%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN353+1 : TPTP v9.3.1. Released v2.0.0.
% 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 : n003.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 : Sun Sep 27 09:17:19 AM UTC 2026
% Result : Theorem 3.45s 2.53s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 0 equ; 0 cnn)
% Maximal formula atoms : 36 ( 19 avg)
% Number of connectives : 307 ( 6 ~; 3 |; 20 &; 228 @)
% ( 8 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 2 ( 1 usr; 1 con; 0-3 aty)
% Number of variables : 15 ( 0 ^; 6 !; 9 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(big_f_decl,type,
big_f: $i > $i > $i > $o ).
thf(1,conjecture,
! [A: $i] :
? [B: $i,C: $i,D: $i] :
! [E: $i] :
( ( ( D @ ( C @ ( B @ big_f ) ) )
=> ( ( E @ ( A @ ( A @ big_f ) ) )
=> ( ( C @ ( B @ ( D @ big_f ) ) )
| ( B @ ( D @ ( C @ big_f ) ) ) ) ) )
=> ( ( ( ( C @ ( B @ ( D @ big_f ) ) )
=> ( ( B @ ( D @ ( C @ big_f ) ) )
& ( D @ ( C @ ( B @ big_f ) ) ) ) )
<=> ( E @ ( B @ ( C @ big_f ) ) ) )
=> ( ( ( ( B @ ( D @ ( C @ big_f ) ) )
=> ( ( C @ ( B @ ( D @ big_f ) ) )
& ( D @ ( C @ ( B @ big_f ) ) ) ) )
<=> ( C @ ( E @ ( B @ big_f ) ) ) )
=> ( ( ( ( ( C @ ( B @ ( D @ big_f ) ) )
=> ~ ( B @ ( D @ ( C @ big_f ) ) ) )
=> ( D @ ( C @ ( B @ big_f ) ) ) )
<=> ( B @ ( C @ ( E @ big_f ) ) ) )
=> ( ( ( C @ ( B @ ( D @ big_f ) ) )
& ( B @ ( D @ ( C @ big_f ) ) )
& ( D @ ( C @ ( B @ big_f ) ) ) )
<=> ( E @ ( E @ ( E @ big_f ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_18_5) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
? [B: $i,C: $i,D: $i] :
! [E: $i] :
( ( ( D @ ( C @ ( B @ big_f ) ) )
=> ( ( E @ ( A @ ( A @ big_f ) ) )
=> ( ( C @ ( B @ ( D @ big_f ) ) )
| ( B @ ( D @ ( C @ big_f ) ) ) ) ) )
=> ( ( ( ( C @ ( B @ ( D @ big_f ) ) )
=> ( ( B @ ( D @ ( C @ big_f ) ) )
& ( D @ ( C @ ( B @ big_f ) ) ) ) )
<=> ( E @ ( B @ ( C @ big_f ) ) ) )
=> ( ( ( ( B @ ( D @ ( C @ big_f ) ) )
=> ( ( C @ ( B @ ( D @ big_f ) ) )
& ( D @ ( C @ ( B @ big_f ) ) ) ) )
<=> ( C @ ( E @ ( B @ big_f ) ) ) )
=> ( ( ( ( ( C @ ( B @ ( D @ big_f ) ) )
=> ~ ( B @ ( D @ ( C @ big_f ) ) ) )
=> ( D @ ( C @ ( B @ big_f ) ) ) )
<=> ( B @ ( C @ ( E @ big_f ) ) ) )
=> ( ( ( C @ ( B @ ( D @ big_f ) ) )
& ( B @ ( D @ ( C @ big_f ) ) )
& ( D @ ( C @ ( B @ big_f ) ) ) )
<=> ( E @ ( E @ ( E @ big_f ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i] :
? [B: $i,C: $i,D: $i] :
! [E: $i] :
( ( ( D @ ( C @ ( B @ big_f ) ) )
=> ( ( E @ ( A @ ( A @ big_f ) ) )
=> ( ( C @ ( B @ ( D @ big_f ) ) )
| ( B @ ( D @ ( C @ big_f ) ) ) ) ) )
=> ( ( ( ( E @ ( B @ ( C @ big_f ) ) )
=> ( ( C @ ( B @ ( D @ big_f ) ) )
=> ( ( B @ ( D @ ( C @ big_f ) ) )
& ( D @ ( C @ ( B @ big_f ) ) ) ) ) )
& ( ( ( C @ ( B @ ( D @ big_f ) ) )
=> ( ( B @ ( D @ ( C @ big_f ) ) )
& ( D @ ( C @ ( B @ big_f ) ) ) ) )
=> ( E @ ( B @ ( C @ big_f ) ) ) ) )
=> ( ( ( ( C @ ( E @ ( B @ big_f ) ) )
=> ( ( B @ ( D @ ( C @ big_f ) ) )
=> ( ( C @ ( B @ ( D @ big_f ) ) )
& ( D @ ( C @ ( B @ big_f ) ) ) ) ) )
& ( ( ( B @ ( D @ ( C @ big_f ) ) )
=> ( ( C @ ( B @ ( D @ big_f ) ) )
& ( D @ ( C @ ( B @ big_f ) ) ) ) )
=> ( C @ ( E @ ( B @ big_f ) ) ) ) )
=> ( ( ( ( B @ ( C @ ( E @ big_f ) ) )
=> ( ( ( C @ ( B @ ( D @ big_f ) ) )
=> ~ ( B @ ( D @ ( C @ big_f ) ) ) )
=> ( D @ ( C @ ( B @ big_f ) ) ) ) )
& ( ( ( ( C @ ( B @ ( D @ big_f ) ) )
=> ~ ( B @ ( D @ ( C @ big_f ) ) ) )
=> ( D @ ( C @ ( B @ big_f ) ) ) )
=> ( B @ ( C @ ( E @ big_f ) ) ) ) )
=> ( ( ( E @ ( E @ ( E @ big_f ) ) )
=> ( ( C @ ( B @ ( D @ big_f ) ) )
& ( B @ ( D @ ( C @ big_f ) ) )
& ( D @ ( C @ ( B @ big_f ) ) ) ) )
& ( ( ( C @ ( B @ ( D @ big_f ) ) )
& ( B @ ( D @ ( C @ big_f ) ) )
& ( D @ ( C @ ( B @ big_f ) ) ) )
=> ( E @ ( E @ ( E @ big_f ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN353+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % 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
% 0.13/0.38 % Computer : n003.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sat Sep 26 17:39:09 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 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
% 0.96/1.07 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/1.30 % [INFO] Parsing done (225ms).
% 1.30/1.31 % [INFO] Running in sequential loop mode.
% 1.76/1.74 % [INFO] eprover registered as external prover.
% 1.76/1.75 % [INFO] Scanning for conjecture ...
% 1.94/1.88 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.09/1.95 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.09/1.96 % [INFO] Problem is first-order (TPTP FOF).
% 2.09/1.96 % [INFO] Type checking passed.
% 2.09/1.97 % [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 ...
% 3.45/2.53 % External prover 'e' found a proof!
% 3.45/2.53 % [INFO] Killing All external provers ...
% 3.45/2.53 % Time passed: 2006ms (effective reasoning time: 1219ms)
% 3.45/2.53 % 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)>
% 3.45/2.53 % Axioms used in derivation (0):
% 3.45/2.53 % No. of inferences in proof: 4
% 3.45/2.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2006 ms resp. 1219 ms w/o parsing
% 3.45/2.57 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.45/2.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------