TSTP Solution File: NUM393+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM393+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 11:40:27 EDT 2023
% Result : Theorem 3.31s 1.72s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 25
% Syntax : Number of formulae : 43 ( 7 unt; 9 typ; 0 def)
% Number of atoms : 91 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 210 ( 4 ~; 5 |; 19 &; 149 @)
% ( 3 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 60 ( 0 ^; 56 !; 4 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(ordinal_type,type,
ordinal: $i > $o ).
thf(inclusion_comparable_type,type,
inclusion_comparable: $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(epsilon_transitive_type,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_type,type,
epsilon_connected: $i > $o ).
thf(ordinal_subset_type,type,
ordinal_subset: $i > $i > $o ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( inclusion_comparable @ A @ B )
=> ( inclusion_comparable @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r3_xboole_0) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( inclusion_comparable @ A @ B )
=> ( inclusion_comparable @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(28,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(53,plain,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( inclusion_comparable @ A @ B )
<=> ( ( subset @ A @ B )
| ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_xboole_0) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( ( inclusion_comparable @ A @ B )
=> ( ( subset @ A @ B )
| ( subset @ B @ A ) ) )
& ( ( ( subset @ A @ B )
| ( subset @ B @ A ) )
=> ( inclusion_comparable @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(10,axiom,
! [A: $i,B: $i] : ( inclusion_comparable @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r3_xboole_0) ).
thf(39,plain,
! [A: $i] : ( inclusion_comparable @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(35,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(50,plain,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(26,plain,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( ( element @ A @ ( powerset @ B ) )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( element @ A @ ( powerset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
thf(62,plain,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ( ordinal_subset @ A @ B )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( ordinal_subset @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(37,plain,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ordinal_subset @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ordinal_subset @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( inclusion_comparable @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_ordinal1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( inclusion_comparable @ A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(18,plain,
~ ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( inclusion_comparable @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(65,plain,
$false,
inference(e,[status(thm)],[57,28,53,41,39,35,50,26,30,62,24,37,22,59,48,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM393+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n023.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 17:16:15 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.90/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.96 % [INFO] Parsing done (127ms).
% 1.22/0.97 % [INFO] Running in sequential loop mode.
% 1.69/1.16 % [INFO] eprover registered as external prover.
% 1.69/1.17 % [INFO] cvc4 registered as external prover.
% 1.69/1.17 % [INFO] Scanning for conjecture ...
% 1.69/1.22 % [INFO] Found a conjecture and 36 axioms. Running axiom selection ...
% 1.89/1.26 % [INFO] Axiom selection finished. Selected 15 axioms (removed 21 axioms).
% 2.03/1.29 % [INFO] Problem is first-order (TPTP FOF).
% 2.03/1.29 % [INFO] Type checking passed.
% 2.03/1.29 % [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 ...
% 3.31/1.71 % External prover 'e' found a proof!
% 3.31/1.71 % [INFO] Killing All external provers ...
% 3.31/1.71 % Time passed: 1198ms (effective reasoning time: 743ms)
% 3.31/1.71 % 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)>
% 3.31/1.71 % Axioms used in derivation (15): redefinition_r1_ordinal1, t1_subset, d9_xboole_0, reflexivity_r3_xboole_0, cc2_ordinal1, t4_subset, cc1_ordinal1, symmetry_r3_xboole_0, connectedness_r1_ordinal1, reflexivity_r1_tarski, reflexivity_r1_ordinal1, antisymmetry_r2_hidden, t3_subset, existence_m1_subset_1, rc1_ordinal1
% 3.31/1.71 % No. of inferences in proof: 34
% 3.31/1.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1198 ms resp. 743 ms w/o parsing
% 3.51/1.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.51/1.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------