TSTP Solution File: SEU630^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU630^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 03:38:42 EDT 2024
% Result : Theorem 4.81s 2.06s
% Output : Refutation 4.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 18 ( 5 unt; 10 typ; 4 def)
% Number of atoms : 36 ( 6 equ; 0 cnn)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 150 ( 2 ~; 0 |; 4 &; 124 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 6 ^ 26 !; 4 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrI_type,type,
dsetconstrI: $o ).
thf(dsetconstrI_def,definition,
( dsetconstrI
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( in @ C @ ( dsetconstr @ A @ B ) ) ) ) ) ) ).
thf(binunion_type,type,
binunion: $i > $i > $i ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(kpair_def,definition,
( kpair
= ( ^ [A: $i,B: $i] : ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(cartprod_def,definition,
( cartprod
= ( ^ [A: $i,B: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) )
@ ^ [C: $i] :
? [D: $i] :
( ( in @ D @ A )
& ? [E: $i] :
( ( in @ E @ B )
& ( C
= ( kpair @ D @ E ) ) ) ) ) ) ) ).
thf(ubforcartprodlem3_type,type,
ubforcartprodlem3: $o ).
thf(ubforcartprodlem3_def,definition,
( ubforcartprodlem3
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( in @ ( kpair @ C @ D ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
thf(1,conjecture,
( dsetconstrI
=> ( ubforcartprodlem3
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( in @ ( kpair @ C @ D ) @ ( cartprod @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(2,negated_conjecture,
~ ( dsetconstrI
=> ( ubforcartprodlem3
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( in @ ( kpair @ C @ D ) @ ( cartprod @ A @ B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( in @ C @ ( dsetconstr @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ C @ emptyset ) @ ( setadjoin @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ C @ emptyset ) @ ( setadjoin @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) @ emptyset ) )
@ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) )
@ ^ [E: $i] :
? [F: $i] :
( ( in @ F @ A )
& ? [G: $i] :
( ( in @ G @ B )
& ( E
= ( setadjoin @ ( setadjoin @ F @ emptyset ) @ ( setadjoin @ ( setadjoin @ F @ ( setadjoin @ G @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU630^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 16:06:24 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.88/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.97 % [INFO] Parsing done (111ms).
% 1.18/0.98 % [INFO] Running in sequential loop mode.
% 1.55/1.17 % [INFO] eprover registered as external prover.
% 1.55/1.18 % [INFO] cvc4 registered as external prover.
% 1.72/1.18 % [INFO] Scanning for conjecture ...
% 1.72/1.25 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.72/1.27 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.72/1.27 % [INFO] Problem is higher-order (TPTP THF).
% 1.72/1.27 % [INFO] Type checking passed.
% 1.72/1.27 % [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 ...
% 4.81/2.05 % External prover 'e' found a proof!
% 4.81/2.06 % [INFO] Killing All external provers ...
% 4.81/2.06 % Time passed: 1534ms (effective reasoning time: 1073ms)
% 4.81/2.06 % 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)>
% 4.81/2.06 % Axioms used in derivation (0):
% 4.81/2.06 % No. of inferences in proof: 4
% 4.81/2.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1534 ms resp. 1073 ms w/o parsing
% 4.81/2.09 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.81/2.09 % [INFO] Killing All external provers ...
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