%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL636+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 : n005.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 07:52:13 AM UTC 2026
% Result : Theorem 4.43s 7.78s
% Output : Refutation 4.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 1
% Syntax : Number of formulae : 4 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 208 ( 0 equ; 0 cnn)
% Maximal formula atoms : 69 ( 52 avg)
% Number of connectives : 638 ( 185 ~; 123 |; 81 &; 249 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 16 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 45 ( 0 ^; 42 !; 3 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(r1_decl,type,
r1: $i > $i > $o ).
thf(p2_decl,type,
p2: $i > $o ).
thf(p102_decl,type,
p102: $i > $o ).
thf(p101_decl,type,
p101: $i > $o ).
thf(p100_decl,type,
p100: $i > $o ).
thf(p1_decl,type,
p1: $i > $o ).
thf(1,conjecture,
~ ? [A: $i] :
~ ( ~ ( ( A @ p100 )
& ~ ( A @ p101 )
& ( ~ ( A @ p101 )
| ( A @ p100 ) )
& ( ~ ( A @ p102 )
| ( A @ p101 ) )
& ( ~ ( A @ p100 )
| ( ( ~ ( A @ p1 )
| ! [B: $i] :
( ~ ( B @ p100 )
| ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) ) )
& ( ( A @ p1 )
| ! [B: $i] :
( ~ ( B @ p100 )
| ~ ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) )
& ( ~ ( A @ p101 )
| ( ( ~ ( A @ p2 )
| ! [B: $i] :
( ~ ( B @ p101 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) ) )
& ( ( A @ p2 )
| ! [B: $i] :
( ~ ( B @ p101 )
| ~ ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) )
& ( ~ ( ( A @ p100 )
& ~ ( A @ p101 ) )
| ( ~ ! [B: $i] :
( ~ ( ( B @ p101 )
& ~ ( B @ p102 )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ~ ! [B: $i] :
( ~ ( ( B @ p101 )
& ~ ( B @ p102 )
& ~ ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) ) ) )
& ! [B: $i] :
( ( ( ~ ( B @ p101 )
| ( B @ p100 ) )
& ( ~ ( B @ p102 )
| ( B @ p101 ) )
& ( ~ ( B @ p100 )
| ( ( ~ ( B @ p1 )
| ! [C: $i] :
( ~ ( C @ p100 )
| ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) ) )
& ( ( B @ p1 )
| ! [C: $i] :
( ~ ( C @ p100 )
| ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) ) ) ) )
& ( ~ ( B @ p101 )
| ( ( ~ ( B @ p2 )
| ! [C: $i] :
( ~ ( C @ p101 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) ) )
& ( ( B @ p2 )
| ! [C: $i] :
( ~ ( C @ p101 )
| ~ ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) ) ) ) )
& ( ~ ( ( B @ p100 )
& ~ ( B @ p101 ) )
| ( ~ ! [C: $i] :
( ~ ( ( C @ p101 )
& ~ ( C @ p102 )
& ( C @ p2 ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ~ ( ( C @ p101 )
& ~ ( C @ p102 )
& ~ ( C @ p2 ) )
| ~ ( C @ ( B @ r1 ) ) ) ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ! [B: $i] :
( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
thf(2,negated_conjecture,
~ ~ ? [A: $i] :
~ ( ~ ( ( A @ p100 )
& ~ ( A @ p101 )
& ( ~ ( A @ p101 )
| ( A @ p100 ) )
& ( ~ ( A @ p102 )
| ( A @ p101 ) )
& ( ~ ( A @ p100 )
| ( ( ~ ( A @ p1 )
| ! [B: $i] :
( ~ ( B @ p100 )
| ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) ) )
& ( ( A @ p1 )
| ! [B: $i] :
( ~ ( B @ p100 )
| ~ ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) )
& ( ~ ( A @ p101 )
| ( ( ~ ( A @ p2 )
| ! [B: $i] :
( ~ ( B @ p101 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) ) )
& ( ( A @ p2 )
| ! [B: $i] :
( ~ ( B @ p101 )
| ~ ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) )
& ( ~ ( ( A @ p100 )
& ~ ( A @ p101 ) )
| ( ~ ! [B: $i] :
( ~ ( ( B @ p101 )
& ~ ( B @ p102 )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ~ ! [B: $i] :
( ~ ( ( B @ p101 )
& ~ ( B @ p102 )
& ~ ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) ) ) )
& ! [B: $i] :
( ( ( ~ ( B @ p101 )
| ( B @ p100 ) )
& ( ~ ( B @ p102 )
| ( B @ p101 ) )
& ( ~ ( B @ p100 )
| ( ( ~ ( B @ p1 )
| ! [C: $i] :
( ~ ( C @ p100 )
| ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) ) )
& ( ( B @ p1 )
| ! [C: $i] :
( ~ ( C @ p100 )
| ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) ) ) ) )
& ( ~ ( B @ p101 )
| ( ( ~ ( B @ p2 )
| ! [C: $i] :
( ~ ( C @ p101 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) ) )
& ( ( B @ p2 )
| ! [C: $i] :
( ~ ( C @ p101 )
| ~ ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) ) ) ) )
& ( ~ ( ( B @ p100 )
& ~ ( B @ p101 ) )
| ( ~ ! [C: $i] :
( ~ ( ( C @ p101 )
& ~ ( C @ p102 )
& ( C @ p2 ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ~ ( ( C @ p101 )
& ~ ( C @ p102 )
& ~ ( C @ p2 ) )
| ~ ( C @ ( B @ r1 ) ) ) ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ! [B: $i] :
( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ? [A: $i] :
~ ( ~ ( ( A @ p100 )
& ~ ( A @ p101 )
& ( ~ ( A @ p101 )
| ( A @ p100 ) )
& ( ~ ( A @ p102 )
| ( A @ p101 ) )
& ( ~ ( A @ p100 )
| ( ( ~ ( A @ p1 )
| ! [B: $i] :
( ~ ( B @ p100 )
| ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) ) )
& ( ( A @ p1 )
| ! [B: $i] :
( ~ ( B @ p100 )
| ~ ( B @ p1 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) )
& ( ~ ( A @ p101 )
| ( ( ~ ( A @ p2 )
| ! [B: $i] :
( ~ ( B @ p101 )
| ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) ) )
& ( ( A @ p2 )
| ! [B: $i] :
( ~ ( B @ p101 )
| ~ ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) ) ) ) )
& ( ~ ( ( A @ p100 )
& ~ ( A @ p101 ) )
| ( ~ ! [B: $i] :
( ~ ( ( B @ p101 )
& ~ ( B @ p102 )
& ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) )
& ~ ! [B: $i] :
( ~ ( ( B @ p101 )
& ~ ( B @ p102 )
& ~ ( B @ p2 ) )
| ~ ( B @ ( A @ r1 ) ) ) ) )
& ! [B: $i] :
( ( ( ~ ( B @ p101 )
| ( B @ p100 ) )
& ( ~ ( B @ p102 )
| ( B @ p101 ) )
& ( ~ ( B @ p100 )
| ( ( ~ ( B @ p1 )
| ! [C: $i] :
( ~ ( C @ p100 )
| ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) ) )
& ( ( B @ p1 )
| ! [C: $i] :
( ~ ( C @ p100 )
| ~ ( C @ p1 )
| ~ ( C @ ( B @ r1 ) ) ) ) ) )
& ( ~ ( B @ p101 )
| ( ( ~ ( B @ p2 )
| ! [C: $i] :
( ~ ( C @ p101 )
| ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) ) )
& ( ( B @ p2 )
| ! [C: $i] :
( ~ ( C @ p101 )
| ~ ( C @ p2 )
| ~ ( C @ ( B @ r1 ) ) ) ) ) )
& ( ~ ( ( B @ p100 )
& ~ ( B @ p101 ) )
| ( ~ ! [C: $i] :
( ~ ( ( C @ p101 )
& ~ ( C @ p102 )
& ( C @ p2 ) )
| ~ ( C @ ( B @ r1 ) ) )
& ~ ! [C: $i] :
( ~ ( ( C @ p101 )
& ~ ( C @ p102 )
& ~ ( C @ p2 ) )
| ~ ( C @ ( B @ r1 ) ) ) ) ) )
| ~ ( B @ ( A @ r1 ) ) ) )
| ~ ! [B: $i] :
( ( B @ p2 )
| ~ ( B @ ( A @ r1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(56,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL636+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.15/5.61 % Computer : n005.cluster.edu
% 0.15/5.61 % Model : x86_64 x86_64
% 0.15/5.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.61 % Memory : 8046.5625MB
% 0.15/5.61 % OS : Linux 6.8.0-71-generic
% 0.15/5.61 % CPULimit : 300
% 0.15/5.61 % WCLimit : 300
% 0.15/5.61 % DateTime : Fri Sep 25 22:48:52 UTC 2026
% 0.15/5.61 % CPUTime :
% 0.15/5.61 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
% 0.94/6.19 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/6.40 % [INFO] Parsing done (204ms).
% 1.20/6.42 % [INFO] Running in sequential loop mode.
% 2.14/6.84 % [INFO] eprover registered as external prover.
% 2.14/6.85 % [INFO] Scanning for conjecture ...
% 2.35/6.98 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.35/7.03 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.65/7.03 % [INFO] Problem is first-order (TPTP FOF).
% 2.65/7.04 % [INFO] Type checking passed.
% 2.65/7.05 % [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 ...
% 4.43/7.78 % External prover 'e' found a proof!
% 4.43/7.78 % [INFO] Killing All external provers ...
% 4.43/7.78 % Time passed: 2019ms (effective reasoning time: 1348ms)
% 4.43/7.78 % 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)>
% 4.43/7.78 % Axioms used in derivation (0):
% 4.43/7.78 % No. of inferences in proof: 4
% 4.43/7.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2019 ms resp. 1348 ms w/o parsing
% 4.74/7.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.74/7.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------