TSTP Solution File: SEU802^2 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU802^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 03:43:52 EDT 2024
% Result : Theorem 31.00s 5.71s
% Output : Refutation 31.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 38 ( 11 unt; 12 typ; 3 def)
% Number of atoms : 69 ( 22 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 242 ( 24 ~; 13 |; 6 &; 185 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 50 ( 8 ^ 36 !; 6 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(dsetconstrER_def,definition,
( dsetconstrER
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) ) ) ) ).
thf(funcSet_type,type,
funcSet: $i > $i > $i ).
thf(ap_type,type,
ap: $i > $i > $i > $i > $i ).
thf(surjective_type,type,
surjective: $i > $i > $i > $o ).
thf(surjective_def,definition,
( surjective
= ( ^ [A: $i,B: $i,C: $i] :
! [D: $i] :
( ( in @ D @ B )
=> ? [E: $i] :
( ( in @ E @ A )
& ( ( ap @ A @ B @ C @ E )
= D ) ) ) ) ) ).
thf(surjFuncSet_type,type,
surjFuncSet: $i > $i > $i ).
thf(surjFuncSet_def,definition,
( surjFuncSet
= ( ^ [A: $i,B: $i] : ( dsetconstr @ ( funcSet @ A @ B ) @ ( surjective @ A @ B ) ) ) ) ).
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(sk5_type,type,
sk5: $i > $i ).
thf(1,conjecture,
( dsetconstrER
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( surjFuncSet @ A @ B ) )
=> ( surjective @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjFuncSetFuncSurj) ).
thf(2,negated_conjecture,
~ ( dsetconstrER
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( surjFuncSet @ A @ B ) )
=> ( surjective @ A @ B @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C
@ ( dsetconstr @ ( funcSet @ A @ B )
@ ^ [D: $i] :
! [E: $i] :
( ( in @ E @ B )
=> ? [F: $i] :
( ( in @ F @ A )
& ( ( ap @ A @ B @ D @ F )
= E ) ) ) ) )
=> ! [D: $i] :
( ( in @ D @ B )
=> ? [E: $i] :
( ( in @ E @ A )
& ( ( ap @ A @ B @ C @ E )
= D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( in @ sk3
@ ( dsetconstr @ ( funcSet @ sk1 @ sk2 )
@ ^ [A: $i] :
! [B: $i] :
( ( in @ B @ sk2 )
=> ? [C: $i] :
( ( in @ C @ sk1 )
& ( ( ap @ sk1 @ sk2 @ A @ C )
= B ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( B @ C ) ),
inference(cnf,[status(esa)],[3]) ).
thf(17,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( ( in @ sk3
@ ( dsetconstr @ ( funcSet @ sk1 @ sk2 )
@ ^ [D: $i] :
! [E: $i] :
( ( in @ E @ sk2 )
=> ? [F: $i] :
( ( in @ F @ sk1 )
& ( ( ap @ sk1 @ sk2 @ D @ F )
= E ) ) ) ) )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,7]) ).
thf(18,plain,
! [A: $i] :
( ( in @ A @ sk2 )
=> ? [B: $i] :
( ( in @ B @ sk1 )
& ( ( ap @ sk1 @ sk2 @ sk3 @ B )
= A ) ) ),
inference(pattern_uni,[status(thm)],[17:[bind(A,$thf( funcSet @ sk1 @ sk2 )),bind(B,$thf( ^ [D: $i] : ! [E: $i] : ( ( in @ E @ sk2 ) => ? [F: $i] : ( ( in @ F @ sk1 ) & ( ( ap @ sk1 @ sk2 @ D @ F ) = E ) ) ) )),bind(C,$thf( sk3 ))]]) ).
thf(35,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ( ( ap @ sk1 @ sk2 @ sk3 @ ( sk5 @ A ) )
= A ) ),
inference(cnf,[status(esa)],[18]) ).
thf(36,plain,
! [A: $i] :
( ( ( ap @ sk1 @ sk2 @ sk3 @ ( sk5 @ A ) )
= A )
| ~ ( in @ A @ sk2 ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(5,plain,
in @ sk4 @ sk2,
inference(cnf,[status(esa)],[3]) ).
thf(34,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ( in @ ( sk5 @ A ) @ sk1 ) ),
inference(cnf,[status(esa)],[18]) ).
thf(554,plain,
! [A: $i] :
( ( in @ ( sk5 @ A ) @ sk1 )
| ( ( in @ sk4 @ sk2 )
!= ( in @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[5,34]) ).
thf(555,plain,
in @ ( sk5 @ sk4 ) @ sk1,
inference(pattern_uni,[status(thm)],[554:[bind(A,$thf( sk4 ))]]) ).
thf(4,plain,
! [A: $i] :
( ~ ( in @ A @ sk1 )
| ( ( ap @ sk1 @ sk2 @ sk3 @ A )
!= sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
! [A: $i] :
( ( ( ap @ sk1 @ sk2 @ sk3 @ A )
!= sk4 )
| ~ ( in @ A @ sk1 ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(9,plain,
! [A: $i] :
( ( ( ap @ sk1 @ sk2 @ sk3 @ A )
!= sk4 )
| ~ ( in @ A @ sk1 ) ),
inference(simp,[status(thm)],[8]) ).
thf(679,plain,
! [A: $i] :
( ( ( ap @ sk1 @ sk2 @ sk3 @ A )
!= sk4 )
| ( ( in @ ( sk5 @ sk4 ) @ sk1 )
!= ( in @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[555,9]) ).
thf(680,plain,
( ( ap @ sk1 @ sk2 @ sk3 @ ( sk5 @ sk4 ) )
!= sk4 ),
inference(pattern_uni,[status(thm)],[679:[bind(A,$thf( sk5 @ sk4 ))]]) ).
thf(1461,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ( A != sk4 )
| ( ( ap @ sk1 @ sk2 @ sk3 @ ( sk5 @ A ) )
!= ( ap @ sk1 @ sk2 @ sk3 @ ( sk5 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,680]) ).
thf(1462,plain,
( ~ ( in @ sk4 @ sk2 )
| ( sk4 != sk4 ) ),
inference(pattern_uni,[status(thm)],[1461:[bind(A,$thf( sk4 ))]]) ).
thf(1517,plain,
~ ( in @ sk4 @ sk2 ),
inference(simp,[status(thm)],[1462]) ).
thf(1568,plain,
~ $true,
inference(rewrite,[status(thm)],[1517,5]) ).
thf(1569,plain,
$false,
inference(simp,[status(thm)],[1568]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU802^2 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n007.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sun May 19 17:32:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.04/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.08 % [INFO] Parsing done (125ms).
% 1.26/1.09 % [INFO] Running in sequential loop mode.
% 1.69/1.29 % [INFO] nitpick registered as external prover.
% 1.69/1.29 % [INFO] Scanning for conjecture ...
% 1.90/1.36 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.90/1.37 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.90/1.37 % [INFO] Problem is higher-order (TPTP THF).
% 2.07/1.38 % [INFO] Type checking passed.
% 2.07/1.38 % [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 ...
% 31.00/5.71 % [INFO] Killing All external provers ...
% 31.00/5.71 % Time passed: 5159ms (effective reasoning time: 4614ms)
% 31.00/5.71 % 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)>
% 31.00/5.71 % Axioms used in derivation (0):
% 31.00/5.71 % No. of inferences in proof: 23
% 31.00/5.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5159 ms resp. 4614 ms w/o parsing
% 31.00/5.75 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 31.00/5.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------