%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN319+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 : n013.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 09:17:11 AM UTC 2026
% Result : Theorem 3.09s 2.26s
% Output : Refutation 3.09s
% 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 : 37 ( 0 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 74 ( 5 ~; 6 |; 6 &; 36 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 12 ( 0 ^; 6 !; 6 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(big_f_decl,type,
big_f: $i > $o ).
thf(big_g_decl,type,
big_g: $i > $o ).
thf(big_h_decl,type,
big_h: $i > $o ).
thf(1,conjecture,
? [A: $i,B: $i] :
! [C: $i,D: $i] :
( ( ( ( B @ big_f )
=> ( C @ big_g ) )
=> ( ~ ( C @ big_f )
& ( A @ big_g ) ) )
=> ( ( ( ( A @ big_g )
| ( A @ big_f ) )
=> ( A @ big_h ) )
=> ( ( ( B @ big_h )
=> ( ( ( D @ big_g )
| ( D @ big_f ) )
=> ( D @ big_h ) ) )
& ( D @ big_h ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_2_5) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i] :
! [C: $i,D: $i] :
( ( ( ( B @ big_f )
=> ( C @ big_g ) )
=> ( ~ ( C @ big_f )
& ( A @ big_g ) ) )
=> ( ( ( ( A @ big_g )
| ( A @ big_f ) )
=> ( A @ big_h ) )
=> ( ( ( B @ big_h )
=> ( ( ( D @ big_g )
| ( D @ big_f ) )
=> ( D @ big_h ) ) )
& ( D @ big_h ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: $i,B: $i] :
! [C: $i,D: $i] :
( ( ( ( B @ big_f )
=> ( C @ big_g ) )
=> ( ~ ( C @ big_f )
& ( A @ big_g ) ) )
=> ( ( ( ( A @ big_g )
| ( A @ big_f ) )
=> ( A @ big_h ) )
=> ( ( ( B @ big_h )
=> ( ( ( D @ big_g )
| ( D @ big_f ) )
=> ( D @ big_h ) ) )
& ( D @ big_h ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN319+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.08 % 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
% 0.14/0.40 % Computer : n013.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 17:32:41 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.86/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.16 % [INFO] Parsing done (174ms).
% 1.23/1.18 % [INFO] Running in sequential loop mode.
% 1.76/1.57 % [INFO] eprover registered as external prover.
% 1.76/1.58 % [INFO] Scanning for conjecture ...
% 1.94/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.10/1.71 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.10/1.71 % [INFO] Problem is first-order (TPTP FOF).
% 2.10/1.72 % [INFO] Type checking passed.
% 2.10/1.72 % [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 ...
% 3.09/2.25 % External prover 'e' found a proof!
% 3.09/2.25 % [INFO] Killing All external provers ...
% 3.09/2.25 % Time passed: 1708ms (effective reasoning time: 1071ms)
% 3.09/2.25 % 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)>
% 3.09/2.26 % Axioms used in derivation (0):
% 3.09/2.26 % No. of inferences in proof: 4
% 3.09/2.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1708 ms resp. 1071 ms w/o parsing
% 3.09/2.29 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.09/2.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------