TSTP Solution File: SEU224+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU224+1 : TPTP v8.1.2. Released v3.3.0.
% 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 11:57:40 EDT 2023
% Result : Theorem 4.00s 1.96s
% Output : Refutation 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 45
% Syntax : Number of formulae : 80 ( 15 unt; 12 typ; 0 def)
% Number of atoms : 195 ( 22 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 464 ( 18 ~; 2 |; 74 &; 319 @)
% ( 5 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 104 ( 0 ^; 86 !; 18 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_type,type,
relation: $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(relation_dom_type,type,
relation_dom: $i > $i ).
thf(relation_dom_restriction_type,type,
relation_dom_restriction: $i > $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(set_intersection2_type,type,
set_intersection2: $i > $i > $i ).
thf(element_type,type,
element: $i > $i > $o ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(relation_empty_yielding_type,type,
relation_empty_yielding: $i > $o ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(56,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(74,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(33,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(160,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(21,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(92,plain,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(96,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( set_intersection2 @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
& ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
& ( in @ D @ B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
& ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
& ( in @ D @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( set_intersection2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(76,plain,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(43,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(79,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(52,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(125,plain,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(32,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(156,plain,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(53,plain,
! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(27,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(141,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(11,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(64,plain,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(30,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(149,plain,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(13,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(71,plain,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(144,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(5,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(49,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( B
= ( relation_dom_restriction @ C @ A ) )
<=> ( ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
thf(130,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( B
= ( relation_dom_restriction @ C @ A ) )
=> ( ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) )
& ( ( ( ( relation_dom @ B )
= ( set_intersection2 @ ( relation_dom @ C ) @ A ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) )
=> ( B
= ( relation_dom_restriction @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
<=> ( ( in @ B @ ( relation_dom @ C ) )
& ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
<=> ( ( in @ B @ ( relation_dom @ C ) )
& ( in @ B @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) )
=> ( ( in @ B @ ( relation_dom @ C ) )
& ( in @ B @ A ) ) )
& ( ( ( in @ B @ ( relation_dom @ C ) )
& ( in @ B @ A ) )
=> ( in @ B @ ( relation_dom @ ( relation_dom_restriction @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(67,plain,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(25,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(127,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation_empty_yielding @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( relation_empty_yielding @ ( relation_dom_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_relat_1) ).
thf(151,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation_empty_yielding @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( relation_empty_yielding @ ( relation_dom_restriction @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(29,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(146,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(4,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(47,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(163,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(10,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(62,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(20,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(90,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(23,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(122,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(168,plain,
$false,
inference(e,[status(thm)],[88,56,74,85,160,92,96,59,76,43,79,52,125,156,53,141,64,149,71,144,49,130,35,67,127,151,146,47,163,62,90,122,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU224+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 12:48:10 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.93/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.03 % [INFO] Parsing done (141ms).
% 1.28/1.04 % [INFO] Running in sequential loop mode.
% 1.81/1.24 % [INFO] eprover registered as external prover.
% 1.81/1.24 % [INFO] cvc4 registered as external prover.
% 1.81/1.24 % [INFO] Scanning for conjecture ...
% 1.92/1.30 % [INFO] Found a conjecture and 37 axioms. Running axiom selection ...
% 2.12/1.35 % [INFO] Axiom selection finished. Selected 32 axioms (removed 5 axioms).
% 2.22/1.38 % [INFO] Problem is first-order (TPTP FOF).
% 2.22/1.39 % [INFO] Type checking passed.
% 2.22/1.39 % [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 ...
% 4.00/1.96 % External prover 'e' found a proof!
% 4.00/1.96 % [INFO] Killing All external provers ...
% 4.00/1.96 % Time passed: 1422ms (effective reasoning time: 914ms)
% 4.00/1.96 % 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)>
% 4.00/1.96 % Axioms used in derivation (32): idempotence_k3_xboole_0, t2_boole, rc3_funct_1, rc1_funct_1, fc13_relat_1, rc2_funct_1, fc5_relat_1, dt_k7_relat_1, rc2_relat_1, rc1_relat_1, t68_funct_1, rc2_xboole_0, fc1_xboole_0, fc4_relat_1, fc4_funct_1, t1_subset, cc1_relat_1, commutativity_k3_xboole_0, rc3_relat_1, t6_boole, t7_boole, cc1_funct_1, cc2_funct_1, existence_m1_subset_1, fc1_relat_1, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1, d3_xboole_0, antisymmetry_r2_hidden
% 4.00/1.96 % No. of inferences in proof: 68
% 4.00/1.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1422 ms resp. 914 ms w/o parsing
% 4.09/2.01 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.09/2.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------