TSTP Solution File: NUM004-1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM004-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 11:39:43 EDT 2023
% Result : Unsatisfiable 2.97s 1.65s
% Output : Refutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 19
% Syntax : Number of formulae : 33 ( 17 unt; 6 typ; 0 def)
% Number of atoms : 47 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 254 ( 22 ~; 20 |; 0 &; 212 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 70 ( 0 ^; 70 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(equalish_type,type,
equalish: $i > $i > $o ).
thf(subtract_type,type,
subtract: $i > $i > $i ).
thf(add_type,type,
add: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(1,negated_conjecture,
~ ( equalish @ ( subtract @ ( add @ a @ b ) @ c ) @ ( add @ a @ ( subtract @ b @ c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
thf(14,plain,
~ ( equalish @ ( subtract @ ( add @ a @ b ) @ c ) @ ( add @ a @ ( subtract @ b @ c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [B: $i,A: $i] : ( equalish @ ( subtract @ ( add @ A @ B ) @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_inverts_subtraction1) ).
thf(21,plain,
! [B: $i,A: $i] : ( equalish @ ( subtract @ ( add @ A @ B ) @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,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(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ B @ C )
| ( equalish @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] : ( equalish @ ( add @ ( subtract @ A @ B ) @ C ) @ ( subtract @ ( add @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity1) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] : ( equalish @ ( add @ ( subtract @ A @ B ) @ C ) @ ( subtract @ ( add @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( equalish @ ( add @ A @ B ) @ ( add @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
thf(19,plain,
! [B: $i,A: $i] : ( equalish @ ( add @ A @ B ) @ ( add @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] : ( equalish @ ( subtract @ ( add @ A @ B ) @ C ) @ ( add @ ( subtract @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity2) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] : ( equalish @ ( subtract @ ( add @ A @ B ) @ C ) @ ( add @ ( subtract @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ C @ ( add @ A @ D ) )
| ( equalish @ C @ ( add @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_substitution1) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ C @ ( add @ A @ D ) )
| ( equalish @ C @ ( add @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( equalish @ ( add @ A @ ( add @ B @ C ) ) @ ( add @ ( add @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] : ( equalish @ ( add @ A @ ( add @ B @ C ) ) @ ( add @ ( add @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ C @ ( subtract @ A @ D ) )
| ( equalish @ C @ ( subtract @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_substitution1) ).
thf(29,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ C @ ( subtract @ A @ D ) )
| ( equalish @ C @ ( subtract @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
! [B: $i,A: $i] : ( equalish @ A @ ( subtract @ ( add @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_inverts_subtraction2) ).
thf(22,plain,
! [B: $i,A: $i] : ( equalish @ A @ ( subtract @ ( add @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ C @ ( add @ D @ A ) )
| ( equalish @ C @ ( add @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_substitution2) ).
thf(27,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ C @ ( add @ D @ A ) )
| ( equalish @ C @ ( add @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,axiom,
! [A: $i] : ( equalish @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(16,plain,
! [A: $i] : ( equalish @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ C @ ( subtract @ D @ A ) )
| ( equalish @ C @ ( subtract @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_substitution2) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ C @ ( subtract @ D @ A ) )
| ( equalish @ C @ ( subtract @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(36,plain,
$false,
inference(e,[status(thm)],[14,21,17,23,19,24,25,20,29,22,27,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM004-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.16/0.35 % Computer : n027.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu May 18 17:14:51 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.85/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.96 % [INFO] Parsing done (121ms).
% 1.20/0.97 % [INFO] Running in sequential loop mode.
% 1.52/1.17 % [INFO] eprover registered as external prover.
% 1.52/1.17 % [INFO] cvc4 registered as external prover.
% 1.52/1.17 % [INFO] Scanning for conjecture ...
% 1.82/1.22 % [INFO] Found a conjecture and 12 axioms. Running axiom selection ...
% 1.92/1.24 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 1.92/1.26 % [INFO] Problem is propositional (TPTP CNF).
% 1.92/1.26 % [INFO] Type checking passed.
% 1.92/1.26 % [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 ...
% 2.70/1.61 % External prover 'e' found a proof!
% 2.70/1.61 % [INFO] Killing All external provers ...
% 2.70/1.61 % Time passed: 1090ms (effective reasoning time: 637ms)
% 2.70/1.61 % 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)>
% 2.70/1.61 % Axioms used in derivation (12): addition_inverts_subtraction1, addition_inverts_subtraction2, subtract_substitution1, reflexivity, transitivity, add_substitution2, commutativity1, associativity_of_addition, commutativity_of_addition, commutativity2, add_substitution1, subtract_substitution2
% 2.70/1.61 % No. of inferences in proof: 27
% 2.97/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1090 ms resp. 637 ms w/o parsing
% 3.12/1.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.12/1.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------