TSTP Solution File: SET924+1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET924+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 4.24s 2.05s
% Output : Refutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 7 unt; 7 typ; 0 def)
% Number of atoms : 75 ( 35 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 279 ( 37 ~; 23 |; 4 &; 204 @)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 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(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(6,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) )
<=> ~ ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_zfmisc_1) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) )
=> ~ ( in @ A @ B ) )
& ( ~ ( in @ A @ B )
=> ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,plain,
( ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) )
=> ~ ( in @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) ) ) ),
inference(miniscope,[status(thm)],[23]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( in @ A @ B )
| ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) )
| ( in @ A @ B ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) )
| ( in @ A @ B ) ),
inference(simp,[status(thm)],[27]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) )
<=> ~ ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) )
<=> ~ ( in @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: $i,B: $i] :
( ( ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) )
=> ~ ( in @ A @ B ) )
& ( ~ ( in @ A @ B )
=> ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
~ ( ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) )
=> ~ ( in @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( ( set_difference @ ( singleton @ A ) @ B )
= ( singleton @ A ) ) ) ),
inference(miniscope,[status(thm)],[7]) ).
thf(10,plain,
( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
= ( singleton @ sk1 ) )
| ( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
!= ( singleton @ sk3 ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(14,plain,
( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
= ( singleton @ sk1 ) )
| ( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
!= ( singleton @ sk3 ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(12,plain,
( ( in @ sk1 @ sk2 )
| ( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
!= ( singleton @ sk3 ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(15,plain,
( ( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
!= ( singleton @ sk3 ) )
| ( in @ sk1 @ sk2 ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( in @ A @ B )
| ( ( singleton @ A )
!= ( singleton @ sk3 ) )
| ( in @ sk1 @ sk2 )
| ( ( set_difference @ ( singleton @ A ) @ B )
!= ( set_difference @ ( singleton @ sk3 ) @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[28,15]) ).
thf(51,plain,
( ( in @ sk3 @ sk4 )
| ( ( singleton @ sk3 )
!= ( singleton @ sk3 ) )
| ( in @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(67,plain,
( ( in @ sk3 @ sk4 )
| ( in @ sk1 @ sk2 ) ),
inference(simp,[status(thm)],[51]) ).
thf(11,plain,
( ( in @ sk1 @ sk2 )
| ~ ( in @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(143,plain,
( ( in @ sk1 @ sk2 )
| ( ( in @ sk3 @ sk4 )
!= ( in @ sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[67,11]) ).
thf(144,plain,
in @ sk1 @ sk2,
inference(pattern_uni,[status(thm)],[143:[]]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
!= ( singleton @ A ) )
| ~ ( in @ A @ B ) ),
inference(cnf,[status(esa)],[24]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
!= ( singleton @ A ) )
| ~ ( in @ A @ B ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
!= ( singleton @ A ) )
| ( ( in @ sk1 @ sk2 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[144,29]) ).
thf(170,plain,
( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
!= ( singleton @ sk1 ) ),
inference(pattern_uni,[status(thm)],[169:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(181,plain,
( ( set_difference @ ( singleton @ sk3 ) @ sk4 )
!= ( singleton @ sk3 ) ),
inference(simplifyReflect,[status(thm)],[14,170]) ).
thf(220,plain,
! [B: $i,A: $i] :
( ( in @ A @ B )
| ( ( singleton @ A )
!= ( singleton @ sk3 ) )
| ( ( set_difference @ ( singleton @ A ) @ B )
!= ( set_difference @ ( singleton @ sk3 ) @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[28,181]) ).
thf(221,plain,
( ( in @ sk3 @ sk4 )
| ( ( singleton @ sk3 )
!= ( singleton @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[220:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(234,plain,
in @ sk3 @ sk4,
inference(simp,[status(thm)],[221]) ).
thf(9,plain,
( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
= ( singleton @ sk1 ) )
| ~ ( in @ sk3 @ sk4 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(13,plain,
( ( ( set_difference @ ( singleton @ sk1 ) @ sk2 )
= ( singleton @ sk1 ) )
| ~ ( in @ sk3 @ sk4 ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(182,plain,
~ ( in @ sk3 @ sk4 ),
inference(simplifyReflect,[status(thm)],[13,170]) ).
thf(235,plain,
$false,
inference(rewrite,[status(thm)],[234,182]) ).
thf(236,plain,
$false,
inference(simp,[status(thm)],[235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET924+1 : TPTP v8.2.0. Released v3.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n006.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 12:29:54 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.93/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.94 % [INFO] Parsing done (99ms).
% 1.18/0.95 % [INFO] Running in sequential loop mode.
% 1.54/1.16 % [INFO] nitpick registered as external prover.
% 1.54/1.17 % [INFO] Scanning for conjecture ...
% 1.64/1.22 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.80/1.25 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.80/1.25 % [INFO] Problem is first-order (TPTP FOF).
% 1.80/1.25 % [INFO] Type checking passed.
% 1.80/1.26 % [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 ...
% 4.24/2.04 % [INFO] Killing All external provers ...
% 4.24/2.05 % Time passed: 1544ms (effective reasoning time: 1097ms)
% 4.24/2.05 % 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)>
% 4.24/2.05 % Axioms used in derivation (1): l34_zfmisc_1
% 4.24/2.05 % No. of inferences in proof: 33
% 4.24/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1544 ms resp. 1097 ms w/o parsing
% 4.32/2.10 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.32/2.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------