf(33,plain,
! [B: $i,A: $i] :
( ~ ( divides @ A @ B )
| ( less @ A @ B )
| ( equalish @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ~ ( divides @ A @ B )
| ( less @ A @ B )
| ( equalish @ A @ B ) ),
inference(cnf,[status(esa)],[33]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( less @ A @ B )
| ( equalish @ A @ B )
| ( ( divides @ c @ a )
!= ( divides @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20,34]) ).
thf(190,plain,
( ( less @ c @ a )
| ( equalish @ c @ a ) ),
inference(pattern_uni,[status(thm)],[189:[bind(A,$thf( c )),bind(B,$thf( a ))]]) ).
thf(6,axiom,
less @ b @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_less_than_c) ).
thf(29,plain,
less @ b @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ C @ A )
| ( less @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ C @ A )
| ( less @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ C @ A )
| ( less @ C @ B ) ),
inference(cnf,[status(esa)],[23]) ).
thf(5,axiom,
~ ( less @ b @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_greater_equal_a) ).
thf(27,plain,
~ ( less @ b @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,plain,
~ ( less @ b @ a ),
inference(polarity_switch,[status(thm)],[27]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ C @ A )
| ( ( less @ C @ B )
!= ( less @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[24,28]) ).
thf(59,plain,
! [A: $i] :
( ~ ( less @ A @ a )
| ~ ( less @ b @ A ) ),
inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( A )),bind(B,$thf( a )),bind(C,$thf( b ))]]) ).
thf(93,plain,
! [A: $i] :
( ~ ( less @ A @ a )
| ( ( less @ b @ c )
!= ( less @ b @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,59]) ).
thf(94,plain,
~ ( less @ c @ a ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( c ))]]) ).
thf(256,plain,
( $false
| ( equalish @ c @ a ) ),
inference(rewrite,[status(thm)],[190,94]) ).
thf(257,plain,
equalish @ c @ a,
inference(simp,[status(thm)],[256]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ B @ C )
| ( equalish @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ B @ C )
| ( equalish @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ B @ C )
| ( equalish @ A @ C ) ),
inference(cnf,[status(esa)],[36]) ).
thf(316,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ A @ C )
| ( ( equalish @ c @ a )
!= ( equalish @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[257,37]) ).
thf(317,plain,
! [A: $i] :
( ~ ( equalish @ A @ c )
| ( equalish @ A @ a ) ),
inference(pattern_uni,[status(thm)],[316:[bind(A,$thf( A )),bind(B,$thf( c )),bind(C,$thf( a ))]]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ ( add @ ( successor @ A ) @ B ) @ C )
| ( less @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',smaller_number) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ ( add @ ( successor @ A ) @ B ) @ C )
| ( less @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ ( add @ ( successor @ A ) @ B ) @ C )
| ( less @ B @ C ) ),
inference(cnf,[status(esa)],[31]) ).
thf(116,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ ( add @ ( successor @ A ) @ B ) @ C )
| ( ( less @ B @ C )
!= ( less @ b @ a ) ) ),
inference(paramod_ordered,[status(thm)],[32,28]) ).
thf(117,plain,
! [A: $i] :
~ ( equalish @ ( add @ ( successor @ A ) @ b ) @ a ),
inference(pattern_uni,[status(thm)],[116:[bind(A,$thf( A )),bind(B,$thf( b )),bind(C,$thf( a ))]]) ).
thf(477,plain,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ c )
| ( ( equalish @ A @ a )
!= ( equalish @ ( add @ ( successor @ B ) @ b ) @ a ) ) ),
inference(paramod_ordered,[status(thm)],[317,117]) ).
thf(478,plain,
! [A: $i] :
~ ( equalish @ ( add @ ( successor @ A ) @ b ) @ c ),
inference(pattern_uni,[status(thm)],[477:[bind(A,$thf( add @ ( successor @ E ) @ b )),bind(B,$thf( E ))]]) ).
thf(509,plain,
! [A: $i] :
~ ( equalish @ ( add @ ( successor @ A ) @ b ) @ c ),
inference(simp,[status(thm)],[478]) ).
thf(1176,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ A @ B )
| ( ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ B @ A ) ) @ A ) @ B )
!= ( equalish @ ( add @ ( successor @ C ) @ b ) @ c ) ) ),
inference(paramod_ordered,[status(thm)],[46,509]) ).
thf(1177,plain,
~ ( less @ b @ c ),
inference(pattern_uni,[status(thm)],[1176:[bind(A,$thf( b )),bind(B,$thf( c )),bind(C,$thf( predecessor_of_1st_minus_2nd @ c @ b ))]]) ).
thf(1236,plain,
~ $true,
inference(rewrite,[status(thm)],[1177,29]) ).
thf(1237,plain,
$false,
inference(simp,[status(thm)],[1236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM021-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n005.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 : Mon May 6 19:35:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.98/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.40/1.04 % [INFO] Parsing done (135ms).
% 1.40/1.04 % [INFO] Running in sequential loop mode.
% 1.85/1.25 % [INFO] nitpick registered as external prover.
% 1.85/1.25 % [INFO] Scanning for conjecture ...
% 1.85/1.30 % [INFO] Found a conjecture and 17 axioms. Running axiom selection ...
% 2.02/1.34 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 2.02/1.35 % [INFO] Problem is propositional (TPTP CNF).
% 2.02/1.35 % [INFO] Type checking passed.
% 2.02/1.36 % [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 ...
% 12.57/3.18 % [INFO] Killing All external provers ...
% 12.57/3.18 % Time passed: 2653ms (effective reasoning time: 2135ms)
% 12.57/3.18 % 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)>
% 12.57/3.19 % Axioms used in derivation (7): b_greater_equal_a, less_lemma, divides_only_less_or_equal, transitivity_of_less, transitivity, smaller_number, b_less_than_c
% 12.57/3.19 % No. of inferences in proof: 41
% 12.57/3.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2653 ms resp. 2135 ms w/o parsing
% 12.57/3.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.57/3.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------