TSTP Solution File: SEU691^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU691^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 03:39:06 EDT 2024
% Result : Theorem 4.02s 1.95s
% Output : Refutation 4.02s
% 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 : 92 ( 18 equ; 0 cnn)
% Maximal formula atoms : 40 ( 11 avg)
% Number of connectives : 322 ( 2 ~; 0 |; 9 &; 253 @)
% ( 0 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 70 ( 12 ^ 54 !; 4 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
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(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(ap_type,type,
ap: $i > $i > $i > $i > $i ).
thf(funcGraphProp1_type,type,
funcGraphProp1: $o ).
thf(funcGraphProp1_def,definition,
( funcGraphProp1
= ( ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( kpair @ D @ ( ap @ A @ B @ C @ D ) ) @ C ) ) ) ) ) ).
thf(funcGraphProp2_type,type,
funcGraphProp2: $o ).
thf(funcGraphProp2_def,definition,
( funcGraphProp2
= ( ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ ( kpair @ D @ E ) @ C )
=> ( ( ap @ A @ B @ C @ D )
= E ) ) ) ) ) ) ) ).
thf(eqbreln_type,type,
eqbreln: $o ).
thf(eqbreln_def,definition,
( eqbreln
= ( ! [A: $i,B: $i,C: $i] :
( ( breln @ A @ B @ C )
=> ! [D: $i] :
( ( breln @ A @ B @ D )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( in @ ( kpair @ E @ F ) @ D ) ) ) )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ D )
=> ( in @ ( kpair @ E @ F ) @ C ) ) ) )
=> ( C = D ) ) ) ) ) ) ) ).
thf(1,conjecture,
( funcGraphProp1
=> ( funcGraphProp2
=> ( eqbreln
=> ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ! [D: $i] :
( ( func @ A @ B @ D )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ( ( ap @ A @ B @ C @ E )
= ( ap @ A @ B @ D @ E ) ) )
=> ( C = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(2,negated_conjecture,
~ ( funcGraphProp1
=> ( funcGraphProp2
=> ( eqbreln
=> ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ! [D: $i] :
( ( func @ A @ B @ D )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ( ( ap @ A @ B @ C @ E )
= ( ap @ A @ B @ D @ E ) ) )
=> ( C = D ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [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 @ ( kpair @ D @ ( ap @ A @ B @ C @ D ) ) @ C ) ) )
=> ( ! [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 @ B )
=> ( ( in @ ( kpair @ D @ E ) @ C )
=> ( ( ap @ A @ B @ C @ D )
= E ) ) ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ ( cartprod @ A @ B ) )
=> ! [D: $i] :
( ( subset @ D @ ( cartprod @ A @ B ) )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( in @ ( kpair @ E @ F ) @ D ) ) ) )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ D )
=> ( in @ ( kpair @ E @ F ) @ C ) ) ) )
=> ( C = D ) ) ) ) )
=> ! [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] :
( ( ( subset @ D @ ( cartprod @ A @ B ) )
& ! [E: $i] :
( ( in @ E @ A )
=> ? [F: $i] :
( ( in @ F
@ ( dsetconstr @ B
@ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) ) )
& ( ( dsetconstr @ B
@ ^ [G: $i] : ( in @ ( kpair @ E @ G ) @ D ) )
= ( setadjoin @ F @ emptyset ) ) ) ) )
=> ( ! [E: $i] :
( ( in @ E @ A )
=> ( ( ap @ A @ B @ C @ E )
= ( ap @ A @ B @ D @ E ) ) )
=> ( C = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(82,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SEU691^2 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n010.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun May 19 18:20:54 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.96/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.98 % [INFO] Parsing done (114ms).
% 1.23/0.99 % [INFO] Running in sequential loop mode.
% 1.71/1.19 % [INFO] eprover registered as external prover.
% 1.71/1.19 % [INFO] cvc4 registered as external prover.
% 1.71/1.20 % [INFO] Scanning for conjecture ...
% 1.89/1.29 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.89/1.31 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.89/1.31 % [INFO] Problem is higher-order (TPTP THF).
% 1.89/1.31 % [INFO] Type checking passed.
% 1.89/1.31 % [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 ...
% 4.02/1.94 % External prover 'e' found a proof!
% 4.02/1.94 % [INFO] Killing All external provers ...
% 4.02/1.95 % Time passed: 1419ms (effective reasoning time: 953ms)
% 4.02/1.95 % 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)>
% 4.02/1.95 % Axioms used in derivation (0):
% 4.02/1.95 % No. of inferences in proof: 4
% 4.02/1.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1419 ms resp. 953 ms w/o parsing
% 4.02/1.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.02/1.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------