TSTP Solution File: SET611^5 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SET611^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 03:03:11 EDT 2024
% Result : Theorem 9.87s 3.73s
% Output : Refutation 9.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 10 unt; 5 typ; 0 def)
% Number of atoms : 167 ( 33 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 261 ( 62 ~; 45 |; 30 &; 124 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 27 ^ 21 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_type,type,
sk1: a > $o ).
thf(sk2_type,type,
sk2: a > $o ).
thf(sk5_type,type,
sk5: a ).
thf(sk6_type,type,
sk6: a ).
thf(1,conjecture,
! [A: a > $o,B: a > $o] :
( ( ( ^ [C: a] :
( ( A @ C )
& ( B @ C ) ) )
= ( ^ [C: a] : $false ) )
= ( ( ^ [C: a] :
( ( A @ C )
& ~ ( B @ C ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_84_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o] :
( ( ( ^ [C: a] :
( ( A @ C )
& ( B @ C ) ) )
= ( ^ [C: a] : $false ) )
= ( ( ^ [C: a] :
( ( A @ C )
& ~ ( B @ C ) ) )
= A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o] :
( ( ( ^ [C: a] :
( ( A @ C )
& ( B @ C ) ) )
= ( ^ [C: a] : $false ) )
= ( ( ^ [C: a] :
( ( A @ C )
& ~ ( B @ C ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
!= ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= sk1 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= sk1 )
!= ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= sk1 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(9,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= sk1 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(13,plain,
( ( ( ( sk1 @ sk5 )
& ~ ( sk2 @ sk5 ) )
!= ( sk1 @ sk5 ) )
| ( ( sk1 @ sk6 )
& ( sk2 @ sk6 ) ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(15,plain,
( ( sk1 @ sk6 )
| ( ( ( sk1 @ sk5 )
& ~ ( sk2 @ sk5 ) )
!= ( sk1 @ sk5 ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(109,plain,
( ( sk1 @ sk6 )
| ( ( sk1 @ sk5 )
& ~ ( sk2 @ sk5 ) )
| ( sk1 @ sk5 ) ),
inference(bool_ext,[status(thm)],[15]) ).
thf(121,plain,
( ( sk1 @ sk5 )
| ( sk1 @ sk5 )
| ( sk1 @ sk6 ) ),
inference(cnf,[status(esa)],[109]) ).
thf(122,plain,
( ( sk1 @ sk5 )
| ( sk1 @ sk6 ) ),
inference(simp,[status(thm)],[121]) ).
thf(14,plain,
( ( sk2 @ sk6 )
| ( ( ( sk1 @ sk5 )
& ~ ( sk2 @ sk5 ) )
!= ( sk1 @ sk5 ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(47,plain,
( ( sk2 @ sk6 )
| ( ( sk1 @ sk5 )
& ~ ( sk2 @ sk5 ) )
| ( sk1 @ sk5 ) ),
inference(bool_ext,[status(thm)],[14]) ).
thf(53,plain,
( ( sk1 @ sk5 )
| ( sk1 @ sk5 )
| ( sk2 @ sk6 ) ),
inference(cnf,[status(esa)],[47]) ).
thf(54,plain,
( ( sk1 @ sk5 )
| ( sk2 @ sk6 ) ),
inference(simp,[status(thm)],[53]) ).
thf(8,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= sk1 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(10,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= sk1 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(16,plain,
! [B: a,A: a] :
( ( ( ( sk1 @ A )
& ~ ( sk2 @ A ) )
= ( sk1 @ A ) )
| ~ ( ( sk1 @ B )
& ( sk2 @ B ) ) ),
inference(func_ext,[status(esa)],[10]) ).
thf(26,plain,
! [B: a,A: a] :
( ~ ( sk1 @ B )
| ~ ( sk2 @ B )
| ( ( ( sk1 @ A )
& ~ ( sk2 @ A ) )
= ( sk1 @ A ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(230,plain,
! [B: a,A: a] :
( ~ ( sk1 @ B )
| ~ ( sk2 @ B )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) )
| ~ ( sk1 @ A ) ),
inference(bool_ext,[status(thm)],[26]) ).
thf(272,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ A )
| ~ ( sk2 @ B )
| ~ ( sk1 @ B ) ),
inference(cnf,[status(esa)],[230]) ).
thf(318,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ A )
| ~ ( sk1 @ B )
| ( ( sk2 @ B )
!= ( sk2 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[272]) ).
thf(319,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ A )
| ~ ( sk1 @ A ) ),
inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( B ))]]) ).
thf(326,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ A ) ),
inference(simp,[status(thm)],[319]) ).
thf(331,plain,
! [A: a] :
( ( sk1 @ sk5 )
| ~ ( sk1 @ A )
| ( ( sk2 @ sk6 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[54,326]) ).
thf(332,plain,
( ( sk1 @ sk5 )
| ~ ( sk1 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[331:[bind(A,$thf( sk6 ))]]) ).
thf(366,plain,
( ( sk1 @ sk5 )
| ( ( sk1 @ sk6 )
!= ( sk1 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[122,332]) ).
thf(367,plain,
sk1 @ sk5,
inference(pattern_uni,[status(thm)],[366:[]]) ).
thf(376,plain,
( ( sk1 @ sk6 )
| ~ ( $true
& ~ ( sk2 @ sk5 ) ) ),
inference(rewrite,[status(thm)],[15,367]) ).
thf(377,plain,
( ( sk1 @ sk6 )
| ( sk2 @ sk5 ) ),
inference(simp,[status(thm)],[376]) ).
thf(372,plain,
( ( sk2 @ sk6 )
| ~ ( $true
& ~ ( sk2 @ sk5 ) ) ),
inference(rewrite,[status(thm)],[14,367]) ).
thf(373,plain,
( ( sk2 @ sk6 )
| ( sk2 @ sk5 ) ),
inference(simp,[status(thm)],[372]) ).
thf(380,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( ( sk1 @ sk5 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[367,326]) ).
thf(381,plain,
~ ( sk2 @ sk5 ),
inference(pattern_uni,[status(thm)],[380:[bind(A,$thf( sk5 ))]]) ).
thf(385,plain,
( ( sk2 @ sk6 )
| $false ),
inference(rewrite,[status(thm)],[373,381]) ).
thf(386,plain,
sk2 @ sk6,
inference(simp,[status(thm)],[385]) ).
thf(389,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( ( sk2 @ sk6 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[386,326]) ).
thf(390,plain,
~ ( sk1 @ sk6 ),
inference(pattern_uni,[status(thm)],[389:[bind(A,$thf( sk6 ))]]) ).
thf(409,plain,
( $false
| $false ),
inference(rewrite,[status(thm)],[377,390,381]) ).
thf(410,plain,
$false,
inference(simp,[status(thm)],[409]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET611^5 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.13 % Command : run_Leo-III %s %d
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon May 20 13:13:24 EDT 2024
% 0.12/0.34 % CPUTime :
% 1.15/1.11 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.54/1.30 % [INFO] Parsing done (178ms).
% 1.54/1.31 % [INFO] Running in sequential loop mode.
% 2.23/1.77 % [INFO] eprover registered as external prover.
% 2.23/1.78 % [INFO] cvc4 registered as external prover.
% 2.23/1.78 % [INFO] Scanning for conjecture ...
% 2.44/1.88 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.44/1.92 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.44/1.92 % [INFO] Problem is higher-order (TPTP THF).
% 2.44/1.92 % [INFO] Type checking passed.
% 2.44/1.93 % [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 ...
% 9.87/3.72 % [INFO] Killing All external provers ...
% 9.87/3.72 % Time passed: 3205ms (effective reasoning time: 2405ms)
% 9.87/3.73 % 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)>
% 9.87/3.73 % Axioms used in derivation (0):
% 9.87/3.73 % No. of inferences in proof: 41
% 9.87/3.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3205 ms resp. 2405 ms w/o parsing
% 9.87/3.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.87/3.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------