TSTP Solution File: SEU742^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU742^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 03:39:30 EDT 2024
% Result : Theorem 2.83s 1.69s
% Output : Refutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 14 ( 4 unt; 7 typ; 3 def)
% Number of atoms : 61 ( 3 equ; 0 cnn)
% Maximal formula atoms : 21 ( 8 avg)
% Number of connectives : 211 ( 2 ~; 0 |; 0 &; 161 @)
% ( 0 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 0 ^ 41 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(binunion_type,type,
binunion: $i > $i > $i ).
thf(binintersect_type,type,
binintersect: $i > $i > $i ).
thf(binintersectI_type,type,
binintersectI: $o ).
thf(binintersectI_def,definition,
( binintersectI
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ B )
=> ( in @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
thf(inIntersectImpInUnion_type,type,
inIntersectImpInUnion: $o ).
thf(inIntersectImpInUnion_def,definition,
( inIntersectImpInUnion
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ ( powerset @ A ) )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ E @ ( binintersect @ B @ C ) )
=> ( in @ E @ ( binunion @ B @ D ) ) ) ) ) ) ) ) ) ).
thf(inIntersectImpInUnion2_type,type,
inIntersectImpInUnion2: $o ).
thf(inIntersectImpInUnion2_def,definition,
( inIntersectImpInUnion2
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ ( powerset @ A ) )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ E @ ( binintersect @ B @ C ) )
=> ( in @ E @ ( binunion @ C @ D ) ) ) ) ) ) ) ) ) ).
thf(1,conjecture,
( binintersectI
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ ( powerset @ A ) )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ E @ ( binintersect @ B @ C ) )
=> ( in @ E @ ( binintersect @ ( binunion @ B @ D ) @ ( binunion @ C @ D ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions) ).
thf(2,negated_conjecture,
~ ( binintersectI
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ ( powerset @ A ) )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ E @ ( binintersect @ B @ C ) )
=> ( in @ E @ ( binintersect @ ( binunion @ B @ D ) @ ( binunion @ C @ D ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ B )
=> ( in @ C @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ ( powerset @ A ) )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ E @ ( binintersect @ B @ C ) )
=> ( in @ E @ ( binunion @ B @ D ) ) ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ ( powerset @ A ) )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ E @ ( binintersect @ B @ C ) )
=> ( in @ E @ ( binunion @ C @ D ) ) ) ) ) ) )
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ ( powerset @ A ) )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ E @ ( binintersect @ B @ C ) )
=> ( in @ E @ ( binintersect @ ( binunion @ B @ D ) @ ( binunion @ C @ D ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
$false,
inference(cvc4,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU742^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n026.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 : Sun May 19 18:04:39 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.86/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.97 % [INFO] Parsing done (108ms).
% 1.17/0.98 % [INFO] Running in sequential loop mode.
% 1.72/1.19 % [INFO] eprover registered as external prover.
% 1.74/1.19 % [INFO] cvc4 registered as external prover.
% 1.74/1.19 % [INFO] Scanning for conjecture ...
% 1.85/1.27 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.85/1.29 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.85/1.29 % [INFO] Problem is higher-order (TPTP THF).
% 1.85/1.30 % [INFO] Type checking passed.
% 1.85/1.30 % [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 ...
% 2.83/1.63 % External prover 'cvc4' found a proof!
% 2.83/1.64 % [INFO] Killing All external provers ...
% 2.83/1.64 % Time passed: 1117ms (effective reasoning time: 659ms)
% 2.83/1.64 % 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)>
% 2.83/1.69 % Axioms used in derivation (0):
% 2.83/1.69 % No. of inferences in proof: 4
% 2.83/1.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1117 ms resp. 659 ms w/o parsing
% 3.15/1.72 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.15/1.72 % [INFO] Killing All external provers ...
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