%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL096-10 : TPTP v9.3.1. Released v7.3.0.
% 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 07:50:48 AM UTC 2026
% Result : Unsatisfiable 24.94s 6.89s
% Output : Refutation 25.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 164 ( 2 ~; 0 |; 0 &; 162 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 38 ( 0 ^; 38 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $i ).
thf(equivalent_decl,type,
equivalent: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(true_decl,type,
true: $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_2) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ equivalent ) @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ equivalent ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
( ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lg_1) ).
thf(7,plain,
( ( c @ ( c @ ( a @ ( b @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_4) ).
thf(18,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( E @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_3) ).
thf(16,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( D @ ( C @ ( A @ equivalent ) @ ( B @ ( A @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ equivalent ) @ is_a_theorem )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(768,plain,
$false,
inference(e,[status(thm)],[10,14,12,7,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL096-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.13 % 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
% 0.24/0.50 % Computer : n015.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 21:53:58 UTC 2026
% 0.24/0.51 % CPUTime :
% 0.24/0.51 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
% 0.92/1.03 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.48/1.26 % [INFO] Parsing done (225ms).
% 1.48/1.28 % [INFO] Running in sequential loop mode.
% 2.34/1.71 % [INFO] eprover registered as external prover.
% 2.34/1.72 % [INFO] Scanning for conjecture ...
% 2.56/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.56/1.85 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.56/1.87 % [INFO] Problem is propositional (TPTP CNF).
% 2.56/1.88 % [INFO] Type checking passed.
% 2.56/1.88 % [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 ...
% 24.94/6.88 % External prover 'e' found a proof!
% 24.94/6.88 % [INFO] Killing All external provers ...
% 24.94/6.89 % Time passed: 6237ms (effective reasoning time: 5594ms)
% 24.94/6.89 % Axioms used in derivation (5): ifeq_axiom, condensed_detachment, lg_2, lg_3, lg_4
% 24.94/6.89 % No. of inferences in proof: 13
% 24.94/6.89 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 6237 ms resp. 5594 ms w/o parsing
% 25.44/6.94 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.44/6.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------