TSTP Solution File: SEU619^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU619^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 03:43:00 EDT 2024
% Result : Theorem 4.29s 2.80s
% Output : Refutation 4.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 24 ( 7 unt; 9 typ; 3 def)
% Number of atoms : 39 ( 8 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 372 ( 15 ~; 8 |; 4 &; 339 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 31 ( 1 ^ 26 !; 4 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(iskpair_type,type,
iskpair: $i > $o ).
thf(iskpair_def,definition,
( iskpair
= ( ^ [A: $i] :
? [B: $i] :
( ( in @ B @ ( setunion @ A ) )
& ? [C: $i] :
( ( in @ C @ ( setunion @ A ) )
& ( A
= ( setadjoin @ ( setadjoin @ B @ emptyset ) @ ( setadjoin @ ( setadjoin @ B @ ( setadjoin @ C @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
thf(setukpairIL_type,type,
setukpairIL: $o ).
thf(setukpairIL_def,definition,
( setukpairIL
= ( ! [A: $i,B: $i] : ( in @ A @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
thf(setukpairIR_type,type,
setukpairIR: $o ).
thf(setukpairIR_def,definition,
( setukpairIR
= ( ! [A: $i,B: $i] : ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(1,conjecture,
( setukpairIL
=> ( setukpairIR
=> ! [A: $i,B: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(2,negated_conjecture,
~ ( setukpairIL
=> ( setukpairIR
=> ! [A: $i,B: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] : ( in @ A @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [A: $i,B: $i] : ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) )
=> ! [A: $i,B: $i] :
? [C: $i] :
( ( in @ C @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) )
& ? [D: $i] :
( ( in @ D @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ C @ emptyset ) @ ( setadjoin @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ( ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ A @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(8,plain,
! [B: $i,A: $i] :
( ( ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ A @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(11,plain,
( ~ ( in @ sk2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ( in @ sk1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(pattern_uni,[status(thm)],[8:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(6,plain,
! [B: $i,A: $i] : ( in @ A @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [B: $i,A: $i] : ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
! [B: $i,A: $i] : ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ),
inference(simp,[status(thm)],[5]) ).
thf(27,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[11,6,9]) ).
thf(28,plain,
$false,
inference(simp,[status(thm)],[27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU619^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n018.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun May 19 16:23:24 EDT 2024
% 0.15/0.38 % CPUTime :
% 1.22/1.13 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.51/1.33 % [INFO] Parsing done (198ms).
% 1.66/1.35 % [INFO] Running in sequential loop mode.
% 2.24/1.79 % [INFO] nitpick registered as external prover.
% 2.24/1.80 % [INFO] Scanning for conjecture ...
% 2.63/1.94 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.63/1.98 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.63/1.98 % [INFO] Problem is higher-order (TPTP THF).
% 2.72/1.98 % [INFO] Type checking passed.
% 2.72/1.99 % [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 ...
% 4.29/2.78 % [INFO] Killing All external provers ...
% 4.29/2.79 % Time passed: 2233ms (effective reasoning time: 1429ms)
% 4.29/2.79 % 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)>
% 4.29/2.80 % Axioms used in derivation (0):
% 4.29/2.80 % No. of inferences in proof: 12
% 4.29/2.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2233 ms resp. 1429 ms w/o parsing
% 4.67/2.89 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.67/2.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------