%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN339+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 : 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 09:17:15 AM UTC 2026
% Result : Theorem 5.11s 3.24s
% Output : Refutation 5.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 6 unt; 0 typ; 1 def)
% Number of atoms : 24 ( 3 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 83 ( 10 ~; 1 |; 1 &; 66 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-3 aty)
% Number of variables : 34 ( 1 ^; 23 !; 9 ?; 34 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(big_f_decl,type,
big_f: $i > $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ! [C: $i] : ( C @ ( B @ ( A @ big_f ) ) )
=> ? [C: $i] : ( C @ ( C @ ( B @ big_f ) ) ) ) ) ) ).
thf(1,conjecture,
? [A: $i] :
! [B: $i] :
? [C: $i] :
( ( C @ ( B @ ( A @ big_f ) ) )
=> ( C @ ( C @ ( B @ big_f ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',church_46_15_4) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
! [B: $i] :
? [C: $i] :
( ( C @ ( B @ ( A @ big_f ) ) )
=> ( C @ ( C @ ( B @ big_f ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: $i] :
! [B: $i] :
? [C: $i] :
( ( C @ ( B @ ( A @ big_f ) ) )
=> ( C @ ( C @ ( B @ big_f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ? [A: $i] :
! [B: $i] :
( ! [C: $i] : ( C @ ( B @ ( A @ big_f ) ) )
=> ? [C: $i] : ( C @ ( C @ ( B @ big_f ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( A @ sk1 @ big_f ) ) )
& ( B @ ( A @ sk1 @ ( A @ big_f ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
! [B: $i,A: $i] : ( B @ ( A @ sk1 @ ( A @ big_f ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(7,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ ( A @ sk1 @ big_f ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(8,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ ( A @ sk1 @ big_f ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(9,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ sk1 @ ( A @ big_f ) ) )
!= ( D @ ( D @ ( C @ sk1 @ big_f ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6,8]) ).
thf(10,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ sk1 @ ( A @ big_f ) ) )
!= ( D @ ( D @ ( C @ sk1 @ big_f ) ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(11,plain,
$false,
inference(pattern_uni,[status(thm)],[10:[bind(A,$thf( I @ sk1 )),bind(B,$thf( I @ sk1 @ sk1 )),bind(C,$thf( I )),bind(D,$thf( I @ sk1 @ sk1 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN339+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.11 % 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
% 0.22/0.48 % Computer : n015.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Sat Sep 26 17:39:13 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 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
% 1.43/1.31 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.82/1.56 % [INFO] Parsing done (242ms).
% 1.82/1.58 % [INFO] Running in sequential loop mode.
% 2.82/2.18 % [INFO] eprover registered as external prover.
% 2.82/2.19 % [INFO] Scanning for conjecture ...
% 3.13/2.32 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.13/2.36 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.13/2.37 % [INFO] Problem is first-order (TPTP FOF).
% 3.13/2.37 % [INFO] Type checking passed.
% 3.13/2.38 % [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 ...
% 5.11/3.23 % [INFO] Killing All external provers ...
% 5.11/3.23 % Time passed: 2540ms (effective reasoning time: 1641ms)
% 5.11/3.23 % 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)>
% 5.11/3.24 % Axioms used in derivation (0):
% 5.11/3.24 % No. of inferences in proof: 11
% 5.11/3.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2540 ms resp. 1641 ms w/o parsing
% 5.29/3.32 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.29/3.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------