TSTP Solution File: SET928+1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET928+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 03:07:24 EDT 2024
% Result : Theorem 8.89s 3.54s
% Output : Refutation 9.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 16
% Syntax : Number of formulae : 71 ( 13 unt; 11 typ; 0 def)
% Number of atoms : 148 ( 36 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 494 ( 76 ~; 48 |; 19 &; 340 @)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 84 ( 0 ^ 78 !; 6 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_difference_type,type,
set_difference: $i > $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(disjoint_type,type,
disjoint: $i > $i > $o ).
thf(sk1_type,type,
sk1: $o ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(1,conjecture,
! [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(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( unordered_pair @ A @ B ) )
<=> ( ~ ( in @ A @ C )
& ~ ( in @ B @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,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)],[2]) ).
thf(12,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)],[11]) ).
thf(16,plain,
( ( ( set_difference @ ( unordered_pair @ sk2 @ sk3 ) @ sk4 )
= ( unordered_pair @ sk2 @ sk3 ) )
| ~ sk1 ),
inference(cnf,[status(esa)],[12]) ).
thf(19,plain,
( ( ( set_difference @ ( unordered_pair @ sk2 @ sk3 ) @ sk4 )
= ( unordered_pair @ sk2 @ sk3 ) )
| ~ sk1 ),
inference(lifteq,[status(thm)],[16]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( ( disjoint @ A @ B )
=> ( ( set_difference @ A @ B )
= A ) )
& ( ( ( set_difference @ A @ B )
= A )
=> ( disjoint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(39,plain,
( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( ( set_difference @ A @ B )
= A ) )
& ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= A )
=> ( disjoint @ A @ B ) ) ),
inference(miniscope,[status(thm)],[38]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) ),
inference(cnf,[status(esa)],[39]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) ),
inference(simp,[status(thm)],[42]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ~ sk1
| ( ( unordered_pair @ sk2 @ sk3 )
!= A )
| ( disjoint @ A @ B )
| ( ( set_difference @ ( unordered_pair @ sk2 @ sk3 ) @ sk4 )
!= ( set_difference @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19,43]) ).
thf(82,plain,
( ~ sk1
| ( ( unordered_pair @ sk2 @ sk3 )
!= ( unordered_pair @ sk2 @ sk3 ) )
| ( disjoint @ ( unordered_pair @ sk2 @ sk3 ) @ sk4 ) ),
inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( unordered_pair @ sk2 @ sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(83,plain,
( ~ sk1
| ( disjoint @ ( unordered_pair @ sk2 @ sk3 ) @ sk4 ) ),
inference(simp,[status(thm)],[82]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( in @ A @ B )
& ~ ( in @ C @ B )
& ~ ( disjoint @ ( unordered_pair @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_zfmisc_1) ).
thf(35,plain,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( in @ A @ B )
& ~ ( in @ C @ B )
& ~ ( disjoint @ ( unordered_pair @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(36,plain,
~ ? [A: $i,B: $i] :
( ~ ( in @ A @ B )
& ? [C: $i] :
( ~ ( in @ C @ B )
& ~ ( disjoint @ ( unordered_pair @ A @ C ) @ B ) ) ),
inference(miniscope,[status(thm)],[35]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ A @ B )
| ( in @ C @ B )
| ( disjoint @ ( unordered_pair @ A @ C ) @ B ) ),
inference(cnf,[status(esa)],[36]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ),
inference(cnf,[status(esa)],[39]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( ( set_difference @ A @ B )
= A )
| ~ ( disjoint @ A @ B ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(13,plain,
( sk1
| ( ( set_difference @ ( unordered_pair @ sk5 @ sk6 ) @ sk7 )
!= ( unordered_pair @ sk5 @ sk6 ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(18,plain,
( ( ( set_difference @ ( unordered_pair @ sk5 @ sk6 ) @ sk7 )
!= ( unordered_pair @ sk5 @ sk6 ) )
| sk1 ),
inference(lifteq,[status(thm)],[13]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ~ ( disjoint @ A @ B )
| ( A
!= ( unordered_pair @ sk5 @ sk6 ) )
| sk1
| ( ( set_difference @ A @ B )
!= ( set_difference @ ( unordered_pair @ sk5 @ sk6 ) @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[44,18]) ).
thf(147,plain,
( ~ ( disjoint @ ( unordered_pair @ sk5 @ sk6 ) @ sk7 )
| ( ( unordered_pair @ sk5 @ sk6 )
!= ( unordered_pair @ sk5 @ sk6 ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( unordered_pair @ sk5 @ sk6 )),bind(B,$thf( sk7 ))]]) ).
thf(162,plain,
( ~ ( disjoint @ ( unordered_pair @ sk5 @ sk6 ) @ sk7 )
| sk1 ),
inference(simp,[status(thm)],[147]) ).
thf(188,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ A @ B )
| ( in @ C @ B )
| sk1
| ( ( disjoint @ ( unordered_pair @ A @ C ) @ B )
!= ( disjoint @ ( unordered_pair @ sk5 @ sk6 ) @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[37,162]) ).
thf(189,plain,
( ( in @ sk5 @ sk7 )
| ( in @ sk6 @ sk7 )
| sk1 ),
inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( sk5 )),bind(B,$thf( sk7 )),bind(C,$thf( sk6 ))]]) ).
thf(14,plain,
( sk1
| ~ ( in @ sk6 @ sk7 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(192,plain,
( ( in @ sk5 @ sk7 )
| sk1
| ( ( in @ sk6 @ sk7 )
!= ( in @ sk6 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[189,14]) ).
thf(193,plain,
( ( in @ sk5 @ sk7 )
| sk1 ),
inference(pattern_uni,[status(thm)],[192:[]]) ).
thf(17,plain,
( sk1
| ~ ( in @ sk5 @ sk7 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(224,plain,
( sk1
| ( ( in @ sk5 @ sk7 )
!= ( in @ sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[193,17]) ).
thf(225,plain,
sk1,
inference(pattern_uni,[status(thm)],[224:[]]) ).
thf(236,plain,
( ~ $true
| ( disjoint @ ( unordered_pair @ sk2 @ sk3 ) @ sk4 ) ),
inference(rewrite,[status(thm)],[83,225]) ).
thf(237,plain,
disjoint @ ( unordered_pair @ sk2 @ sk3 ) @ sk4,
inference(simp,[status(thm)],[236]) ).
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(22,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(cnf,[status(esa)],[22]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(15,plain,
( ( in @ sk2 @ sk4 )
| ( in @ sk3 @ sk4 )
| ~ sk1 ),
inference(cnf,[status(esa)],[12]) ).
thf(240,plain,
( ( in @ sk2 @ sk4 )
| ( in @ sk3 @ sk4 )
| ~ $true ),
inference(rewrite,[status(thm)],[15,225]) ).
thf(241,plain,
( ( in @ sk2 @ sk4 )
| ( in @ sk3 @ sk4 ) ),
inference(simp,[status(thm)],[240]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( disjoint @ ( unordered_pair @ A @ B ) @ C )
& ( in @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_zfmisc_1) ).
thf(32,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( disjoint @ ( unordered_pair @ A @ B ) @ C )
& ( in @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( disjoint @ ( unordered_pair @ A @ B ) @ C )
& ( in @ A @ C ) ),
inference(miniscope,[status(thm)],[32]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( disjoint @ ( unordered_pair @ A @ B ) @ C )
| ~ ( in @ A @ C ) ),
inference(cnf,[status(esa)],[33]) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk1
| ~ ( in @ A @ C )
| ( ( disjoint @ ( unordered_pair @ sk2 @ sk3 ) @ sk4 )
!= ( disjoint @ ( unordered_pair @ A @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[83,34]) ).
thf(171,plain,
( ~ sk1
| ~ ( in @ sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).
thf(238,plain,
( ~ $true
| ~ ( in @ sk2 @ sk4 ) ),
inference(rewrite,[status(thm)],[171,225]) ).
thf(239,plain,
~ ( in @ sk2 @ sk4 ),
inference(simp,[status(thm)],[238]) ).
thf(287,plain,
( $false
| ( in @ sk3 @ sk4 ) ),
inference(rewrite,[status(thm)],[241,239]) ).
thf(288,plain,
in @ sk3 @ sk4,
inference(simp,[status(thm)],[287]) ).
thf(293,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( disjoint @ ( unordered_pair @ A @ B ) @ C )
| ( ( in @ sk3 @ sk4 )
!= ( in @ A @ C ) ) ),
inference(paramod_ordered,[status(thm)],[288,34]) ).
thf(294,plain,
! [A: $i] :
~ ( disjoint @ ( unordered_pair @ sk3 @ A ) @ sk4 ),
inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(301,plain,
! [A: $i] :
~ ( disjoint @ ( unordered_pair @ sk3 @ A ) @ sk4 ),
inference(simp,[status(thm)],[294]) ).
thf(328,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( disjoint @ ( unordered_pair @ A @ B ) @ sk4 )
| ( ( unordered_pair @ B @ A )
!= ( unordered_pair @ sk3 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[24,301]) ).
thf(329,plain,
! [A: $i] :
~ ( disjoint @ ( unordered_pair @ A @ sk3 ) @ sk4 ),
inference(pattern_uni,[status(thm)],[328:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(369,plain,
$false,
inference(rewrite,[status(thm)],[237,329]) ).
thf(370,plain,
$false,
inference(simp,[status(thm)],[369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET928+1 : TPTP v8.2.0. Released v3.2.0.
% 0.12/0.13 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 12:40:54 EDT 2024
% 0.13/0.34 % CPUTime :
% 1.09/1.05 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.44/1.23 % [INFO] Parsing done (179ms).
% 1.49/1.24 % [INFO] Running in sequential loop mode.
% 2.06/1.65 % [INFO] nitpick registered as external prover.
% 2.06/1.66 % [INFO] Scanning for conjecture ...
% 2.23/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.40/1.82 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.40/1.84 % [INFO] Problem is first-order (TPTP FOF).
% 2.40/1.85 % [INFO] Type checking passed.
% 2.40/1.85 % [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 ...
% 8.89/3.52 % [INFO] Killing All external provers ...
% 8.89/3.54 % Time passed: 3037ms (effective reasoning time: 2286ms)
% 8.89/3.54 % 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)>
% 8.89/3.54 % Axioms used in derivation (4): t83_xboole_1, t57_zfmisc_1, commutativity_k2_tarski, t55_zfmisc_1
% 8.89/3.54 % No. of inferences in proof: 60
% 8.89/3.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3037 ms resp. 2286 ms w/o parsing
% 9.04/3.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.04/3.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------