%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL682+1.001 : TPTP v9.3.1. Released v4.0.0.
% 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 : n018.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 07:52:32 AM UTC 2026
% Result : Theorem 3.32s 2.92s
% Output : Refutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 0 equ; 0 cnn)
% Maximal formula atoms : 21 ( 9 avg)
% Number of connectives : 247 ( 65 ~; 60 |; 2 &; 118 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 50 ( 0 ^; 47 !; 3 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(r1_decl,type,
r1: $i > $i > $o ).
thf(p16_decl,type,
p16: $i > $o ).
thf(p12_decl,type,
p12: $i > $o ).
thf(p14_decl,type,
p14: $i > $o ).
thf(p15_decl,type,
p15: $i > $o ).
thf(p13_decl,type,
p13: $i > $o ).
thf(p11_decl,type,
p11: $i > $o ).
thf(1,conjecture,
~ ? [A: $i] :
~ ( ! [B: $i] :
( ! [C: $i] :
( ( C @ p11 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p12 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p13 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p15 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ~ ! [C: $i] :
( ( C @ p12 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ( C @ p14 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ( C @ p12 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ( C @ p16 )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
thf(2,negated_conjecture,
~ ~ ? [A: $i] :
~ ( ! [B: $i] :
( ! [C: $i] :
( ( C @ p11 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p12 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p13 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p15 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ~ ! [C: $i] :
( ( C @ p12 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ( C @ p14 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ( C @ p12 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ( C @ p16 )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ~ ? [A: $i] :
~ ( ! [B: $i] :
( ! [C: $i] :
( ( C @ p11 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p12 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p13 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ( C @ p15 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ( B @ ( A @ r1 ) ) )
| ~ ! [B: $i] :
( ~ ( ~ ! [C: $i] :
( ( C @ p12 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ( C @ p14 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ( C @ p12 )
| ~ ( C @ ( B @ r1 ) ) )
| ~ ! [C: $i] :
( ( C @ p16 )
| ~ ( C @ ( B @ r1 ) ) ) )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] : ( A @ ( A @ r1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(28,plain,
! [A: $i] : ( A @ ( A @ r1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1 ) )
& ( B @ ( A @ r1 ) ) )
=> ( C @ ( A @ r1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(30,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1 ) )
& ( B @ ( A @ r1 ) ) )
=> ( C @ ( A @ r1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(32,plain,
$false,
inference(e,[status(thm)],[5,28,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL682+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % 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
% 0.10/0.43 % Computer : n018.cluster.edu
% 0.10/0.43 % Model : x86_64 x86_64
% 0.10/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.43 % Memory : 8046.5625MB
% 0.10/0.43 % OS : Linux 6.8.0-71-generic
% 0.10/0.43 % CPULimit : 300
% 0.10/0.43 % WCLimit : 300
% 0.10/0.43 % DateTime : Fri Sep 25 23:21:20 UTC 2026
% 0.10/0.43 % CPUTime :
% 0.10/0.43 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
% 0.82/1.24 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.12/1.44 % [INFO] Parsing done (196ms).
% 1.12/1.46 % [INFO] Running in sequential loop mode.
% 1.61/1.87 % [INFO] eprover registered as external prover.
% 1.61/1.88 % [INFO] Scanning for conjecture ...
% 1.79/2.03 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.00/2.09 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.00/2.10 % [INFO] Problem is first-order (TPTP FOF).
% 2.00/2.11 % [INFO] Type checking passed.
% 2.00/2.12 % [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 ...
% 3.32/2.91 % External prover 'e' found a proof!
% 3.32/2.91 % [INFO] Killing All external provers ...
% 3.32/2.91 % Time passed: 2254ms (effective reasoning time: 1444ms)
% 3.32/2.91 % 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)>
% 3.32/2.92 % Axioms used in derivation (2): reflexivity, transitivity
% 3.32/2.92 % No. of inferences in proof: 8
% 3.32/2.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2254 ms resp. 1444 ms w/o parsing
% 3.32/2.99 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.32/2.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------