TSTP Solution File: SET930+1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET930+1 : TPTP v8.2.0. Released v3.2.0.
% 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 : Tue May 21 03:07:25 EDT 2024
% Result : Theorem 15.61s 3.51s
% Output : Refutation 15.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 62 ( 18 unt; 8 typ; 0 def)
% Number of atoms : 153 ( 75 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 652 ( 79 ~; 45 |; 33 &; 480 @)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 97 ( 0 ^ 94 !; 3 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_difference_type,type,
set_difference: $i > $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( unordered_pair @ A @ B ) )
<=> ( ~ ( in @ A @ C )
& ~ ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).
thf(44,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( unordered_pair @ A @ B ) )
=> ( ~ ( in @ A @ C )
& ~ ( in @ B @ C ) ) )
& ( ( ~ ( in @ A @ C )
& ~ ( in @ B @ C ) )
=> ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( unordered_pair @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(45,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( unordered_pair @ A @ B ) )
=> ( ~ ( in @ A @ C )
& ~ ( in @ B @ C ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ~ ( in @ A @ C )
& ~ ( in @ B @ C ) )
=> ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( unordered_pair @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[44]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ A @ C )
| ( in @ B @ C )
| ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( unordered_pair @ A @ B ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( unordered_pair @ A @ B ) )
| ( in @ A @ C )
| ( in @ B @ C ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( unordered_pair @ A @ B ) )
| ( in @ A @ C )
| ( in @ B @ C ) ),
inference(simp,[status(thm)],[49]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
~ ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= empty_set )
& ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= ( singleton @ A ) )
& ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= ( singleton @ B ) )
& ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= ( unordered_pair @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
~ ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= empty_set )
& ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= ( singleton @ A ) )
& ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= ( singleton @ B ) )
& ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= ( unordered_pair @ A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i,B: $i,C: $i] :
~ ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= empty_set )
& ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= ( singleton @ A ) )
& ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= ( singleton @ B ) )
& ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= ( unordered_pair @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,plain,
~ ~ ? [A: $i,B: $i,C: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= empty_set )
& ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= ( singleton @ A ) )
& ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= ( singleton @ B ) )
& ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= ( unordered_pair @ A @ B ) ) ),
inference(miniscope,[status(thm)],[11]) ).
thf(13,plain,
( ( set_difference @ ( unordered_pair @ sk1 @ sk2 ) @ sk3 )
!= ( unordered_pair @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(17,plain,
( ( set_difference @ ( unordered_pair @ sk1 @ sk2 ) @ sk3 )
!= ( unordered_pair @ sk1 @ sk2 ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(289,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ A @ C )
| ( in @ B @ C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ sk1 @ sk2 ) )
| ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= ( set_difference @ ( unordered_pair @ sk1 @ sk2 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[50,17]) ).
thf(290,plain,
( ( in @ sk1 @ sk3 )
| ( in @ sk2 @ sk3 )
| ( ( unordered_pair @ sk1 @ sk2 )
!= ( unordered_pair @ sk1 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[289:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(321,plain,
( ( in @ sk1 @ sk3 )
| ( in @ sk2 @ sk3 ) ),
inference(simp,[status(thm)],[290]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( singleton @ A ) )
<=> ( ~ ( in @ A @ C )
& ( ( in @ B @ C )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).
thf(27,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( singleton @ A ) )
=> ( ~ ( in @ A @ C )
& ( ( in @ B @ C )
| ( A = B ) ) ) )
& ( ( ~ ( in @ A @ C )
& ( ( in @ B @ C )
| ( A = B ) ) )
=> ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( singleton @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( singleton @ A ) )
=> ( ~ ( in @ A @ C )
& ( ( in @ B @ C )
| ( A = B ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ~ ( in @ A @ C )
& ( ( in @ B @ C )
| ( A = B ) ) )
=> ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( singleton @ A ) ) ) ),
inference(miniscope,[status(thm)],[27]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ A @ C )
| ~ ( in @ B @ C )
| ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( singleton @ A ) ) ),
inference(cnf,[status(esa)],[28]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( singleton @ A ) )
| ( in @ A @ C )
| ~ ( in @ B @ C ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( singleton @ A ) )
| ( in @ A @ C )
| ~ ( in @ B @ C ) ),
inference(simp,[status(thm)],[35]) ).
thf(15,plain,
( ( set_difference @ ( unordered_pair @ sk1 @ sk2 ) @ sk3 )
!= ( singleton @ sk1 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(19,plain,
( ( set_difference @ ( unordered_pair @ sk1 @ sk2 ) @ sk3 )
!= ( singleton @ sk1 ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(198,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ A @ C )
| ~ ( in @ B @ C )
| ( ( singleton @ A )
!= ( singleton @ sk1 ) )
| ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= ( set_difference @ ( unordered_pair @ sk1 @ sk2 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[36,19]) ).
thf(199,plain,
( ( in @ sk1 @ sk3 )
| ~ ( in @ sk2 @ sk3 )
| ( ( singleton @ sk1 )
!= ( singleton @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(203,plain,
( ( in @ sk1 @ sk3 )
| ~ ( in @ sk2 @ sk3 ) ),
inference(simp,[status(thm)],[199]) ).
thf(495,plain,
( ( in @ sk1 @ sk3 )
| ( ( in @ sk2 @ sk3 )
!= ( in @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[321,203]) ).
thf(496,plain,
in @ sk1 @ sk3,
inference(pattern_uni,[status(thm)],[495:[]]) ).
thf(534,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( singleton @ A ) )
| ( in @ A @ C )
| ( ( in @ sk1 @ sk3 )
!= ( in @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[496,36]) ).
thf(535,plain,
! [A: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ sk1 ) @ sk3 )
= ( singleton @ A ) )
| ( in @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[534:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk3 ))]]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= empty_set )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).
thf(53,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= empty_set )
=> ( ( in @ A @ C )
& ( in @ B @ C ) ) )
& ( ( ( in @ A @ C )
& ( in @ B @ C ) )
=> ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(54,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= empty_set )
=> ( ( in @ A @ C )
& ( in @ B @ C ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ C )
& ( in @ B @ C ) )
=> ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= empty_set ) ) ),
inference(miniscope,[status(thm)],[53]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= empty_set ) ),
inference(cnf,[status(esa)],[54]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= empty_set )
| ~ ( in @ A @ C )
| ~ ( in @ B @ C ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= empty_set )
| ~ ( in @ A @ C )
| ~ ( in @ B @ C ) ),
inference(simp,[status(thm)],[58]) ).
thf(16,plain,
( ( set_difference @ ( unordered_pair @ sk1 @ sk2 ) @ sk3 )
!= empty_set ),
inference(cnf,[status(esa)],[12]) ).
thf(20,plain,
( ( set_difference @ ( unordered_pair @ sk1 @ sk2 ) @ sk3 )
!= empty_set ),
inference(lifteq,[status(thm)],[16]) ).
thf(934,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
!= ( set_difference @ ( unordered_pair @ sk1 @ sk2 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[59,20]) ).
thf(935,plain,
( ~ ( in @ sk1 @ sk3 )
| ~ ( in @ sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[934:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(1169,plain,
( ~ $true
| ~ ( in @ sk2 @ sk3 ) ),
inference(rewrite,[status(thm)],[935,496]) ).
thf(1170,plain,
~ ( in @ sk2 @ sk3 ),
inference(simp,[status(thm)],[1169]) ).
thf(3031,plain,
! [A: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ sk1 ) @ sk3 )
= ( singleton @ A ) )
| ( ( in @ A @ sk3 )
!= ( in @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[535,1170]) ).
thf(3032,plain,
( ( set_difference @ ( unordered_pair @ sk2 @ sk1 ) @ sk3 )
= ( singleton @ sk2 ) ),
inference(pattern_uni,[status(thm)],[3031:[bind(A,$thf( sk2 ))]]) ).
thf(14,plain,
( ( set_difference @ ( unordered_pair @ sk1 @ sk2 ) @ sk3 )
!= ( singleton @ sk2 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(18,plain,
( ( set_difference @ ( unordered_pair @ sk1 @ sk2 ) @ sk3 )
!= ( singleton @ sk2 ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(3226,plain,
( ( set_difference @ ( unordered_pair @ sk2 @ sk1 ) @ sk3 )
!= ( set_difference @ ( unordered_pair @ sk1 @ sk2 ) @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[3032,18]) ).
thf(3255,plain,
( ( ( unordered_pair @ sk2 @ sk1 )
!= ( unordered_pair @ sk1 @ sk2 ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[3226]) ).
thf(3289,plain,
( ( unordered_pair @ sk2 @ sk1 )
!= ( unordered_pair @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[3255]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(3330,plain,
$false,
inference(simplifyReflect,[status(thm)],[3289,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SET930+1 : TPTP v8.2.0. Released v3.2.0.
% 0.12/0.13 % Command : run_Leo-III %s %d
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon May 20 11:25:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.70/0.75 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.01/0.85 % [INFO] Parsing done (97ms).
% 1.01/0.86 % [INFO] Running in sequential loop mode.
% 1.32/1.06 % [INFO] nitpick registered as external prover.
% 1.32/1.06 % [INFO] Scanning for conjecture ...
% 1.51/1.15 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 1.67/1.18 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.67/1.19 % [INFO] Problem is first-order (TPTP FOF).
% 1.80/1.20 % [INFO] Type checking passed.
% 1.80/1.20 % [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 ...
% 15.61/3.50 % [INFO] Killing All external provers ...
% 15.61/3.51 % Time passed: 3026ms (effective reasoning time: 2644ms)
% 15.61/3.51 % 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)>
% 15.61/3.51 % Axioms used in derivation (4): t72_zfmisc_1, l39_zfmisc_1, t73_zfmisc_1, commutativity_k2_tarski
% 15.61/3.51 % No. of inferences in proof: 54
% 15.61/3.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3026 ms resp. 2644 ms w/o parsing
% 15.61/3.58 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.61/3.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------