%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN332+1 : TPTP v9.3.1. Released v2.0.0.
% 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 : n015.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 09:17:14 AM UTC 2026
% Result : Theorem 3.17s 7.33s
% Output : Refutation 3.17s
% 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 : 57 ( 0 equ; 0 cnn)
% Maximal formula atoms : 30 ( 14 avg)
% Number of connectives : 168 ( 3 ~; 0 |; 11 &; 112 @)
% ( 10 <=>; 30 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 2 ( 1 usr; 1 con; 0-2 aty)
% Number of variables : 9 ( 0 ^; 3 !; 6 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
thf(big_f_decl,type,
big_f: $i > $i > $o ).
thf(1,conjecture,
? [A: $i,B: $i] :
! [C: $i] :
( ( ( ( A @ ( B @ big_f ) )
& ( B @ ( A @ big_f ) ) )
<~> ( C @ ( A @ big_f ) ) )
=> ( ( ( C @ ( A @ big_f ) )
<=> ( A @ ( C @ big_f ) ) )
=> ( ( ( C @ ( A @ big_f ) )
<=> ( C @ ( B @ big_f ) ) )
=> ( ( ( ( A @ ( B @ big_f ) )
=> ( B @ ( A @ big_f ) ) )
<=> ( C @ ( C @ big_f ) ) )
=> ( ( ( B @ ( A @ big_f ) )
<=> ( A @ ( B @ big_f ) ) )
<=> ( B @ ( C @ big_f ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_14_4) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i] :
! [C: $i] :
( ( ( ( A @ ( B @ big_f ) )
& ( B @ ( A @ big_f ) ) )
<~> ( C @ ( A @ big_f ) ) )
=> ( ( ( C @ ( A @ big_f ) )
<=> ( A @ ( C @ big_f ) ) )
=> ( ( ( C @ ( A @ big_f ) )
<=> ( C @ ( B @ big_f ) ) )
=> ( ( ( ( A @ ( B @ big_f ) )
=> ( B @ ( A @ big_f ) ) )
<=> ( C @ ( C @ big_f ) ) )
=> ( ( ( B @ ( A @ big_f ) )
<=> ( A @ ( B @ big_f ) ) )
<=> ( B @ ( C @ big_f ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: $i,B: $i] :
! [C: $i] :
( ~ ( ( ( C @ ( A @ big_f ) )
=> ( ( A @ ( B @ big_f ) )
& ( B @ ( A @ big_f ) ) ) )
& ( ( ( A @ ( B @ big_f ) )
& ( B @ ( A @ big_f ) ) )
=> ( C @ ( A @ big_f ) ) ) )
=> ( ( ( ( A @ ( C @ big_f ) )
=> ( C @ ( A @ big_f ) ) )
& ( ( C @ ( A @ big_f ) )
=> ( A @ ( C @ big_f ) ) ) )
=> ( ( ( ( C @ ( B @ big_f ) )
=> ( C @ ( A @ big_f ) ) )
& ( ( C @ ( A @ big_f ) )
=> ( C @ ( B @ big_f ) ) ) )
=> ( ( ( ( C @ ( C @ big_f ) )
=> ( ( A @ ( B @ big_f ) )
=> ( B @ ( A @ big_f ) ) ) )
& ( ( ( A @ ( B @ big_f ) )
=> ( B @ ( A @ big_f ) ) )
=> ( C @ ( C @ big_f ) ) ) )
=> ( ( ( B @ ( C @ big_f ) )
=> ( ( ( A @ ( B @ big_f ) )
=> ( B @ ( A @ big_f ) ) )
& ( ( B @ ( A @ big_f ) )
=> ( A @ ( B @ big_f ) ) ) ) )
& ( ( ( ( A @ ( B @ big_f ) )
=> ( B @ ( A @ big_f ) ) )
& ( ( B @ ( A @ big_f ) )
=> ( A @ ( B @ big_f ) ) ) )
=> ( B @ ( C @ big_f ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN332+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.11 % 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
% 0.20/5.46 % Computer : n015.cluster.edu
% 0.20/5.46 % Model : x86_64 x86_64
% 0.20/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/5.46 % Memory : 8046.5625MB
% 0.20/5.46 % OS : Linux 6.8.0-71-generic
% 0.20/5.46 % CPULimit : 300
% 0.20/5.46 % WCLimit : 300
% 0.20/5.46 % DateTime : Sat Sep 26 17:38:34 UTC 2026
% 0.20/5.46 % CPUTime :
% 0.20/5.46 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
% 1.04/6.05 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/6.23 % [INFO] Parsing done (172ms).
% 1.33/6.24 % [INFO] Running in sequential loop mode.
% 1.86/6.65 % [INFO] eprover registered as external prover.
% 1.86/6.66 % [INFO] Scanning for conjecture ...
% 2.04/6.75 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.04/6.79 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.04/6.79 % [INFO] Problem is first-order (TPTP FOF).
% 2.04/6.79 % [INFO] Type checking passed.
% 2.20/6.80 % [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 ...
% 3.17/7.33 % External prover 'e' found a proof!
% 3.17/7.33 % [INFO] Killing All external provers ...
% 3.17/7.33 % Time passed: 1723ms (effective reasoning time: 1081ms)
% 3.17/7.33 % 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)>
% 3.17/7.33 % Axioms used in derivation (0):
% 3.17/7.33 % No. of inferences in proof: 4
% 3.17/7.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1723 ms resp. 1081 ms w/o parsing
% 3.17/7.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.17/7.36 % [INFO] Killing All external provers ...
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