%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU696^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:29:03 AM UTC 2026
% Result : Theorem 5.19s 2.77s
% Output : Refutation 5.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 9 ( 6 unt; 0 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 : 5 ( 5 >; 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_decl,type,
in: $i > $i > $o ).
thf(dpsetconstr_decl,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_decl,type,
func: $i > $i > $i > $o ).
thf(ap_decl,type,
ap: $i > $i > $i > $i > $i ).
thf(app_decl,type,
app: $o ).
thf(lam_decl,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(lamp_decl,type,
lamp: $o ).
thf(funcext_decl,type,
funcext: $o ).
thf(beta1_decl,type,
beta1: $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_def,definition,
( lam
= ( ^ [A: $i,B: $i,C: $i > $i] :
( dpsetconstr @ A @ B
@ ^ [D: $i] : ( (=) @ $i @ ( C @ D ) ) ) ) ) ).
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_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_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(79,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU696^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.23 % Computer : n007.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Tue Sep 29 14:09:25 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.06/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.01 % [INFO] Parsing done (202ms).
% 1.24/1.03 % [INFO] Running in sequential loop mode.
% 2.13/1.44 % [INFO] eprover registered as external prover.
% 2.13/1.45 % [INFO] Scanning for conjecture ...
% 2.34/1.59 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.54/1.62 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.54/1.62 % [INFO] Problem is higher-order (TPTP THF).
% 2.54/1.63 % [INFO] Type checking passed.
% 2.54/1.63 % [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 ...
% 5.19/2.76 % External prover 'e' found a proof!
% 5.19/2.76 % [INFO] Killing All external provers ...
% 5.19/2.76 % Time passed: 2390ms (effective reasoning time: 1731ms)
% 5.19/2.76 % 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)>
% 5.19/2.77 % Axioms used in derivation (0):
% 5.19/2.77 % No. of inferences in proof: 4
% 5.19/2.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2390 ms resp. 1731 ms w/o parsing
% 5.92/2.81 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.92/2.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------