TSTP Solution File: SET925+1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET925+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 03:07:22 EDT 2024
% Result : Theorem 6.89s 3.14s
% Output : Refutation 6.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 5 unt; 8 typ; 0 def)
% Number of atoms : 71 ( 33 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 238 ( 28 ~; 21 |; 4 &; 174 @)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 34 ( 0 ^ 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_difference_type,type,
set_difference: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(empty_set_type,type,
empty_set: $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(sk4_type,type,
sk4: $i ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
<=> ( in @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: $i,B: $i] :
( ( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
=> ( in @ A @ B ) )
& ( ( in @ A @ B )
=> ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
~ ( ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
=> ( in @ A @ B ) )
& ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set ) ) ),
inference(miniscope,[status(thm)],[8]) ).
thf(10,plain,
( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
= empty_set )
| ( in @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[9]) ).
thf(14,plain,
( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
= empty_set )
| ( in @ sk3 @ sk4 ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
=> ( in @ A @ B ) )
& ( ( in @ A @ B )
=> ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,plain,
( ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
=> ( in @ A @ B ) )
& ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set ) ) ),
inference(miniscope,[status(thm)],[25]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set ) ),
inference(cnf,[status(esa)],[26]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
| ~ ( in @ A @ B ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
| ~ ( in @ A @ B ) ),
inference(simp,[status(thm)],[29]) ).
thf(11,plain,
( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
= empty_set )
| ( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
!= empty_set ) ),
inference(cnf,[status(esa)],[9]) ).
thf(15,plain,
( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
= empty_set )
| ( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
!= empty_set ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
= empty_set )
| ( ( set_difference @ ( singleton @ A ) @ B )
!= ( set_difference @ ( singleton @ sk3 ) @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[30,15]) ).
thf(121,plain,
( ~ ( in @ sk3 @ sk4 )
| ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(149,plain,
( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
= empty_set )
| ( ( in @ sk3 @ sk4 )
!= ( in @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[14,121]) ).
thf(150,plain,
( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
= empty_set ),
inference(pattern_uni,[status(thm)],[149:[]]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
!= empty_set )
| ( in @ A @ B ) ),
inference(cnf,[status(esa)],[26]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
!= empty_set )
| ( in @ A @ B ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( in @ A @ B )
| ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
!= ( set_difference @ ( singleton @ A ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[150,31]) ).
thf(185,plain,
in @ sk1 @ sk2,
inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(12,plain,
( ~ ( in @ sk1 @ sk2 )
| ( in @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[9]) ).
thf(13,plain,
( ~ ( in @ sk1 @ sk2 )
| ( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
!= empty_set ) ),
inference(cnf,[status(esa)],[9]) ).
thf(16,plain,
( ( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
!= empty_set )
| ~ ( in @ sk1 @ sk2 ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ sk1 @ sk2 )
| ( ( set_difference @ ( singleton @ A ) @ B )
!= ( set_difference @ ( singleton @ sk3 ) @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[30,16]) ).
thf(119,plain,
( ~ ( in @ sk3 @ sk4 )
| ~ ( in @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(135,plain,
( ~ ( in @ sk1 @ sk2 )
| ( ( in @ sk3 @ sk4 )
!= ( in @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[12,119]) ).
thf(136,plain,
~ ( in @ sk1 @ sk2 ),
inference(pattern_uni,[status(thm)],[135:[]]) ).
thf(191,plain,
$false,
inference(rewrite,[status(thm)],[185,136]) ).
thf(192,plain,
$false,
inference(simp,[status(thm)],[191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET925+1 : TPTP v8.2.0. Released v3.2.0.
% 0.13/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 20 13:13:54 EDT 2024
% 0.20/0.35 % CPUTime :
% 1.18/1.09 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.49/1.26 % [INFO] Parsing done (170ms).
% 1.49/1.28 % [INFO] Running in sequential loop mode.
% 2.15/1.70 % [INFO] nitpick registered as external prover.
% 2.15/1.71 % [INFO] Scanning for conjecture ...
% 2.40/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.40/1.85 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.40/1.86 % [INFO] Problem is first-order (TPTP FOF).
% 2.40/1.86 % [INFO] Type checking passed.
% 2.40/1.87 % [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 ...
% 6.70/3.13 % [INFO] Killing All external provers ...
% 6.89/3.14 % Time passed: 2612ms (effective reasoning time: 1848ms)
% 6.89/3.14 % 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)>
% 6.89/3.14 % Axioms used in derivation (1): l36_zfmisc_1
% 6.89/3.14 % No. of inferences in proof: 31
% 6.89/3.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2612 ms resp. 1848 ms w/o parsing
% 6.89/3.19 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.89/3.19 % [INFO] Killing All external provers ...
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