TSTP Solution File: SET974+1 by Leo-III-SAT---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET974+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 03:07:29 EDT 2024
% Result : Theorem 58.60s 9.17s
% Output : Refutation 58.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 58 ( 12 unt; 12 typ; 0 def)
% Number of atoms : 115 ( 16 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 576 ( 46 ~; 34 |; 18 &; 475 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-5 aty)
% Number of variables : 142 ( 0 ^ 127 !; 15 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
thf(disjoint_type,type,
disjoint: $i > $i > $o ).
thf(cartesian_product2_type,type,
cartesian_product2: $i > $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(set_intersection2_type,type,
set_intersection2: $i > $i > $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk7_type,type,
sk7: $i > $i > $i > $i > $i > $i ).
thf(sk8_type,type,
sk8: $i > $i > $i > $i > $i > $i ).
thf(sk9_type,type,
sk9: $i > $i > $i ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( disjoint @ A @ B )
| ( disjoint @ C @ D ) )
=> ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( disjoint @ A @ B )
| ( disjoint @ C @ D ) )
=> ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( disjoint @ A @ B )
| ( disjoint @ C @ D ) )
=> ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
~ ( disjoint @ ( cartesian_product2 @ sk1 @ sk3 ) @ ( cartesian_product2 @ sk2 @ sk4 ) ),
inference(cnf,[status(esa)],[14]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(47,plain,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(48,plain,
( ~ ? [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
& ~ ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ? [A: $i,B: $i] :
( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
inference(miniscope,[status(thm)],[47]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sk9 @ B @ A ) @ ( set_intersection2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[48]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
& ! [F: $i,G: $i] :
~ ( ( A
= ( ordered_pair @ F @ G ) )
& ( in @ F @ ( set_intersection2 @ B @ D ) )
& ( in @ G @ ( set_intersection2 @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_zfmisc_1) ).
thf(41,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
~ ( ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
& ! [F: $i,G: $i] :
~ ( ( A
= ( ordered_pair @ F @ G ) )
& ( in @ F @ ( set_intersection2 @ B @ D ) )
& ( in @ G @ ( set_intersection2 @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(42,plain,
~ ? [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
& ~ ? [F: $i,G: $i] :
( ( A
= ( ordered_pair @ F @ G ) )
& ( in @ F @ ( set_intersection2 @ B @ D ) )
& ( in @ G @ ( set_intersection2 @ C @ E ) ) ) ),
inference(miniscope,[status(thm)],[41]) ).
thf(44,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
| ( in @ ( sk7 @ E @ D @ C @ B @ A ) @ ( set_intersection2 @ B @ D ) ) ),
inference(cnf,[status(esa)],[42]) ).
thf(264,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sk7 @ G @ F @ E @ D @ C ) @ ( set_intersection2 @ D @ F ) )
| ( ( in @ ( sk9 @ B @ A ) @ ( set_intersection2 @ A @ B ) )
!= ( in @ C @ ( set_intersection2 @ ( cartesian_product2 @ D @ E ) @ ( cartesian_product2 @ F @ G ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[50,44]) ).
thf(265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( disjoint @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ ( sk7 @ D @ C @ B @ A @ ( sk9 @ ( cartesian_product2 @ C @ D ) @ ( cartesian_product2 @ A @ B ) ) ) @ ( set_intersection2 @ A @ C ) ) ),
inference(pattern_uni,[status(thm)],[264:[bind(A,$thf( cartesian_product2 @ J @ K )),bind(B,$thf( cartesian_product2 @ L @ M )),bind(C,$thf( sk9 @ ( cartesian_product2 @ L @ M ) @ ( cartesian_product2 @ J @ K ) )),bind(D,$thf( J )),bind(E,$thf( K )),bind(F,$thf( L )),bind(G,$thf( M ))]]) ).
thf(280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( disjoint @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ ( sk7 @ D @ C @ B @ A @ ( sk9 @ ( cartesian_product2 @ C @ D ) @ ( cartesian_product2 @ A @ B ) ) ) @ ( set_intersection2 @ A @ C ) ) ),
inference(simp,[status(thm)],[265]) ).
thf(5,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(22,plain,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(cnf,[status(esa)],[22]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( disjoint @ C @ D )
| ( in @ ( sk9 @ D @ C ) @ ( set_intersection2 @ B @ A ) )
| ( ( set_intersection2 @ A @ B )
!= ( set_intersection2 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[24,50]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sk9 @ B @ A ) @ ( set_intersection2 @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1281,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( disjoint @ C @ D )
| ( in @ ( sk9 @ D @ C ) @ ( set_intersection2 @ B @ A ) )
| ( ( set_intersection2 @ A @ B )
!= ( set_intersection2 @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[24,254]) ).
thf(1282,plain,
! [B: $i,A: $i] :
( ( disjoint @ B @ A )
| ( in @ ( sk9 @ A @ B ) @ ( set_intersection2 @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[1281:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(45,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
| ( in @ ( sk8 @ E @ D @ C @ B @ A ) @ ( set_intersection2 @ C @ E ) ) ),
inference(cnf,[status(esa)],[42]) ).
thf(16,plain,
( ( disjoint @ sk1 @ sk2 )
| ( disjoint @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[14]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ),
inference(cnf,[status(esa)],[48]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ),
inference(simp,[status(thm)],[49]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( disjoint @ sk1 @ sk2 )
| ~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ( ( disjoint @ sk3 @ sk4 )
!= ( disjoint @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16,51]) ).
thf(89,plain,
! [A: $i] :
( ( disjoint @ sk1 @ sk2 )
| ~ ( in @ A @ ( set_intersection2 @ sk3 @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(95,plain,
! [A: $i] :
( ( disjoint @ sk1 @ sk2 )
| ~ ( in @ A @ ( set_intersection2 @ sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(331,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
| ( disjoint @ sk1 @ sk2 )
| ( ( in @ ( sk8 @ E @ D @ C @ B @ A ) @ ( set_intersection2 @ C @ E ) )
!= ( in @ F @ ( set_intersection2 @ sk3 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[45,95]) ).
thf(332,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( set_intersection2 @ ( cartesian_product2 @ B @ sk3 ) @ ( cartesian_product2 @ A @ sk4 ) ) )
| ( disjoint @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[331:[bind(A,$thf( K )),bind(B,$thf( J )),bind(C,$thf( sk3 )),bind(D,$thf( H )),bind(E,$thf( sk4 )),bind(F,$thf( sk8 @ sk4 @ H @ sk3 @ J @ K ))]]) ).
thf(345,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( set_intersection2 @ ( cartesian_product2 @ B @ sk3 ) @ ( cartesian_product2 @ A @ sk4 ) ) )
| ( disjoint @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[332]) ).
thf(6789,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( disjoint @ B @ A )
| ( disjoint @ sk1 @ sk2 )
| ( ( in @ ( sk9 @ A @ B ) @ ( set_intersection2 @ B @ A ) )
!= ( in @ E @ ( set_intersection2 @ ( cartesian_product2 @ D @ sk3 ) @ ( cartesian_product2 @ C @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1282,345]) ).
thf(6790,plain,
! [B: $i,A: $i] :
( ( disjoint @ ( cartesian_product2 @ A @ sk3 ) @ ( cartesian_product2 @ B @ sk4 ) )
| ( disjoint @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6789:[bind(A,$thf( cartesian_product2 @ J @ sk4 )),bind(B,$thf( cartesian_product2 @ H @ sk3 )),bind(C,$thf( J )),bind(D,$thf( H )),bind(E,$thf( sk9 @ ( cartesian_product2 @ J @ sk4 ) @ ( cartesian_product2 @ H @ sk3 ) ))]]) ).
thf(6809,plain,
! [B: $i,A: $i] :
( ( disjoint @ ( cartesian_product2 @ A @ sk3 ) @ ( cartesian_product2 @ B @ sk4 ) )
| ( disjoint @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[6790]) ).
thf(6852,plain,
! [B: $i,A: $i] :
( ( disjoint @ sk1 @ sk2 )
| ( ( disjoint @ ( cartesian_product2 @ A @ sk3 ) @ ( cartesian_product2 @ B @ sk4 ) )
!= ( disjoint @ ( cartesian_product2 @ sk1 @ sk3 ) @ ( cartesian_product2 @ sk2 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6809,15]) ).
thf(6853,plain,
disjoint @ sk1 @ sk2,
inference(pattern_uni,[status(thm)],[6852:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(6879,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ( ( disjoint @ sk1 @ sk2 )
!= ( disjoint @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6853,51]) ).
thf(6880,plain,
! [A: $i] :
~ ( in @ A @ ( set_intersection2 @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6879:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(6886,plain,
! [A: $i] :
~ ( in @ A @ ( set_intersection2 @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[6880]) ).
thf(6916,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( disjoint @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( ( in @ ( sk7 @ D @ C @ B @ A @ ( sk9 @ ( cartesian_product2 @ C @ D ) @ ( cartesian_product2 @ A @ B ) ) ) @ ( set_intersection2 @ A @ C ) )
!= ( in @ E @ ( set_intersection2 @ sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[280,6886]) ).
thf(6917,plain,
! [B: $i,A: $i] : ( disjoint @ ( cartesian_product2 @ sk1 @ B ) @ ( cartesian_product2 @ sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[6916:[bind(A,$thf( sk1 )),bind(B,$thf( P )),bind(C,$thf( sk2 )),bind(D,$thf( N )),bind(E,$thf( sk7 @ N @ sk2 @ P @ sk1 @ ( sk9 @ ( cartesian_product2 @ sk2 @ N ) @ ( cartesian_product2 @ sk1 @ P ) ) ))]]) ).
thf(6951,plain,
! [B: $i,A: $i] : ( disjoint @ ( cartesian_product2 @ sk1 @ B ) @ ( cartesian_product2 @ sk2 @ A ) ),
inference(simp,[status(thm)],[6917]) ).
thf(7469,plain,
~ $true,
inference(rewrite,[status(thm)],[15,6951]) ).
thf(7470,plain,
$false,
inference(simp,[status(thm)],[7469]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET974+1 : TPTP v8.2.0. Released v3.2.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n016.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 20 12:34:54 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.93/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/0.98 % [INFO] Parsing done (114ms).
% 1.25/0.99 % [INFO] Running in sequential loop mode.
% 1.70/1.19 % [INFO] nitpick registered as external prover.
% 1.70/1.20 % [INFO] Scanning for conjecture ...
% 1.87/1.25 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 1.87/1.27 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.87/1.29 % [INFO] Problem is first-order (TPTP FOF).
% 1.87/1.30 % [INFO] Type checking passed.
% 1.87/1.30 % [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 ...
% 58.60/9.16 % [INFO] Killing All external provers ...
% 58.60/9.17 % Time passed: 8636ms (effective reasoning time: 8175ms)
% 58.60/9.17 % 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)>
% 58.60/9.17 % Axioms used in derivation (3): t4_xboole_0, t104_zfmisc_1, commutativity_k3_xboole_0
% 58.60/9.17 % No. of inferences in proof: 46
% 58.60/9.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8636 ms resp. 8175 ms w/o parsing
% 58.60/9.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 58.60/9.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------