TSTP Solution File: FLD067-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : FLD067-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 11:08:06 EDT 2023
% Result : Unsatisfiable 3.76s 1.86s
% Output : Refutation 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 45
% Syntax : Number of formulae : 79 ( 19 unt; 12 typ; 0 def)
% Number of atoms : 159 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 556 ( 90 ~; 92 |; 0 &; 374 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 100 ( 0 ^; 100 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_or_equal_type,type,
less_or_equal: $i > $i > $o ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(equalish_type,type,
equalish: $i > $i > $o ).
thf(add_type,type,
add: $i > $i > $i ).
thf(additive_inverse_type,type,
additive_inverse: $i > $i ).
thf(u_type,type,
u: $i ).
thf(additive_identity_type,type,
additive_identity: $i ).
thf(defined_type,type,
defined: $i > $o ).
thf(multiplicative_identity_type,type,
multiplicative_identity: $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(multiplicative_inverse_type,type,
multiplicative_inverse: $i > $i ).
thf(14,axiom,
defined @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).
thf(56,plain,
defined @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
! [A: $i] :
( ( equalish @ A @ A )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_equality) ).
thf(42,plain,
! [A: $i] :
( ( equalish @ A @ A )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( equalish @ ( add @ A @ B ) @ ( add @ C @ B ) )
| ~ ( defined @ B )
| ~ ( equalish @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_addition) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( equalish @ ( add @ A @ B ) @ ( add @ C @ B ) )
| ~ ( defined @ B )
| ~ ( equalish @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( equalish @ A @ B )
| ~ ( less_or_equal @ A @ B )
| ~ ( less_or_equal @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( equalish @ A @ B )
| ~ ( less_or_equal @ A @ B )
| ~ ( less_or_equal @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(4,axiom,
defined @ multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
thf(38,plain,
defined @ multiplicative_identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( less_or_equal @ A @ B )
| ~ ( less_or_equal @ A @ C )
| ~ ( less_or_equal @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_order_relation) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( less_or_equal @ A @ B )
| ~ ( less_or_equal @ A @ C )
| ~ ( less_or_equal @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(6,axiom,
defined @ additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
thf(41,plain,
defined @ additive_identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,axiom,
defined @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
thf(73,plain,
defined @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1,negated_conjecture,
less_or_equal @ a @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).
thf(34,plain,
less_or_equal @ a @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(33,axiom,
~ ( equalish @ additive_identity @ multiplicative_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_identities) ).
thf(91,plain,
~ ( equalish @ additive_identity @ multiplicative_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ( less_or_equal @ ( add @ A @ B ) @ ( add @ C @ B ) )
| ~ ( defined @ B )
| ~ ( less_or_equal @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( less_or_equal @ ( add @ A @ B ) @ ( add @ C @ B ) )
| ~ ( defined @ B )
| ~ ( less_or_equal @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(3,negated_conjecture,
~ ( less_or_equal @ additive_identity @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_6) ).
thf(36,plain,
~ ( less_or_equal @ additive_identity @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(32,axiom,
defined @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
thf(90,plain,
defined @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(21,axiom,
! [A: $i] :
( ( defined @ ( additive_inverse @ A ) )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
thf(69,plain,
! [A: $i] :
( ( defined @ ( additive_inverse @ A ) )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( equalish @ ( multiply @ A @ ( multiply @ B @ C ) ) @ ( multiply @ ( multiply @ A @ B ) @ C ) )
| ~ ( defined @ A )
| ~ ( defined @ B )
| ~ ( defined @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_multiplication) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( equalish @ ( multiply @ A @ ( multiply @ B @ C ) ) @ ( multiply @ ( multiply @ A @ B ) @ C ) )
| ~ ( defined @ A )
| ~ ( defined @ B )
| ~ ( defined @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( equalish @ A @ B )
| ~ ( equalish @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_equality) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( equalish @ A @ B )
| ~ ( equalish @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( defined @ ( add @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_addition) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( defined @ ( add @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(26,axiom,
! [A: $i] :
( ( defined @ ( multiplicative_inverse @ A ) )
| ~ ( defined @ A )
| ( equalish @ A @ additive_identity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
thf(78,plain,
! [A: $i] :
( ( defined @ ( multiplicative_inverse @ A ) )
| ~ ( defined @ A )
| ( equalish @ A @ additive_identity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(17,axiom,
! [A: $i] :
( ( equalish @ ( multiply @ multiplicative_identity @ A ) @ A )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
thf(61,plain,
! [A: $i] :
( ( equalish @ ( multiply @ multiplicative_identity @ A ) @ A )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( less_or_equal @ A @ B )
| ( less_or_equal @ B @ A )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_order_relation) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( less_or_equal @ A @ B )
| ( less_or_equal @ B @ A )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( less_or_equal @ additive_identity @ ( multiply @ A @ B ) )
| ~ ( less_or_equal @ additive_identity @ A )
| ~ ( less_or_equal @ additive_identity @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_multiplication) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( less_or_equal @ additive_identity @ ( multiply @ A @ B ) )
| ~ ( less_or_equal @ additive_identity @ A )
| ~ ( less_or_equal @ additive_identity @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [A: $i] :
( ( equalish @ ( add @ additive_identity @ A ) @ A )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_addition) ).
thf(59,plain,
! [A: $i] :
( ( equalish @ ( add @ additive_identity @ A ) @ A )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( less_or_equal @ A @ B )
| ~ ( less_or_equal @ C @ B )
| ~ ( equalish @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_order_relation) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( less_or_equal @ A @ B )
| ~ ( less_or_equal @ C @ B )
| ~ ( equalish @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( equalish @ A @ B )
| ~ ( equalish @ A @ C )
| ~ ( equalish @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_equality) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( equalish @ A @ B )
| ~ ( equalish @ A @ C )
| ~ ( equalish @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ( equalish @ ( add @ A @ ( add @ B @ C ) ) @ ( add @ ( add @ A @ B ) @ C ) )
| ~ ( defined @ A )
| ~ ( defined @ B )
| ~ ( defined @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_addition) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( equalish @ ( add @ A @ ( add @ B @ C ) ) @ ( add @ ( add @ A @ B ) @ C ) )
| ~ ( defined @ A )
| ~ ( defined @ B )
| ~ ( defined @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( equalish @ ( multiply @ A @ B ) @ ( multiply @ B @ A ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_multiplication) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( equalish @ ( multiply @ A @ B ) @ ( multiply @ B @ A ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( defined @ ( multiply @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplication) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( defined @ ( multiply @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(27,axiom,
! [A: $i] :
( ( equalish @ ( multiply @ A @ ( multiplicative_inverse @ A ) ) @ multiplicative_identity )
| ~ ( defined @ A )
| ( equalish @ A @ additive_identity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
thf(80,plain,
! [A: $i] :
( ( equalish @ ( multiply @ A @ ( multiplicative_inverse @ A ) ) @ multiplicative_identity )
| ~ ( defined @ A )
| ( equalish @ A @ additive_identity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(2,negated_conjecture,
equalish @ ( add @ b @ ( additive_inverse @ a ) ) @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_equals_u_5) ).
thf(35,plain,
equalish @ ( add @ b @ ( additive_inverse @ a ) ) @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( equalish @ ( multiply @ A @ B ) @ ( multiply @ C @ B ) )
| ~ ( defined @ B )
| ~ ( equalish @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_multiplication) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( equalish @ ( multiply @ A @ B ) @ ( multiply @ C @ B ) )
| ~ ( defined @ B )
| ~ ( equalish @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( equalish @ ( add @ ( multiply @ A @ B ) @ ( multiply @ C @ B ) ) @ ( multiply @ ( add @ A @ C ) @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ C )
| ~ ( defined @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( equalish @ ( add @ ( multiply @ A @ B ) @ ( multiply @ C @ B ) ) @ ( multiply @ ( add @ A @ C ) @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ C )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(11,axiom,
! [A: $i] :
( ( equalish @ ( add @ A @ ( additive_inverse @ A ) ) @ additive_identity )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
thf(50,plain,
! [A: $i] :
( ( equalish @ ( add @ A @ ( additive_inverse @ A ) ) @ additive_identity )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( equalish @ ( add @ A @ B ) @ ( add @ B @ A ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_addition) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( equalish @ ( add @ A @ B ) @ ( add @ B @ A ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(93,plain,
$false,
inference(e,[status(thm)],[56,42,52,84,38,65,41,73,34,91,82,36,90,69,88,46,57,78,61,74,44,59,71,54,86,76,39,80,35,48,63,50,67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : FLD067-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 22:56:31 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.94/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.05 % [INFO] Parsing done (142ms).
% 1.25/1.05 % [INFO] Running in sequential loop mode.
% 1.83/1.27 % [INFO] eprover registered as external prover.
% 1.83/1.27 % [INFO] cvc4 registered as external prover.
% 1.96/1.27 % [INFO] Scanning for conjecture ...
% 1.96/1.33 % [INFO] Found a conjecture and 30 axioms. Running axiom selection ...
% 2.23/1.37 % [INFO] Axiom selection finished. Selected 30 axioms (removed 0 axioms).
% 2.23/1.40 % [INFO] Problem is propositional (TPTP CNF).
% 2.23/1.40 % [INFO] Type checking passed.
% 2.23/1.41 % [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 ...
% 3.76/1.86 % External prover 'e' found a proof!
% 3.76/1.86 % [INFO] Killing All external provers ...
% 3.76/1.86 % Time passed: 1329ms (effective reasoning time: 804ms)
% 3.76/1.86 % 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)>
% 3.76/1.86 % Axioms used in derivation (30): existence_of_identity_multiplication, transitivity_of_order_relation, associativity_multiplication, well_definedness_of_additive_identity, compatibility_of_order_relation_and_multiplication, well_definedness_of_multiplication, existence_of_identity_addition, transitivity_of_equality, reflexivity_of_equality, commutativity_addition, commutativity_multiplication, existence_of_inverse_addition, well_definedness_of_addition, compatibility_of_equality_and_multiplication, a_is_defined, antisymmetry_of_order_relation, associativity_addition, b_is_defined, totality_of_order_relation, compatibility_of_equality_and_addition, existence_of_inverse_multiplication, well_definedness_of_multiplicative_identity, well_definedness_of_additive_inverse, symmetry_of_equality, different_identities, well_definedness_of_multiplicative_inverse, compatibility_of_equality_and_order_relation, compatibility_of_order_relation_and_addition, u_is_defined, distributivity
% 3.76/1.86 % No. of inferences in proof: 67
% 3.76/1.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1329 ms resp. 804 ms w/o parsing
% 4.07/1.96 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.07/1.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------