TSTP Solution File: NUM020-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM020-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n031.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 11:39:46 EDT 2023
% Result : Unsatisfiable 2.48s 1.53s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 19
% Syntax : Number of formulae : 32 ( 17 unt; 7 typ; 0 def)
% Number of atoms : 35 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 146 ( 14 ~; 10 |; 0 &; 122 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 ^; 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(equalish_type,type,
equalish: $i > $i > $o ).
thf(add_type,type,
add: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(successor_type,type,
successor: $i > $i ).
thf(n0_type,type,
n0: $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(n1_type,type,
n1: $i ).
thf(9,axiom,
! [A: $i] : ( equalish @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(25,plain,
! [A: $i] : ( equalish @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2,negated_conjecture,
! [A: $i] :
~ ( equalish @ ( successor @ A ) @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_contradiction) ).
thf(14,plain,
! [A: $i] :
~ ( equalish @ ( successor @ A ) @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [B: $i,A: $i] : ( equalish @ ( multiply @ A @ ( successor @ B ) ) @ ( add @ ( multiply @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times) ).
thf(20,plain,
! [B: $i,A: $i] : ( equalish @ ( multiply @ A @ ( successor @ B ) ) @ ( add @ ( multiply @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
~ ( equalish @ ( add @ a @ ( successor @ n0 ) ) @ ( successor @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',deny_addition_lemma) ).
thf(13,plain,
~ ( equalish @ ( add @ a @ ( successor @ n0 ) ) @ ( successor @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,axiom,
! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',adding_zero) ).
thf(17,plain,
! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( equalish @ ( add @ A @ ( successor @ B ) ) @ ( successor @ ( add @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition) ).
thf(18,plain,
! [B: $i,A: $i] : ( equalish @ ( add @ A @ ( successor @ B ) ) @ ( successor @ ( add @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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(28,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(7,axiom,
! [B: $i,A: $i] :
( ~ ( equalish @ ( successor @ A ) @ ( successor @ B ) )
| ( equalish @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_equality1) ).
thf(21,plain,
! [B: $i,A: $i] :
( ~ ( equalish @ ( successor @ A ) @ ( successor @ B ) )
| ( equalish @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( successor @ A ) @ ( successor @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_substitution) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( successor @ A ) @ ( successor @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
equalish @ n1 @ ( successor @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_succeeds_zero) ).
thf(30,plain,
equalish @ n1 @ ( successor @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [A: $i] : ( equalish @ ( multiply @ A @ n0 ) @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_zero) ).
thf(19,plain,
! [A: $i] : ( equalish @ ( multiply @ A @ n0 ) @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(33,plain,
$false,
inference(e,[status(thm)],[25,14,20,13,17,18,28,21,26,23,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM020-1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.07/0.14 % Command : run_Leo-III %s %d
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 18 18:10:11 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.93/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.94 % [INFO] Parsing done (110ms).
% 1.23/0.95 % [INFO] Running in sequential loop mode.
% 1.64/1.14 % [INFO] eprover registered as external prover.
% 1.64/1.15 % [INFO] cvc4 registered as external prover.
% 1.64/1.15 % [INFO] Scanning for conjecture ...
% 1.72/1.20 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.72/1.22 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.89/1.23 % [INFO] Problem is propositional (TPTP CNF).
% 1.89/1.23 % [INFO] Type checking passed.
% 1.89/1.23 % [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 ...
% 2.48/1.53 % External prover 'e' found a proof!
% 2.48/1.53 % [INFO] Killing All external provers ...
% 2.48/1.53 % Time passed: 1017ms (effective reasoning time: 571ms)
% 2.48/1.53 % 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)>
% 2.48/1.53 % Axioms used in derivation (10): successor_equality1, successor_substitution, reflexivity, addition, times_zero, times, adding_zero, transitivity, one_succeeds_zero, symmetry
% 2.48/1.53 % No. of inferences in proof: 25
% 2.48/1.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1017 ms resp. 571 ms w/o parsing
% 2.76/1.55 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.76/1.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------