TSTP Solution File: SEU186+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU186+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 11:57:27 EDT 2023
% Result : Theorem 3.27s 1.74s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 29
% Syntax : Number of formulae : 52 ( 19 unt; 8 typ; 0 def)
% Number of atoms : 81 ( 14 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 198 ( 29 ~; 2 |; 16 &; 132 @)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 0 ^; 64 !; 10 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_type,type,
relation: $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(element_type,type,
element: $i > $i > $o ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(29,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(41,plain,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(73,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(21,axiom,
! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(76,plain,
! [A: $i] :
( ( ( relation @ A )
=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) )
& ( ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) )
=> ( relation @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(35,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(63,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(58,plain,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(51,plain,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(60,plain,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(22,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(85,plain,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(38,plain,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(33,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(12,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(54,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(49,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(55,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,conjecture,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(23,plain,
~ ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(47,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(68,plain,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(90,plain,
$false,
inference(e,[status(thm)],[29,41,73,44,76,66,35,63,58,51,60,85,38,33,71,54,49,55,23,47,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU186+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n018.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 13:14:58 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.87/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.95 % [INFO] Parsing done (112ms).
% 1.22/0.95 % [INFO] Running in sequential loop mode.
% 1.53/1.15 % [INFO] eprover registered as external prover.
% 1.53/1.15 % [INFO] cvc4 registered as external prover.
% 1.53/1.15 % [INFO] Scanning for conjecture ...
% 1.74/1.21 % [INFO] Found a conjecture and 25 axioms. Running axiom selection ...
% 1.87/1.25 % [INFO] Axiom selection finished. Selected 20 axioms (removed 5 axioms).
% 1.87/1.27 % [INFO] Problem is first-order (TPTP FOF).
% 1.87/1.27 % [INFO] Type checking passed.
% 1.87/1.28 % [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 ...
% 3.27/1.73 % External prover 'e' found a proof!
% 3.27/1.73 % [INFO] Killing All external provers ...
% 3.27/1.73 % Time passed: 1219ms (effective reasoning time: 776ms)
% 3.27/1.73 % 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)>
% 3.27/1.74 % Axioms used in derivation (20): fc1_zfmisc_1, cc1_relat_1, fc3_subset_1, fc2_subset_1, t7_boole, rc2_relat_1, rc1_relat_1, t2_subset, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, d5_tarski, fc4_relat_1, t1_subset, t6_boole, d1_relat_1, existence_m1_subset_1, commutativity_k2_tarski, t8_boole, rc1_xboole_0
% 3.27/1.74 % No. of inferences in proof: 44
% 3.27/1.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1219 ms resp. 776 ms w/o parsing
% 3.45/1.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.45/1.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------