%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO387^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n009.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 08:45:42 AM UTC 2026
% Result : Theorem 3.99s 2.39s
% Output : Refutation 4.23s
% 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 : 139 ( 0 equ; 0 cnn)
% Maximal formula atoms : 46 ( 34 avg)
% Number of connectives : 557 ( 68 ~; 60 |; 75 &; 354 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 28 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 117 ( 0 ^; 117 !; 0 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
thf(cQ_5_decl,type,
cQ_5: $i > $i > $i > $o ).
thf(f_decl,type,
f: $i > $i ).
thf(cP_4_decl,type,
cP_4: $i > $i > $o ).
thf(cQ_4_decl,type,
cQ_4: $i > $i > $i > $o ).
thf(d_decl,type,
d: $i ).
thf(c_decl,type,
c: $i ).
thf(b_decl,type,
b: $i ).
thf(a_decl,type,
a: $i ).
thf(cP_3_decl,type,
cP_3: $i > $i > $o ).
thf(cQ_3_decl,type,
cQ_3: $i > $i > $i > $o ).
thf(cP_2_decl,type,
cP_2: $i > $i > $o ).
thf(cQ_2_decl,type,
cQ_2: $i > $i > $i > $o ).
thf(cP_1_decl,type,
cP_1: $i > $i > $o ).
thf(cQ_1_decl,type,
cQ_1: $i > $i > $i > $o ).
thf(1,conjecture,
~ ( ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ! [A: $i] : ( cP_1 @ d @ A )
& ! [A: $i,B: $i] :
( ~ ( cP_1 @ A @ B )
| ( cP_1 @ ( f @ A ) @ B ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( cQ_1 @ A @ B @ C )
| ~ ( cP_1 @ ( f @ A ) @ D )
| ~ ( cP_1 @ ( f @ B ) @ E )
| ~ ( cP_1 @ ( f @ C ) @ F )
| ( cQ_2 @ D @ E @ F ) )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ! [A: $i] : ( cP_2 @ d @ A )
& ! [A: $i,B: $i] :
( ~ ( cP_2 @ A @ B )
| ( cP_2 @ ( f @ A ) @ B ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( cQ_2 @ A @ B @ C )
| ~ ( cP_2 @ ( f @ A ) @ D )
| ~ ( cP_2 @ ( f @ B ) @ E )
| ~ ( cP_2 @ ( f @ C ) @ F )
| ( cQ_3 @ D @ E @ F ) )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ! [A: $i] : ( cP_3 @ d @ A )
& ! [A: $i,B: $i] :
( ~ ( cP_3 @ A @ B )
| ( cP_3 @ ( f @ A ) @ B ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( cQ_3 @ A @ B @ C )
| ~ ( cP_3 @ ( f @ A ) @ D )
| ~ ( cP_3 @ ( f @ B ) @ E )
| ~ ( cP_3 @ ( f @ C ) @ F )
| ( cQ_4 @ D @ E @ F ) )
& ( cP_4 @ a @ a )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ! [A: $i] : ( cP_4 @ d @ A )
& ! [A: $i,B: $i] :
( ~ ( cP_4 @ A @ B )
| ( cP_4 @ ( f @ A ) @ B ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( cQ_4 @ A @ B @ C )
| ~ ( cP_4 @ ( f @ A ) @ D )
| ~ ( cP_4 @ ( f @ B ) @ E )
| ~ ( cP_4 @ ( f @ C ) @ F )
| ( cQ_5 @ D @ E @ F ) )
& ! [A: $i,B: $i,C: $i] :
~ ( cQ_5 @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM409_4) ).
thf(2,negated_conjecture,
~ ~ ( ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ! [A: $i] : ( cP_1 @ d @ A )
& ! [A: $i,B: $i] :
( ~ ( cP_1 @ A @ B )
| ( cP_1 @ ( f @ A ) @ B ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( cQ_1 @ A @ B @ C )
| ~ ( cP_1 @ ( f @ A ) @ D )
| ~ ( cP_1 @ ( f @ B ) @ E )
| ~ ( cP_1 @ ( f @ C ) @ F )
| ( cQ_2 @ D @ E @ F ) )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ! [A: $i] : ( cP_2 @ d @ A )
& ! [A: $i,B: $i] :
( ~ ( cP_2 @ A @ B )
| ( cP_2 @ ( f @ A ) @ B ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( cQ_2 @ A @ B @ C )
| ~ ( cP_2 @ ( f @ A ) @ D )
| ~ ( cP_2 @ ( f @ B ) @ E )
| ~ ( cP_2 @ ( f @ C ) @ F )
| ( cQ_3 @ D @ E @ F ) )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ! [A: $i] : ( cP_3 @ d @ A )
& ! [A: $i,B: $i] :
( ~ ( cP_3 @ A @ B )
| ( cP_3 @ ( f @ A ) @ B ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( cQ_3 @ A @ B @ C )
| ~ ( cP_3 @ ( f @ A ) @ D )
| ~ ( cP_3 @ ( f @ B ) @ E )
| ~ ( cP_3 @ ( f @ C ) @ F )
| ( cQ_4 @ D @ E @ F ) )
& ( cP_4 @ a @ a )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ! [A: $i] : ( cP_4 @ d @ A )
& ! [A: $i,B: $i] :
( ~ ( cP_4 @ A @ B )
| ( cP_4 @ ( f @ A ) @ B ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( cQ_4 @ A @ B @ C )
| ~ ( cP_4 @ ( f @ A ) @ D )
| ~ ( cP_4 @ ( f @ B ) @ E )
| ~ ( cP_4 @ ( f @ C ) @ F )
| ( cQ_5 @ D @ E @ F ) )
& ! [A: $i,B: $i,C: $i] :
~ ( cQ_5 @ A @ B @ C ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ( ( cQ_1 @ a @ b @ c )
& ( cP_1 @ a @ a )
& ( cP_1 @ b @ b )
& ( cP_1 @ c @ c )
& ! [A: $i] : ( cP_1 @ d @ A )
& ! [A: $i,B: $i] :
( ~ ( cP_1 @ A @ B )
| ( cP_1 @ ( f @ A ) @ B ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( cQ_1 @ A @ B @ C )
| ~ ( cP_1 @ ( f @ A ) @ D )
| ~ ( cP_1 @ ( f @ B ) @ E )
| ~ ( cP_1 @ ( f @ C ) @ F )
| ( cQ_2 @ D @ E @ F ) )
& ( cP_2 @ a @ a )
& ( cP_2 @ b @ b )
& ( cP_2 @ c @ c )
& ! [A: $i] : ( cP_2 @ d @ A )
& ! [A: $i,B: $i] :
( ~ ( cP_2 @ A @ B )
| ( cP_2 @ ( f @ A ) @ B ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( cQ_2 @ A @ B @ C )
| ~ ( cP_2 @ ( f @ A ) @ D )
| ~ ( cP_2 @ ( f @ B ) @ E )
| ~ ( cP_2 @ ( f @ C ) @ F )
| ( cQ_3 @ D @ E @ F ) )
& ( cP_3 @ a @ a )
& ( cP_3 @ b @ b )
& ( cP_3 @ c @ c )
& ! [A: $i] : ( cP_3 @ d @ A )
& ! [A: $i,B: $i] :
( ~ ( cP_3 @ A @ B )
| ( cP_3 @ ( f @ A ) @ B ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( cQ_3 @ A @ B @ C )
| ~ ( cP_3 @ ( f @ A ) @ D )
| ~ ( cP_3 @ ( f @ B ) @ E )
| ~ ( cP_3 @ ( f @ C ) @ F )
| ( cQ_4 @ D @ E @ F ) )
& ( cP_4 @ a @ a )
& ( cP_4 @ b @ b )
& ( cP_4 @ c @ c )
& ! [A: $i] : ( cP_4 @ d @ A )
& ! [A: $i,B: $i] :
( ~ ( cP_4 @ A @ B )
| ( cP_4 @ ( f @ A ) @ B ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( cQ_4 @ A @ B @ C )
| ~ ( cP_4 @ ( f @ A ) @ D )
| ~ ( cP_4 @ ( f @ B ) @ E )
| ~ ( cP_4 @ ( f @ C ) @ F )
| ( cQ_5 @ D @ E @ F ) )
& ! [A: $i,B: $i,C: $i] :
~ ( cQ_5 @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(45,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO387^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.10/0.21 % Computer : n009.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 16:50:15 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 1.06/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.47/1.06 % [INFO] Parsing done (213ms).
% 1.47/1.07 % [INFO] Running in sequential loop mode.
% 2.18/1.46 % [INFO] eprover registered as external prover.
% 2.18/1.47 % [INFO] Scanning for conjecture ...
% 2.55/1.62 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.55/1.68 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.55/1.69 % [INFO] Problem is higher-order (TPTP THF).
% 2.55/1.69 % [INFO] Type checking passed.
% 2.72/1.70 % [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 ...
% 3.99/2.39 % External prover 'e' found a proof!
% 3.99/2.39 % [INFO] Killing All external provers ...
% 3.99/2.39 % Time passed: 2068ms (effective reasoning time: 1312ms)
% 3.99/2.39 % 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)>
% 3.99/2.39 % Axioms used in derivation (0):
% 3.99/2.39 % No. of inferences in proof: 4
% 3.99/2.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2068 ms resp. 1312 ms w/o parsing
% 4.23/2.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.23/2.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------