%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL121-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n014.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 07:50:54 AM UTC 2026
% Result : Unsatisfiable 35.48s 9.04s
% Output : Refutation 36.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of formulae : 7 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 11 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 72 ( 6 ~; 4 |; 0 &; 62 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $o ).
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(1,negated_conjecture,
~ ( b @ ( c @ ( c @ equivalent ) @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lg_1) ).
thf(4,plain,
~ ( b @ ( c @ ( c @ equivalent ) @ ( b @ equivalent ) @ equivalent ) @ ( a @ equivalent ) @ ( a @ equivalent ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
thf(6,plain,
! [B: $i,A: $i] :
( ( B @ is_a_theorem )
| ~ ( A @ is_a_theorem )
| ~ ( B @ ( A @ equivalent ) @ is_a_theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_2) ).
thf(8,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ equivalent ) @ ( D @ ( B @ equivalent ) @ equivalent ) @ ( C @ ( B @ equivalent ) @ equivalent ) @ ( A @ equivalent ) @ ( A @ equivalent ) @ is_a_theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1373,plain,
$false,
inference(e,[status(thm)],[4,6,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL121-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % 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
% 0.13/0.39 % Computer : n014.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 21:53:03 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.16 % [INFO] Parsing done (179ms).
% 1.28/1.18 % [INFO] Running in sequential loop mode.
% 1.83/1.59 % [INFO] eprover registered as external prover.
% 1.83/1.59 % [INFO] Scanning for conjecture ...
% 2.02/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.19/1.72 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.19/1.73 % [INFO] Problem is propositional (TPTP CNF).
% 2.19/1.73 % [INFO] Type checking passed.
% 2.19/1.73 % [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 ...
% 35.48/9.03 % External prover 'e' found a proof!
% 35.48/9.03 % [INFO] Killing All external provers ...
% 35.48/9.04 % Time passed: 8500ms (effective reasoning time: 7855ms)
% 35.48/9.04 % Axioms used in derivation (2): condensed_detachment, lg_2
% 35.48/9.04 % No. of inferences in proof: 7
% 35.48/9.04 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 8500 ms resp. 7855 ms w/o parsing
% 36.01/9.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 36.01/9.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------