TSTP Solution File: SEU734^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU734^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 03:39:26 EDT 2024
% Result : Theorem 3.20s 1.81s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 17 ( 5 unt; 9 typ; 4 def)
% Number of atoms : 58 ( 4 equ; 0 cnn)
% Maximal formula atoms : 19 ( 7 avg)
% Number of connectives : 188 ( 2 ~; 0 |; 0 &; 144 @)
% ( 0 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 35 ( 0 ^ 35 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(binintersect_type,type,
binintersect: $i > $i > $i ).
thf(setminus_type,type,
setminus: $i > $i > $i ).
thf(binintersectT_lem_type,type,
binintersectT_lem: $o ).
thf(binintersectT_lem_def,definition,
( binintersectT_lem
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( in @ ( binintersect @ B @ C ) @ ( powerset @ A ) ) ) ) ) ) ).
thf(complementT_lem_type,type,
complementT_lem: $o ).
thf(complementT_lem_def,definition,
( complementT_lem
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ B ) @ ( powerset @ A ) ) ) ) ) ).
thf(subsetTI_type,type,
subsetTI: $o ).
thf(subsetTI_def,definition,
( subsetTI
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ B )
=> ( in @ D @ C ) ) )
=> ( subset @ B @ C ) ) ) ) ) ) ).
thf(complementImpComplementIntersect_type,type,
complementImpComplementIntersect: $o ).
thf(complementImpComplementIntersect_def,definition,
( complementImpComplementIntersect
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ ( setminus @ A @ B ) )
=> ( in @ D @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ) ) ).
thf(1,conjecture,
( binintersectT_lem
=> ( complementT_lem
=> ( subsetTI
=> ( complementImpComplementIntersect
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ B ) @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementSubsetComplementIntersect) ).
thf(2,negated_conjecture,
~ ( binintersectT_lem
=> ( complementT_lem
=> ( subsetTI
=> ( complementImpComplementIntersect
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ B ) @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( in @ ( binintersect @ B @ C ) @ ( powerset @ A ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ B ) @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ B )
=> ( in @ D @ C ) ) )
=> ( subset @ B @ C ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( in @ D @ ( setminus @ A @ B ) )
=> ( in @ D @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) )
=> ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ B ) @ ( setminus @ A @ ( binintersect @ B @ C ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU734^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n017.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 18:13:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.98/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/1.00 % [INFO] Parsing done (126ms).
% 1.38/1.01 % [INFO] Running in sequential loop mode.
% 1.74/1.24 % [INFO] eprover registered as external prover.
% 1.74/1.24 % [INFO] cvc4 registered as external prover.
% 1.74/1.24 % [INFO] Scanning for conjecture ...
% 1.94/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.94/1.35 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.94/1.35 % [INFO] Problem is higher-order (TPTP THF).
% 1.94/1.35 % [INFO] Type checking passed.
% 1.94/1.35 % [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 ...
% 3.20/1.81 % External prover 'e' found a proof!
% 3.20/1.81 % [INFO] Killing All external provers ...
% 3.20/1.81 % Time passed: 1271ms (effective reasoning time: 790ms)
% 3.20/1.81 % 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)>
% 3.20/1.81 % Axioms used in derivation (0):
% 3.20/1.81 % No. of inferences in proof: 4
% 3.20/1.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1271 ms resp. 790 ms w/o parsing
% 3.37/1.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.37/1.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------