%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LDA003-1 : 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 : n007.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 08:00:08 AM UTC 2026
% Result : Unsatisfiable 4.78s 3.19s
% Output : Refutation 5.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of formulae : 15 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 8 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 66 ( 6 ~; 4 |; 0 &; 56 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(left_decl,type,
left: $i > $i > $o ).
thf(n3_decl,type,
n3: $i ).
thf(u_decl,type,
u: $i ).
thf(f_decl,type,
f: $i > $i > $i ).
thf(n2_decl,type,
n2: $i ).
thf(n1_decl,type,
n1: $i ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ f ) @ ( A @ f ) )
= ( C @ ( A @ f ) @ ( B @ ( A @ f ) @ f ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ f ) @ ( A @ f ) )
= ( C @ ( A @ f ) @ ( B @ ( A @ f ) @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ left ) )
| ~ ( C @ ( B @ left ) )
| ~ ( B @ ( A @ left ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ left ) )
| ~ ( C @ ( B @ left ) )
| ~ ( B @ ( A @ left ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
( n3
= ( n1 @ ( n2 @ f ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(17,plain,
( n3
= ( n1 @ ( n2 @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( B @ ( A @ f ) @ ( A @ left ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(12,plain,
! [B: $i,A: $i] : ( B @ ( A @ f ) @ ( A @ left ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
~ ( u @ ( n3 @ left ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
thf(8,plain,
~ ( u @ ( n3 @ left ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
( u
= ( n2 @ ( n2 @ f ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(19,plain,
( u
= ( n2 @ ( n2 @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
( n2
= ( n1 @ ( n1 @ f ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(15,plain,
( n2
= ( n1 @ ( n1 @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[10,13,17,12,8,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LDA003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.13 % 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
% 0.24/0.50 % Computer : n007.cluster.edu
% 0.24/0.50 % Model : x86_64 x86_64
% 0.24/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.50 % Memory : 8046.5625MB
% 0.24/0.50 % OS : Linux 6.8.0-71-generic
% 0.24/0.50 % CPULimit : 300
% 0.24/0.50 % WCLimit : 300
% 0.24/0.50 % DateTime : Fri Sep 25 23:53:24 UTC 2026
% 0.24/0.51 % CPUTime :
% 0.24/0.51 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
% 1.40/1.38 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.94/1.64 % [INFO] Parsing done (260ms).
% 1.94/1.66 % [INFO] Running in sequential loop mode.
% 2.83/2.29 % [INFO] eprover registered as external prover.
% 3.05/2.30 % [INFO] Scanning for conjecture ...
% 3.22/2.43 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 3.22/2.48 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 3.22/2.50 % [INFO] Problem is propositional (TPTP CNF).
% 3.38/2.51 % [INFO] Type checking passed.
% 3.38/2.51 % [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 ...
% 4.78/3.19 % External prover 'e' found a proof!
% 4.78/3.19 % [INFO] Killing All external provers ...
% 4.78/3.19 % Time passed: 2468ms (effective reasoning time: 1517ms)
% 4.78/3.19 % Axioms used in derivation (6): clause_5, clause_4, a3, clause_6, a1, a2
% 4.78/3.19 % No. of inferences in proof: 15
% 4.78/3.19 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2468 ms resp. 1517 ms w/o parsing
% 5.02/3.22 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.02/3.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------