%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN066-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : Sun Sep 27 09:16:42 AM UTC 2026
% Result : Unsatisfiable 4.77s 8.05s
% Output : Refutation 4.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 82 ( 8 ~; 8 |; 0 &; 66 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(big_r_decl,type,
big_r: $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(big_p_decl,type,
big_p: $i > $i > $o ).
thf(f_decl,type,
f: $i > $i > $i ).
thf(g_decl,type,
g: $i > $i ).
thf(big_q_decl,type,
big_q: $i > $i > $o ).
thf(h_decl,type,
h: $i > $i > $i ).
thf(i_decl,type,
i: $i > $i > $i ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ i ) @ big_q ) )
| ( B @ ( A @ big_p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ i ) @ big_q ) )
| ( B @ ( A @ big_p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ g @ ( A @ ( B @ f ) @ big_p ) )
| ~ ( B @ ( A @ big_p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( B @ g @ ( A @ ( B @ f ) @ big_p ) )
| ~ ( B @ ( A @ big_p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A @ g @ ( B @ ( A @ h ) @ big_q ) )
| ~ ( A @ g @ ( B @ ( A @ f ) @ big_p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( A @ g @ ( B @ ( A @ h ) @ big_q ) )
| ~ ( A @ g @ ( B @ ( A @ f ) @ big_p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( A @ ( a @ big_r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(7,plain,
! [A: $i] :
~ ( A @ ( a @ big_r ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ big_r ) )
| ~ ( B @ ( A @ big_q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ big_r ) )
| ~ ( B @ ( A @ big_q ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ f ) @ big_p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
thf(11,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ f ) @ big_p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,plain,
$false,
inference(e,[status(thm)],[14,9,12,7,16,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN066-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.14/5.43 % Computer : n009.cluster.edu
% 0.14/5.43 % Model : x86_64 x86_64
% 0.14/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.43 % Memory : 8046.5625MB
% 0.14/5.43 % OS : Linux 6.8.0-71-generic
% 0.14/5.43 % CPULimit : 300
% 0.14/5.43 % WCLimit : 300
% 0.14/5.43 % DateTime : Sat Sep 26 17:08:49 UTC 2026
% 0.14/5.44 % CPUTime :
% 0.14/5.44 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
% 1.25/6.28 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.77/6.54 % [INFO] Parsing done (254ms).
% 1.77/6.56 % [INFO] Running in sequential loop mode.
% 2.64/7.11 % [INFO] eprover registered as external prover.
% 2.64/7.12 % [INFO] Scanning for conjecture ...
% 2.93/7.25 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 3.09/7.30 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 3.09/7.31 % [INFO] Problem is propositional (TPTP CNF).
% 3.09/7.32 % [INFO] Type checking passed.
% 3.09/7.32 % [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 ...
% 4.34/8.05 % External prover 'e' found a proof!
% 4.34/8.05 % [INFO] Killing All external provers ...
% 4.77/8.05 % Time passed: 2406ms (effective reasoning time: 1487ms)
% 4.77/8.05 % Axioms used in derivation (5): clause_5, clause_2, clause_1, clause_4, clause_3
% 4.77/8.05 % No. of inferences in proof: 13
% 4.77/8.05 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2406 ms resp. 1487 ms w/o parsing
% 4.77/8.11 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.77/8.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------