TSTP Solution File: SEU696^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU696^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 03:39:08 EDT 2024
% Result : Theorem 3.27s 1.72s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 18 ( 6 unt; 9 typ; 5 def)
% Number of atoms : 58 ( 18 equ; 4 cnn)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 187 ( 2 ~; 0 |; 0 &; 148 @)
% ( 0 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 52 ( 7 ^ 45 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(dpsetconstr_type,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_type,type,
func: $i > $i > $i > $o ).
thf(ap_type,type,
ap: $i > $i > $i > $i > $i ).
thf(app_type,type,
app: $o ).
thf(app_def,definition,
( app
= ( ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( ap @ A @ B @ C @ D ) @ B ) ) ) ) ) ).
thf(lam_type,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(lam_def,definition,
( lam
= ( ^ [A: $i,B: $i,C: $i > $i] :
( dpsetconstr @ A @ B
@ ^ [D: $i] : ( (=) @ $i @ ( C @ D ) ) ) ) ) ).
thf(lamp_type,type,
lamp: $o ).
thf(lamp_def,definition,
( lamp
= ( ! [A: $i,B: $i,C: $i > $i] :
( ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( C @ D ) @ B ) )
=> ( func @ A @ B @ ( lam @ A @ B @ C ) ) ) ) ) ).
thf(funcext_type,type,
funcext: $o ).
thf(funcext_def,definition,
( funcext
= ( ! [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 ) ) ) ) ) ) ).
thf(beta1_type,type,
beta1: $o ).
thf(beta1_def,definition,
( beta1
= ( ! [A: $i,B: $i,C: $i > $i] :
( ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( C @ D ) @ B ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( ap @ A @ B @ ( lam @ A @ B @ C ) @ D )
= ( C @ D ) ) ) ) ) ) ).
thf(1,conjecture,
( app
=> ( lamp
=> ( funcext
=> ( beta1
=> ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ( ( lam @ A @ B @ ( ap @ A @ B @ C ) )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(2,negated_conjecture,
~ ( app
=> ( lamp
=> ( funcext
=> ( beta1
=> ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ( ( lam @ A @ B @ ( ap @ A @ B @ C ) )
= C ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( ap @ A @ B @ C @ D ) @ B ) ) )
=> ( ! [A: $i,B: $i,C: $i > $i] :
( ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( C @ D ) @ B ) )
=> ( func @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [D: $i] : ( (=) @ $i @ ( C @ D ) ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [A: $i,B: $i,C: $i > $i] :
( ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( C @ D ) @ B ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( ap @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [E: $i] : ( (=) @ $i @ ( C @ E ) ) )
@ D )
= ( C @ D ) ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( func @ A @ B @ C )
=> ( ( dpsetconstr @ A @ B
@ ^ [D: $i] : ( (=) @ $i @ ( ap @ A @ B @ C @ D ) ) )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
$false,
inference(cvc4,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU696^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n021.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 15:40:39 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.95/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.15/0.97 % [INFO] Parsing done (105ms).
% 1.15/0.98 % [INFO] Running in sequential loop mode.
% 1.70/1.18 % [INFO] eprover registered as external prover.
% 1.70/1.18 % [INFO] cvc4 registered as external prover.
% 1.70/1.19 % [INFO] Scanning for conjecture ...
% 1.88/1.27 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.01/1.29 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.01/1.29 % [INFO] Problem is higher-order (TPTP THF).
% 2.01/1.29 % [INFO] Type checking passed.
% 2.01/1.29 % [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 ...
% 3.27/1.71 % External prover 'cvc4' found a proof!
% 3.27/1.72 % [INFO] Killing All external provers ...
% 3.27/1.72 % Time passed: 1183ms (effective reasoning time: 732ms)
% 3.27/1.72 % 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)>
% 3.27/1.72 % Axioms used in derivation (0):
% 3.27/1.72 % No. of inferences in proof: 4
% 3.27/1.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1183 ms resp. 732 ms w/o parsing
% 3.40/1.77 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.40/1.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------