%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN353-1 : TPTP v9.3.1. Released v1.2.0.
% 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 : n004.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 : Unsatisfiable 6.80s 3.72s
% Output : Refutation 7.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 17
% Syntax : Number of formulae : 35 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 95 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 538 ( 46 ~; 60 |; 0 &; 432 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 3 usr; 2 con; 0-3 aty)
% Number of variables : 102 ( 0 ^; 102 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
thf(f_decl,type,
f: $i > $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(z_decl,type,
z: $i > $i > $i > $i ).
thf(5,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ z ) ) @ ( A @ ( B @ f ) ) )
| ~ ( A @ ( C @ ( B @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause5) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ z ) ) @ ( A @ ( B @ f ) ) )
| ~ ( A @ ( C @ ( B @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( A @ ( C @ z ) ) @ f ) ) )
| ( B @ ( A @ ( C @ f ) ) )
| ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause11) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( A @ ( C @ z ) ) @ f ) ) )
| ( B @ ( A @ ( C @ f ) ) )
| ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ ( A @ z ) ) @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause13) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ ( A @ z ) ) @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(2,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ z ) ) @ ( B @ ( C @ f ) ) )
| ( A @ ( C @ ( B @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause2) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ z ) ) @ ( B @ ( C @ f ) ) )
| ( A @ ( C @ ( B @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ z ) ) @ ( C @ ( B @ ( A @ z ) ) @ ( C @ ( B @ ( A @ z ) ) @ f ) ) )
| ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause14) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ z ) ) @ ( C @ ( B @ ( A @ z ) ) @ ( C @ ( B @ ( A @ z ) ) @ f ) ) )
| ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ z ) ) @ ( B @ ( C @ f ) ) )
| ( B @ ( A @ ( C @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause3) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ z ) ) @ ( B @ ( C @ f ) ) )
| ( B @ ( A @ ( C @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ z ) ) @ ( C @ f ) ) )
| ( A @ ( C @ ( B @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause7) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ z ) ) @ ( C @ f ) ) )
| ( A @ ( C @ ( B @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ f ) ) )
| ( A @ ( C @ ( B @ f ) ) )
| ~ ( C @ ( B @ ( A @ z ) ) @ ( a @ ( a @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ f ) ) )
| ( A @ ( C @ ( B @ f ) ) )
| ~ ( C @ ( B @ ( A @ z ) ) @ ( a @ ( a @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ z ) ) @ ( B @ ( C @ f ) ) )
| ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause4) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ z ) ) @ ( B @ ( C @ f ) ) )
| ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ z ) ) @ ( C @ f ) ) )
| ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ z ) ) @ ( C @ f ) ) )
| ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ z ) ) @ ( B @ ( A @ ( C @ z ) ) @ ( B @ ( A @ ( C @ z ) ) @ f ) ) )
| ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause15) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ z ) ) @ ( B @ ( A @ ( C @ z ) ) @ ( B @ ( A @ ( C @ z ) ) @ f ) ) )
| ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ z ) ) @ ( C @ f ) ) )
| ( B @ ( A @ ( C @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause6) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ z ) ) @ ( C @ f ) ) )
| ( B @ ( A @ ( C @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( C @ ( B @ z ) ) @ f ) ) )
| ~ ( B @ ( A @ ( C @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause12) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ ( C @ ( B @ z ) ) @ f ) ) )
| ~ ( B @ ( A @ ( C @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ z ) ) @ ( C @ ( B @ ( A @ z ) ) @ ( C @ ( B @ ( A @ z ) ) @ f ) ) )
| ~ ( B @ ( A @ ( C @ f ) ) )
| ~ ( A @ ( C @ ( B @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause17) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ z ) ) @ ( C @ ( B @ ( A @ z ) ) @ ( C @ ( B @ ( A @ z ) ) @ f ) ) )
| ~ ( B @ ( A @ ( C @ f ) ) )
| ~ ( A @ ( C @ ( B @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ z ) ) @ ( A @ f ) ) )
| ~ ( B @ ( A @ ( C @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause9) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ z ) ) @ ( A @ f ) ) )
| ~ ( B @ ( A @ ( C @ f ) ) )
| ~ ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ z ) ) @ ( A @ ( C @ ( B @ z ) ) @ ( A @ ( C @ ( B @ z ) ) @ f ) ) )
| ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause16) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ z ) ) @ ( A @ ( C @ ( B @ z ) ) @ ( A @ ( C @ ( B @ z ) ) @ f ) ) )
| ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ ( C @ ( B @ z ) ) @ f ) ) )
| ( A @ ( C @ ( B @ f ) ) )
| ( C @ ( B @ ( A @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause10) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ ( C @ ( B @ z ) ) @ f ) ) )
| ( A @ ( C @ ( B @ f ) ) )
| ( C @ ( B @ ( A @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(56,plain,
$false,
inference(e,[status(thm)],[18,31,24,25,20,29,28,21,33,32,34,22,27,26,23,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN353-1 : TPTP v9.3.1. Released v1.2.0.
% 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
% 0.26/0.49 % Computer : n004.cluster.edu
% 0.26/0.49 % Model : x86_64 x86_64
% 0.26/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.49 % Memory : 8046.5625MB
% 0.26/0.49 % OS : Linux 6.8.0-71-generic
% 0.26/0.49 % CPULimit : 300
% 0.26/0.49 % WCLimit : 300
% 0.26/0.49 % DateTime : Sat Sep 26 17:37:06 UTC 2026
% 0.26/0.49 % CPUTime :
% 0.26/0.49 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
% 1.41/1.38 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.93/1.68 % [INFO] Parsing done (298ms).
% 2.20/1.70 % [INFO] Running in sequential loop mode.
% 3.26/2.35 % [INFO] eprover registered as external prover.
% 3.26/2.36 % [INFO] Scanning for conjecture ...
% 3.64/2.56 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.85/2.67 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.85/2.67 % [INFO] Problem is propositional (TPTP CNF).
% 3.85/2.68 % [INFO] Type checking passed.
% 3.85/2.69 % [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 ...
% 6.80/3.72 % External prover 'e' found a proof!
% 6.80/3.72 % [INFO] Killing All external provers ...
% 6.80/3.72 % Time passed: 3005ms (effective reasoning time: 2005ms)
% 6.80/3.72 % Axioms used in derivation (0):
% 6.80/3.72 % No. of inferences in proof: 35
% 6.80/3.72 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3005 ms resp. 2005 ms w/o parsing
% 7.02/3.80 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.02/3.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------