%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL899+1 : TPTP v9.3.1. Released v5.5.0.
% 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 : n006.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 07:53:20 AM UTC 2026
% Result : Theorem 3.79s 17.86s
% Output : Refutation 4.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 30 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 15 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 180 ( 2 ~; 0 |; 5 &; 160 @)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 0 ^; 59 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf('==>_decl',type,
'==>': $i > $i > $i ).
thf('1_decl',type,
'1': $i ).
thf('+_decl',type,
'+': $i > $i > $i ).
thf('0_decl',type,
'0': $i ).
thf('>=_decl',type,
'>=': $i > $i > $o ).
thf(5,axiom,
! [A: $i] :
( ( '0' @ ( A @ '+' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).
thf(25,plain,
! [A: $i] :
( ( '0' @ ( A @ '+' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,axiom,
! [A: $i] :
( ( '1' @ ( A @ '+' ) )
= '1' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_12) ).
thf(52,plain,
! [A: $i] :
( ( '1' @ ( A @ '+' ) )
= '1' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ '>=' ) )
=> ( C @ ( A @ '==>' ) @ ( C @ ( B @ '==>' ) @ '>=' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_10) ).
thf(46,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ '>=' ) )
=> ( C @ ( A @ '==>' ) @ ( C @ ( B @ '==>' ) @ '>=' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $i] : ( A @ ( A @ '>=' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_04) ).
thf(28,plain,
! [A: $i] : ( A @ ( A @ '>=' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: $i] : ( '0' @ ( A @ '>=' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
thf(41,plain,
! [A: $i] : ( '0' @ ( A @ '>=' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ '>=' ) )
& ( B @ ( A @ '>=' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ '>=' ) )
& ( B @ ( A @ '>=' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ '+' ) )
= ( A @ ( B @ '+' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ '+' ) )
= ( A @ ( B @ '+' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ '>=' ) )
=> ( B @ ( C @ '==>' ) @ ( A @ ( C @ '==>' ) @ '>=' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_11) ).
thf(49,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ '>=' ) )
=> ( B @ ( C @ '==>' ) @ ( A @ ( C @ '==>' ) @ '>=' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ '+' ) @ '>=' ) )
<=> ( C @ ( A @ '==>' ) @ ( B @ '>=' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
thf(35,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ '==>' ) @ ( B @ '>=' ) )
=> ( C @ ( B @ ( A @ '+' ) @ '>=' ) ) )
& ( ( C @ ( B @ ( A @ '+' ) @ '>=' ) )
=> ( C @ ( A @ '==>' ) @ ( B @ '>=' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
! [A: $i] :
( ( '1' @ ( '1' @ ( A @ '==>' ) @ '==>' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( '1' @ ( '1' @ ( A @ '==>' ) @ '==>' ) )
= A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i] :
( ( '1' @ ( '1' @ ( A @ '==>' ) @ '==>' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ '>=' ) )
=> ( C @ ( B @ '+' ) @ ( C @ ( A @ '+' ) @ '>=' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).
thf(43,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ '>=' ) )
=> ( C @ ( B @ '+' ) @ ( C @ ( A @ '+' ) @ '>=' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ '==>' ) @ '==>' ) )
= ( A @ ( A @ ( B @ '==>' ) @ '==>' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_13) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ '==>' ) @ '==>' ) )
= ( A @ ( A @ ( B @ '==>' ) @ '==>' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '>=' ) )
& ( B @ ( A @ '>=' ) ) )
=> ( C @ ( A @ '>=' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_05) ).
thf(30,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ '>=' ) )
& ( B @ ( A @ '>=' ) ) )
=> ( C @ ( A @ '>=' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ '+' ) @ '+' ) )
= ( C @ ( B @ '+' ) @ ( A @ '+' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_01) ).
thf(19,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ '+' ) @ '+' ) )
= ( C @ ( B @ '+' ) @ ( A @ '+' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(58,plain,
$false,
inference(e,[status(thm)],[25,52,46,28,41,32,22,49,35,16,43,55,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.43 % Problem : LCL899+1 : TPTP v9.3.1. Released v5.5.0.
% 0.03/0.49 % 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
% 0.13/15.83 % Computer : n006.cluster.edu
% 0.13/15.83 % Model : x86_64 x86_64
% 0.13/15.83 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/15.83 % Memory : 8046.5625MB
% 0.13/15.83 % OS : Linux 6.8.0-71-generic
% 0.13/15.83 % CPULimit : 300
% 0.13/15.83 % WCLimit : 300
% 0.13/15.83 % DateTime : Fri Sep 25 23:46:30 UTC 2026
% 0.13/15.84 % CPUTime :
% 0.13/15.84 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
% 0.98/16.43 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/16.63 % [INFO] Parsing done (196ms).
% 1.33/16.64 % [INFO] Running in sequential loop mode.
% 2.05/17.04 % [INFO] eprover registered as external prover.
% 2.05/17.05 % [INFO] Scanning for conjecture ...
% 2.23/17.14 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 2.23/17.18 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.35/17.21 % [INFO] Problem is first-order (TPTP FOF).
% 2.35/17.22 % [INFO] Type checking passed.
% 2.35/17.22 % [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 ...
% 3.79/17.86 % External prover 'e' found a proof!
% 3.79/17.86 % [INFO] Killing All external provers ...
% 3.79/17.86 % Time passed: 1879ms (effective reasoning time: 1213ms)
% 3.79/17.86 % Solved by 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)>
% 3.79/17.86 % Axioms used in derivation (13): sos_01, sos_05, sos_02, sos_11, sos_07, sos_13, sos_08, sos_12, sos_06, sos_09, sos_03, sos_04, sos_10
% 3.79/17.86 % No. of inferences in proof: 30
% 3.79/17.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1879 ms resp. 1213 ms w/o parsing
% 4.06/17.92 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.06/17.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------