TSTP Solution File: FLD059-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : FLD059-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 11:08:02 EDT 2023
% Result : Unsatisfiable 3.39s 1.73s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 43
% Syntax : Number of formulae : 76 ( 17 unt; 11 typ; 0 def)
% Number of atoms : 157 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 552 ( 90 ~; 92 |; 0 &; 370 @)
% ( 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 ( 11 usr; 5 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(additive_identity_type,type,
additive_identity: $i ).
thf(a_type,type,
a: $i ).
thf(equalish_type,type,
equalish: $i > $i > $o ).
thf(add_type,type,
add: $i > $i > $i ).
thf(u_type,type,
u: $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(additive_inverse_type,type,
additive_inverse: $i > $i ).
thf(multiplicative_inverse_type,type,
multiplicative_inverse: $i > $i ).
thf(15,axiom,
defined @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).
thf(57,plain,
defined @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(32,axiom,
~ ( equalish @ additive_identity @ multiplicative_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_identities) ).
thf(89,plain,
~ ( equalish @ additive_identity @ multiplicative_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(13,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(53,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)],[13]) ).
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(77,plain,
! [A: $i] :
( ( defined @ ( multiplicative_inverse @ A ) )
| ~ ( defined @ A )
| ( equalish @ A @ additive_identity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
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(73,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(11,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(49,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)],[11]) ).
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(81,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(20,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(66,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)],[20]) ).
thf(3,negated_conjecture,
~ ( less_or_equal @ additive_identity @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_5) ).
thf(35,plain,
~ ( less_or_equal @ additive_identity @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
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(87,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(12,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(51,plain,
! [A: $i] :
( ( equalish @ ( add @ A @ ( additive_inverse @ A ) ) @ additive_identity )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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(79,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(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(83,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(7,axiom,
defined @ additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
thf(42,plain,
defined @ additive_identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
defined @ multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
thf(37,plain,
defined @ multiplicative_identity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,axiom,
! [A: $i] :
( ( equalish @ ( add @ additive_identity @ A ) @ A )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_addition) ).
thf(60,plain,
! [A: $i] :
( ( equalish @ ( add @ additive_identity @ A ) @ A )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
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(85,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(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(38,plain,
! [B: $i,A: $i] :
( ( defined @ ( multiply @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
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(70,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(1,negated_conjecture,
less_or_equal @ additive_identity @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
thf(33,plain,
less_or_equal @ additive_identity @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,negated_conjecture,
equalish @ ( add @ a @ a ) @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_equals_u_4) ).
thf(34,plain,
equalish @ ( add @ a @ a ) @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,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(45,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)],[9]) ).
thf(19,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(64,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)],[19]) ).
thf(23,axiom,
defined @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
thf(72,plain,
defined @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(8,axiom,
! [A: $i] :
( ( equalish @ A @ A )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_equality) ).
thf(43,plain,
! [A: $i] :
( ( equalish @ A @ A )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: $i] :
( ( defined @ ( additive_inverse @ A ) )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
thf(40,plain,
! [A: $i] :
( ( defined @ ( additive_inverse @ A ) )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,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(55,plain,
! [C: $i,B: $i,A: $i] :
( ( equalish @ A @ B )
| ~ ( equalish @ A @ C )
| ~ ( equalish @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
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(75,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(16,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(58,plain,
! [B: $i,A: $i] :
( ( defined @ ( add @ A @ B ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( equalish @ A @ B )
| ~ ( equalish @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_equality) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( equalish @ A @ B )
| ~ ( equalish @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(21,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(68,plain,
! [B: $i,A: $i] :
( ( equalish @ ( add @ A @ B ) @ ( add @ B @ A ) )
| ~ ( defined @ A )
| ~ ( defined @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(18,axiom,
! [A: $i] :
( ( equalish @ ( multiply @ multiplicative_identity @ A ) @ A )
| ~ ( defined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
thf(62,plain,
! [A: $i] :
( ( equalish @ ( multiply @ multiplicative_identity @ A ) @ A )
| ~ ( defined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(91,plain,
$false,
inference(e,[status(thm)],[57,89,53,77,73,49,81,66,35,87,51,79,83,42,37,60,85,38,70,33,34,45,64,72,43,40,55,75,58,47,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : FLD059-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 22:45:40 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.84/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/0.96 % [INFO] Parsing done (120ms).
% 1.29/0.96 % [INFO] Running in sequential loop mode.
% 1.76/1.17 % [INFO] eprover registered as external prover.
% 1.76/1.17 % [INFO] cvc4 registered as external prover.
% 1.76/1.17 % [INFO] Scanning for conjecture ...
% 1.85/1.23 % [INFO] Found a conjecture and 29 axioms. Running axiom selection ...
% 1.93/1.27 % [INFO] Axiom selection finished. Selected 29 axioms (removed 0 axioms).
% 1.93/1.30 % [INFO] Problem is propositional (TPTP CNF).
% 1.93/1.30 % [INFO] Type checking passed.
% 1.93/1.30 % [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 ...
% 3.39/1.73 % External prover 'e' found a proof!
% 3.39/1.73 % [INFO] Killing All external provers ...
% 3.39/1.73 % Time passed: 1217ms (effective reasoning time: 763ms)
% 3.39/1.73 % 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)>
% 3.39/1.73 % Axioms used in derivation (29): 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, totality_of_order_relation, 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, 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
% 3.39/1.73 % No. of inferences in proof: 65
% 3.39/1.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1217 ms resp. 763 ms w/o parsing
% 3.67/1.82 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.67/1.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------