%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU695^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n026.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 4.27s 2.31s
% Output : Refutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 8 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 51 ( 12 equ; 3 cnn)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 173 ( 2 ~; 0 |; 0 &; 135 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 49 ( 6 ^; 43 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(kpair_decl,type,
kpair: $i > $i > $i ).
thf(dpsetconstr_decl,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(dpsetconstrI_decl,type,
dpsetconstrI: $o ).
thf(func_decl,type,
func: $i > $i > $i > $o ).
thf(ap_decl,type,
ap: $i > $i > $i > $i > $i ).
thf(lam_decl,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(lamp_decl,type,
lamp: $o ).
thf(funcGraphProp2_decl,type,
funcGraphProp2: $o ).
thf(dpsetconstrI_def,definition,
( dpsetconstrI
= ( ! [A: $i,B: $i,C: $i > $i > $o,D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( C @ D @ E )
=> ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) ) ) ) ) ) ) ).
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(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(1,conjecture,
( dpsetconstrI
=> ( lamp
=> ( funcGraphProp2
=> ! [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 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta1) ).
thf(2,negated_conjecture,
~ ( dpsetconstrI
=> ( lamp
=> ( funcGraphProp2
=> ! [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 ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i > $i > $o,D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( C @ D @ E )
=> ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) ) ) ) )
=> ( ! [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] :
( ( 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 > $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 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU695^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:13:57 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/0.99 % [INFO] Parsing done (201ms).
% 1.25/1.01 % [INFO] Running in sequential loop mode.
% 2.18/1.42 % [INFO] eprover registered as external prover.
% 2.18/1.43 % [INFO] Scanning for conjecture ...
% 2.38/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.57/1.60 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.57/1.61 % [INFO] Problem is higher-order (TPTP THF).
% 2.57/1.61 % [INFO] Type checking passed.
% 2.57/1.62 % [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 ...
% 4.27/2.31 % External prover 'e' found a proof!
% 4.27/2.31 % [INFO] Killing All external provers ...
% 4.27/2.31 % Time passed: 1971ms (effective reasoning time: 1299ms)
% 4.27/2.31 % 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)>
% 4.27/2.31 % Axioms used in derivation (0):
% 4.27/2.31 % No. of inferences in proof: 4
% 4.27/2.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1971 ms resp. 1299 ms w/o parsing
% 4.27/2.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.27/2.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------