TSTP Solution File: NUM027-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM027-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 11:39:47 EDT 2023
% Result : Unsatisfiable 3.17s 1.64s
% Output : Refutation 3.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 31
% Syntax : Number of formulae : 53 ( 21 unt; 10 typ; 0 def)
% Number of atoms : 73 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 292 ( 34 ~; 30 |; 0 &; 228 @)
% ( 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 : 11 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 72 ( 0 ^; 72 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(equalish_type,type,
equalish: $i > $i > $o ).
thf(c_type,type,
c: $i ).
thf(n0_type,type,
n0: $i ).
thf(less_type,type,
less: $i > $i > $o ).
thf(b_type,type,
b: $i ).
thf(a_type,type,
a: $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(add_type,type,
add: $i > $i > $i ).
thf(successor_type,type,
successor: $i > $i ).
thf(predecessor_of_1st_minus_2nd_type,type,
predecessor_of_1st_minus_2nd: $i > $i > $i ).
thf(20,axiom,
! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',adding_zero) ).
thf(56,plain,
! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( equalish @ ( successor @ A ) @ ( successor @ B ) )
| ( equalish @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_equality1) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ ( equalish @ ( successor @ A ) @ ( successor @ B ) )
| ( equalish @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [B: $i,A: $i] : ( equalish @ ( multiply @ A @ ( successor @ B ) ) @ ( add @ ( multiply @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times) ).
thf(39,plain,
! [B: $i,A: $i] : ( equalish @ ( multiply @ A @ ( successor @ B ) ) @ ( add @ ( multiply @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality_preserved_over_times) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( less @ A @ B )
| ~ ( equalish @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_and_equal) ).
thf(31,plain,
! [B: $i,A: $i] :
( ~ ( less @ A @ B )
| ~ ( equalish @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ A @ B )
| ( equalish @ C @ n0 )
| ( less @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_lemma) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ A @ B )
| ( equalish @ C @ n0 )
| ( less @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,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(42,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ B @ C )
| ( equalish @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2,axiom,
~ ( less @ b @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_not_less_than_a) ).
thf(24,plain,
~ ( less @ b @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( less @ A @ B )
| ( equalish @ B @ A )
| ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',numbers_either_less_or_equal) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( less @ A @ B )
| ( equalish @ B @ A )
| ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
less @ ( multiply @ b @ c ) @ ( multiply @ a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_c_less_than_a_times_c) ).
thf(46,plain,
less @ ( multiply @ b @ c ) @ ( multiply @ a @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(21,axiom,
! [B: $i,A: $i] : ( equalish @ ( add @ A @ ( successor @ B ) ) @ ( successor @ ( add @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition) ).
thf(57,plain,
! [B: $i,A: $i] : ( equalish @ ( add @ A @ ( successor @ B ) ) @ ( successor @ ( add @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(4,axiom,
! [A: $i] :
~ ( less @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',number_not_less_than_itself) ).
thf(28,plain,
! [A: $i] :
~ ( less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,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(33,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ ( add @ ( successor @ A ) @ B ) @ C )
| ( less @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
~ ( equalish @ c @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_is_0) ).
thf(22,plain,
~ ( equalish @ c @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( successor @ A ) @ ( successor @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_substitution) ).
thf(44,plain,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( successor @ A ) @ ( successor @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,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(54,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)],[19]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(49,plain,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [A: $i] :
~ ( equalish @ ( successor @ A ) @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_the_first_number) ).
thf(40,plain,
! [A: $i] :
~ ( equalish @ ( successor @ A ) @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
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(26,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(5,axiom,
! [A: $i] : ( equalish @ ( multiply @ A @ n0 ) @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_zero) ).
thf(30,plain,
! [A: $i] : ( equalish @ ( multiply @ A @ n0 ) @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,axiom,
! [A: $i] : ( equalish @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(51,plain,
! [A: $i] : ( equalish @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(58,plain,
$false,
inference(e,[status(thm)],[56,52,39,35,31,47,42,24,37,46,57,28,33,22,44,54,49,40,26,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM027-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n002.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 : Thu May 18 17:26:50 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.94/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/0.96 % [INFO] Parsing done (117ms).
% 1.31/0.97 % [INFO] Running in sequential loop mode.
% 1.68/1.17 % [INFO] eprover registered as external prover.
% 1.68/1.17 % [INFO] cvc4 registered as external prover.
% 1.77/1.18 % [INFO] Scanning for conjecture ...
% 1.77/1.23 % [INFO] Found a conjecture and 20 axioms. Running axiom selection ...
% 1.94/1.26 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 1.94/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 1.94/1.28 % [INFO] Type checking passed.
% 1.94/1.28 % [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 ...
% 3.17/1.63 % External prover 'e' found a proof!
% 3.17/1.63 % [INFO] Killing All external provers ...
% 3.17/1.64 % Time passed: 1106ms (effective reasoning time: 659ms)
% 3.17/1.64 % 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)>
% 3.17/1.64 % Axioms used in derivation (20): numbers_either_less_or_equal, successor_equality1, equality_preserved_over_times, less_lemma, successor_substitution, reflexivity, addition, times_zero, not_less_and_equal, adding_zero, number_not_less_than_itself, transitivity, multiply_lemma, symmetry, smaller_number, b_times_c_less_than_a_times_c, b_not_less_than_a, times, transitivity_of_less, zero_is_the_first_number
% 3.17/1.64 % No. of inferences in proof: 43
% 3.17/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1106 ms resp. 659 ms w/o parsing
% 3.17/1.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.17/1.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------