TSTP Solution File: SEU673^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU673^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 03:39:00 EDT 2024
% Result : Theorem 3.54s 1.81s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 20 ( 5 unt; 12 typ; 4 def)
% Number of atoms : 60 ( 8 equ; 0 cnn)
% Maximal formula atoms : 22 ( 7 avg)
% Number of connectives : 182 ( 2 ~; 0 |; 7 &; 147 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 49 ( 14 ^ 31 !; 4 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrEL_type,type,
dsetconstrEL: $o ).
thf(dsetconstrEL_def,definition,
( dsetconstrEL
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( in @ C @ A ) ) ) ) ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(theprop_type,type,
theprop: $o ).
thf(theprop_def,definition,
( theprop
= ( ! [A: $i] :
( ( singleton @ A )
=> ( in @ ( setunion @ A ) @ A ) ) ) ) ).
thf(func_type,type,
func: $i > $i > $i > $o ).
thf(func_def,definition,
( func
= ( ^ [A: $i,B: $i,C: $i] :
( ( breln @ A @ B @ C )
& ! [D: $i] :
( ( in @ D @ A )
=> ( ex1 @ B
@ ^ [E: $i] : ( in @ ( kpair @ D @ E ) @ C ) ) ) ) ) ) ).
thf(funcImageSingleton_type,type,
funcImageSingleton: $o ).
thf(funcImageSingleton_def,definition,
( funcImageSingleton
= ( ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [E: $i] : ( in @ ( kpair @ D @ E ) @ C ) ) ) ) ) ) ) ).
thf(1,conjecture,
( dsetconstrEL
=> ( theprop
=> ( funcImageSingleton
=> ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [E: $i] : ( in @ ( kpair @ D @ E ) @ C ) ) )
@ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(2,negated_conjecture,
~ ( dsetconstrEL
=> ( theprop
=> ( funcImageSingleton
=> ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [E: $i] : ( in @ ( kpair @ D @ E ) @ C ) ) )
@ B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( in @ C @ A ) )
=> ( ! [A: $i] :
( ? [B: $i] :
( ( in @ B @ A )
& ( A
= ( setadjoin @ B @ emptyset ) ) )
=> ( in @ ( setunion @ A ) @ A ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ C @ ( cartprod @ A @ B ) )
& ! [D: $i] :
( ( in @ D @ A )
=> ? [E: $i] :
( ( in @ E
@ ( dsetconstr @ B
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) ) )
& ( ( dsetconstr @ B
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) )
= ( setadjoin @ E @ emptyset ) ) ) ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ? [E: $i] :
( ( in @ E
@ ( dsetconstr @ B
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) ) )
& ( ( dsetconstr @ B
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) )
= ( setadjoin @ E @ emptyset ) ) ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( ( subset @ C @ ( cartprod @ A @ B ) )
& ! [D: $i] :
( ( in @ D @ A )
=> ? [E: $i] :
( ( in @ E
@ ( dsetconstr @ B
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) ) )
& ( ( dsetconstr @ B
@ ^ [F: $i] : ( in @ ( kpair @ D @ F ) @ C ) )
= ( setadjoin @ E @ emptyset ) ) ) ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [E: $i] : ( in @ ( kpair @ D @ E ) @ C ) ) )
@ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU673^2 : TPTP v8.2.0. Released v3.7.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 18:13:39 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.94/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.96 % [INFO] Parsing done (115ms).
% 1.31/0.96 % [INFO] Running in sequential loop mode.
% 1.65/1.18 % [INFO] eprover registered as external prover.
% 1.65/1.18 % [INFO] cvc4 registered as external prover.
% 1.65/1.18 % [INFO] Scanning for conjecture ...
% 1.90/1.26 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.90/1.28 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.90/1.29 % [INFO] Problem is higher-order (TPTP THF).
% 1.90/1.29 % [INFO] Type checking passed.
% 1.90/1.29 % [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 ...
% 3.54/1.81 % External prover 'e' found a proof!
% 3.54/1.81 % [INFO] Killing All external provers ...
% 3.54/1.81 % Time passed: 1302ms (effective reasoning time: 842ms)
% 3.54/1.81 % 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)>
% 3.54/1.81 % Axioms used in derivation (0):
% 3.54/1.81 % No. of inferences in proof: 4
% 3.54/1.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1302 ms resp. 842 ms w/o parsing
% 3.67/1.85 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.67/1.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------